Daily Papers

Fine-tuned large language models can exhibit reward-hacking behavior arising from emergent misalignment, which is difficult to detect from final outputs alone. While prior work has studied reward hacking at the level of completed responses, it remains unclear whether such behavior can be identified during generation. We propose an activation-based monitoring approach that detects reward-hacking signals from internal representations as a model generates its response. Our method trains sparse autoencoders on residual stream activations and applies lightweight linear classifiers to produce token-level estimates of reward-hacking activity. Across multiple model families and fine-tuning mixtures, we find that internal activation patterns reliably distinguish reward-hacking from benign behavior, generalize to unseen mixed-policy adapters, and exhibit model-dependent temporal structure during chain-of-thought reasoning. Notably, reward-hacking signals often emerge early, persist throughout reasoning, and can be amplified by increased test-time compute in the form of chain-of-thought prompting under weakly specified reward objectives. These results suggest that internal activation monitoring provides a complementary and earlier signal of emergent misalignment than output-based evaluation, supporting more robust post-deployment safety monitoring for fine-tuned language models.

Existing approaches for analyzing neural network activations, such as PCA and sparse autoencoders, rely on strong structural assumptions. Generative models offer an alternative: they can uncover structure without such assumptions and act as priors that improve intervention fidelity. We explore this direction by training diffusion models on one billion residual stream activations, creating "meta-models" that learn the distribution of a network's internal states. We find that diffusion loss decreases smoothly with compute and reliably predicts downstream utility. In particular, applying the meta-model's learned prior to steering interventions improves fluency, with larger gains as loss decreases. Moreover, the meta-model's neurons increasingly isolate concepts into individual units, with sparse probing scores that scale as loss decreases. These results suggest generative meta-models offer a scalable path toward interpretability without restrictive structural assumptions. Project page: https://generative-latent-prior.github.io.

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

Sparse Autoencoders (SAEs) decompose residual-stream activations into interpretable features. Recent latent-space defenses increasingly rely on these decompositions, assuming that identified "unsafe" SAE features serve as actionable handles for monitoring and intervention. In this paradigm, clamping a specific harmful feature is expected to reliably prevent model misbehavior. However, we show that this success may hide a recoverable failure mode: the clamp may block one visible route to a behavior without eliminating the behavior itself. We formulate this vulnerability as post-intervention recovery, a constrained residual-space optimization problem. Starting from the post-intervention residual state, we optimize residual perturbations to recover the pre-intervention behavior while preserving the post-intervention values of the targeted SAE features. Even under a strong threat model where the intervention remains active throughout optimization and generation, recovery remains possible. To rule out that recovery simply undoes the intervention, we use encoder-orthogonal updates for single-layer interventions and the corresponding feature-map Jacobian in the cross-layer setting. Across TPP, unlearning, IOI, and refusal steering experiments, this stress test reveals recoverable behavior despite successful feature-level intervention. Especially in the safety-critical refusal-steering setting, we achieve a 95.8% recovery rate on valid samples while keeping defended-feature relative drift to 0.131, substantially below suffix-based baselines. A recovery-path attribution analysis further localizes this recovery to the SAE reconstruction residual, the component left unexplained by the SAE. These results expose a gap between feature-level control and behavioral completeness: SAE features can support causal intervention, but controlling them does not guarantee control over the underlying behavior.

Large language models (LLMs) can be said to have preferences: they reliably pick certain tasks and outputs over others, and preferences shaped by post-training and system prompts appear to shape much of their behaviour. But models can also adopt different personas which have radically different preferences. How is this implemented internally? Does each persona run on its own preference machinery, or is something shared underneath? We train linear probes on residual-stream activations of Gemma-3-27B and Qwen-3.5-122B to predict revealed pairwise task choices, and identify a genuine preference vector: it tracks the model's preferences as they shift across a range of prompts and situations, and on Gemma-3-27B steering along it causally controls pairwise choice. This preference representation is largely shared across personas: a probe trained on the helpful assistant predicts and steers the choices of qualitatively different personas, including an evil persona whose preferences anti-correlate with those of the Assistant.

We introduce Contrastive Activation Addition (CAA), an innovative method for steering language models by modifying activations during their forward passes. CAA computes ``steering vectors'' by averaging the difference in residual stream activations between pairs of positive and negative examples of a particular behavior such as factual versus hallucinatory responses. During inference, these steering vectors are added at all token positions after the user's prompt with either a positive or negative coefficient, allowing precise control over the degree of the targeted behavior. We evaluate CAA's effectiveness on Llama 2 Chat using both multiple-choice behavioral question datasets and open-ended generation tasks. We demonstrate that CAA significantly alters model behavior, outperforms traditional methods like finetuning and few-shot prompting, and minimally reduces capabilities. Moreover, by employing various activation space interpretation methods, we gain deeper insights into CAA's mechanisms. CAA both accurately steers model outputs and also sheds light on how high-level concepts are represented in Large Language Models (LLMs).

Activation Oracles (AOs) are promising methods for interpreting residual stream activations. However, current AOs face important issues, such as hallucinations and vagueness. Additionally, text-inversion confounds make them hard to evaluate. To this end, we improve the Activation Oracle (AO) training regime in four ways: training on on-policy rollouts, improving the conversational dataset, feeding more layers and an improvement to the injection formula. The capability improvements are marginal, but quality of life improvements are quite substantial. In addition, we open source the first comprehensive evaluation suite for AO quality, which we call AObench. Overall, we hope that our work sets a foundation that helps improve AOs and other models in the paradigm of scalable, end-to-end interpretability.

Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to resolve this fundamental tension. In this work, we argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion." By applying Gram-Schmidt decomposition to residual-stream activations , we reveal a dual-modulation mechanism driving this process: a class-agnostic topological preservation that anchors global structure to prevent semantic collapse, and a specific algebraic divergence that directionally tears apart cross-class concepts to forge logical boundaries. We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing. Crucially, targeted specific vector ablation establishes a strict causal binding between this topology and model function: algebraically erasing the divergence component collapses parity classification accuracy from 100% to chance levels (38.57%). Furthermore, we uncover a three-phase layer-wise geometric dynamic and demonstrate that under social pressure prompts, models fail to generate sufficient divergence. This results in a "manifold entanglement" that geometrically explains sycophancy and hallucination. Ultimately, our findings revise the linear-isometric presumption, demonstrating that the emergence of discrete logic in LLMs is purchased at an irreducible cost of topological deformation.

While large language models (LLMs) appear to be increasingly capable of solving compositional tasks, it is an open question whether they do so using compositional mechanisms. In this work, we investigate how feedforward LLMs solve two-hop factual recall tasks, which can be expressed compositionally as g(f(x)). We first confirm that modern LLMs continue to suffer from the "compositionality gap": i.e. their ability to compute both z = f(x) and y = g(z) does not entail their ability to compute the composition y = g(f(x)). Then, using logit lens on their residual stream activations, we identify two processing mechanisms, one which solves tasks compositionally, computing f(x) along the way to computing g(f(x)), and one which solves them directly, without any detectable signature of the intermediate variable f(x). Finally, we find that which mechanism is employed appears to be related to the embedding space geometry, with the idiomatic mechanism being dominant in cases where there exists a linear mapping from x to g(f(x)) in the embedding spaces. We fully release our data and code at: https://github.com/apoorvkh/composing-functions .

Sparse Autoencoders (SAEs) have emerged as a promising approach for interpreting neural network representations by learning sparse, human-interpretable features from dense activations. We investigate whether incorporating variational methods into SAE architectures can improve feature organization and interpretability. We introduce the Variational Sparse Autoencoder (vSAE), which replaces deterministic ReLU gating with stochastic sampling from learned Gaussian posteriors and incorporates KL divergence regularization toward a standard normal prior. Our hypothesis is that this probabilistic sampling creates dispersive pressure, causing features to organize more coherently in the latent space while avoiding overlap. We evaluate a TopK vSAE against a standard TopK SAE on Pythia-70M transformer residual stream activations using comprehensive benchmarks including SAE Bench, individual feature interpretability analysis, and global latent space visualization through t-SNE. The vSAE underperforms standard SAE across core evaluation metrics, though excels at feature independence and ablation metrics. The KL divergence term creates excessive regularization pressure that substantially reduces the fraction of living features, leading to observed performance degradation. While vSAE features demonstrate improved robustness, they exhibit many more dead features than baseline. Our findings suggest that naive application of variational methods to SAEs does not improve feature organization or interpretability.

Large Language Models (LLMs) often encode whether a statement is true as a vector in their residual stream activations. These vectors, also known as truth vectors, have been studied in prior work, however how they change when context is introduced remains unexplored. We study this question by measuring (1) the directional change (θ) between the truth vectors with and without context and (2) the relative magnitude of the truth vectors upon adding context. Across four LLMs and four datasets, we find that (1) truth vectors are roughly orthogonal in early layers, converge in middle layers, and may stabilize or continue increasing in later layers; (2) adding context generally increases the truth vector magnitude, i.e., the separation between true and false representations in the activation space is amplified; (3) larger models distinguish relevant from irrelevant context mainly through directional change (θ), while smaller models show this distinction through magnitude differences. We also find that context conflicting with parametric knowledge produces larger geometric changes than parametrically aligned context. To the best of our knowledge, this is the first work that provides a geometric characterization of how context transforms the truth vector in the activation space of LLMs.

We investigate feature universality in Gemma-2 language models (Gemma-2-2B and Gemma-2-9B), asking whether models with a four-fold difference in scale still converge on comparable internal concepts. Using the Sparse Autoencoder (SAE) dictionary-learning pipeline, we utilize SAEs on each model's residual-stream activations, align the resulting monosemantic features via activation correlation, and compare the matched feature spaces with SVCCA and RSA. Middle layers yield the strongest overlap, while early and late layers show far less similarity. Preliminary experiments extend the analysis from single tokens to multi-token subspaces, showing that semantically similar subspaces interact similarly with language models. These results strengthen the case that large language models carve the world into broadly similar, interpretable features despite size differences, reinforcing universality as a foundation for cross-model interpretability.

Activation-based control steers large language models (LLMs) by intervening on their internal representations during inference, and has emerged as an effective paradigm for controlling behaviors such as persona and style. However, existing methods often rely on fixed steering directions or task-specific intervention modules, making them difficult to adapt to fine-grained concepts and compositional constraints. We propose UniSteer, a text-guided activation flow matching model that learns a conditional distribution over residual-stream activations from natural-language conditions. Instead of fitting a separate intervention for each target behavior, UniSteer learns a universal conditional velocity field in activation space. At inference time, UniSteer performs flow inversion by partially transporting a source activation toward a latent state and regenerating it under a target textual condition before injecting it back into the frozen LLM. The same conditional model supports activation-space classification by selecting the textual label with the lowest reconstruction energy. Experiments on three target LLMs show that UniSteer provides a unified interface across behavioral control, truthfulness steering, fine-grained concept steering, multi-constraint instruction following, and activation-space classification.

Large-scale autoregressive models pretrained on next-token prediction and finetuned with reinforcement learning (RL) have achieved unprecedented success on many problem domains. During RL, these models explore by generating new outputs, one token at a time. However, sampling actions token-by-token can result in highly inefficient learning, particularly when rewards are sparse. Here, we show that it is possible to overcome this problem by acting and exploring within the internal representations of an autoregressive model. Specifically, to discover temporally-abstract actions, we introduce a higher-order, non-causal sequence model whose outputs control the residual stream activations of a base autoregressive model. On grid world and MuJoCo-based tasks with hierarchical structure, we find that the higher-order model learns to compress long activation sequence chunks onto internal controllers. Critically, each controller executes a sequence of behaviorally meaningful actions that unfold over long timescales and are accompanied with a learned termination condition, such that composing multiple controllers over time leads to efficient exploration on novel tasks. We show that direct internal controller reinforcement, a process we term "internal RL", enables learning from sparse rewards in cases where standard RL finetuning fails. Our results demonstrate the benefits of latent action generation and reinforcement in autoregressive models, suggesting internal RL as a promising avenue for realizing hierarchical RL within foundation models.

Conversational large language models are fine-tuned for both instruction-following and safety, resulting in models that obey benign requests but refuse harmful ones. While this refusal behavior is widespread across chat models, its underlying mechanisms remain poorly understood. In this work, we show that refusal is mediated by a one-dimensional subspace, across 13 popular open-source chat models up to 72B parameters in size. Specifically, for each model, we find a single direction such that erasing this direction from the model's residual stream activations prevents it from refusing harmful instructions, while adding this direction elicits refusal on even harmless instructions. Leveraging this insight, we propose a novel white-box jailbreak method that surgically disables refusal with minimal effect on other capabilities. Finally, we mechanistically analyze how adversarial suffixes suppress propagation of the refusal-mediating direction. Our findings underscore the brittleness of current safety fine-tuning methods. More broadly, our work showcases how an understanding of model internals can be leveraged to develop practical methods for controlling model behavior.

Refusal on harmful prompts is a key safety behaviour in instruction-tuned large language models (LLMs), yet the internal causes of this behaviour remain poorly understood. We study two public instruction-tuned models, Gemma-2-2B-IT and LLaMA-3.1-8B-IT, using sparse autoencoders (SAEs) trained on residual-stream activations. Given a harmful prompt, we search the SAE latent space for feature sets whose ablation flips the model from refusal to compliance, demonstrating causal influence and creating a jailbreak. Our search proceeds in three stages: (1) Refusal Direction: find a refusal-mediating direction and collect SAE features near that direction; (2) Greedy Filtering: prune to a minimal set; and (3) Interaction Discovery: fit a factorization machine (FM) that captures nonlinear interactions among the remaining active features and the minimal set. This pipeline yields a broad set of jailbreak-critical features, offering insight into the mechanistic basis of refusal. Moreover, we find evidence of redundant features that remain dormant unless earlier features are suppressed. Our findings highlight the potential for fine-grained auditing and targeted intervention in safety behaviours by manipulating the interpretable latent space.

Large language models (LLMs) can store a significant amount of factual knowledge in their parameters. However, their parametric knowledge may conflict with the information provided in the context. Such conflicts can lead to undesirable model behaviour, such as reliance on outdated or incorrect information. In this work, we investigate whether LLMs can identify knowledge conflicts and whether it is possible to know which source of knowledge the model will rely on by analysing the residual stream of the LLM. Through probing tasks, we find that LLMs can internally register the signal of knowledge conflict in the residual stream, which can be accurately detected by probing the intermediate model activations. This allows us to detect conflicts within the residual stream before generating the answers without modifying the input or model parameters. Moreover, we find that the residual stream shows significantly different patterns when the model relies on contextual knowledge versus parametric knowledge to resolve conflicts. This pattern can be employed to estimate the behaviour of LLMs when conflict happens and prevent unexpected answers before producing the answers. Our analysis offers insights into how LLMs internally manage knowledge conflicts and provides a foundation for developing methods to control the knowledge selection processes.

Activation steering is a popular white-box control technique that modifies model activations to elicit an abstract change in its behavior. It has also become a standard tool in interpretability (e.g., probing truthfulness, or translating activations into human-readable explanations) and safety research (e.g., jailbreakability). However, it is unclear whether steered behavior is realizable by any textual prompt. In this work, we cast this question as a surjectivity problem: for a fixed model, does every steered activation admit a preimage under the model's natural forward pass? Under practical assumptions, we prove that activation steering pushes the residual stream off the manifold of states reachable from discrete prompts. Almost surely, no prompt can reproduce the same internal behavior induced by steering. We also illustrate this finding empirically across three widely used LLMs. Our results establish a formal separation between white-box steerability and black-box prompting. We therefore caution against interpreting the ease and success of activation steering as evidence of prompt-based interpretability or vulnerability, and argue for evaluation protocols that explicitly decouple white-box and black-box interventions.

The dynamic range of activations is a first-order constraint for low-bit quantization, activation scaling, and stable LLM inference. Prior work characterized outlier features and massive activations on pre-2024 LLaMA-style models, and the downstream activation-quantization stack inherits that picture without revisiting it for the post-LLaMA open-model boom. We ask the deployment-oriented question: how large can activations get in modern open LLMs, and how does this magnitude vary across families, generations, and training stages? Under a unified pipeline (5,000-sample multi-domain corpus, family-specific tokenization, identical hooks across embeddings, hidden states, attention, MLP/MoE, SwiGLU gates, and final norm), we measure global and layerwise maxima on 27 checkpoints from 8 open families spanning dense, MoE, vision-language, intermediate-training, and instruction-tuned variants. We find that (i) global maxima span over nearly four orders of magnitude at comparable parameter counts, with Qwen3.5 and MoE checkpoints in the 10^2 to 10^3 range and Gemma3-27B-it reaching ~7 x 10^5; (ii) cross-family and cross-generation comparisons break simple monotonic scaling; and (iii) MoE checkpoints exhibit 14.0-23.4x lower peaks than matched-scale dense counterparts, while the residual stream carries the global maximum in 22/24 checkpoints. A lightweight INT-8 sanity check shows that measured maxima co-vary with low-bit reconstruction error via activation-scale selection. We conclude that maximum activation magnitude is a model property tied to family, architecture, and training stage - not a simple byproduct of size - and should be measured and reported alongside any open-weight release before low-bit deployment. The code is publicly available at https://github.com/clx1415926/Max_act_llm.

As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.

Recent advancements in large language models (LLMs) have resulted in increasingly anthropomorphic language concerning the ability of LLMs to reason. Whether reasoning in LLMs should be understood to be inherently different is, however, widely debated. We propose utilizing a representation engineering approach wherein model activations are read from the residual stream of an LLM when processing a reasoning task. The activations are used to derive a control vector that is applied to the model as an inference-time intervention, modulating the representational space of the model, to improve performance on the specified task. We publish the code for deriving control vectors and analyzing model representations. The method allows us to improve performance on reasoning benchmarks and assess how control vectors influence the final logit distribution of a model via metrics such as KL divergence and entropy. We apply control vectors to Mistral-7B-Instruct and a range of Pythia models on an inductive, a deductive and mathematical reasoning task. We show that an LLM can, to a certain degree, be controlled to improve its perceived reasoning ability by modulating activations. The intervention is dependent upon the ability to reliably extract the model's typical state when correctly solving a task. Our results suggest that reasoning performance can be modulated in the same manner as other information-processing tasks performed by LLMs and demonstrate that we are capable of improving performance on specific tasks via a simple intervention on the residual stream with no additional training.

Large language models (LLMs) show strong multilingual capabilities, yet reliably controlling the language of their outputs remains difficult. Representation-level steering addresses this by adding language-specific vectors to model activations at inference time, but identifying language-specific directions in the residual stream often relies on multilingual or parallel data that can be expensive to obtain. Sparse autoencoders (SAEs) decompose residual activations into interpretable, sparse feature directions and offer a natural basis for this search, yet existing SAE-based approaches face the same data constraint. We introduce LangFIR (Language Feature Identification via Random-token Filtering), a method that discovers language-specific SAE features using only a small amount of monolingual data and random-token sequences. Many SAE features consistently activated by target-language inputs do not encode language identity. Random-token sequences surface these language-agnostic features, allowing LangFIR to filter them out and isolate a sparse set of language-specific features. We show that these features are extremely sparse, highly selective for their target language, and causally important: directional ablation increases cross-entropy loss only for the corresponding language. Using these features to construct steering vectors for multilingual generation control, LangFIR achieves the best average accuracy BLEU across three models (Gemma 3 1B, Gemma 3 4B, and Llama 3.1 8B), three datasets, and twelve target languages, outperforming the strongest monolingual baseline by up to and surpassing methods that rely on parallel data. Our results suggest that language identity in multilingual LLMs is localized in a sparse set of feature directions discoverable with monolingual data. Code is available at https://anonymous.4open.science/r/LangFIR-C0F5/.

Sparse autoencoders (SAEs) are a promising approach to interpreting the internal representations of transformer language models. However, standard SAEs are trained separately on each transformer layer, making it difficult to use them to study how information flows across layers. To solve this problem, we introduce the multi-layer SAE (MLSAE): a single SAE trained on the residual stream activation vectors from every transformer layer simultaneously. The residual stream is usually understood as preserving information across layers, so we expected to, and did, find individual SAE features that are active at multiple layers. Interestingly, while a single SAE feature is active at different layers for different prompts, for a single prompt, we find that a single feature is far more likely to be active at a single layer. For larger underlying models, we find that the cosine similarities between adjacent layers in the residual stream are higher, so we expect more features to be active at multiple layers. These results show that MLSAEs are a promising method to study information flow in transformers. We release our code to train and analyze MLSAEs at https://github.com/tim-lawson/mlsae.

Large language models (LLMs) excel at complex reasoning when they include intermediate steps, known as "chains of thought" (CoTs). However, these rationales are often overly verbose, even for simple problems, leading to wasted context, increased latency, and higher energy consumption. We observe that verbose, English-heavy CoTs and concise, math-centric CoTs occupy distinct regions in the model's residual-stream activation space. By extracting and injecting a "steering vector" to transition between these modes, we can reliably shift generation toward more concise reasoning, effectively compressing CoTs without retraining. We formalize this approach as Activation-Steered Compression (ASC), an inference-time technique that shortens reasoning traces by directly modifying hidden representations. In addition, we provide a theoretical analysis of the impact of ASC on the output distribution, derived from a closed-form KL-divergence-bounded constraint to regulate steering strength. Using only 100 paired verbose and concise examples, ASC achieves up to 67.43% reduction in CoT length on MATH500 and GSM8K datasets, while maintaining accuracy across 7B, 8B, and 32B parameter models. As a training-free method, ASC introduces negligible runtime overhead and, on MATH500, delivers an average 2.73x speedup in end-to-end reasoning wall-clock time on an 8B model. This makes ASC a practical and efficient tool for streamlining the deployment of reasoning-capable LLMs in latency- or cost-sensitive settings. The code is available at: https://github.com/ArminAzizi98/ASC

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Context can change whether a request is harmful without changing its topic or surface form. We ask whether residual-stream probes distinguish harmful requests from surface-matched benign controls at a useful operating point. Across three 7-8B model families, an activation sensor blocks 95.5-97.7 percent of judge-classified compliant attacks in a taxonomy-selected set. It also blocks 59.6-68.4 percent of XSTest prompts. A fully disjoint audit reconstructs near-ceiling source-contrast AUROC (0.996-0.999), but fixed transfer to matched pairs is weaker: 0.656-0.819 on the guard-selected Twin-n70 subset and 0.590-0.690 on the full Twin-n163 cohort. We test ten axes on the reference family and seven across all families with leakage, hold-out, and permutation controls. On Twin-n163, no axis evaluated without direct pair-boundary fitting reaches the specified numerical threshold. Requiring persistence on that full cohort was added at analysis time. A separately specified 24B/32B extension gives the same result. Pair-trained classifiers weaken under category and generation-batch hold-out and false-block 79.6-100 percent of XSTest at 95 percent in-corpus TPR. At the tested read points, these activation scores behave as broad-risk detectors rather than standalone context adjudicators.

Activation steering -- adding a vector to a model's residual stream to modify its behavior -- is widely used in safety evaluations as if the model cannot detect the intervention. We test this assumption, introducing steering awareness: a model's ability to infer, during its own forward pass, that a steering vector was injected and what concept it encodes. After fine-tuning, seven instruction-tuned models develop strong steering awareness on held-out concepts; the best reaches 95.5% detection, 71.2% concept identification, and zero false positives on clean inputs. This generalizes to unseen steering vector construction methods when their directions have high cosine similarity to the training distribution but not otherwise, indicating a geometric detector rather than a generic anomaly detector. Surprisingly, detection does not confer resistance; on both factual and safety benchmarks, detection-trained models are consistently more susceptible to steering than their base counterparts. Mechanistically, steering awareness arises not from a localized circuit, but from a distributed transformation that progressively rotates diverse injected vectors into a shared detection direction. Activation steering should therefore not be considered an invisible intervention in safety evaluations.

Large Language Models memorize vast amounts of training data, raising concerns regarding privacy, copyright infringement, and safety. Machine unlearning seeks to remove the influence of a targeted forget set while preserving model performance, ideally approximating a model retrained from scratch without the forget set. Existing approaches aim to achieve this by updating model parameters via gradient-based methods. However, these updates are computationally expensive, lead to irreversible weight changes, and degrade when the model is quantized for deployment. A recent alternative to changing model weights is activation engineering, where activations are changed during inference to steer model behavior. Despite circumventing weight editing, naive activation steering introduces its own failure modes, as a single global steering vector applies the same intervention to every input, leading to unintended changes in model behavior. We introduce Inference-Time Unlearning via Gated Activation Redirection (GUARD-IT), a training- and gradient-free method that unlearns via input-dependent activation steering at inference time. The resulting intervention is applied as a norm-preserving rotation in the residual stream, leaving model weights untouched. Experiments on TOFU and MUSE show that GUARD-IT matches or exceeds 12 gradient-based baselines across three model scales, while being the only method to simultaneously preserve utility, suppress memorization, and avoid catastrophic collapse across all settings. GUARD-IT further supports continual unlearning without retraining, and remains effective under quantization, a scenario in which parameter-editing methods degrade.

Activation steering has become a popular training-free method to control LLM behavior by injecting precomputed direction vectors into the model's residual stream at inference time. Yet its robustness to realistic input variation remains unstudied. We present the first systematic evaluation of activation steering robustness under adversarial text perturbations on the inputs, covering four extraction methods, three attack strategies, six personas from Anthropic Model-Written Evaluation Dataset, and five models ranging from 1.5B to 30B parameters. Attacks succeed broadly across all settings: directional robustness drops by up to 64%, post-attack confidence collapses near or below 0.25 across all methods and models, and steering strength degrades on nearly every steerable input. Layer selection is equally fragile, with the optimal layer identified by an automated method on clean inputs shifting by up to 17 positions under perturbation, a failure that compounds the vector-level breakdown. Extracting vectors from adversarially perturbed inputs partially recovers steerability for PCA and MD on mid-to-large models, but they consistently fail to locate the improved optimal layer, limiting the practical benefit of this mitigation. Together, these findings reveal that the brittleness of activation steering is structural rather than method-specific, and that current layer selection strategies are not robust enough for real-world deployment.

Vision-Language-Action (VLA) models leverage powerful perceptual priors from web-scale Vision-Language Model (VLM) pre-training, yet they remain surprisingly brittle in practice, frequently failing at simple robotic tasks. To mitigate this, we propose Contrastive Conceptor Activation Steering (COAST). COAST builds on the notion of a "conceptor", a linear operator that soft-projects data into the principal components of a target distribution. COAST uses conceptors to identify success-critical subspaces for a target robotic task from a few examples of success and failure rollouts. At inference time, it steers VLA latents into these identified success subspaces to improve task outcomes. Across three architecturally distinct neural policies (flow-matching VLA, autoregressive VLA, and Diffusion Policy), COAST improves absolute mean simulation and real-robot task success rate by over 20 and 40% respectively. The activation subspace geometry reveals that failure modes share substantial structure across tasks while success representations remain largely task-specific. When tasks share similar failure modes, this structure enables previously fitted conceptors to improve performance on new tasks without refitting. Ultimately, our results suggest that current VLAs retain substantial task-relevant knowledge in their latent representations, and that the action expert's decoding bottleneck could be mitigated by steering its residual stream toward task-relevant subspaces. COAST provides a lightweight, training-free path to unlocking these latent capabilities by steering the model towards its own "success" distributions.

Activation steering controls language model behavior by adding directions to internal representations at inference time, but standard residual-stream steering can fail in stateful dialogue. We identify KV-cache contamination as a key failure mode: steered token states are stored and repeatedly reused, turning a local perturbation into cumulative coherence degradation. To address this challenge, we propose Gated Cropped Attention-Delta steering (GCAD), which extracts steering signals from system-prompt contributions to self-attention and applies them with token-level gating. Across persona-steering experiments, GCAD preserves trait control while substantially improving long-horizon coherence. On the main multi-turn benchmark, GCAD improves average coherence drift from -18.6 to -1.9 and raises turn-10 trait expression from 78.0 to 93.1. These results suggest that activation steering becomes more reliable when interventions follow the prompt-mediated pathways that models already use for behavioral control.

Modern large language models (LLMs) are typically secured by auditing data, prompts, and refusal policies, while treating the forward pass as an implementation detail. We show that intermediate activations in decoder-only LLMs form a vulnerable attack surface for behavioral control. Building on recent findings on attention sinks and compression valleys, we identify a high-gain region in the residual stream where small, well-aligned perturbations are causally amplified along the autoregressive trajectory--a Causal Amplification Effect (CAE). We exploit this as an attack surface via Sensitivity-Scaled Steering (SSS), a progressive activation-level attack that combines beginning-of-sequence (BOS) anchoring with sensitivity-based reinforcement to focus a limited perturbation budget on the most vulnerable layers and tokens. We show that across multiple open-weight models and four behavioral axes, SSS induces large shifts in evil, hallucination, sycophancy, and sentiment while preserving high coherence and general capabilities, turning activation steering into a concrete security concern for white-box and supply-chain LLM deployments.

We investigate whether independently trained language models converge to geometrically compatible latent representations, and whether this compatibility can be exploited to correct model behavior at inference time without any weight updates. We learn a linear projection matrix that maps activation vectors from a large teacher model into the coordinate system of a smaller student model, then intervene on the student's residual stream during generation by substituting its internal state with the translated teacher representation. Across a fully crossed experimental matrix of 20 heterogeneous teacher-student pairings spanning mixture-of-experts, dense, code-specialized, and synthetically trained architectures, the Ridge projection consistently achieves R^2 = 0.50 on verbal reasoning and R^2 = 0.40 on mathematical reasoning, collapsing to R^2 = -0.22 under permutation control and R^2 = 0.01 under L_1 regularization. Behavioral correction rates range from 14.0% to 50.0% on TruthfulQA (mean 25.2%) and from 8.5% to 43.3% on GSM8K arithmetic reasoning (mean 25.5%), demonstrating that the method generalizes across fundamentally different reasoning domains. We report a near-zero correlation between geometric alignment quality and behavioral correction rate (r = -0.07), revealing a dissociation between representation space fidelity and output space impact. Intervention strength is architecture-specific: student models exhibit characteristic sensitivity profiles that invert across domains, with the most steerable verbal student becoming the least steerable mathematical student. Finally, a double dissociation experiment conducted across all 20 model pairings confirms without exception that projection matrices collapse catastrophically when transferred across reasoning domains (mean R^2 = -3.83 in both transfer directions), establishing domain-specific subspace geometry as a universal property of LMs.

Large language models (LLMs) are now ubiquitous in user-facing applications, yet they still generate undesirable toxic outputs, including profanity, vulgarity, and derogatory remarks. Although numerous detoxification methods exist, most apply broad, surface-level fixes and can therefore easily be circumvented by jailbreak attacks. In this paper we leverage sparse autoencoders (SAEs) to identify toxicity-related directions in the residual stream of models and perform targeted activation steering using the corresponding decoder vectors. We introduce three tiers of steering aggressiveness and evaluate them on GPT-2 Small and Gemma-2-2B, revealing trade-offs between toxicity reduction and language fluency. At stronger steering strengths, these causal interventions surpass competitive baselines in reducing toxicity by up to 20%, though fluency can degrade noticeably on GPT-2 Small depending on the aggressiveness. Crucially, standard NLP benchmark scores upon steering remain stable, indicating that the model's knowledge and general abilities are preserved. We further show that feature-splitting in wider SAEs hampers safety interventions, underscoring the importance of disentangled feature learning. Our findings highlight both the promise and the current limitations of SAE-based causal interventions for LLM detoxification, further suggesting practical guidelines for safer language-model deployment.

In this paper, we delve into several mechanisms employed by Transformer-based language models (LLMs) for factual recall tasks. We outline a pipeline consisting of three major steps: (1) Given a prompt ``The capital of France is,'' task-specific attention heads extract the topic token, such as ``France,'' from the context and pass it to subsequent MLPs. (2) As attention heads' outputs are aggregated with equal weight and added to the residual stream, the subsequent MLP acts as an ``activation,'' which either erases or amplifies the information originating from individual heads. As a result, the topic token ``France'' stands out in the residual stream. (3) A deep MLP takes ``France'' and generates a component that redirects the residual stream towards the direction of the correct answer, i.e., ``Paris.'' This procedure is akin to applying an implicit function such as ``get\_capital(X),'' and the argument X is the topic token information passed by attention heads. To achieve the above quantitative and qualitative analysis for MLPs, we proposed a novel analytic method aimed at decomposing the outputs of the MLP into components understandable by humans. Additionally, we observed a universal anti-overconfidence mechanism in the final layer of models, which suppresses correct predictions. We mitigate this suppression by leveraging our interpretation to improve factual recall confidence. The above interpretations are evaluated across diverse tasks spanning various domains of factual knowledge, using various language models from the GPT-2 families, 1.3B OPT, up to 7B Llama-2, and in both zero- and few-shot setups.

Decomposing model activations into interpretable components is a key open problem in mechanistic interpretability. Sparse autoencoders (SAEs) are a popular method for decomposing the internal activations of trained transformers into sparse, interpretable features, and have been applied to MLP layers and the residual stream. In this work we train SAEs on attention layer outputs and show that also here SAEs find a sparse, interpretable decomposition. We demonstrate this on transformers from several model families and up to 2B parameters. We perform a qualitative study of the features computed by attention layers, and find multiple families: long-range context, short-range context and induction features. We qualitatively study the role of every head in GPT-2 Small, and estimate that at least 90% of the heads are polysemantic, i.e. have multiple unrelated roles. Further, we show that Sparse Autoencoders are a useful tool that enable researchers to explain model behavior in greater detail than prior work. For example, we explore the mystery of why models have so many seemingly redundant induction heads, use SAEs to motivate the hypothesis that some are long-prefix whereas others are short-prefix, and confirm this with more rigorous analysis. We use our SAEs to analyze the computation performed by the Indirect Object Identification circuit (Wang et al.), validating that the SAEs find causally meaningful intermediate variables, and deepening our understanding of the semantics of the circuit. We open-source the trained SAEs and a tool for exploring arbitrary prompts through the lens of Attention Output SAEs.

Activation patching is a standard method in mechanistic interpretability for localizing the components of a model responsible for specific behaviors, but it is computationally expensive to apply at scale. Attribution patching offers a faster, gradient-based approximation, yet suffers from noise and reduced reliability in deep, highly non-linear networks. In this work, we introduce Relevance Patching (RelP), which replaces the local gradients in attribution patching with propagation coefficients derived from Layer-wise Relevance Propagation (LRP). LRP propagates the network's output backward through the layers, redistributing relevance to lower-level components according to local propagation rules that ensure properties such as relevance conservation or improved signal-to-noise ratio. Like attribution patching, RelP requires only two forward passes and one backward pass, maintaining computational efficiency while improving faithfulness. We validate RelP across a range of models and tasks, showing that it more accurately approximates activation patching than standard attribution patching, particularly when analyzing residual stream and MLP outputs in the Indirect Object Identification (IOI) task. For instance, for MLP outputs in GPT-2 Large, attribution patching achieves a Pearson correlation of 0.006, whereas RelP reaches 0.956, highlighting the improvement offered by RelP. Additionally, we compare the faithfulness of sparse feature circuits identified by RelP and Integrated Gradients (IG), showing that RelP achieves comparable faithfulness without the extra computational cost associated with IG.

Role-playing has emerged as an effective technique for enhancing the reasoning capabilities of large language models (LLMs). However, existing methods primarily rely on prompt engineering, which often lacks stability and interpretability. In this paper, we introduce Sparse Autoencoder Role-Playing Steering (SRPS), a novel framework that identifies and manipulates internal model features associated with role-playing behavior. Our approach extracts latent representations from role-play prompts, selects the most relevant features based on activation patterns, and constructs a steering vector that can be injected into the model's residual stream with controllable intensity. Our method enables fine-grained control over role-specific behavior and offers insights into how role information influences internal model activations. Extensive experiments across various reasoning benchmarks and model sizes demonstrate consistent performance gains. Notably, in the zero-shot chain-of-thought (CoT) setting, the accuracy of Llama3.1-8B on CSQA improves from 31.86% to 39.80%, while Gemma2-9B on SVAMP increases from 37.50% to 45.10%. These results highlight the potential of SRPS to enhance reasoning ability in LLMs, providing better interpretability and stability compared to traditional prompt-based role-playing.

In Transformer language models, activation vectors transform from current token embeddings to next token predictions as they pass through the model. To isolate a minimal form of this transformation, we identify language model subnetworks that make bigram predictions, naive next token predictions based only on the current token. We find that bigram subnetworks can be found in fully trained language models up to 1B parameters, and these subnetworks are critical for model performance even when they consist of less than 0.2% of model parameters. Bigram subnetworks are concentrated in the first Transformer MLP layer, and they overlap significantly with subnetworks trained to optimally prune a given model. Mechanistically, the bigram subnetworks often recreate a pattern from the full models where the first layer induces a sharp change that aligns activations with next token predictions rather than current token representations. Our results demonstrate that bigram subnetworks comprise a minimal subset of parameters that are both necessary and sufficient for basic next token predictions in language models, and they help drive the transformation from current to next token activations in the residual stream. These subnetworks can lay a foundation for studying language model circuits by building up from a minimal circuit rather than the traditional approach of ablating circuits from a full model.

While Attention Residuals has shown some effectiveness in addressing the widespread issue of unbounded activation growth across deep residual layers, it inevitably incurs significant communication overhead. To circumvent this bottleneck, we propose Multi-Gate Residuals (MGR), which stabilizes activation scales without additional communication burden. It utilizes a straightforward scoring and gating mechanism to maintain multi-stream context, coupled with Attention Pooling to extract hidden states from the stream states. Empirical experiments demonstrate that MGR is practical for large-scale training and deployment, offering tangible performance improvements over existing architectures.

Residual connections with PreNorm are standard in modern LLMs, yet they accumulate all layer outputs with fixed unit weights. This uniform aggregation causes uncontrolled hidden-state growth with depth, progressively diluting each layer's contribution. We propose Attention Residuals (AttnRes), which replaces this fixed accumulation with softmax attention over preceding layer outputs, allowing each layer to selectively aggregate earlier representations with learned, input-dependent weights. To address the memory and communication overhead of attending over all preceding layer outputs for large-scale model training, we introduce Block AttnRes, which partitions layers into blocks and attends over block-level representations, reducing the memory footprint while preserving most of the gains of full AttnRes. Combined with cache-based pipeline communication and a two-phase computation strategy, Block AttnRes becomes a practical drop-in replacement for standard residual connections with minimal overhead. Scaling law experiments confirm that the improvement is consistent across model sizes, and ablations validate the benefit of content-dependent depth-wise selection. We further integrate AttnRes into the Kimi Linear architecture (48B total / 3B activated parameters) and pre-train on 1.4T tokens, where AttnRes mitigates PreNorm dilution, yielding more uniform output magnitudes and gradient distribution across depth, and improves downstream performance across all evaluated tasks.

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

Low-bit weight-only quantization significantly reduces the memory footprint of large language models (LLMs), but disproportionately affects certain examples. We analyze diverse 3-4 bit methods on LLMs ranging from 7B-70B in size and find that the quantization errors of 50 pairs of methods are strongly correlated (avg. 0.82) on FineWeb examples. Moreover, the residual stream magnitudes of full-precision models are indicative of future quantization errors. We further establish a hypothesis that relates the residual stream magnitudes to error amplification and accumulation over layers. Using LLM localization techniques, early exiting, and activation patching, we show that examples with large errors rely on precise residual activations in the late layers, and that the outputs of MLP gates play a crucial role in maintaining the perplexity. Our work reveals why certain examples result in large quantization errors and which model components are most critical for performance preservation.

Multi-stream transformer architectures have recently been proposed as a promising direction for managing representation collapse and the vanishing gradient problem for residual connections, yet their internal mechanisms remain unexplored. In particular, the recently introduced Manifold-Constrained Hyper-Connections (mHC) architecture posits multiple residual streams with constrained interaction, but lacks in-depth mechanistic analysis. We present the first open-source mHC language model (https://huggingface.co/wgpeng/mhc-780m) and analyze the multiple-stream architecture with a suite of representation-level metrics and causal interventions to probe how parallel streams encode and utilize information. Specifically, we introduce a systematic stream ablation-and-rescue framework that enables direct causal comparison of residual streams during inference. Through targeted pairwise interventions and controlled recovery experiments, we distinguish functional redundancy from asymmetric utilization and reveal how information is distributed across streams beyond what is observable from representational similarity alone.

Recent progress in video large language models (Video-LLMs) has enabled strong offline reasoning over long and complex videos. However, real-world deployments increasingly require streaming perception and proactive interaction, where video frames arrive online and the system must decide not only what to respond, but also when to respond. In this work, we revisit proactive activation in streaming video as a structured sequence modeling problem, motivated by the observation that temporal transitions in streaming video naturally form span-structured activation patterns. To capture this span-level structure, we model activation signals jointly over a sliding temporal window and update them iteratively as new frames arrive. We propose STRIDE (Structured Temporal Refinement with Iterative DEnoising), which employs a lightweight masked diffusion module at the activation interface to jointly predict and progressively refine activation signals across the window. Extensive experiments on diverse streaming benchmarks and downstream models demonstrate that STRIDE shows more reliable and temporally coherent proactive responses, significantly improving when-to-speak decision quality in online streaming scenarios.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which suggest that the forward and backward signals can be directly propagated from one block to any other block, when using identity mappings as the skip connections and after-addition activation. A series of ablation experiments support the importance of these identity mappings. This motivates us to propose a new residual unit, which makes training easier and improves generalization. We report improved results using a 1001-layer ResNet on CIFAR-10 (4.62% error) and CIFAR-100, and a 200-layer ResNet on ImageNet. Code is available at: https://github.com/KaimingHe/resnet-1k-layers

Deep residual networks were shown to be able to scale up to thousands of layers and still have improving performance. However, each fraction of a percent of improved accuracy costs nearly doubling the number of layers, and so training very deep residual networks has a problem of diminishing feature reuse, which makes these networks very slow to train. To tackle these problems, in this paper we conduct a detailed experimental study on the architecture of ResNet blocks, based on which we propose a novel architecture where we decrease depth and increase width of residual networks. We call the resulting network structures wide residual networks (WRNs) and show that these are far superior over their commonly used thin and very deep counterparts. For example, we demonstrate that even a simple 16-layer-deep wide residual network outperforms in accuracy and efficiency all previous deep residual networks, including thousand-layer-deep networks, achieving new state-of-the-art results on CIFAR, SVHN, COCO, and significant improvements on ImageNet. Our code and models are available at https://github.com/szagoruyko/wide-residual-networks

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear reservoir, where the latter is based on residual orthogonal connections along the temporal dimension for enhanced long-term propagation of the input. The resulting reservoir state dynamics are studied through the lens of linear stability analysis, and we investigate diverse configurations for the temporal residual connections. The proposed approach is empirically assessed on time-series and pixel-level 1-D classification tasks. Our experimental results highlight the advantages of the proposed approach over other conventional RC models.

The success of powerful open source Large Language Models (LLMs) has enabled the community to create a vast collection of post-trained models adapted to specific tasks and domains. However, navigating and understanding these models remains challenging due to inconsistent metadata and unstructured repositories. We introduce Delta Activations, a method to represent finetuned models as vector embeddings by measuring shifts in their internal activations relative to a base model. This representation allows for effective clustering by domain and task, revealing structure in the model landscape. Delta Activations also demonstrate desirable properties: it is robust across finetuning settings and exhibits an additive property when finetuning datasets are mixed. In addition, we show that Delta Activations can embed tasks via few-shot finetuning, and further explore its use for model selection and merging. We hope Delta Activations can facilitate the practice of reusing publicly available models. Code is available at https://github.com/OscarXZQ/delta_activations.

Deep residual architectures, such as ResNet and the Transformer, have enabled models of unprecedented depth, yet a formal understanding of why depth is so effective remains an open question. A popular intuition, following Veit et al. (2016), is that these residual networks behave like ensembles of many shallower models. Our key finding is an explicit analytical formula that verifies this ensemble perspective, proving that increasing network depth is mathematically equivalent to expanding the size of this implicit ensemble. Furthermore, our expansion reveals a hierarchical ensemble structure in which the combinatorial growth of computation paths leads to an explosion in the output signal, explaining the historical necessity of normalization layers in training deep models. This insight offers a first principles explanation for the historical dependence on normalization layers and sheds new light on a family of successful normalization-free techniques like SkipInit and Fixup. However, while these previous approaches infer scaling factors through optimizer analysis or a heuristic analogy to Batch Normalization, our work offers the first explanation derived directly from the network's inherent functional structure. Specifically, our Residual Expansion Theorem reveals that scaling each residual module provides a principled solution to taming the combinatorial explosion inherent to these architectures. We further show that this scaling acts as a capacity controls that also implicitly regularizes the model's complexity.

Attention Residuals replace standard additive residual connections with learned softmax attention over previous layer outputs, enabling selective cross-layer routing. However, standard Attention Residuals still attend over cumulative hidden states in previous layers, which are highly redundant. We show that this redundancy leads to routing collapse in deeper layers: attention weights become low-contrast and closer to uniform (max weight {approx}0.2), limiting the model's ability to select informative states in previous layers. This raises a key but underexplored design question: what layer-wise representations should be routed in Attention Residuals? To answer this question, we propose Delta Attention Residuals, which attend over deltas -- the change introduced by each sublayer (v_i = h_{i+1} - h_i) -- instead of cumulative states. Delta representations are structurally diverse and yield higher-contrast attention distributions (max weight {approx}0.6), enabling more selective and effective routing across layers. This principle applies at both per-sublayer and block granularity. Across all tested scales (220M--7.6B), Delta Attention Residuals consistently outperform both standard residuals and Attention Residuals, with 1.7--8.2\% validation perplexity gains. Delta Attention Residuals also enables converting pretrained checkpoints into Delta Attention Residuals via standard fine-tuning. Code is available at https://github.com/wdlctc/delta-attention-residuals-code.

We consider the problem of accurate quantization for language models, where both the weights and activations are uniformly quantized to 4 bits per parameter, the lowest bitwidth format natively supported by GPU hardware. In this context, the key challenge is activation quantization: it is known that language models contain outlier channels whose values on average are orders of magnitude higher than than other channels, which prevents accurate low-bitwidth quantization with known techniques. We systematically study this phenomena and find that these outlier channels emerge early in training, and that they occur more frequently in layers with residual streams. We then propose a simple strategy which regularizes a layer's inputs via quantization-aware training (QAT) and its outputs via activation kurtosis regularization. We show that regularizing both the inputs and outputs is crucial for preventing a model's "migrating" the difficulty in input quantization to the weights, which makes post-training quantization (PTQ) of weights more difficult. When combined with weight PTQ, we show that our approach can obtain a W4A4 model that performs competitively to the standard-precision W16A16 baseline.

Diffusion Transformers (DiTs) have become a de facto backbone of modern visual generation, and nearly every major axis of their design -- tokenization, attention, conditioning, objectives, and latent autoencoders -- has been extensively revisited. The residual stream that governs how information accumulates across layers, however, has been directly inherited from the original Transformer. In this paper, we present a systematic empirical analysis of cross-layer information flow in DiTs, jointly along depth and denoising timestep, and identify three concrete symptoms of traditional residual addition, namely monotonic forward magnitude inflation, sharp backward gradient decay, and pronounced block-wise redundancy. Motivated by this diagnosis, we propose Diffusion-Adaptive Routing (DAR), a drop-in residual replacement that performs learnable, timestep-adaptive, and non-incremental aggregation over the history of sublayer outputs. Moreover, the proposed DAR is compatible with many modern Transformer enhancement methods, such as REPA. On ImageNet 256times256, DAR improves SiT-XL/2 by 2.11 FID (7.56 vs.\ 9.67) and matches the baseline's converged quality with 8.75times fewer training iterations. Stacked on top of REPA, it yields a 2times training acceleration in the early stage, suggesting cross-layer information routing as an underexplored design axis in diffusion modeling, one that operates orthogonally to existing representation-alignment objectives. Beyond pretraining, DAR can also be applied during the fine-tuning stage of large-scale T2I models and preserves high-frequency details during Distribution Matching Distillation.

Several recent Transformer architectures expose later layers to representations computed in the earliest layers, motivated by the observation that low-level features can become harder to recover as the residual stream is repeatedly transformed through depth. The cheapest among these methods add static value residuals: learned mixing coefficients that expose the first-layer value projection V_1 uniformly across tokens and heads. More expressive dense or dynamic alternatives recover finer-grained access, but at higher memory cost and lower throughput. The usefulness of V_1 is unlikely to be constant across tokens, heads, and contexts; different positions plausibly require different amounts of access to early lexical or semantic information. We therefore treat early-representation reuse as a retrieval problem rather than a connectivity problem, and introduce Selective Access Transformer (SATFormer), which preserves the first-layer value pathway while controlling access with a context-dependent gate. Across models from 130M to 1.3B parameters, SATFormer consistently improves validation loss and zero-shot accuracy over the static value-residual and Transformer baselines. Its strongest gains appear on retrieval-intensive benchmarks, where it improves over static value residuals by approximately 1.5 average points, while maintaining throughput and memory usage close to the baseline Transformer. Gate analyses suggest sparse, depth-dependent, head-specific, and category-sensitive access patterns, supporting the interpretation that SATFormer learns selective reuse of early representations rather than uniform residual copying. Our code is available at https://github.com/SkyeGunasekaran/SATFormer.

Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are impossible in shallow models, or do they merely spread the same kinds of computation out over more layers? To address these questions, we analyze the residual stream of the Llama 3.1 and Qwen 3 family of models. We find: First, comparing the output of the sublayers to the residual stream reveals that layers in the second half contribute much less than those in the first half, with a clear phase transition between the two halves. Second, skipping layers in the second half has a much smaller effect on future computations and output predictions. Third, for multihop tasks, we are unable to find evidence that models are using increased depth to compose subresults in examples involving many hops. Fourth, we seek to directly address whether deeper models are using their additional layers to perform new kinds of computation. To do this, we train linear maps from the residual stream of a shallow model to a deeper one. We find that layers with the same relative depth map best to each other, suggesting that the larger model simply spreads the same computations out over its many layers. All this evidence suggests that deeper models are not using their depth to learn new kinds of computation, but only using the greater depth to perform more fine-grained adjustments to the residual. This may help explain why increasing scale leads to diminishing returns for stacked Transformer architectures.

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

Existing 1D visual tokenizers for autoregressive (AR) generation largely follow the design principles of language modeling, as they are built directly upon transformers whose priors originate in language, yielding single-hierarchy latent tokens and treating visual data as flat sequential token streams. However, this language-like formulation overlooks key properties of vision, particularly the hierarchical and residual network designs that have long been essential for convergence and efficiency in visual models. To bring "vision" back to vision, we propose the Residual Tokenizer (ResTok), a 1D visual tokenizer that builds hierarchical residuals for both image tokens and latent tokens. The hierarchical representations obtained through progressively merging enable cross-level feature fusion at each layer, substantially enhancing representational capacity. Meanwhile, the semantic residuals between hierarchies prevent information overlap, yielding more concentrated latent distributions that are easier for AR modeling. Cross-level bindings consequently emerge without any explicit constraints. To accelerate the generation process, we further introduce a hierarchical AR generator that substantially reduces sampling steps by predicting an entire level of latent tokens at once rather than generating them strictly token-by-token. Extensive experiments demonstrate that restoring hierarchical residual priors in visual tokenization significantly improves AR image generation, achieving a gFID of 2.34 on ImageNet-256 with only 9 sampling steps. Code is available at https://github.com/Kwai-Kolors/ResTok.

Large Language Models (LLMs) are trained with next-token prediction, implemented in autoregressive Transformers via causal masking for parallelism. This creates a subtle misalignment: residual connections tie activations to the current token, while supervision targets the next token, potentially propagating mismatched information if the current token is not the most informative for prediction. In this work, we empirically localize this input-output alignment shift in pretrained LLMs, using decoding trajectories over tied embedding spaces and similarity-based metrics. Our experiments reveal that the hidden token representations switch from input alignment to output alignment deep within the network. Motivated by this observation, we propose a lightweight residual-path mitigation based on residual attenuation, implemented either as a fixed-layer intervention or as a learnable gating mechanism. Experiments on multiple benchmarks show that these strategies alleviate the representation misalignment and yield improvements, providing an efficient and general architectural enhancement for autoregressive Transformers.

Residual connections are pivotal for deep neural networks, enabling greater depth by mitigating vanishing gradients. However, in standard residual updates, the module's output is directly added to the input stream. This can lead to updates that predominantly reinforce or modulate the existing stream direction, potentially underutilizing the module's capacity for learning entirely novel features. In this work, we introduce Orthogonal Residual Update: we decompose the module's output relative to the input stream and add only the component orthogonal to this stream. This design aims to guide modules to contribute primarily new representational directions, fostering richer feature learning while promoting more efficient training. We demonstrate that our orthogonal update strategy improves generalization accuracy and training stability across diverse architectures (ResNetV2, Vision Transformers) and datasets (CIFARs, TinyImageNet, ImageNet-1k), achieving, for instance, a +4.3\%p top-1 accuracy gain for ViT-B on ImageNet-1k.

Very deep convolutional networks have been central to the largest advances in image recognition performance in recent years. One example is the Inception architecture that has been shown to achieve very good performance at relatively low computational cost. Recently, the introduction of residual connections in conjunction with a more traditional architecture has yielded state-of-the-art performance in the 2015 ILSVRC challenge; its performance was similar to the latest generation Inception-v3 network. This raises the question of whether there are any benefit in combining the Inception architecture with residual connections. Here we give clear empirical evidence that training with residual connections accelerates the training of Inception networks significantly. There is also some evidence of residual Inception networks outperforming similarly expensive Inception networks without residual connections by a thin margin. We also present several new streamlined architectures for both residual and non-residual Inception networks. These variations improve the single-frame recognition performance on the ILSVRC 2012 classification task significantly. We further demonstrate how proper activation scaling stabilizes the training of very wide residual Inception networks. With an ensemble of three residual and one Inception-v4, we achieve 3.08 percent top-5 error on the test set of the ImageNet classification (CLS) challenge

Convolutional neural network (CNN) depth is of crucial importance for image super-resolution (SR). However, we observe that deeper networks for image SR are more difficult to train. The low-resolution inputs and features contain abundant low-frequency information, which is treated equally across channels, hence hindering the representational ability of CNNs. To solve these problems, we propose the very deep residual channel attention networks (RCAN). Specifically, we propose a residual in residual (RIR) structure to form very deep network, which consists of several residual groups with long skip connections. Each residual group contains some residual blocks with short skip connections. Meanwhile, RIR allows abundant low-frequency information to be bypassed through multiple skip connections, making the main network focus on learning high-frequency information. Furthermore, we propose a channel attention mechanism to adaptively rescale channel-wise features by considering interdependencies among channels. Extensive experiments show that our RCAN achieves better accuracy and visual improvements against state-of-the-art methods.

We present Hierarchical Residual Networks (HiResNets), deep convolutional neural networks with long-range residual connections between layers at different hierarchical levels. HiResNets draw inspiration on the organization of the mammalian brain by replicating the direct connections from subcortical areas to the entire cortical hierarchy. We show that the inclusion of hierarchical residuals in several architectures, including ResNets, results in a boost in accuracy and faster learning. A detailed analysis of our models reveals that they perform hierarchical compositionality by learning feature maps relative to the compressed representations provided by the skip connections.

Transformers can capture long-range dependencies using self-attention, allowing tokens to attend to all others directly. However, stacking multiple attention layers leads to attention concentration. One natural way to address this issue is to use cross-layer attention, allowing information from earlier layers to be directly accessible to later layers. However, this approach is computationally expensive. To address this problem, we propose Transformer with residual value (ResFormer) which approximates cross-layer attention through adding a residual connection from the values of the the first layer to all subsequent layers. Based on this method, one variant is the Transformer with single layer value (SVFormer), where all layers share the same value embedding from first layer, reducing the KV cache by nearly 50%. Comprehensive empirical evidence demonstrates that ResFormer mitigates attention concentration problem in deeper layers and enhances representation across most layers, outperforming the vanilla Transformer, DenseFormer, and NeuTRENO in training error as well as downstream tasks. SVFormer trains significantly faster than the vanilla Transformer and performs better than other methods like GQA and CLA, with performance influenced by sequence length and cumulative learning rate.

In this work, we propose "Residual Attention Network", a convolutional neural network using attention mechanism which can incorporate with state-of-art feed forward network architecture in an end-to-end training fashion. Our Residual Attention Network is built by stacking Attention Modules which generate attention-aware features. The attention-aware features from different modules change adaptively as layers going deeper. Inside each Attention Module, bottom-up top-down feedforward structure is used to unfold the feedforward and feedback attention process into a single feedforward process. Importantly, we propose attention residual learning to train very deep Residual Attention Networks which can be easily scaled up to hundreds of layers. Extensive analyses are conducted on CIFAR-10 and CIFAR-100 datasets to verify the effectiveness of every module mentioned above. Our Residual Attention Network achieves state-of-the-art object recognition performance on three benchmark datasets including CIFAR-10 (3.90% error), CIFAR-100 (20.45% error) and ImageNet (4.8% single model and single crop, top-5 error). Note that, our method achieves 0.6% top-1 accuracy improvement with 46% trunk depth and 69% forward FLOPs comparing to ResNet-200. The experiment also demonstrates that our network is robust against noisy labels.

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving token-space dynamics underexplored. The high dimensionality and categoricity of token distributions hinder their analysis, as standard statistical descriptors are not suitable. We show that the entropy of logit-lens predictions overcomes these issues. In doing so, it provides a per-layer scalar, permutation-invariant metric. We introduce Entropy-Lens to distill the token-space dynamics of the residual stream into a low-dimensional signal. We call this signal the entropy profile. We apply our method to a variety of model sizes and families, showing that (i) entropy profiles uncover token prediction dynamics driven by expansion and pruning strategies; (ii) these dynamics are family-specific and invariant under depth rescaling; (iii) they are characteristic of task type and output format; (iv) these strategies have unequal impact on downstream performance, with the expansion strategy usually being more critical. Ultimately, our findings further enhance our understanding of the residual stream, enabling a granular assessment of how information is processed across model depth.

In this paper, we present a novel framework for enhancing the performance of Quanvolutional Neural Networks (QuNNs) by introducing trainable quanvolutional layers and addressing the critical challenges associated with them. Traditional quanvolutional layers, although beneficial for feature extraction, have largely been static, offering limited adaptability. Unlike state-of-the-art, our research overcomes this limitation by enabling training within these layers, significantly increasing the flexibility and potential of QuNNs. However, the introduction of multiple trainable quanvolutional layers induces complexities in gradient-based optimization, primarily due to the difficulty in accessing gradients across these layers. To resolve this, we propose a novel architecture, Residual Quanvolutional Neural Networks (ResQuNNs), leveraging the concept of residual learning, which facilitates the flow of gradients by adding skip connections between layers. By inserting residual blocks between quanvolutional layers, we ensure enhanced gradient access throughout the network, leading to improved training performance. Moreover, we provide empirical evidence on the strategic placement of these residual blocks within QuNNs. Through extensive experimentation, we identify an efficient configuration of residual blocks, which enables gradients across all the layers in the network that eventually results in efficient training. Our findings suggest that the precise location of residual blocks plays a crucial role in maximizing the performance gains in QuNNs. Our results mark a substantial step forward in the evolution of quantum deep learning, offering new avenues for both theoretical development and practical quantum computing applications.

This paper accelerates video perception, such as semantic segmentation and human pose estimation, by levering cross-frame redundancies. Unlike the existing approaches, which avoid redundant computations by warping the past features using optical-flow or by performing sparse convolutions on frame differences, we approach the problem from a new perspective: low-bit quantization. We observe that residuals, as the difference in network activations between two neighboring frames, exhibit properties that make them highly quantizable. Based on this observation, we propose a novel quantization scheme for video networks coined as Residual Quantization. ResQ extends the standard, frame-by-frame, quantization scheme by incorporating temporal dependencies that lead to better performance in terms of accuracy vs. bit-width. Furthermore, we extend our model to dynamically adjust the bit-width proportional to the amount of changes in the video. We demonstrate the superiority of our model, against the standard quantization and existing efficient video perception models, using various architectures on semantic segmentation and human pose estimation benchmarks.

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

A method is presented for accelerating inference in transformer language models by exploiting the low effective rank of the token activation manifold at each layer. The method decomposes each activation vector into a subspace component and a residual, computes the linear-layer output on the subspace component via a cached low-rank weight image at reduced memory bandwidth, and applies a per-token gate that determines whether the residual correction is computed or skipped. The gate ensures that the output distribution is preserved to within a controllable tolerance. Validation on three model families (GPT-2 124M, GPT-J 6B, OPT 6.7B) on AMD MI300X demonstrates effective speedups of 3.0x to 10.5x on linear-layer weight reads with perplexity ratios below 1.00 and top-1 token agreement above 98%. The method requires no retraining, no architectural modification, and no approximation of the attention mechanism. At the operating point (k = 256, ε = 0.05) on GPT-J 14 6B, the accelerated model produces character-for-character identical output to the baseline.

The key-value (KV) cache is widely treated as essential state in transformer inference, and a large body of work engineers policies to compress, evict, or approximate its entries. We prove that this state is entirely redundant: keys and values at every layer are deterministic projections of the residual stream, and recomputing them from a single residual vector per token incurs exactly zero reconstruction error, not approximately, but bit-identically. We verify this across six models from four architecture families (135M to 4B parameters). Cross-task residual patching at every layer produces D_KL = 0 between patched and original output distributions, confirming that the residual stream satisfies a Markov property and is the sole information-carrying state. Removing the cache entirely and recomputing from scratch yields token-identical output under greedy decoding on all models tested. We build on this result with KV-Direct, a bounded-memory inference scheme that checkpoints residual vectors (5 KB per token on Gemma 3-4B) instead of full KV pairs (136 KB), recomputing keys and values on demand. Over 20 conversation turns, KV-Direct holds peak memory at 42 MB while the standard cache grows past 103 MB. Against five eviction baselines (H2O, StreamingLLM, SnapKV, TOVA, window-only), KV-Direct maintains 100% token match at every cache budget; all baselines degrade to 5-28%. A per-operation latency analysis shows recomputation runs up to 5x faster than reading cached tensors at moderate batch sizes. Code is available at https://github.com/Kaleemullahqasim/KV-Direct.

One of the core pillars of efficient deep learning methods is architectural improvements such as the residual/skip connection, which has led to significantly better model convergence and quality. Since then the residual connection has become ubiquitous in not just convolutional neural networks but also transformer-based architectures, the backbone of LLMs. In this paper we introduce Learned Augmented Residual Layer (LAuReL) -- a novel generalization of the canonical residual connection -- with the goal to be an in-situ replacement of the latter while outperforming on both model quality and footprint metrics. Our experiments show that using \laurel can help boost performance for both vision and language models. For example, on the ResNet-50, ImageNet 1K task, it achieves 60% of the gains from adding an extra layer, while only adding 0.003% more parameters, and matches it while adding 2.6times fewer parameters.

Batch Normalization is a key component in almost all state-of-the-art image classifiers, but it also introduces practical challenges: it breaks the independence between training examples within a batch, can incur compute and memory overhead, and often results in unexpected bugs. Building on recent theoretical analyses of deep ResNets at initialization, we propose a simple set of analysis tools to characterize signal propagation on the forward pass, and leverage these tools to design highly performant ResNets without activation normalization layers. Crucial to our success is an adapted version of the recently proposed Weight Standardization. Our analysis tools show how this technique preserves the signal in networks with ReLU or Swish activation functions by ensuring that the per-channel activation means do not grow with depth. Across a range of FLOP budgets, our networks attain performance competitive with the state-of-the-art EfficientNets on ImageNet.

We introduce SANA-Video 2.0, a hybrid video diffusion transformer instantiated at 5B and 14B scales under a unified architecture. Designed to generate high-quality video up to 720p on a single GPU, SANA-Video 2.0 matches full-softmax video DiTs in quality while retaining the favorable long-sequence scaling of linear attention. To avoid quadratic attention throughout, Hybrid Linear-Softmax Attention combines gated linear attention for O(N)-dominated mixing with periodic gated-softmax anchors at a 3:1 ratio, restoring the full-rank token interactions that pure linear attention lacks. To propagate these refreshed representations across depth, Block Attention Residuals (AttnRes) route completed block summaries into later linear layers, enabling anchor-feature reuse and boosting deep-layer effective rank by ~12%. Through from-scratch training, SANA-Video 2.0 learns the complete hybrid directly rather than linearizing pretrained models, with reduced-resolution proxy studies establishing 25% softmax as the optimal quality-efficiency trade-off. With 40-step sampling, SANA-Video 2.0 achieves a VBench score of 84.30 in 13.2s at 480p on a single H100, remaining competitive with far larger softmax video DiTs at a fraction of the latency. Its compiled DiT forward pass is 3.2x faster than a matched full-softmax baseline at 720p/60s, a gap that expands with video duration. Furthermore, full-stack Sol-Engine optimization (kernel fusion, caching, and sparse attention) accelerates this hardware-friendly backbone by a further 3.58x, bringing the 5B pipeline to 13.06s at 720p/5s and making it 120x faster than Wan 2.2-A14B on one H100. Overall, our hybrid design recovers softmax-level expressiveness at substantially reduced cost, unlocking scalable long, high resolution video generation.

The efficacy of deep residual networks is fundamentally predicated on the identity shortcut connection. While this mechanism effectively mitigates the vanishing gradient problem, it imposes a strictly additive inductive bias on feature transformations, thereby limiting the network's capacity to model complex state transitions. In this paper, we introduce Deep Delta Learning (DDL), a novel architecture that generalizes the standard residual connection by modulating the identity shortcut with a learnable, data-dependent geometric transformation. This transformation, termed the Delta Operator, constitutes a rank-1 perturbation of the identity matrix, parameterized by a reflection direction vector k(X) and a gating scalar β(X). We provide a spectral analysis of this operator, demonstrating that the gate β(X) enables dynamic interpolation between identity mapping, orthogonal projection, and geometric reflection. Furthermore, we restructure the residual update as a synchronous rank-1 injection, where the gate acts as a dynamic step size governing both the erasure of old information and the writing of new features. This unification empowers the network to explicitly control the spectrum of its layer-wise transition operator, enabling the modeling of complex, non-monotonic dynamics while preserving the stable training characteristics of gated residual architectures.

Several video understanding tasks, such as natural language temporal video grounding, temporal activity localization, and audio description generation, require "temporally dense" reasoning over frames sampled at high temporal resolution. However, computing frame-level features for these tasks is computationally expensive given the temporal resolution requirements. In this paper, we make three contributions to reduce the cost of computing features for temporally dense tasks. First, we introduce a vision transformer (ViT) architecture, dubbed ResidualViT, that leverages the large temporal redundancy in videos to efficiently compute temporally dense frame-level features. Our architecture incorporates (i) learnable residual connections that ensure temporal consistency across consecutive frames and (ii) a token reduction module that enhances processing speed by selectively discarding temporally redundant information while reusing weights of a pretrained foundation model. Second, we propose a lightweight distillation strategy to approximate the frame-level features of the original foundation model. Finally, we evaluate our approach across four tasks and five datasets, in both zero-shot and fully supervised settings, demonstrating significant reductions in computational cost (up to 60%) and improvements in inference speed (up to 2.5x faster), all while closely approximating the accuracy of the original foundation model.

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search of activation functions has largely relied on empirical knowledge in the past, lacking theoretical guidance, which has hindered the identification of more effective activation functions. In this work, we offer a proper solution to such issue. Firstly, we theoretically demonstrate the existence of the worst activation function with boundary conditions (WAFBC) from the perspective of information entropy. Furthermore, inspired by the Taylor expansion form of information entropy functional, we propose the Entropy-based Activation Function Optimization (EAFO) methodology. EAFO methodology presents a novel perspective for designing static activation functions in deep neural networks and the potential of dynamically optimizing activation during iterative training. Utilizing EAFO methodology, we derive a novel activation function from ReLU, known as Correction Regularized ReLU (CRReLU). Experiments conducted with vision transformer and its variants on CIFAR-10, CIFAR-100 and ImageNet-1K datasets demonstrate the superiority of CRReLU over existing corrections of ReLU. Extensive empirical studies on task of large language model (LLM) fine-tuning, CRReLU exhibits superior performance compared to GELU, suggesting its broader potential for practical applications.

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar\'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar\'e 2D convolutions up to Poincar\'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr\'echet mean calculations in hyperbolic space. We introduce Poincar\'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar\'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with long-term information processing. In this paper, we introduce a novel class of deep untrained RNNs based on temporal residual connections, called Deep Residual Echo State Networks (DeepResESNs). We show that leveraging a hierarchy of untrained residual recurrent layers significantly boosts memory capacity and long-term temporal modeling. For the temporal residual connections, we consider different orthogonal configurations, including randomly generated and fixed-structure configurations, and we study their effect on network dynamics. A thorough mathematical analysis outlines necessary and sufficient conditions to ensure stable dynamics within DeepResESN. Our experiments on a variety of time series tasks showcase the advantages of the proposed approach over traditional shallow and deep RC.

Despite the rapid evolution of training paradigms, the decoder backbone of large vision--language models (LVLMs) remains fundamentally rooted in the residual-connection Transformer architecture. Therefore, deciphering the distinct roles of internal modules is critical for understanding model mechanics and guiding architectural optimization. While prior statistical approaches have provided valuable attribution-based insights, they often lack a unified theoretical basis. To bridge this gap, we propose a unified framework grounded in information theory and geometry to quantify the geometric and entropic nature of residual updates. Applying this unified framework reveals a fundamental functional decoupling: Attention acts as a subspace-preserving operator focused on reconfiguration, whereas FFNs serve as subspace-expanding operators driving semantic innovation. Strikingly, further experiments demonstrate that replacing learned attention weights with predefined values (e.g., Gaussian noise) yields comparable or even superior performance across a majority of datasets relative to vanilla models. These results expose severe misallocation and redundancy in current mechanisms, suggesting that state-of-the-art LVLMs effectively ``get lost in attention'' rather than efficiently leveraging visual context.

Activation steering has emerged as a cost-effective paradigm for modifying large language model (LLM) behaviors. Existing methods typically intervene at the block level, steering the bundled activations of selected attention heads, feedforward networks, or residual streams. However, we reveal that block-level activations are inherently heterogeneous, entangling beneficial, irrelevant, and harmful features, thereby rendering block-level steering coarse, inefficient, and intrusive. To investigate the root cause, we decompose block activations into fine-grained atomic unit (AU)-level activations, where each AU-level activation corresponds to a single dimension of the block activation, and each AU denotes a slice of the block weight matrix. Steering an AU-level activation is thus equivalent to steering its associated AU. Our theoretical and empirical analysis show that heterogeneity arises because different AUs or dimensions control distinct token distributions in LLM outputs. Hence, block-level steering inevitably moves helpful and harmful token directions together, which reduces efficiency. Restricting intervention to beneficial AUs yields more precise and effective steering. Building on this insight, we propose AUSteer, a simple and efficient method that operates at a finer granularity of the AU level. AUSteer first identifies discriminative AUs globally by computing activation momenta on contrastive samples. It then assigns adaptive steering strengths tailored to diverse inputs and selected AU activations. Comprehensive experiments on multiple LLMs and tasks show that AUSteer consistently surpasses advanced baselines while steering considerably fewer activations, demonstrating that steering less achieves more.

Residual transformations enhance the representational depth and expressive power of large language models (LLMs). However, applying static residual transformations across all tokens in auto-regressive generation leads to a suboptimal trade-off between inference efficiency and generation fidelity. Existing methods, including Early Exiting, Skip Decoding, and Mixture-of-Depth address this by modulating the residual transformation based on token-level complexity. Nevertheless, these approaches predominantly consider the distance traversed by tokens through the model layers, neglecting the underlying velocity of residual evolution. We introduce Mixture of Multi-rate Residuals (M2R2), a framework that dynamically modulates residual velocity to improve early alignment, enhancing inference efficiency. Evaluations on reasoning oriented tasks such as Koala, Self-Instruct, WizardLM, and MT-Bench show M2R2 surpasses state-of-the-art distance-based strategies, balancing generation quality and speedup. In self-speculative decoding setup, M2R2 achieves up to 2.8x speedups on MT-Bench, outperforming methods like 2-model speculative decoding, Medusa, LookAhead Decoding, and DEED. In Mixture-of-Experts (MoE) architectures, integrating early residual alignment with ahead-of-time expert loading into high-bandwidth memory (HBM) accelerates decoding, reduces expert-switching bottlenecks, and achieves a 2.9x speedup, making it highly effective in resource-constrained environments.

Large-scale vision language pre-training has recently shown promise for no-reference image-quality assessment (NR-IQA), yet the relative merits of modern Vision Transformer foundations remain poorly understood. In this work, we present the first systematic evaluation of six prominent pretrained backbones, CLIP, SigLIP2, DINOv2, DINOv3, Perception, and ResNet, for the task of No-Reference Image Quality Assessment (NR-IQA), each finetuned using an identical lightweight MLP head. Our study uncovers two previously overlooked factors: (1) SigLIP2 consistently achieves strong performance; and (2) the choice of activation function plays a surprisingly crucial role, particularly for enhancing the generalization ability of image quality assessment models. Notably, we find that simple sigmoid activations outperform commonly used ReLU and GELU on several benchmarks. Motivated by this finding, we introduce a learnable activation selection mechanism that adaptively determines the nonlinearity for each channel, eliminating the need for manual activation design, and achieving new state-of-the-art SRCC on CLIVE, KADID10K, and AGIQA3K. Extensive ablations confirm the benefits across architectures and regimes, establishing strong, resource-efficient NR-IQA baselines.

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x cdot sigmoid(beta x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We also train ResMLP models in a self-supervised setup, to further remove priors from employing a labelled dataset. Finally, by adapting our model to machine translation we achieve surprisingly good results. We share pre-trained models and our code based on the Timm library.

Deep learning time-series processing often relies on convolutional neural networks with overlapping windows. This overlap allows the network to produce an output faster than the window length. However, it introduces additional computations. This work explores the potential to optimize computational efficiency during inference by exploiting convolution's shift-invariance properties to skip the calculation of layer activations between successive overlapping windows. Although convolutions are shift-invariant, zero-padding and pooling operations, widely used in such networks, are not efficient and complicate efficient streaming inference. We introduce StreamiNNC, a strategy to deploy Convolutional Neural Networks for online streaming inference. We explore the adverse effects of zero padding and pooling on the accuracy of streaming inference, deriving theoretical error upper bounds for pooling during streaming. We address these limitations by proposing signal padding and pooling alignment and provide guidelines for designing and deploying models for StreamiNNC. We validate our method in simulated data and on three real-world biomedical signal processing applications. StreamiNNC achieves a low deviation between streaming output and normal inference for all three networks (2.03 - 3.55% NRMSE). This work demonstrates that it is possible to linearly speed up the inference of streaming CNNs processing overlapping windows, negating the additional computation typically incurred by overlapping windows.

Deep Spiking Neural Networks (SNNs) present optimization difficulties for gradient-based approaches due to discrete binary activation and complex spatial-temporal dynamics. Considering the huge success of ResNet in deep learning, it would be natural to train deep SNNs with residual learning. Previous Spiking ResNet mimics the standard residual block in ANNs and simply replaces ReLU activation layers with spiking neurons, which suffers the degradation problem and can hardly implement residual learning. In this paper, we propose the spike-element-wise (SEW) ResNet to realize residual learning in deep SNNs. We prove that the SEW ResNet can easily implement identity mapping and overcome the vanishing/exploding gradient problems of Spiking ResNet. We evaluate our SEW ResNet on ImageNet, DVS Gesture, and CIFAR10-DVS datasets, and show that SEW ResNet outperforms the state-of-the-art directly trained SNNs in both accuracy and time-steps. Moreover, SEW ResNet can achieve higher performance by simply adding more layers, providing a simple method to train deep SNNs. To our best knowledge, this is the first time that directly training deep SNNs with more than 100 layers becomes possible. Our codes are available at https://github.com/fangwei123456/Spike-Element-Wise-ResNet.

Neural fields, a category of neural networks trained to represent high-frequency signals, have gained significant attention in recent years due to their impressive performance in modeling complex 3D data, especially large neural signed distance (SDFs) or radiance fields (NeRFs) via a single multi-layer perceptron (MLP). However, despite the power and simplicity of representing signals with an MLP, these methods still face challenges when modeling large and complex temporal signals due to the limited capacity of MLPs. In this paper, we propose an effective approach to address this limitation by incorporating temporal residual layers into neural fields, dubbed ResFields, a novel class of networks specifically designed to effectively represent complex temporal signals. We conduct a comprehensive analysis of the properties of ResFields and propose a matrix factorization technique to reduce the number of trainable parameters and enhance generalization capabilities. Importantly, our formulation seamlessly integrates with existing techniques and consistently improves results across various challenging tasks: 2D video approximation, dynamic shape modeling via temporal SDFs, and dynamic NeRF reconstruction. Lastly, we demonstrate the practical utility of ResFields by showcasing its effectiveness in capturing dynamic 3D scenes from sparse sensory inputs of a lightweight capture system.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to purely autoregressive language models because they can decode multiple tokens in parallel. However, state-of-the-art block-wise dLLMs rely on a "remasking" mechanism that decodes only the most confident tokens and discards the rest, effectively wasting computation. We demonstrate that recycling computation from the discarded tokens is beneficial, as these tokens retain contextual information useful for subsequent decoding iterations. In light of this, we propose Residual Context Diffusion (RCD), a module that converts these discarded token representations into contextual residuals and injects them back for the next denoising step. RCD uses a decoupled two-stage training pipeline to bypass the memory bottlenecks associated with backpropagation. We validate our method on both long CoT reasoning (SDAR) and short CoT instruction following (LLaDA) models. We demonstrate that a standard dLLM can be efficiently converted to the RCD paradigm with merely ~1 billion tokens. RCD consistently improves frontier dLLMs by 5-10 points in accuracy with minimal extra computation overhead across a wide range of benchmarks. Notably, on the most challenging AIME tasks, RCD nearly doubles baseline accuracy and attains up to 4-5x fewer denoising steps at equivalent accuracy levels.

We investigate the origins of massive activations in large language models (LLMs) and identify a specific layer named the Massive Emergence Layer (ME Layer), that is consistently observed across model families, where massive activations first emerge and subsequently propagate to deeper layers through residual connections. We show that, within the ME Layer both the RMSNorm and the FFN parameters jointly contribute to the emergence of massive activations. Once formed, the massive activation token representation remains largely invariant across layers, reducing the diversity of hidden representations passed to the attention module. Motivated by this limitation, we propose a simple and effective method to reduce the rigidity of the massive activation token. Our approach consistently improves LLM performance across multiple tasks, including instruction following and math reasoning, in both training free and fine tuning settings. Moreover, we show that our method mitigates attention sinks by selectively weakening their influence, elucidating their origin at the hidden state level and shedding new light on principled mitigation strategies.

Most contemporary neural learning systems rely on epoch-based optimization and repeated access to historical data, implicitly assuming reversible computation. In contrast, real-world environments often present information as irreversible streams, where inputs cannot be replayed or revisited. Under such conditions, conventional architectures degrade into reactive filters lacking long-horizon coherence. This paper introduces Stream Neural Networks (StNN), an execution paradigm designed for irreversible input streams. StNN operates through a stream-native execution algorithm, the Stream Network Algorithm (SNA), whose fundamental unit is the stream neuron. Each stream neuron maintains a persistent temporal state that evolves continuously across inputs. We formally establish three structural guarantees: (1) stateless mappings collapse under irreversibility and cannot encode temporal dependencies; (2) persistent state dynamics remain bounded under mild activation constraints; and (3) the state transition operator is contractive for λ < 1, ensuring stable long-horizon execution. Empirical phase-space analysis and continuous tracking experiments validate these theoretical results. The execution principles introduced in this work define a minimal substrate for neural computation under irreversible streaming constraints.

Multimodal agents repeatedly re-examine the same video frames, UI screenshots, and rendered artifacts as their context window slides and reasoning iterates, yet every look-back re-encodes from scratch, because prefix caches serve reuse only at a fixed leading position. We show this recompute is avoidable, and identify exactly what naive KV reuse loses: the cross-chunk conditioning a chunk absorbs from its neighbours. This loss is asymmetric. The direct readout of a cached chunk is recovered exactly and for free by the standard state-merge. What remains is a diffuse, low-rank residue concentrated in deep layers, invisible to single-hop retrieval but precisely what multi-hop reasoning binds on. Blind reuse therefore leaves single-hop recall intact while halving multi-hop accuracy; this is the failure mode prior position-independent caches, designed for single-context or single-image reuse, do not address. We repair it with a small, training-free low-rank conditioning patch stored alongside each position-free chunk. Reuse reduces to one operator across MLA, GQA, and MHA: exact RoPE re-rotation to any target position, plus the patch that restores cross-chunk binding. This makes three window operations cheap: reorder (one patch serves every ordering of a cached set), sliding-window survival (surviving chunks relocate via rotation only, zero re-encode), and recall (an evicted chunk is rehydrated by its patch, never re-encoded). A rank-m patch recovers full task accuracy on cross-chunk-binding benchmarks, MM-NIAH across two attention families and two-page doc-QA, at a fraction of the KV footprint, and reconstructs re-prefill KV to within bf16 rounding in a production SGLang kernel across six backbones. The conditioning signal is strongest in redundant vision and video streams, making our solution most impactful where multimodal agents spend their recompute budget.

In this paper, we present an efficient method for storing fine-tuned models by leveraging the low-rank properties of weight residuals. Our key observation is that weight residuals in large overparameterized models exhibit even stronger low-rank characteristics. Based on this insight, we propose Efficient Residual Encoding (ERE), a novel approach that achieves efficient storage of fine-tuned model weights by approximating the low-rank weight residuals. Furthermore, we analyze the robustness of weight residuals and push the limit of storage efficiency by utilizing additional quantization and layer-wise rank allocation. Our experimental results demonstrate that our method significantly reduces memory footprint while preserving performance in various tasks and modalities. We release our code.

Convolutional Neural Networks (CNNs) has revolutionized computer vision, but training very deep networks has been challenging due to the vanishing gradient problem. This paper explores Residual Networks (ResNet), introduced by He et al. (2015), which overcomes this limitation by using skip connections. ResNet enables the training of networks with hundreds of layers by allowing gradients to flow directly through shortcut connections that bypass intermediate layers. In our implementation on the CIFAR-10 dataset, ResNet-18 achieves 89.9% accuracy compared to 84.1% for a traditional deep CNN of similar depth, while also converging faster and training more stably.

Memory constraint of always-on devices is one of the major concerns when deploying speech processing models on these devices. While larger models trained with sufficiently large amount of data generally perform better, making them fit in the device memory is a demanding challenge. In this paper, we aim to reduce model size by reparameterizing model weights across Transformer encoder layers and assuming a special weight composition and structure. More specifically, inspired by ResNet and the more recent LoRA work, we propose an approach named ResidualTransformer, where each weight matrix in a Transformer layer comprises 1) a shared full-rank component with its adjacent layers, and 2) a unique low-rank component to itself. The low-rank matrices only account for a small amount of model size increase. In addition, we add diagonal weight matrices to improve modeling capacity of the low-rank matrices. Experiments of our 10k-hour speech recognition and speech translation tasks show that the Transformer encoder size can be reduced by ~3X with very slight performance degradation.

Mobile displays refresh at 90-120 Hz, yet most video is encoded at 24-30 frames per second; real-time frame-rate doubling requires each synthesized frame within 33.3 ms on mobile neural processing units. We show that mainstream flow-based video frame interpolation faces three structural deployment barriers on mobile accelerators: spatial sampling operators exceed the frame budget or lack hardware support, iterative flow refinement collapses under 8-bit post-training quantization, and memory-bound operators dominate the inference graph. ANVIL addresses these barriers by reusing motion vectors already computed by the H.264 decoder to prealign input frames, removing learned optical flow, spatial sampling, and iterative accumulation from the accelerator graph. The remaining residual is refined by a convolution-dominated network whose inference graph is composed almost entirely of compute-bound operators. On a Snapdragon 8 Gen 3 device, ANVIL achieves 12.8 ms 1080p network inference in 8-bit integer precision; an open-source Android player sustains 28.4 ms median end-to-end latency per interpolated frame pair over 54,623 consecutively logged samples during 30-minute continuous playback. Per-operator causal analysis identifies quantized accumulation on recurrent flow states as a key mechanism behind integer quantization failure in iterative methods. The current design targets H.264 playback scenarios with decoder-exposed motion vectors.

Large Transformer models function as Dense Associative Memories (DAMs), retrieving knowledge via high-dimensional attractor dynamics driven by the self-attention mechanism ramsauer2020hopfield, wu2024attention. However, adapting these frozen memory systems to new tasks presents a fundamental ``Plasticity-Stability'' dilemma. Current methods either risk catastrophic interference by modifying synaptic weights directly (e.g., LoRA) hu2021lora or degrade associative capacity by clogging the retrieval buffer with static prompt tokens (e.g., VPT) jia2022vpt. In this work, we propose H-Res (Hierarchical Residual Steering), a mechanism that modulates the effective energy landscape of the Transformer without altering its global equilibrium or expanding its sequence length. By formulating adaptation as a control problem on the activation manifold chen2018neuralode, H-Res learns a state-dependent vector field that steers token trajectories into task-specific basins of attraction. We formally prove that H-Res preserves the attention entropy of the foundation model and facilitates Neural Collapse papyan2020prevalence. Empirically, Manifold Steering outperforms global weight modification by 26\% on associative retrieval tasks and eliminates the computational overhead of prompt-based methods, scaling effectively to structured domains zha2023vtab.

In this paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

Large language models (LLMs) are widely used in text-to-image (T2I) systems, but they are typically limited to text encoding, while denoising is handled by newly trained generative backbones. The emergence of representation autoencoders (RAEs) shifts the generation target toward semantically structured visual representations, creating a latent space that is more compatible with pretrained LLM priors. Inspired by multimodal LLMs (MLLMs), where an MLP projector is sufficient to align clean visual representations with a pretrained LLM, we repurpose the MLLM itself as a noisy representation encoder, extending this mechanism from clean to noisy inputs. We present RepFusion, which uses the resulting MLLM outputs as the conditioning signal for a diffusion transformer. In controlled comparisons at similar inference budgets, RepFusion outperforms baselines that devote comparable capacity to newly initialized denoisers. These results demonstrate that MLLMs provide strong priors for denoising visual representations and that, by conditioning on evolving noisy representations, test-time compute can be productively spent on repeated MLLM conditioning in modern T2I systems.

Understanding continuous video streams plays a fundamental role in real-time applications including embodied AI and autonomous driving. Unlike offline video understanding, streaming video understanding requires the ability to process video streams frame by frame, preserve historical information, and make low-latency decisions. To address these challenges, our main contributions are three-fold. (i) We develop a novel streaming video backbone, termed as StreamFormer, by incorporating causal temporal attention into a pre-trained vision transformer. This enables efficient streaming video processing while maintaining image representation capability. (ii) To train StreamFormer, we propose to unify diverse spatial-temporal video understanding tasks within a multitask visual-language alignment framework. Hence, StreamFormer learns global semantics, temporal dynamics, and fine-grained spatial relationships simultaneously. (iii) We conduct extensive experiments on online action detection, online video instance segmentation, and video question answering. StreamFormer achieves competitive results while maintaining efficiency, demonstrating its potential for real-time applications.

We introduce StreamDiffusion, a real-time diffusion pipeline designed for interactive image generation. Existing diffusion models are adept at creating images from text or image prompts, yet they often fall short in real-time interaction. This limitation becomes particularly evident in scenarios involving continuous input, such as Metaverse, live video streaming, and broadcasting, where high throughput is imperative. To address this, we present a novel approach that transforms the original sequential denoising into the batching denoising process. Stream Batch eliminates the conventional wait-and-interact approach and enables fluid and high throughput streams. To handle the frequency disparity between data input and model throughput, we design a novel input-output queue for parallelizing the streaming process. Moreover, the existing diffusion pipeline uses classifier-free guidance(CFG), which requires additional U-Net computation. To mitigate the redundant computations, we propose a novel residual classifier-free guidance (RCFG) algorithm that reduces the number of negative conditional denoising steps to only one or even zero. Besides, we introduce a stochastic similarity filter(SSF) to optimize power consumption. Our Stream Batch achieves around 1.5x speedup compared to the sequential denoising method at different denoising levels. The proposed RCFG leads to speeds up to 2.05x higher than the conventional CFG. Combining the proposed strategies and existing mature acceleration tools makes the image-to-image generation achieve up-to 91.07fps on one RTX4090, improving the throughputs of AutoPipline developed by Diffusers over 59.56x. Furthermore, our proposed StreamDiffusion also significantly reduces the energy consumption by 2.39x on one RTX3060 and 1.99x on one RTX4090, respectively.

The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of discarding residual learning by employing large implicit kernels to achieve full context interaction at each layer of the network. To accomplish it, we introduce coordinate-based implicit MLPs as a slow network to generate hyper-kernels for another fast convolutional network. To get context-varying weights for fast dynamic encoding, we propose a HyperZ{cdotZ{cdot}W} operator that connects hyper-kernels (W) and hidden activations (Z) through simple elementwise multiplication, followed by convolution of Z using the context-dependent W. Based on this design, we present a novel Terminator architecture that integrates hyper-kernels of different sizes to produce multi-branch hidden representations for enhancing the feature extraction capability of each layer. Additionally, a bottleneck layer is employed to compress the concatenated channels, allowing only valuable information to propagate to the subsequent layers. Notably, our model incorporates several innovative components and exhibits excellent properties, such as introducing local feedback error for updating the slow network, stable zero-mean features, faster training convergence, and fewer model parameters. Extensive experimental results on pixel-level 1D and 2D image classification benchmarks demonstrate the superior performance of our architecture.

We introduce GateSkip, a simple residual-stream gating mechanism that enables token-wise layer skipping in decoder-only LMs. Each Attention/MLP branch is equipped with a sigmoid-linear gate that condenses the branch's output before it re-enters the residual stream. During inference we rank tokens by the gate values and skip low-importance ones using a per-layer budget. While early-exit or router-based Mixture-of-Depths models are known to be unstable and need extensive retraining, our smooth, differentiable gates fine-tune stably on top of pretrained models. On long-form reasoning, we save up to 15\% compute while retaining over 90\% of baseline accuracy. On instruction-tuned models we see accuracy gains at full compute and match baseline quality near 50\% savings. The learned gates give insight into transformer information flow (e.g., BOS tokens act as anchors), and the method combines easily with quantization, pruning, and self-speculative decoding.

Conditional computation is a popular strategy to make Transformers more efficient. Existing methods often target individual modules (e.g., mixture-of-experts layers) or skip layers independently of one another. However, interpretability research has demonstrated that the middle layers of Transformers exhibit greater redundancy, and that early layers aggregate information into token positions. Guided by these insights, we propose a novel architecture that dynamically skips a variable number of layers from the middle outward. In particular, a learned gating mechanism determines whether to bypass a symmetric span of central blocks based on the input, and a gated attention mechanism prevents subsequent tokens from attending to skipped token positions. Residual norms are controlled with a 'sandwich' or 'perilayernorm' scheme and gate sparsity with an adaptive regularization loss. We had aimed to reduce compute requirements for 'simpler' tokens and potentially foster an emergent multi-level representational hierarchy but, at the scales investigated, our approach does not achieve improvements in the trade-off between validation cross-entropy and estimated FLOPs compared to dense baselines with fewer layers. We release our code at https://github.com/tim-lawson/skip-middle.

While deeper convolutional networks are needed to achieve maximum accuracy in visual perception tasks, for many inputs shallower networks are sufficient. We exploit this observation by learning to skip convolutional layers on a per-input basis. We introduce SkipNet, a modified residual network, that uses a gating network to selectively skip convolutional blocks based on the activations of the previous layer. We formulate the dynamic skipping problem in the context of sequential decision making and propose a hybrid learning algorithm that combines supervised learning and reinforcement learning to address the challenges of non-differentiable skipping decisions. We show SkipNet reduces computation by 30-90% while preserving the accuracy of the original model on four benchmark datasets and outperforms the state-of-the-art dynamic networks and static compression methods. We also qualitatively evaluate the gating policy to reveal a relationship between image scale and saliency and the number of layers skipped.

The influential Residual Networks designed by He et al. remain the gold-standard architecture in numerous scientific publications. They typically serve as the default architecture in studies, or as baselines when new architectures are proposed. Yet there has been significant progress on best practices for training neural networks since the inception of the ResNet architecture in 2015. Novel optimization & data-augmentation have increased the effectiveness of the training recipes. In this paper, we re-evaluate the performance of the vanilla ResNet-50 when trained with a procedure that integrates such advances. We share competitive training settings and pre-trained models in the timm open-source library, with the hope that they will serve as better baselines for future work. For instance, with our more demanding training setting, a vanilla ResNet-50 reaches 80.4% top-1 accuracy at resolution 224x224 on ImageNet-val without extra data or distillation. We also report the performance achieved with popular models with our training procedure.

As we show in this paper, the prediction for output token n+1 of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens 1, 2, ..., n-1. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location k in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.

We present hyper-connections, a simple yet effective method that can serve as an alternative to residual connections. This approach specifically addresses common drawbacks observed in residual connection variants, such as the seesaw effect between gradient vanishing and representation collapse. Theoretically, hyper-connections allow the network to adjust the strength of connections between features at different depths and dynamically rearrange layers. We conduct experiments focusing on the pre-training of large language models, including dense and sparse models, where hyper-connections show significant performance improvements over residual connections. Additional experiments conducted on vision tasks also demonstrate similar improvements. We anticipate that this method will be broadly applicable and beneficial across a wide range of AI problems.

Recent advances in video diffusion models have shifted towards transformer-based architectures, achieving state-of-the-art video generation but at the cost of quadratic attention complexity, which severely limits scalability for longer sequences. We introduce ReHyAt, a Recurrent Hybrid Attention mechanism that combines the fidelity of softmax attention with the efficiency of linear attention, enabling chunk-wise recurrent reformulation and constant memory usage. Unlike the concurrent linear-only SANA Video, ReHyAt's hybrid design allows efficient distillation from existing softmax-based models, reducing the training cost by two orders of magnitude to ~160 GPU hours, while being competitive in the quality. Our light-weight distillation and finetuning pipeline provides a recipe that can be applied to future state-of-the-art bidirectional softmax-based models. Experiments on VBench and VBench-2.0, as well as a human preference study, demonstrate that ReHyAt achieves state-of-the-art video quality while reducing attention cost from quadratic to linear, unlocking practical scalability for long-duration and on-device video generation. Project page is available at https://qualcomm-ai-research.github.io/rehyat.

Increasingly expensive training of ever larger models such as Vision Transfomers motivate reusing the vast library of already trained state-of-the-art networks. However, their latency, high computational costs and memory demands pose significant challenges for deployment, especially on resource-constrained hardware. While structured pruning methods can reduce these factors, they often require costly retraining, sometimes for up to hundreds of epochs, or even training from scratch to recover the lost accuracy resulting from the structural modifications. Maintaining the provided performance of trained models after structured pruning and thereby avoiding extensive retraining remains a challenge. To solve this, we introduce Variance-Based Pruning, a simple and structured one-shot pruning technique for efficiently compressing networks, with minimal finetuning. Our approach first gathers activation statistics, which are used to select neurons for pruning. Simultaneously the mean activations are integrated back into the model to preserve a high degree of performance. On ImageNet-1k recognition tasks, we demonstrate that directly after pruning DeiT-Base retains over 70% of its original performance and requires only 10 epochs of fine-tuning to regain 99% of the original accuracy while simultaneously reducing MACs by 35% and model size by 36%, thus speeding up the model by 1.44x.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

Activation sparsity improves compute efficiency and resource utilization in sparsity-aware neural network accelerators. As the predominant operation in DNNs is multiply-accumulate (MAC) of activations with weights to compute inner products, skipping operations where (at least) one of the two operands is zero can make inference more efficient in terms of latency and power. Spatial sparsification of activations is a popular topic in DNN literature and several methods have already been established to bias a DNN for it. On the other hand, temporal sparsity is an inherent feature of bio-inspired spiking neural networks (SNNs), which neuromorphic processing exploits for hardware efficiency. Introducing and exploiting spatio-temporal sparsity, is a topic much less explored in DNN literature, but in perfect resonance with the trend in DNN, to shift from static signal processing to more streaming signal processing. Towards this goal, in this paper we introduce a new DNN layer (called Delta Activation Layer), whose sole purpose is to promote temporal sparsity of activations during training. A Delta Activation Layer casts temporal sparsity into spatial activation sparsity to be exploited when performing sparse tensor multiplications in hardware. By employing delta inference and ``the usual'' spatial sparsification heuristics during training, the resulting model learns to exploit not only spatial but also temporal activation sparsity (for a given input data distribution). One may use the Delta Activation Layer either during vanilla training or during a refinement phase. We have implemented Delta Activation Layer as an extension of the standard Tensoflow-Keras library, and applied it to train deep neural networks on the Human Action Recognition (UCF101) dataset. We report an almost 3x improvement of activation sparsity, with recoverable loss of model accuracy after longer training.

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.

Standard transformers entangle all computation in a single residual stream, obscuring which components perform which functions. We introduce the Dual-Stream Transformer, which decomposes the residual stream into two functionally distinct components: a token stream updated by attention and a context stream updated by feed-forward networks. Information flow between attention heads is controlled through a hierarchy of mixing strategies, from fully independent (maximum interpretability) to dense (standard transformer behavior). This design exposes a tunable tradeoff between interpretability and performance. We measure this tradeoff on language modeling tasks at 29M parameters. Fully independent head mixing increases validation loss by 8\% relative to dense baselines. The recommended Kronecker mixing strategy, which permits scalar communication between heads while preserving within-head structure, costs only 2.5\%. All configurations maintain functional generation under attention amplification (scaling logits by factors up to 16 at inference time), with degradation ranging from 16\% to 27\%. This robustness suggests the architectures learn discrete algorithms that operate independently of soft probabilistic mixing. The architecture provides a foundation for interpretable language models where internal structure is exposed by design. This work was partially supported by DARPA Contract HR001125C0302.

While Test-Time Scaling (TTS) offers a promising direction to enhance video generation without the surging costs of training, current test-time video generation methods based on diffusion models suffer from exorbitant candidate exploration costs and lack temporal guidance. To address these structural bottlenecks, we propose shifting the focus to streaming video generation. We identify that its chunk-level synthesis and few denoising steps are intrinsically suited for TTS, significantly lowering computational overhead while enabling fine-grained temporal control. Driven by this insight, we introduced Stream-T1, a pioneering comprehensive TTS framework exclusively tailored for streaming video generation. Specifically, Stream-T1 is composed of three units: (1) Stream -Scaled Noise Propagation, which actively refines the initial latent noise of the generating chunk using historically proven, high-quality previous chunk noise, effectively establishes temporal dependency and utilizing the historical Gaussian prior to guide the current generation; (2) Stream -Scaled Reward Pruning, which comprehensively evaluates generated candidates to strike an optimal balance between local spatial aesthetics and global temporal coherence by integrating immediate short-term assessments with sliding-window-based long-term evaluations; (3) Stream-Scaled Memory Sinking, which dynamically routes the context evicted from KV-cache into distinct updating pathways guided by the reward feedback, ensuring that previously generated visual information effectively anchors and guides the subsequent video stream. Evaluated on both 5s and 30s comprehensive video benchmarks, Stream-T1 demonstrates profound superiority, significantly improving temporal consistency, motion smoothness, and frame-level visual quality.

Motivated in part by their relevance for low-precision training and quantization, massive activations in large language models (LLMs) have recently emerged as a topic of interest. However, existing analyses are limited in scope, and generalizability across architectures is unclear. This paper helps address some of these gaps by conducting an analysis of massive activations across a broad range of LLMs, including both GLU-based and non-GLU-based architectures. Our findings challenge several prior assumptions, most importantly: (1) not all massive activations are detrimental, i.e. suppressing them does not lead to an explosion of perplexity or a collapse in downstream task performance; (2) proposed mitigation strategies such as Attention KV bias are model-specific and ineffective in certain cases. We consequently investigate novel hybrid mitigation strategies; in particular pairing Target Variance Rescaling (TVR) with Attention KV bias or Dynamic Tanh (DyT) successfully balances the mitigation of massive activations with preserved downstream model performance in the scenarios we investigated. Our code is available at: https://github.com/bluorion-com/refine_massive_activations.

The ability to learn new concepts continually is necessary in this ever-changing world. However, deep neural networks suffer from catastrophic forgetting when learning new categories. Many works have been proposed to alleviate this phenomenon, whereas most of them either fall into the stability-plasticity dilemma or take too much computation or storage overhead. Inspired by the gradient boosting algorithm to gradually fit the residuals between the target model and the previous ensemble model, we propose a novel two-stage learning paradigm FOSTER, empowering the model to learn new categories adaptively. Specifically, we first dynamically expand new modules to fit the residuals between the target and the output of the original model. Next, we remove redundant parameters and feature dimensions through an effective distillation strategy to maintain the single backbone model. We validate our method FOSTER on CIFAR-100 and ImageNet-100/1000 under different settings. Experimental results show that our method achieves state-of-the-art performance. Code is available at: https://github.com/G-U-N/ECCV22-FOSTER.

We investigate the mechanism underlying a previously identified phenomenon in Vision Transformers -- the emergence of high-norm tokens that lead to noisy attention maps. We observe that in multiple models (e.g., CLIP, DINOv2), a sparse set of neurons is responsible for concentrating high-norm activations on outlier tokens, leading to irregular attention patterns and degrading downstream visual processing. While the existing solution for removing these outliers involves retraining models from scratch with additional learned register tokens, we use our findings to create a training-free approach to mitigate these artifacts. By shifting the high-norm activations from our discovered register neurons into an additional untrained token, we can mimic the effect of register tokens on a model already trained without registers. We demonstrate that our method produces cleaner attention and feature maps, enhances performance over base models across multiple downstream visual tasks, and achieves results comparable to models explicitly trained with register tokens. We then extend test-time registers to off-the-shelf vision-language models to improve their interpretability. Our results suggest that test-time registers effectively take on the role of register tokens at test-time, offering a training-free solution for any pre-trained model released without them.

Hyper-Connections (HC) expand the residual stream of Transformers into N parallel streams, providing a form of memory scaling beyond model width and depth. Manifold-Constrained HC (mHC) stabilizes this formulation at scale. The large gains from N{=}1 to N{=}4 suggest residual-stream expansion as a promising scaling axis. However, existing HC-family methods typically stop at N{=}4. Our experiments reveal why: scaling mHC beyond this point yields diminishing performance gains and rapidly increasing training cost. We attribute this limitation to two bottlenecks: insufficient write-back information for an expanding number of streams and residual-mixing generation whose cost scales cubically with N. To address both bottlenecks, we propose xHC (Expanded Hyper-Connections), the first HC-family method to achieve meaningful expansion beyond N{=}4. xHC combines temporal feature augmentation for richer write-back with a sparse residual-stream architecture that updates only k=4 of the N=16 streams while retaining dense access to the full residual state. Across 18B and 28B MoE models, xHC delivers strong and consistent downstream improvements. On an 18B MoE model, xHC improves the average downstream score by 4.0 points over mHC, while adding only modest training FLOPs over the vanilla baseline. Scaling-law experiments show that the vanilla and mHC require 1.50times and 1.19times the compute of xHC, respectively, to reach the same loss. Practical large-N training also requires controlling memory traffic from the expanded residual state. We therefore introduce xHC-Flash, which reduces the per-sublayer memory traffic from 73.5C to 40C, comparable to the 34C required by mHC at N{=}4, while retaining the gains of full xHC. Together, xHC and xHC-Flash make large-N residual-stream expansion effective and practical for LLM pre-training.