Daily Papers

We present a neural network architecture and training method designed to enable very rapid training and low implementation complexity. Due to its training speed and very few tunable parameters, the method has strong potential for applications requiring frequent retraining or online training. The approach is characterized by (a) convolutional filters based on biologically inspired visual processing filters, (b) randomly-valued classifier-stage input weights, (c) use of least squares regression to train the classifier output weights in a single batch, and (d) linear classifier-stage output units. We demonstrate the efficacy of the method by applying it to image classification. Our results match existing state-of-the-art results on the MNIST (0.37% error) and NORB-small (2.2% error) image classification databases, but with very fast training times compared to standard deep network approaches. The network's performance on the Google Street View House Number (SVHN) (4% error) database is also competitive with state-of-the art methods.

Linear Sequence Modeling (LSM) like linear attention, state space models and linear RNNs, and Mixture-of-Experts (MoE) have recently emerged as significant architectural improvements. In this paper, we introduce Linear-MoE, a production-level system for modeling and training large-scale models that integrate LSM with MoE. Linear-MoE leverages the advantages of both LSM modules for linear-complexity sequence modeling and MoE layers for sparsely activation, aiming to offer high performance with efficient training. The Linear-MoE system comprises: 1) Modeling subsystem, which provides a unified framework supporting all instances of LSM. and 2) Training subsystem, which facilitates efficient training by incorporating various advanced parallelism technologies, particularly Sequence Parallelism designed for Linear-MoE models. Additionally, we explore hybrid models that combine Linear-MoE layers with standard Transformer-MoE layers with its Sequence Parallelism to further enhance model flexibility and performance. Evaluations on two model series, A0.3B-2B and A1B-7B, demonstrate Linear-MoE achieves efficiency gains while maintaining competitive performance on various benchmarks, showcasing its potential as a next-generation foundational model architecture. Code: https://github.com/OpenSparseLLMs/Linear-MoE.

We introduce the "exponential linear unit" (ELU) which speeds up learning in deep neural networks and leads to higher classification accuracies. Like rectified linear units (ReLUs), leaky ReLUs (LReLUs) and parametrized ReLUs (PReLUs), ELUs alleviate the vanishing gradient problem via the identity for positive values. However, ELUs have improved learning characteristics compared to the units with other activation functions. In contrast to ReLUs, ELUs have negative values which allows them to push mean unit activations closer to zero like batch normalization but with lower computational complexity. Mean shifts toward zero speed up learning by bringing the normal gradient closer to the unit natural gradient because of a reduced bias shift effect. While LReLUs and PReLUs have negative values, too, they do not ensure a noise-robust deactivation state. ELUs saturate to a negative value with smaller inputs and thereby decrease the forward propagated variation and information. Therefore, ELUs code the degree of presence of particular phenomena in the input, while they do not quantitatively model the degree of their absence. In experiments, ELUs lead not only to faster learning, but also to significantly better generalization performance than ReLUs and LReLUs on networks with more than 5 layers. On CIFAR-100 ELUs networks significantly outperform ReLU networks with batch normalization while batch normalization does not improve ELU networks. ELU networks are among the top 10 reported CIFAR-10 results and yield the best published result on CIFAR-100, without resorting to multi-view evaluation or model averaging. On ImageNet, ELU networks considerably speed up learning compared to a ReLU network with the same architecture, obtaining less than 10% classification error for a single crop, single model network.

This paper presents a computationally efficient variant of gradient boosting for multi-class classification and multi-output regression tasks. Standard gradient boosting uses a 1-vs-all strategy for classifications tasks with more than two classes. This strategy translates in that one tree per class and iteration has to be trained. In this work, we propose the use of multi-output regressors as base models to handle the multi-class problem as a single task. In addition, the proposed modification allows the model to learn multi-output regression problems. An extensive comparison with other multi-ouptut based gradient boosting methods is carried out in terms of generalization and computational efficiency. The proposed method showed the best trade-off between generalization ability and training and predictions speeds.

Gated Linear Units (arXiv:1612.08083) consist of the component-wise product of two linear projections, one of which is first passed through a sigmoid function. Variations on GLU are possible, using different nonlinear (or even linear) functions in place of sigmoid. We test these variants in the feed-forward sublayers of the Transformer (arXiv:1706.03762) sequence-to-sequence model, and find that some of them yield quality improvements over the typically-used ReLU or GELU activations.

The two-stage fine-tuning (FT) method, linear probing (LP) then fine-tuning (LP-FT), outperforms linear probing and FT alone. This holds true for both in-distribution (ID) and out-of-distribution (OOD) data. One key reason for its success is the preservation of pre-trained features, achieved by obtaining a near-optimal linear head during LP. However, despite the widespread use of large language models, there has been limited exploration of more complex architectures such as Transformers. In this paper, we analyze the training dynamics of LP-FT for classification tasks on the basis of the neural tangent kernel (NTK) theory. Our analysis decomposes the NTK matrix into two components. This decomposition highlights the importance of the linear head norm alongside the prediction accuracy at the start of the FT stage. We also observe a significant increase in the linear head norm during LP, which stems from training with the cross-entropy (CE) loss. This increase in the linear head norm effectively reduces changes in learned features. Furthermore, we find that this increased norm can adversely affect model calibration, which can be corrected using temperature scaling. Additionally, we extend our analysis with the NTK to the low-rank adaptation (LoRA) method and validate its effectiveness. Our experiments using a Transformer-based model on multiple natural language processing datasets confirm our theoretical analysis. Our study demonstrates the effectiveness of LP-FT for fine-tuning language models. Code is available at https://github.com/tom4649/lp-ft_ntk.

Neural network models have a reputation for being black boxes. We propose to monitor the features at every layer of a model and measure how suitable they are for classification. We use linear classifiers, which we refer to as "probes", trained entirely independently of the model itself. This helps us better understand the roles and dynamics of the intermediate layers. We demonstrate how this can be used to develop a better intuition about models and to diagnose potential problems. We apply this technique to the popular models Inception v3 and Resnet-50. Among other things, we observe experimentally that the linear separability of features increase monotonically along the depth of the model.

Rectified activation units (rectifiers) are essential for state-of-the-art neural networks. In this work, we study rectifier neural networks for image classification from two aspects. First, we propose a Parametric Rectified Linear Unit (PReLU) that generalizes the traditional rectified unit. PReLU improves model fitting with nearly zero extra computational cost and little overfitting risk. Second, we derive a robust initialization method that particularly considers the rectifier nonlinearities. This method enables us to train extremely deep rectified models directly from scratch and to investigate deeper or wider network architectures. Based on our PReLU networks (PReLU-nets), we achieve 4.94% top-5 test error on the ImageNet 2012 classification dataset. This is a 26% relative improvement over the ILSVRC 2014 winner (GoogLeNet, 6.66%). To our knowledge, our result is the first to surpass human-level performance (5.1%, Russakovsky et al.) on this visual recognition challenge.

We propose the Gaussian Error Linear Unit (GELU), a high-performing neural network activation function. The GELU activation function is xPhi(x), where Phi(x) the standard Gaussian cumulative distribution function. The GELU nonlinearity weights inputs by their value, rather than gates inputs by their sign as in ReLUs (x1_{x>0}). We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all considered computer vision, natural language processing, and speech tasks.

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

Classification is one of the most widespread tasks in AI applications, serving often as the first step in filtering, sorting, and categorizing data. Since modern AI systems must handle large volumes of input data and early pipeline stages can propagate errors downstream, achieving high efficiency and accuracy is critical. Moreover, classification requirements can change dynamically based on user needs, necessitating models with strong zero-shot capabilities. While generative LLMs have become mainstream for zero-shot classification due to their versatility, they suffer from inconsistent instruction following and computational inefficiency. Cross-encoders, commonly used as rerankers in RAG pipelines, face a different bottleneck: they must process text-label pairs sequentially, significantly reducing efficiency with large label sets. Embedding-based approaches offer good efficiency but struggle with complex scenarios involving logical and semantic constraints. We propose GLiClass, a novel method that adapts the GLiNER architecture for sequence classification tasks. Our approach achieves strong accuracy and efficiency comparable to embedding-based methods, while maintaining the flexibility needed for zero-shot and few-shot learning scenarios. Additionally, we adapted proximal policy optimization (PPO) for multi-label text classification, enabling training classifiers in data-sparse conditions or from human feedback.

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output units (e.g. an O-class classifier), however, the eNTK on N inputs is of size NO times NO, taking O((NO)^2) memory and up to O((NO)^3) computation. Most existing applications have therefore used one of a handful of approximations yielding N times N kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits", converges to the true eNTK at initialization for any network with a wide final "readout" layer. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

Gated Recurrent Unit (GRU) is a recently-developed variation of the long short-term memory (LSTM) unit, both of which are types of recurrent neural network (RNN). Through empirical evidence, both models have been proven to be effective in a wide variety of machine learning tasks such as natural language processing (Wen et al., 2015), speech recognition (Chorowski et al., 2015), and text classification (Yang et al., 2016). Conventionally, like most neural networks, both of the aforementioned RNN variants employ the Softmax function as its final output layer for its prediction, and the cross-entropy function for computing its loss. In this paper, we present an amendment to this norm by introducing linear support vector machine (SVM) as the replacement for Softmax in the final output layer of a GRU model. Furthermore, the cross-entropy function shall be replaced with a margin-based function. While there have been similar studies (Alalshekmubarak & Smith, 2013; Tang, 2013), this proposal is primarily intended for binary classification on intrusion detection using the 2013 network traffic data from the honeypot systems of Kyoto University. Results show that the GRU-SVM model performs relatively higher than the conventional GRU-Softmax model. The proposed model reached a training accuracy of ~81.54% and a testing accuracy of ~84.15%, while the latter was able to reach a training accuracy of ~63.07% and a testing accuracy of ~70.75%. In addition, the juxtaposition of these two final output layers indicate that the SVM would outperform Softmax in prediction time - a theoretical implication which was supported by the actual training and testing time in the study.

This paper presents a fascinating find: By training an auto-regressive LLM model on text tokens, the text model inherently develops internally an ability to understand images and audio, thereby developing the ability to see and hear just by reading. Popular audio and visual LLM models fine-tune text LLM models to give text output conditioned on images and audio embeddings. On the other hand, our architecture takes in patches of images, audio waveforms or tokens as input. It gives us the embeddings or category labels typical of a classification pipeline. We show the generality of text weights in aiding audio classification for datasets FSD-50K and GTZAN. Further, we show this working for image classification on CIFAR-10 and Fashion-MNIST, as well on image patches. This pushes the notion of text-LLMs learning powerful internal circuits that can be utilized by activating necessary connections for various applications rather than training models from scratch every single time.

This paper introduces a new approach to using Large Language Models (LLMs) for classification tasks, which are typically handled using Machine Learning (ML) models. Unlike ML models that rely heavily on data cleaning and feature engineering, this method streamlines the process using LLMs. This paper proposes a new concept called "Language Model Learning (LML)" powered by a new method called "Data-Augmented Prediction (DAP)". The classification is performed by LLMs using a method similar to humans manually exploring and understanding the data and deciding classifications using data as a reference. Training data is summarized and evaluated to determine the features that lead to the classification of each label the most. In the process of DAP, the system uses the data summary to automatically create a query, which is used to retrieve relevant rows from the dataset. A classification is generated by the LLM using data summary and relevant rows, ensuring satisfactory accuracy even with complex data. Usage of data summary and similar data in DAP ensures context-aware decision-making. The proposed method uses the words "Act as an Explainable Machine Learning Model" in the prompt to enhance the interpretability of the predictions by allowing users to review the logic behind each prediction. In some test cases, the system scored an accuracy above 90%, proving the effectiveness of the system and its potential to outperform conventional ML models in various scenarios. The code is available at https://github.com/Pro-GenAI/LML-DAP

Deploying LLMs raises two coupled challenges: (1) monitoring - estimating where a model underperforms as traffic and domains drift - and (2) improvement - prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response, we compute an output-entropy profile from final-layer next-token probabilities (from top-k logprobs) and summarize it with eleven statistics. A lightweight classifier predicts instance correctness, and averaging predicted probabilities yields a domain-level accuracy estimate. We evaluate on ten STEM reasoning benchmarks with exhaustive train/test compositions (k in {1,2,3,4}; all "10 choose k" combinations), across nine LLMs from six families (3B-20B). Estimates often track held-out benchmark accuracy, and several models show near-monotonic ordering of domains. Output-entropy profiles are thus an accessible signal for scalable monitoring and for targeting data acquisition.

This paper explores the relationship between the condition number of a neural network's weight tensor and the extent of information encoded by the associated processing unit, viewed through the lens of information theory. It argues that a high condition number, though not sufficient for effective knowledge encoding, may indicate that the unit has learned to selectively amplify and compress information. This intuition is formalized for linear units with Gaussian inputs, linking the condition number and the transformation's log-volume scaling factor to the characteristics of the output entropy and the geometric properties of the learned transformation. The analysis demonstrates that for a fixed weight norm, a concentrated distribution of singular values (high condition number) corresponds to reduced overall information transfer, indicating a specialized and efficient encoding strategy. Furthermore, the linear stage entropy bound provides an upper limit on post-activation information for contractive, element-wise nonlinearities, supporting the condition number as a scale-invariant proxy for encoding capacity in practical neural networks. An empirical case study applies these principles to guide selective fine-tuning of Large Language Models for both a new task and a new input modality. The experiments show that the proposed method, named KappaTune, effectively mitigates catastrophic forgetting. Unlike many existing catastrophic forgetting mitigation methods that rely on access to pre-training statistics, which are often unavailable, this selective fine-tuning approach offers a way to bypass this common requirement.

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

Training large models from scratch usually costs a substantial amount of resources. Towards this problem, recent studies such as bert2BERT and LiGO have reused small pretrained models to initialize a large model (termed the ``target model''), leading to a considerable acceleration in training. Despite the successes of these previous studies, they grew pretrained models by mapping partial weights only, ignoring potential correlations across the entire model. As we show in this paper, there are inter- and intra-interactions among the weights of both the pretrained and the target models. As a result, the partial mapping may not capture the complete information and lead to inadequate growth. In this paper, we propose a method that linearly correlates each weight of the target model to all the weights of the pretrained model to further enhance acceleration ability. We utilize multi-linear operators to reduce computational and spacial complexity, enabling acceptable resource requirements. Experiments demonstrate that our method can save 76\% computational costs on DeiT-base transferred from DeiT-small, which outperforms bert2BERT by +12.0\% and LiGO by +20.7\%, respectively.

The training data for fine-tuning large language models (LLMs) is typically structured as input-output pairs. However, for many tasks, there can be multiple equally valid output variations for the same input. Recent studies have observed that the choice of output variation used in training can affect the model's performance. This raises an important question: how can we generate the most effective output from the many possible response generation strategy options? Rather than relying on the traditional but resource-intensive train-and-evaluate approach, this paper proposes a scalable, approximate method for estimating the quality of a small subset of generated training data derived from the same input. We then evaluate how well this small subset of generated output fits the target model we are trying to train. We present a large-scale benchmark covering diverse reasoning-based datasets to support our study. The central idea is that a good output should closely resemble the output generated by the target LLM. We formalize this 'closeness' as the expected alignment score between a candidate output and the output sampled from the target LLM. We connect this measurement to the perplexity metric used in previous literature and demonstrate that leveraging an alignment-based metric can provide better predictions of model performance. Using this strategy, we can evaluate a small subset of the generated output from each response generation strategy option, then select the most effective strategy. We show that an LLM trained on data generated by the selected strategy could lead to a significant performance gain in many cases.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

We introduce the use of rectified linear units (ReLU) as the classification function in a deep neural network (DNN). Conventionally, ReLU is used as an activation function in DNNs, with Softmax function as their classification function. However, there have been several studies on using a classification function other than Softmax, and this study is an addition to those. We accomplish this by taking the activation of the penultimate layer h_{n - 1} in a neural network, then multiply it by weight parameters theta to get the raw scores o_{i}. Afterwards, we threshold the raw scores o_{i} by 0, i.e. f(o) = max(0, o_{i}), where f(o) is the ReLU function. We provide class predictions y through argmax function, i.e. argmax f(x).

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.

We investigate the predictability of large language model (LLM) capabilities: given records of past experiments using different model families, numbers of parameters, tasks, and numbers of in-context examples, can we accurately predict LLM performance on new experiment configurations? Answering this question has practical implications for LLM users (e.g., deciding which models to try), developers (e.g., prioritizing evaluation on representative tasks), and the research community (e.g., identifying hard-to-predict capabilities that warrant further investigation). We study the performance prediction problem on experiment records from BIG-bench. On a random train-test split, an MLP-based predictor achieves an R^2 score greater than 95%, indicating the presence of learnable patterns within the experiment records. We then formulate the problem of searching for "small-bench," an informative subset of BIG-bench tasks from which the performance on the full set can be maximally recovered. We find a subset as informative as BIG-bench Hard for evaluating new model families, while being 3times smaller. Additionally, we find competitive subsets by clustering task representations learned by our MLP-based predictor and selecting tasks close to cluster centroids, highlighting the importance of task diversity in constructing "small-bench."

This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear relationship (Procrustes similarity score of 0.99). However, linearity decreases when the residual component is removed due to a consistently low output norm of the transformer layer. Our experiments show that removing or linearly approximating some of the most linear blocks of transformers does not affect significantly the loss or model performance. Moreover, in our pretraining experiments on smaller models we introduce a cosine-similarity-based regularization, aimed at reducing layer linearity. This regularization improves performance metrics on benchmarks like Tiny Stories and SuperGLUE and as well successfully decreases the linearity of the models. This study challenges the existing understanding of transformer architectures, suggesting that their operation may be more linear than previously assumed.

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

This paper presents a comparison of six machine learning (ML) algorithms: GRU-SVM (Agarap, 2017), Linear Regression, Multilayer Perceptron (MLP), Nearest Neighbor (NN) search, Softmax Regression, and Support Vector Machine (SVM) on the Wisconsin Diagnostic Breast Cancer (WDBC) dataset (Wolberg, Street, & Mangasarian, 1992) by measuring their classification test accuracy and their sensitivity and specificity values. The said dataset consists of features which were computed from digitized images of FNA tests on a breast mass (Wolberg, Street, & Mangasarian, 1992). For the implementation of the ML algorithms, the dataset was partitioned in the following fashion: 70% for training phase, and 30% for the testing phase. The hyper-parameters used for all the classifiers were manually assigned. Results show that all the presented ML algorithms performed well (all exceeded 90% test accuracy) on the classification task. The MLP algorithm stands out among the implemented algorithms with a test accuracy of ~99.04%.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

Early stopping monitors global validation loss and halts all parameter updates simultaneously, which is computationally costly for large transformers due to the extended time required for validation inference. We propose GradES, a novel gradient-based early stopping approach that operates within transformer components (attention projections and Feed-Forward layer matrices). We found that different components converge at varying rates during fine-tuning. GradES tracks the magnitude of gradients in backpropagation for these matrices during training. When a projection matrix's gradients fall below a convergence threshold tau, we exclude that projection matrix from further updates individually, eliminating costly validation passes while allowing slow converging matrices to continue learning. By strategically freezing parameters when their gradients converge, GradES speeds up training time by 1.57--7.22times while simultaneously enhancing generalization through early prevention of overfitting, resulting in 1.2% higher average accuracy.

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem we must look at the articulated decisions in entirety. If we could capture the actions of non-linear units for a particular input, we would be able to replay the whole system back and forth as if it was always linear. It would also reveal the actions of non-linearities because the resulting linear system, a Linear Interpreter, depends on the input image. We introduce a hooking layer, called a LinearScope, which allows us to run the network and the linear interpreter in parallel. Its implementation is simple, flexible and efficient. From here we can make many curious inquiries: how do these linear systems look like? When the rows and columns of the transformation matrix are images, how do they look like? What type of basis do these linear transformations rely on? The answers depend on the problems presented, through which we take a tour to some popular architectures used for classification, super-resolution (SR) and image-to-image translation (I2I). For classification we observe that popular networks use a pixel-wise vote per class strategy and heavily rely on bias parameters. For SR and I2I we find that CNNs use wavelet-type basis similar to the human visual system. For I2I we reveal copy-move and template-creation strategies to generate outputs.

Combination approaches for speech recognition (ASR) systems cover structured sentence-level or word-based merging techniques as well as combination of model scores during beam search. In this work, we compare model combination across popular ASR architectures. Our method leverages the complementary strengths of different models in exploring diverse portions of the search space. We rescore a joint hypothesis list of two model candidates. We then identify the best hypothesis through log-linear combination of these sequence-level scores. While model combination during first-pass recognition may yield improved performance, it introduces variability due to differing decoding methods, making direct comparison more challenging. Our two-pass method ensures consistent comparisons across all system combination results presented in this study. We evaluate model pair candidates with varying architectures and label topologies and units. Experimental results are provided for the Librispeech 960h task.

Quantizing the activation, weight, and gradient to 4-bit is promising to accelerate neural network training. However, existing 4-bit training methods require custom numerical formats which are not supported by contemporary hardware. In this work, we propose a training method for transformers with all matrix multiplications implemented with the INT4 arithmetic. Training with an ultra-low INT4 precision is challenging. To achieve this, we carefully analyze the specific structures of activation and gradients in transformers to propose dedicated quantizers for them. For forward propagation, we identify the challenge of outliers and propose a Hadamard quantizer to suppress the outliers. For backpropagation, we leverage the structural sparsity of gradients by proposing bit splitting and leverage score sampling techniques to quantize gradients accurately. Our algorithm achieves competitive accuracy on a wide range of tasks including natural language understanding, machine translation, and image classification. Unlike previous 4-bit training methods, our algorithm can be implemented on the current generation of GPUs. Our prototypical linear operator implementation is up to 2.2 times faster than the FP16 counterparts and speeds up the training by up to 35.1%.

In this paper, we aim to generate text classification data given arbitrary class definitions (i.e., user instruction), so one can train a small text classifier without any human annotation or raw corpus. Compared with pioneer attempts, our proposed Incubator is the first framework that can handle complicated and even mutually dependent classes (e.g., "TED Talk given by Educator" and "Other"). Specifically, Incubator is an LLM firstly tuned on the instruction-to-data mappings that we obtained from classification datasets and descriptions on HuggingFace together with in-context augmentation by GPT-4. We then refine Incubator by learning on the cluster centers of semantic textual embeddings to emphasize the uniformity and semantic diversity in generations. We compare Incubator on various classification tasks with strong baselines such as direct LLM-based inference and training data generation by prompt engineering. Experiments show Incubator is able to (1) perform well on traditional benchmarks, (2) take label dependency and user preference into consideration, and (3) enable logical text mining by incubating multiple classifiers.

The rise of large language models (LLMs) has created a significant disparity: industrial research labs with their computational resources, expert teams, and advanced infrastructures, can effectively fine-tune LLMs, while individual developers and small organizations face barriers due to limited resources. In this paper, we aim to bridge this gap by presenting a comprehensive study on supervised fine-tuning of LLMs using instruction-tuning datasets spanning diverse knowledge domains and skills. We focus on small-sized LLMs (3B to 7B parameters) for their cost-efficiency and accessibility. We explore various training configurations and strategies across four open-source pre-trained models. We provide detailed documentation of these configurations, revealing findings that challenge several common training practices, including hyperparameter recommendations from TULU and phased training recommended by Orca. Key insights from our work include: (i) larger batch sizes paired with lower learning rates lead to improved model performance on benchmarks such as MMLU, MTBench, and Open LLM Leaderboard; (ii) early-stage training dynamics, such as lower gradient norms and higher loss values, are strong indicators of better final model performance, enabling early termination of sub-optimal runs and significant computational savings; (iii) through a thorough exploration of hyperparameters like warmup steps and learning rate schedules, we provide guidance for practitioners and find that certain simplifications do not compromise performance; and (iv) we observed no significant difference in performance between phased and stacked training strategies, but stacked training is simpler and more sample efficient. With these findings holding robustly across datasets and models, we hope this study serves as a guide for practitioners fine-tuning small LLMs and promotes a more inclusive environment for LLM research.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

It is a common belief that large language models (LLMs) are better than smaller-sized ones. However, larger models also require significantly more time and compute during inference. This begs the question: what happens when both models operate under the same budget? (e.g., compute, run-time). To address this question, we analyze code generation LLMs of various sizes and make comparisons such as running a 70B model once vs. generating five outputs from a 13B model. We consider a standard unit-test setup, which can be used to select the correct output from the smaller model. Our findings reveal that the repeated use of smaller models can yield consistent improvements, with gains of up to 15% across five tasks. On the other hand, in scenarios where unit-tests are unavailable, a ranking-based selection of candidates from the smaller model falls short of the performance of a single output from larger ones. Our results highlight the potential of using smaller models instead of larger ones, and the importance of studying approaches for ranking LLM outputs.

Deep classifiers are known to be sensitive to data distribution shifts, primarily due to their reliance on spurious correlations in training data. It has been suggested that these classifiers can still find useful features in the network's last layer that hold up under such shifts. In this work, we question the use of last-layer representations for out-of-distribution (OOD) generalisation and explore the utility of intermediate layers. To this end, we introduce Intermediate Layer Classifiers (ILCs). We discover that intermediate layer representations frequently offer substantially better generalisation than those from the penultimate layer. In many cases, zero-shot OOD generalisation using earlier-layer representations approaches the few-shot performance of retraining on penultimate layer representations. This is confirmed across multiple datasets, architectures, and types of distribution shifts. Our analysis suggests that intermediate layers are less sensitive to distribution shifts compared to the penultimate layer. These findings highlight the importance of understanding how information is distributed across network layers and its role in OOD generalisation, while also pointing to the limits of penultimate layer representation utility. Code is available at https://github.com/oshapio/intermediate-layer-generalization

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

Gated Linear Units (GLUs) have become essential components in the feed-forward networks of state-of-the-art Large Language Models (LLMs). However, they require twice as many memory reads compared to feed-forward layers without gating, due to the use of separate weight matrices for the gate and value streams. To address this bottleneck, we introduce Masked Gated Linear Units (MGLUs), a novel family of GLUs with an efficient kernel implementation. The core contribution of MGLUs include: (1) the Mixture of Element-wise Gating (MoEG) architecture that learns multiple binary masks, each determining gate or value assignments at the element level on a single shared weight matrix resulting in reduced memory transfer, and (2) FlashMGLU, a hardware-friendly kernel that yields up to a 19.7 times inference-time speed-up over a naive PyTorch MGLU and is 47% more memory-efficient and 34% faster than standard GLUs despite added architectural complexity on an RTX5090 GPU. In LLM experiments, the Swish-activated variant SwiMGLU preserves its memory advantages while matching - or even surpassing - the downstream accuracy of the SwiGLU baseline.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

This paper presents presents three distinct systems developed for the M-DAIGT shared task on detecting AI generated content in news articles and academic abstracts. The systems includes: (1) A fine-tuned RoBERTa-base classifier, (2) A classical TF-IDF + Support Vector Machine (SVM) classifier , and (3) An Innovative ensemble model named Candace, leveraging probabilistic features extracted from multiple Llama-3.2 models processed by a customTransformer encoder.The RoBERTa-based system emerged as the most performant, achieving near-perfect results on both development and test sets.

Production deployments in complex systems require ML architectures to be highly efficient and usable against multiple tasks. Particularly demanding are classification problems in which data arrives in a streaming fashion and each class is presented separately. Recent methods with stochastic gradient learning have been shown to struggle in such setups or have limitations like memory buffers, and being restricted to specific domains that disable its usage in real-world scenarios. For this reason, we present a fully differentiable architecture based on the Mixture of Experts model, that enables the training of high-performance classifiers when examples from each class are presented separately. We conducted exhaustive experiments that proved its applicability in various domains and ability to learn online in production environments. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods.

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive expansion where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in T steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of J neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the T partial models and bias are integrated as a single NN with T times J neurons in the hidden layer. Extensive experiments in classification and regression tasks, as well as in combination with deep neural networks, are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS, SGD and deep models. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.

We describe PromptBoosting, a query-efficient procedure for building a text classifier from a neural language model (LM) without access to the LM's parameters, gradients, or hidden representations. This form of "black-box" classifier training has become increasingly important as the cost of training and inference in large-scale LMs grows. But existing black-box LM classifier learning approaches are themselves computationally inefficient, typically specializing LMs to the target task by searching in a large space of (discrete or continuous) prompts using zeroth-order optimization methods. Instead of directly optimizing in prompt space, PromptBoosting obtains a small pool of prompts via a gradient-free approach and then constructs a large pool of weak learners by pairing these prompts with different elements of the LM's output distribution. These weak learners are then ensembled using the AdaBoost algorithm. The entire learning process requires only a small number of forward passes and no backward pass. Experiments show that PromptBoosting achieves state-of-the-art performance in multiple black-box few-shot classification tasks, and matches or outperforms full fine-tuning in both few-shot and standard learning paradigms, while training 10x faster than existing black-box methods.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

LLMs are commonly trained with a learning rate (LR) warmup, followed by cosine decay to 10% of the maximum (10x decay). In a large-scale empirical study, we show that under an optimal peak LR, a simple linear decay-to-zero (D2Z) schedule consistently outperforms other schedules when training at compute-optimal dataset sizes. D2Z is superior across a range of model sizes, batch sizes, datasets, and vocabularies. Benefits increase as dataset size increases. Leveraging a novel interpretation of AdamW as an exponential moving average of weight updates, we show how linear D2Z optimally balances the demands of early training (moving away from initial conditions) and late training (averaging over more updates in order to mitigate gradient noise). In experiments, a 610M-parameter model trained for 80 tokens-per-parameter (TPP) using D2Z achieves lower loss than when trained for 200 TPP using 10x decay, corresponding to an astonishing 60% compute savings. Models such as Llama2-7B, trained for 286 TPP with 10x decay, could likely have saved a majority of compute by training with D2Z.

Tokenization algorithms that merge the units of a base vocabulary into larger, variable-rate units have become standard in natural language processing tasks. This idea, however, has been mostly overlooked when the vocabulary consists of phonemes or Discrete Acoustic Units (DAUs), an audio-based representation that is playing an increasingly important role due to the success of discrete language-modeling techniques. In this paper, we showcase the advantages of tokenization of phonetic units and of DAUs on three prediction tasks: grapheme-to-phoneme, grapheme-to-DAUs, and unsupervised speech generation using DAU language modeling. We demonstrate that tokenization yields significant improvements in terms of performance, as well as training and inference speed, across all three tasks. We also offer theoretical insights to provide some explanation for the superior performance observed.

An algorithm to estimate the evolution of learning curves on the whole of a training data base, based on the results obtained from a portion and using a functional strategy, is introduced. We approximate iteratively the sought value at the desired time, independently of the learning technique used and once a point in the process, called prediction level, has been passed. The proposal proves to be formally correct with respect to our working hypotheses and includes a reliable proximity condition. This allows the user to fix a convergence threshold with respect to the accuracy finally achievable, which extends the concept of stopping criterion and seems to be effective even in the presence of distorting observations. Our aim is to evaluate the training effort, supporting decision making in order to reduce the need for both human and computational resources during the learning process. The proposal is of interest in at least three operational procedures. The first is the anticipation of accuracy gain, with the purpose of measuring how much work is needed to achieve a certain degree of performance. The second relates the comparison of efficiency between systems at training time, with the objective of completing this task only for the one that best suits our requirements. The prediction of accuracy is also a valuable item of information for customizing systems, since we can estimate in advance the impact of settings on both the performance and the development costs. Using the generation of part-of-speech taggers as an example application, the experimental results are consistent with our expectations.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further aggravates the tension between model capability and resource consumption, highlighting the importance of inference efficiency. However, a unified metric that accurately reflects an LLM's efficiency across different model sizes and architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. Larger models can predict the next token more accurately, achieving greater compression gains but at higher computational costs. Empirical evaluations on mainstream open-source models show that models of varying sizes within a series exhibit consistent information capacity. This metric enables a fair efficiency comparison across model series and accurate performance prediction within a model series. A distinctive feature of information capacity is that it incorporates tokenizer efficiency, which affects both input and output token counts but is often neglected in LLM evaluations. We assess the information capacity of 49 models on 5 heterogeneous datasets and observe consistent results on the influences of tokenizer efficiency, pretraining data, and the mixture-of-experts architecture.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples (x, f(x)) presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods which add new capabilities to the models they are used on. The first adds a recurrence mechanism, which removes the fixed-window sized constraint and improves the efficiency of a transformer decoder. The second allows masked language models (MLMs) to be used for initialization of both the encoder and decoder of a non-autoregressive sequence-to-sequence transformer, opening up generative applications of models which were previously only used for natural language understanding tasks. We also introduce two new techniques for improving the quality of predictions of any transformer decoder without additional finetuning. One, hidden state optimization, can be applied to any transformer decoder to improve the quality of predictions at inference time, especially for few-shot classification. The other, conditional beam search, allows practitioners to search for natural language generation (NLG) model outputs with high likelihood while conditioning on the event that the output is not degenerate (e.g. empty, repetitive, etc.). Finally, we provide theoretical and empirical insights on the divergence of model-likelihood and output quality which has widely been observed in prior work. These insights apply to any model which represents a distribution over text, and apply to language models which are not transformers or even autoregressive. We argue that the NLP community has, to some extent, misunderstood the implications of these findings, and encourage a point of view which has more nuance.

We develop task scaling laws and model ladders to predict the individual task performance of pretrained language models (LMs) in the overtrained setting. Standard power laws for language modeling loss cannot accurately model task performance. Therefore, we leverage a two-step prediction approach: first use model and data size to predict a task-specific loss, and then use this task loss to predict task performance. We train a set of small-scale "ladder" models, collect data points to fit the parameterized functions of the two prediction steps, and make predictions for two target models: a 7B model trained to 4T tokens and a 13B model trained to 5T tokens. Training the ladder models only costs 1% of the compute used for the target models. On four multiple-choice tasks written in ranked classification format, we can predict the accuracy of both target models within 2 points of absolute error. We have higher prediction error on four other tasks (average absolute error 6.9) and find that these are often tasks with higher variance in task metrics. We also find that using less compute to train fewer ladder models tends to deteriorate predictions. Finally, we empirically show that our design choices and the two-step approach lead to superior performance in establishing scaling laws.

Large language models (LLMs) and high-capacity encoders have advanced zero and few-shot classification, but their inference cost and latency limit practical deployment. We propose training lightweight text classifiers using dynamically generated supervision from an LLM. Our method employs an iterative, agentic loop in which the LLM curates training data, analyzes model successes and failures, and synthesizes targeted examples to address observed errors. This closed-loop generation and evaluation process progressively improves data quality and adapts it to the downstream classifier and task. Across four widely used benchmarks, our approach consistently outperforms standard zero and few-shot baselines. These results indicate that LLMs can serve effectively as data curators, enabling accurate and efficient classification without the operational cost of large-model deployment.

Following the rationale of end-to-end modeling, CTC, RNN-T or encoder-decoder-attention models for automatic speech recognition (ASR) use graphemes or grapheme-based subword units based on e.g. byte-pair encoding (BPE). The mapping from pronunciation to spelling is learned completely from data. In contrast to this, classical approaches to ASR employ secondary knowledge sources in the form of phoneme lists to define phonetic output labels and pronunciation lexica. In this work, we do a systematic comparison between grapheme- and phoneme-based output labels for an encoder-decoder-attention ASR model. We investigate the use of single phonemes as well as BPE-based phoneme groups as output labels of our model. To preserve a simplified and efficient decoder design, we also extend the phoneme set by auxiliary units to be able to distinguish homophones. Experiments performed on the Switchboard 300h and LibriSpeech benchmarks show that phoneme-based modeling is competitive to grapheme-based encoder-decoder-attention modeling.

In this technical report, we tackle the challenges of training large-scale Mixture of Experts (MoE) models, focusing on overcoming cost inefficiency and resource limitations prevalent in such systems. To address these issues, we present two differently sized MoE large language models (LLMs), namely Ling-Lite and Ling-Plus (referred to as "Bailing" in Chinese, spelled Bail\'ing in Pinyin). Ling-Lite contains 16.8 billion parameters with 2.75 billion activated parameters, while Ling-Plus boasts 290 billion parameters with 28.8 billion activated parameters. Both models exhibit comparable performance to leading industry benchmarks. This report offers actionable insights to improve the efficiency and accessibility of AI development in resource-constrained settings, promoting more scalable and sustainable technologies. Specifically, to reduce training costs for large-scale MoE models, we propose innovative methods for (1) optimization of model architecture and training processes, (2) refinement of training anomaly handling, and (3) enhancement of model evaluation efficiency. Additionally, leveraging high-quality data generated from knowledge graphs, our models demonstrate superior capabilities in tool use compared to other models. Ultimately, our experimental findings demonstrate that a 300B MoE LLM can be effectively trained on lower-performance devices while achieving comparable performance to models of a similar scale, including dense and MoE models. Compared to high-performance devices, utilizing a lower-specification hardware system during the pre-training phase demonstrates significant cost savings, reducing computing costs by approximately 20%. The models can be accessed at https://huggingface.co/inclusionAI.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

Large language models have demonstrated exceptional capability in natural language understanding and generation. However, their generation speed is limited by the inherently sequential nature of their decoding process, posing challenges for real-time applications. This paper introduces Lexical Unit Decoding (LUD), a novel decoding methodology implemented in a data-driven manner, accelerating the decoding process without sacrificing output quality. The core of our approach is the observation that a pre-trained language model can confidently predict multiple contiguous tokens, forming the basis for a lexical unit, in which these contiguous tokens could be decoded in parallel. Extensive experiments validate that our method substantially reduces decoding time while maintaining generation quality, i.e., 33\% speed up on natural language generation with no quality loss, and 30\% speed up on code generation with a negligible quality loss of 3\%. Distinctively, LUD requires no auxiliary models and does not require changes to existing architectures. It can also be integrated with other decoding acceleration methods, thus achieving an even more pronounced inference efficiency boost. We posit that the foundational principles of LUD could define a new decoding paradigm for future language models, enhancing their applicability for a broader spectrum of applications. All codes are be publicly available at https://github.com/tjunlp-lab/Lexical-Unit-Decoding-LUD-. Keywords: Parallel Decoding, Lexical Unit Decoding, Large Language Model

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.

The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition exhibits the following encoding properties across a variety of deep learning models: (1) {\it determinism}: almost every linear region contains at most one training example. We can therefore represent almost every training example by a unique activation pattern, which is parameterized by a {\it neural code}; and (2) {\it categorization}: according to the neural code, simple algorithms, such as K-Means, K-NN, and logistic regression, can achieve fairly good performance on both training and test data. These encoding properties surprisingly suggest that {\it normal neural networks well-trained for classification behave as hash encoders without any extra efforts.} In addition, the encoding properties exhibit variability in different scenarios. {Further experiments demonstrate that {\it model size}, {\it training time}, {\it training sample size}, {\it regularization}, and {\it label noise} contribute in shaping the encoding properties, while the impacts of the first three are dominant.} We then define an {\it activation hash phase chart} to represent the space expanded by {model size}, training time, training sample size, and the encoding properties, which is divided into three canonical regions: {\it under-expressive regime}, {\it critically-expressive regime}, and {\it sufficiently-expressive regime}. The source code package is available at https://github.com/LeavesLei/activation-code.

The widespread use of Large Language Models (LLMs), celebrated for their ability to generate human-like text, has raised concerns about misinformation and ethical implications. Addressing these concerns necessitates the development of robust methods to detect and attribute text generated by LLMs. This paper investigates "Cross-Model Detection," evaluating whether a classifier trained to distinguish between source LLM-generated and human-written text can also detect text from a target LLM without further training. The study comprehensively explores various LLM sizes and families, and assesses the impact of conversational fine-tuning techniques on classifier generalization. The research also delves into Model Attribution, encompassing source model identification, model family classification, and model size classification. Our results reveal several key findings: a clear inverse relationship between classifier effectiveness and model size, with larger LLMs being more challenging to detect, especially when the classifier is trained on data from smaller models. Training on data from similarly sized LLMs can improve detection performance from larger models but may lead to decreased performance when dealing with smaller models. Additionally, model attribution experiments show promising results in identifying source models and model families, highlighting detectable signatures in LLM-generated text. Overall, our study contributes valuable insights into the interplay of model size, family, and training data in LLM detection and attribution.

The output of Large Language Models (LLMs) are a function of the internal model's parameters and the input provided into the context window. The hypothesis presented here is that under a greedy sampling strategy the variance in the LLM's output is a function of the conceptual certainty embedded in the model's parametric knowledge, as well as the lexical variance in the input. Finetuning the model results in reducing the sensitivity of the model output to the lexical input variations. This is then applied to a classification problem and a probabilistic method is proposed for estimating the certainties of the predicted classes.

Transformer training is notoriously difficult, requiring a careful design of optimizers and use of various heuristics. We make progress towards understanding the subtleties of training Transformers by carefully studying a simple yet canonical linearized shallow Transformer model. Specifically, we train linear Transformers to solve regression tasks, inspired by J.~von Oswald et al.~(ICML 2023), and K.~Ahn et al.~(NeurIPS 2023). Most importantly, we observe that our proposed linearized models can reproduce several prominent aspects of Transformer training dynamics. Consequently, the results obtained in this paper suggest that a simple linearized Transformer model could actually be a valuable, realistic abstraction for understanding Transformer optimization.

Variation in language is ubiquitous and often systematically linked to regional, social, and contextual factors. Tokenizers split texts into smaller units and might behave differently for less common linguistic forms. This might affect downstream LLM performance differently on two types of tasks: Tasks where the model should be robust to language variation (e.g., for semantic tasks like NLI, labels do not depend on whether a text uses British or American spelling) and tasks where the model should be sensitive to language variation (e.g., for form-based tasks like authorship verification, labels depend on whether a text uses British or American spelling). We pre-train BERT base models with the popular Byte-Pair Encoding algorithm to investigate how key tokenization design choices impact the performance of downstream models: the corpus used to train the tokenizer, the pre-tokenizer and the vocabulary size. We find that the best tokenizer varies on the two task types and that the pre-tokenizer has the biggest overall impact on performance. Further, we introduce a new approach to estimate tokenizer impact on downstream LLM performance, showing substantial improvement over metrics like R\'enyi efficiency. We encourage more work on language variation and its relation to tokenizers and thus LLM performance.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Large Language Models (LLMs) have achieved widespread adoption, yet our understanding of their behavior remains limited, particularly in detecting data contamination and hallucinations. While recently proposed probing techniques provide insights through activation analysis, they require "white-box" access to model internals, often unavailable. Current "gray-box" approaches typically analyze only the probability of the actual tokens in the sequence with simple task-specific heuristics. Importantly, these methods overlook the rich information contained in the full token distribution at each processing step. To address these limitations, we propose that gray-box analysis should leverage the complete observable output of LLMs, consisting of both the previously used token probabilities as well as the complete token distribution sequences - a unified data type we term LOS (LLM Output Signature). To this end, we develop a transformer-based approach to process LOS that theoretically guarantees approximation of existing techniques while enabling more nuanced analysis. Our approach achieves superior performance on hallucination and data contamination detection in gray-box settings, significantly outperforming existing baselines. Furthermore, it demonstrates strong transfer capabilities across datasets and LLMs, suggesting that LOS captures fundamental patterns in LLM behavior. Our code is available at: https://github.com/BarSGuy/LLM-Output-Signatures-Network.

Most NLP tasks are modeled as supervised learning and thus require labeled training data to train effective models. However, manually producing such data at sufficient quality and quantity is known to be costly and time-intensive. Current research addresses this bottleneck by exploring a novel paradigm called zero-shot learning via dataset generation. Here, a powerful LLM is prompted with a task description to generate labeled data that can be used to train a downstream NLP model. For instance, an LLM might be prompted to "generate 500 movie reviews with positive overall sentiment, and another 500 with negative sentiment." The generated data could then be used to train a binary sentiment classifier, effectively leveraging an LLM as a teacher to a smaller student model. With this demo, we introduce Fabricator, an open-source Python toolkit for dataset generation. Fabricator implements common dataset generation workflows, supports a wide range of downstream NLP tasks (such as text classification, question answering, and entity recognition), and is integrated with well-known libraries to facilitate quick experimentation. With Fabricator, we aim to support researchers in conducting reproducible dataset generation experiments using LLMs and help practitioners apply this approach to train models for downstream tasks.

Although BERT-style encoder models are heavily used in NLP research, many researchers do not pretrain their own BERTs from scratch due to the high cost of training. In the past half-decade since BERT first rose to prominence, many advances have been made with other transformer architectures and training configurations that have yet to be systematically incorporated into BERT. Here, we introduce MosaicBERT, a BERT-style encoder architecture and training recipe that is empirically optimized for fast pretraining. This efficient architecture incorporates FlashAttention, Attention with Linear Biases (ALiBi), Gated Linear Units (GLU), a module to dynamically remove padded tokens, and low precision LayerNorm into the classic transformer encoder block. The training recipe includes a 30% masking ratio for the Masked Language Modeling (MLM) objective, bfloat16 precision, and vocabulary size optimized for GPU throughput, in addition to best-practices from RoBERTa and other encoder models. When pretrained from scratch on the C4 dataset, this base model achieves a downstream average GLUE (dev) score of 79.6 in 1.13 hours on 8 A100 80 GB GPUs at a cost of roughly $20. We plot extensive accuracy vs. pretraining speed Pareto curves and show that MosaicBERT base and large are consistently Pareto optimal when compared to a competitive BERT base and large. This empirical speed up in pretraining enables researchers and engineers to pretrain custom BERT-style models at low cost instead of finetune on existing generic models. We open source our model weights and code.

The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.

Transformers with linear recurrent modeling offer linear-time training and constant-memory inference. Despite their demonstrated efficiency and performance, pretraining such non-standard architectures from scratch remains costly and risky. The linearization of large language models (LLMs) transforms pretrained standard models into linear recurrent structures, enabling more efficient deployment. However, current linearization methods typically introduce additional feature map modules that require extensive fine-tuning and overlook the gating mechanisms used in state-of-the-art linear recurrent models. To address these issues, this paper presents Liger, short for Linearizing LLMs to gated recurrent structures. Liger is a novel approach for converting pretrained LLMs into gated linear recurrent models without adding extra parameters. It repurposes the pretrained key matrix weights to construct diverse gating mechanisms, facilitating the formation of various gated recurrent structures while avoiding the need to train additional components from scratch. Using lightweight fine-tuning with Low-Rank Adaptation (LoRA), Liger restores the performance of the linearized gated recurrent models to match that of the original LLMs. Additionally, we introduce Liger Attention, an intra-layer hybrid attention mechanism, which significantly recovers 93\% of the Transformer-based LLM at 0.02\% pre-training tokens during the linearization process, achieving competitive results across multiple benchmarks, as validated on models ranging from 1B to 8B parameters. Code is available at https://github.com/OpenSparseLLMs/Linearization.

Large language models have been widely adopted but require significant GPU memory for inference. We develop a procedure for Int8 matrix multiplication for feed-forward and attention projection layers in transformers, which cut the memory needed for inference by half while retaining full precision performance. With our method, a 175B parameter 16/32-bit checkpoint can be loaded, converted to Int8, and used immediately without performance degradation. This is made possible by understanding and working around properties of highly systematic emergent features in transformer language models that dominate attention and transformer predictive performance. To cope with these features, we develop a two-part quantization procedure, LLM.int8(). We first use vector-wise quantization with separate normalization constants for each inner product in the matrix multiplication, to quantize most of the features. However, for the emergent outliers, we also include a new mixed-precision decomposition scheme, which isolates the outlier feature dimensions into a 16-bit matrix multiplication while still more than 99.9% of values are multiplied in 8-bit. Using LLM.int8(), we show empirically it is possible to perform inference in LLMs with up to 175B parameters without any performance degradation. This result makes such models much more accessible, for example making it possible to use OPT-175B/BLOOM on a single server with consumer GPUs. We open-source our software.

Machine learning classification problems are widespread in bioinformatics, but the technical knowledge required to perform model training, optimization, and inference can prevent researchers from utilizing this technology. This article presents an automated tool for machine learning classification problems to simplify the process of training models and producing results while providing informative visualizations and insights into the data. This tool supports both binary and multiclass classification problems, and it provides access to a variety of models and methods. Synthetic data can be generated within the interface to fill missing values, balance class labels, or generate entirely new datasets. It also provides support for feature evaluation and generates explainability scores to indicate which features influence the output the most. We present CLASSify, an open-source tool for simplifying the user experience of solving classification problems without the need for knowledge of machine learning.

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.

Pruning assumes a subnetwork exists in the original deep neural network, which can achieve comparative model performance with less computation than the original. However, it is unclear how the model performance varies with the different subnetwork extractions. In this paper, we choose the representation dimension (or embedding dimension, model dimension, the dimension of the residual stream in the relevant literature) as the entry point to this issue. We investigate the linear transformations in the LLM transformer blocks and consider a specific structured pruning approach, SliceGPT, to extract the subnetworks of different representation dimensions. We mechanistically analyse the activation flow during the model forward passes, and find the representation dimension dominates the linear transformations, model predictions, and, finally, the model performance. Explicit analytical relations are given to calculate the pruned model performance (perplexity and accuracy) without actual evaluation, and are empirically validated with Llama-3-8B-Instruct and Phi-3-mini-4k-Instruct.

We create two German-only decoder models, LL\"aMmlein 120M and 1B, transparently from scratch and publish them, along with the training data, for the German NLP research community to use. The model training involved several key steps, including extensive data preprocessing, the creation of a custom German tokenizer, the training itself, as well as the evaluation of the final models on various benchmarks. Throughout the training process, multiple checkpoints were saved and analyzed using the SuperGLEBer benchmark to monitor the models' learning dynamics. Compared to state-of-the-art models on the SuperGLEBer benchmark, both LL\"aMmlein models performed competitively, consistently matching or surpassing models with similar parameter sizes. The results show that the models' quality scales with size as expected, but performance improvements on some tasks plateaued early, offering valuable insights into resource allocation for future model development.

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input dimension and the network width are proportionally large. Recent work [Cui & al '23] established that linear regression provides Bayes-optimal test error to learn such a function when the number of available samples is only linear in the dimension. That work stressed the open challenge of theoretically analyzing the optimal test error in the more interesting regime where the number of samples is quadratic in the dimension. In this paper, we solve this challenge for quadratic activations and derive a closed-form expression for the Bayes-optimal test error. We also provide an algorithm, that we call GAMP-RIE, which combines approximate message passing with rotationally invariant matrix denoising, and that asymptotically achieves the optimal performance. Technically, our result is enabled by establishing a link with recent works on optimal denoising of extensive-rank matrices and on the ellipsoid fitting problem. We further show empirically that, in the absence of noise, randomly-initialized gradient descent seems to sample the space of weights, leading to zero training loss, and averaging over initialization leads to a test error equal to the Bayes-optimal one.

The rapid advancements in computing dramatically increase the scale and cost of training Large Language Models (LLMs). Accurately predicting downstream task performance prior to model training is crucial for efficient resource allocation, yet remains challenging due to two primary constraints: (1) the "emergence phenomenon", wherein downstream performance metrics become meaningful only after extensive training, which limits the ability to use smaller models for prediction; (2) Uneven task difficulty distributions and the absence of consistent scaling laws, resulting in substantial metric variability. Existing performance prediction methods suffer from limited accuracy and reliability, thereby impeding the assessment of potential LLM capabilities. To address these challenges, we propose a Clustering-On-Difficulty (COD) downstream performance prediction framework. COD first constructs a predictable support subset by clustering tasks based on difficulty features, strategically excluding non-emergent and non-scalable clusters. The scores on the selected subset serve as effective intermediate predictors of downstream performance on the full evaluation set. With theoretical support, we derive a mapping function that transforms performance metrics from the predictable subset to the full evaluation set, thereby ensuring accurate extrapolation of LLM downstream performance. The proposed method has been applied to predict performance scaling for a 70B LLM, providing actionable insights for training resource allocation and assisting in monitoring the training process. Notably, COD achieves remarkable predictive accuracy on the 70B LLM by leveraging an ensemble of small models, demonstrating an absolute mean deviation of 1.36% across eight important LLM evaluation benchmarks.

Autoregressive Large Language Models have transformed the landscape of Natural Language Processing. Pre-train and prompt paradigm has replaced the conventional approach of pre-training and fine-tuning for many downstream NLP tasks. This shift has been possible largely due to LLMs and innovative prompting techniques. LLMs have shown great promise for a variety of downstream tasks owing to their vast parameters and huge datasets that they are pre-trained on. However, in order to fully realize their potential, their outputs must be guided towards the desired outcomes. Prompting, in which a specific input or instruction is provided to guide the LLMs toward the intended output, has become a tool for achieving this goal. In this paper, we discuss the various prompting techniques that have been applied to fully harness the power of LLMs. We present a taxonomy of existing literature on prompting techniques and provide a concise survey based on this taxonomy. Further, we identify some open problems in the realm of prompting in autoregressive LLMs which could serve as a direction for future research.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new closed-form predictor variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at 100 and 300 epochs (top-1 linear accuracy on ImageNet).

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

This research investigates how Machine Learning (ML) algorithms can assist in workload allocation strategies by detecting tasks with node affinity operators (referred to as constraint operators), which constrain their execution to a limited number of nodes. Using real-world Google Cluster Data (GCD) workload traces and the AGOCS framework, the study extracts node attributes and task constraints, then analyses them to identify suitable node-task pairings. It focuses on tasks that can be executed on either a single node or fewer than a thousand out of 12.5k nodes in the analysed GCD cluster. Task constraint operators are compacted, pre-processed with one-hot encoding, and used as features in a training dataset. Various ML classifiers, including Artificial Neural Networks, K-Nearest Neighbours, Decision Trees, Naive Bayes, Ridge Regression, Adaptive Boosting, and Bagging, are fine-tuned and assessed for accuracy and F1-scores. The final ensemble voting classifier model achieved 98% accuracy and a 1.5-1.8% misclassification rate for tasks with a single suitable node.

This paper demonstrates that a single-layer neural network using Parametric Rectified Linear Unit (PReLU) activation can solve the XOR problem, a simple fact that has been overlooked so far. We compare this solution to the multi-layer perceptron (MLP) and the Growing Cosine Unit (GCU) activation function and explain why PReLU enables this capability. Our results show that the single-layer PReLU network can achieve 100\% success rate in a wider range of learning rates while using only three learnable parameters.

Prototypical part network (ProtoPNet) methods have been designed to achieve interpretable classification by associating predictions with a set of training prototypes, which we refer to as trivial prototypes because they are trained to lie far from the classification boundary in the feature space. Note that it is possible to make an analogy between ProtoPNet and support vector machine (SVM) given that the classification from both methods relies on computing similarity with a set of training points (i.e., trivial prototypes in ProtoPNet, and support vectors in SVM). However, while trivial prototypes are located far from the classification boundary, support vectors are located close to this boundary, and we argue that this discrepancy with the well-established SVM theory can result in ProtoPNet models with inferior classification accuracy. In this paper, we aim to improve the classification of ProtoPNet with a new method to learn support prototypes that lie near the classification boundary in the feature space, as suggested by the SVM theory. In addition, we target the improvement of classification results with a new model, named ST-ProtoPNet, which exploits our support prototypes and the trivial prototypes to provide more effective classification. Experimental results on CUB-200-2011, Stanford Cars, and Stanford Dogs datasets demonstrate that ST-ProtoPNet achieves state-of-the-art classification accuracy and interpretability results. We also show that the proposed support prototypes tend to be better localised in the object of interest rather than in the background region.

We introduce GLM-130B, a bilingual (English and Chinese) pre-trained language model with 130 billion parameters. It is an attempt to open-source a 100B-scale model at least as good as GPT-3 and unveil how models of such a scale can be successfully pre-trained. Over the course of this effort, we face numerous unexpected technical and engineering challenges, particularly on loss spikes and disconvergence. In this paper, we introduce the training process of GLM-130B including its design choices, training strategies for both efficiency and stability, and engineering efforts. The resultant GLM-130B model offers significant outperformance over GPT-3 175B on a wide range of popular English benchmarks while the performance advantage is not observed in OPT-175B and BLOOM-176B. It also consistently and significantly outperforms ERNIE TITAN 3.0 260B -- the largest Chinese language model -- across related benchmarks. Finally, we leverage a unique scaling property of GLM-130B to reach INT4 quantization, without quantization aware training and with almost no performance loss, making it the first among 100B-scale models. More importantly, the property allows its effective inference on 4timesRTX 3090 (24G) or 8timesRTX 2080 Ti (11G) GPUs, the most ever affordable GPUs required for using 100B-scale models. The GLM-130B model weights are publicly accessible and its code, training logs, related toolkit, and lessons learned are open-sourced at https://github.com/THUDM/GLM-130B .

Retrained large language models (LLMs) have become extensively used across various sub-disciplines of natural language processing (NLP). In NLP, text classification problems have garnered considerable focus, but still faced with some limitations related to expensive computational cost, time consumption, and robust performance to unseen classes. With the proposal of chain of thought prompting (CoT), LLMs can be implemented using zero-shot learning (ZSL) with the step by step reasoning prompts, instead of conventional question and answer formats. The zero-shot LLMs in the text classification problems can alleviate these limitations by directly utilizing pretrained models to predict both seen and unseen classes. Our research primarily validates the capability of GPT models in text classification. We focus on effectively utilizing prompt strategies to various text classification scenarios. Besides, we compare the performance of zero shot LLMs with other state of the art text classification methods, including traditional machine learning methods, deep learning methods, and ZSL methods. Experimental results demonstrate that the performance of LLMs underscores their effectiveness as zero-shot text classifiers in three of the four datasets analyzed. The proficiency is especially advantageous for small businesses or teams that may not have extensive knowledge in text classification.

Recently the LARS and LAMB optimizers have been proposed for training neural networks faster using large batch sizes. LARS and LAMB add layer-wise normalization to the update rules of Heavy-ball momentum and Adam, respectively, and have become popular in prominent benchmarks and deep learning libraries. However, without fair comparisons to standard optimizers, it remains an open question whether LARS and LAMB have any benefit over traditional, generic algorithms. In this work we demonstrate that standard optimization algorithms such as Nesterov momentum and Adam can match or exceed the results of LARS and LAMB at large batch sizes. Our results establish new, stronger baselines for future comparisons at these batch sizes and shed light on the difficulties of comparing optimizers for neural network training more generally.

Neural networks can approximate complex functions, but they struggle to perform exact arithmetic operations over real numbers. The lack of inductive bias for arithmetic operations leaves neural networks without the underlying logic necessary to extrapolate on tasks such as addition, subtraction, and multiplication. We present two new neural network components: the Neural Addition Unit (NAU), which can learn exact addition and subtraction; and the Neural Multiplication Unit (NMU) that can multiply subsets of a vector. The NMU is, to our knowledge, the first arithmetic neural network component that can learn to multiply elements from a vector, when the hidden size is large. The two new components draw inspiration from a theoretical analysis of recently proposed arithmetic components. We find that careful initialization, restricting parameter space, and regularizing for sparsity is important when optimizing the NAU and NMU. Our proposed units NAU and NMU, compared with previous neural units, converge more consistently, have fewer parameters, learn faster, can converge for larger hidden sizes, obtain sparse and meaningful weights, and can extrapolate to negative and small values.

A central notion in practical and theoretical machine learning is that of a weak learner, classifiers that achieve better-than-random performance (on any given distribution over data), even by a small margin. Such weak learners form the practical basis for canonical machine learning methods such as boosting. In this work, we illustrate that prompt-based large language models can operate effectively as said weak learners. Specifically, we illustrate the use of a large language model (LLM) as a weak learner in a boosting algorithm applied to tabular data. We show that by providing (properly sampled according to the distribution of interest) text descriptions of tabular data samples, LLMs can produce a summary of the samples that serves as a template for classification and achieves the aim of acting as a weak learner on this task. We incorporate these models into a boosting approach, which in some settings can leverage the knowledge within the LLM to outperform traditional tree-based boosting. The model outperforms both few-shot learning and occasionally even more involved fine-tuning procedures, particularly for tasks involving small numbers of data points. The results illustrate the potential for prompt-based LLMs to function not just as few-shot learners themselves, but as components of larger machine learning pipelines.

We propose a novel block for video modelling. It relies on a time-space-channel factorisation with dedicated blocks for each dimension: gated linear recurrent units (LRUs) perform information mixing over time, self-attention layers perform mixing over space, and MLPs over channels. The resulting architecture TRecViT performs well on sparse and dense tasks, trained in supervised or self-supervised regimes. Notably, our model is causal and outperforms or is on par with a pure attention model ViViT-L on large scale video datasets (SSv2, Kinetics400), while having 3times less parameters, 12times smaller memory footprint, and 5times lower FLOPs count. Code and checkpoints will be made available online at https://github.com/google-deepmind/trecvit.

We present a novel inference scheme, self-speculative decoding, for accelerating Large Language Models (LLMs) without the need for an auxiliary model. This approach is characterized by a two-stage process: drafting and verification. The drafting stage generates draft tokens at a slightly lower quality but more quickly, which is achieved by selectively skipping certain intermediate layers during drafting Subsequently, the verification stage employs the original LLM to validate those draft output tokens in one forward pass. This process ensures the final output remains identical to that produced by the unaltered LLM, thereby maintaining output quality. The proposed method requires no additional neural network training and no extra memory footprint, making it a plug-and-play and cost-effective solution for inference acceleration. Benchmarks with LLaMA-2 and its fine-tuned models demonstrated a speedup up to 1.73times.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

The integration of pre-trained text-based large language models (LLM) with speech input has enabled instruction-following capabilities for diverse speech tasks. This integration requires the use of a speech encoder, a speech adapter, and an LLM, trained on diverse tasks. We propose the use of discrete speech units (DSU), rather than continuous-valued speech encoder outputs, that are converted to the LLM token embedding space using the speech adapter. We generate DSU using a self-supervised speech encoder followed by k-means clustering. The proposed model shows robust performance on speech inputs from seen/unseen domains and instruction-following capability in spoken question answering. We also explore various types of DSU extracted from different layers of the self-supervised speech encoder, as well as Mel frequency Cepstral Coefficients (MFCC). Our findings suggest that the ASR task and datasets are not crucial in instruction-tuning for spoken question answering tasks.

The ability of large language models to generate complex texts allows them to be widely integrated into many aspects of life, and their output can quickly fill all network resources. As the impact of LLMs grows, it becomes increasingly important to develop powerful detectors for the generated text. This detector is essential to prevent the potential misuse of these technologies and to protect areas such as social media from the negative effects of false content generated by LLMS. The main goal of LLM-generated text detection is to determine whether text is generated by an LLM, which is a basic binary classification task. In our work, we mainly use three different classification methods based on open source datasets: traditional machine learning techniques such as logistic regression, k-means clustering, Gaussian Naive Bayes, support vector machines, and methods based on converters such as BERT, and finally algorithms that use LLMs to detect LLM-generated text. We focus on model generalization, potential adversarial attacks, and accuracy of model evaluation. Finally, the possible research direction in the future is proposed, and the current experimental results are summarized.

There is debate if phoneme or viseme units are the most effective for a lipreading system. Some studies use phoneme units even though phonemes describe unique short sounds; other studies tried to improve lipreading accuracy by focusing on visemes with varying results. We compare the performance of a lipreading system by modeling visual speech using either 13 viseme or 38 phoneme units. We report the accuracy of our system at both word and unit levels. The evaluation task is large vocabulary continuous speech using the TCD-TIMIT corpus. We complete our visual speech modeling via hybrid DNN-HMMs and our visual speech decoder is a Weighted Finite-State Transducer (WFST). We use DCT and Eigenlips as a representation of mouth ROI image. The phoneme lipreading system word accuracy outperforms the viseme based system word accuracy. However, the phoneme system achieved lower accuracy at the unit level which shows the importance of the dictionary for decoding classification outputs into words.

Recent results indicate that the generic descriptors extracted from the convolutional neural networks are very powerful. This paper adds to the mounting evidence that this is indeed the case. We report on a series of experiments conducted for different recognition tasks using the publicly available code and model of the \overfeat network which was trained to perform object classification on ILSVRC13. We use features extracted from the \overfeat network as a generic image representation to tackle the diverse range of recognition tasks of object image classification, scene recognition, fine grained recognition, attribute detection and image retrieval applied to a diverse set of datasets. We selected these tasks and datasets as they gradually move further away from the original task and data the \overfeat network was trained to solve. Astonishingly, we report consistent superior results compared to the highly tuned state-of-the-art systems in all the visual classification tasks on various datasets. For instance retrieval it consistently outperforms low memory footprint methods except for sculptures dataset. The results are achieved using a linear SVM classifier (or L2 distance in case of retrieval) applied to a feature representation of size 4096 extracted from a layer in the net. The representations are further modified using simple augmentation techniques e.g. jittering. The results strongly suggest that features obtained from deep learning with convolutional nets should be the primary candidate in most visual recognition tasks.

This case study investigates the task of job classification in a real-world setting, where the goal is to determine whether an English-language job posting is appropriate for a graduate or entry-level position. We explore multiple approaches to text classification, including supervised approaches such as traditional models like Support Vector Machines (SVMs) and state-of-the-art deep learning methods such as DeBERTa. We compare them with Large Language Models (LLMs) used in both few-shot and zero-shot classification settings. To accomplish this task, we employ prompt engineering, a technique that involves designing prompts to guide the LLMs towards the desired output. Specifically, we evaluate the performance of two commercially available state-of-the-art GPT-3.5-based language models, text-davinci-003 and gpt-3.5-turbo. We also conduct a detailed analysis of the impact of different aspects of prompt engineering on the model's performance. Our results show that, with a well-designed prompt, a zero-shot gpt-3.5-turbo classifier outperforms all other models, achieving a 6% increase in Precision@95% Recall compared to the best supervised approach. Furthermore, we observe that the wording of the prompt is a critical factor in eliciting the appropriate "reasoning" in the model, and that seemingly minor aspects of the prompt significantly affect the model's performance.

Generative Large Language Models (LLMs) have become the mainstream choice for fewshot and zeroshot learning thanks to the universality of text generation. Many users, however, do not need the broad capabilities of generative LLMs when they only want to automate a classification task. Smaller BERT-like models can also learn universal tasks, which allow them to do any text classification task without requiring fine-tuning (zeroshot classification) or to learn new tasks with only a few examples (fewshot), while being significantly more efficient than generative LLMs. This paper (1) explains how Natural Language Inference (NLI) can be used as a universal classification task that follows similar principles as instruction fine-tuning of generative LLMs, (2) provides a step-by-step guide with reusable Jupyter notebooks for building a universal classifier, and (3) shares the resulting universal classifier that is trained on 33 datasets with 389 diverse classes. Parts of the code we share has been used to train our older zeroshot classifiers that have been downloaded more than 55 million times via the Hugging Face Hub as of December 2023. Our new classifier improves zeroshot performance by 9.4%.

Conventional multi-label classification (MLC) methods assume that all samples are fully labeled and identically distributed. Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and partial labels (PL). To address the problem, we introduce a novel task, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to jointly consider the above two imperfect learning environments. Not surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the PLT-MLC, resulting in significant performance degradation on the two proposed PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework: COrrection rightarrow ModificatIon rightarrow balanCe, abbreviated as \method{}. Our bootstrapping philosophy is to simultaneously correct the missing labels (Correction) with convinced prediction confidence over a class-aware threshold and to learn from these recall labels during training. We next propose a novel multi-focal modifier loss that simultaneously addresses head-tail imbalance and positive-negative imbalance to adaptively modify the attention to different samples (Modification) under the LT class distribution. In addition, we develop a balanced training strategy by distilling the model's learning effect from head and tail samples, and thus design a balanced classifier (Balance) conditioned on the head and tail learning effect to maintain stable performance for all samples. Our experimental study shows that the proposed significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of effectiveness and robustness on our newly created PLT-MLC datasets.

On-device large language models (LLMs) are catalyzing novel mobile applications such as UI task automation and personalized email auto-reply, without giving away users' private data. However, on-device LLMs still suffer from unacceptably long inference latency, especially the time to first token (prefill stage) due to the need of long context for accurate, personalized content generation, as well as the lack of parallel computing capacity of mobile CPU/GPU. To enable practical on-device LLM, we present mllm-NPU, the first-of-its-kind LLM inference system that efficiently leverages on-device Neural Processing Unit (NPU) offloading. Essentially, mllm-NPU is an algorithm-system co-design that tackles a few semantic gaps between the LLM architecture and contemporary NPU design. Specifically, it re-constructs the prompt and model in three levels: (1) At prompt level, it divides variable-length prompts into multiple fixed-sized chunks while maintaining data dependencies; (2) At tensor level, it identifies and extracts significant outliers to run on the CPU/GPU in parallel with minimal overhead; (3) At block level, it schedules Transformer blocks in an out-of-order manner to the CPU/GPU and NPU based on their hardware affinity and sensitivity to accuracy. Compared to competitive baselines, mllm-NPU achieves 22.4x faster prefill speed and 30.7x energy savings on average, and up to 32.8x speedup in an end-to-end real-world application. For the first time, mllm-NPU achieves more than 1,000 tokens/sec prefilling for a billion-sized model (Qwen1.5-1.8B), paving the way towards practical on-device LLM.

Few Shot Class Incremental Learning (FSCIL) with few examples per class for each incremental session is the realistic setting of continual learning since obtaining large number of annotated samples is not feasible and cost effective. We present the framework MASIL as a step towards learning the maximal separable classifier. It addresses the common problem i.e forgetting of old classes and over-fitting to novel classes by learning the classifier weights to be maximally separable between classes forming a simplex Equiangular Tight Frame. We propose the idea of concept factorization explaining the collapsed features for base session classes in terms of concept basis and use these to induce classifier simplex for few shot classes. We further adds fine tuning to reduce any error occurred during factorization and train the classifier jointly on base and novel classes without retaining any base class samples in memory. Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that MASIL outperforms all the benchmarks.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

The goal of voice conversion is to transform source speech into a target voice, keeping the content unchanged. In this paper, we focus on self-supervised representation learning for voice conversion. Specifically, we compare discrete and soft speech units as input features. We find that discrete representations effectively remove speaker information but discard some linguistic content - leading to mispronunciations. As a solution, we propose soft speech units. To learn soft units, we predict a distribution over discrete speech units. By modeling uncertainty, soft units capture more content information, improving the intelligibility and naturalness of converted speech. Samples available at https://ubisoft-laforge.github.io/speech/soft-vc/. Code available at https://github.com/bshall/soft-vc/.

Large language models (LLMs) hold the promise of solving diverse tasks when provided with appropriate natural language prompts. However, prompting often leads models to make predictions with lower accuracy compared to finetuning a model with ample training data. On the other hand, while finetuning LLMs on task-specific data generally improves their performance, abundant annotated datasets are not available for all tasks. Previous work has explored generating task-specific data from state-of-the-art LLMs and using this data to finetune smaller models, but this approach requires access to a language model other than the one being trained, which introduces cost, scalability challenges, and legal hurdles associated with continuously relying on more powerful LLMs. In response to these, we propose SELF-GUIDE, a multi-stage mechanism in which we synthesize task-specific input-output pairs from the student LLM, then use these input-output pairs to finetune the student LLM itself. In our empirical evaluation of the Natural Instructions V2 benchmark, we find that SELF-GUIDE improves the performance of LLM by a substantial margin. Specifically, we report an absolute improvement of approximately 15% for classification tasks and 18% for generation tasks in the benchmark's metrics. This sheds light on the promise of self-synthesized data guiding LLMs towards becoming task-specific experts without any external learning signals.

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear Unit (GELU) activation function has emerged as a dominant method, surpassing traditional functions such as the Rectified Linear Unit (ReLU) in various applications. This study presents a rigorous mathematical investigation of the GELU activation function, exploring its differentiability, boundedness, stationarity, and smoothness properties in detail. Additionally, we conduct an extensive experimental comparison of the GELU function against a broad range of alternative activation functions, utilizing a residual convolutional network trained on the CIFAR-10, CIFAR-100, and STL-10 datasets as the empirical testbed. Our results demonstrate the superior performance of GELU compared to other activation functions, establishing its suitability for a wide range of deep learning applications. This comprehensive study contributes to a more profound understanding of the underlying mathematical properties of GELU and provides valuable insights for practitioners aiming to select activation functions that optimally align with their specific objectives and constraints in deep learning.

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in handling more complex problems remains unexplored. In this paper, we prove that any linear transformer maintains an implicit linear model and can be interpreted as performing a variant of preconditioned gradient descent. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm, surpassing or matching in performance many reasonable baselines. We reverse-engineer this algorithm and show that it is a novel approach incorporating momentum and adaptive rescaling based on noise levels. Our findings show that even linear transformers possess the surprising ability to discover sophisticated optimization strategies.

Transformer-based language models (LMs) create hidden representations of their inputs at every layer, but only use final-layer representations for prediction. This obscures the internal decision-making process of the model and the utility of its intermediate representations. One way to elucidate this is to cast the hidden representations as final representations, bypassing the transformer computation in-between. In this work, we suggest a simple method for such casting, by using linear transformations. We show that our approach produces more accurate approximations than the prevailing practice of inspecting hidden representations from all layers in the space of the final layer. Moreover, in the context of language modeling, our method allows "peeking" into early layer representations of GPT-2 and BERT, showing that often LMs already predict the final output in early layers. We then demonstrate the practicality of our method to recent early exit strategies, showing that when aiming, for example, at retention of 95% accuracy, our approach saves additional 7.9% layers for GPT-2 and 5.4% layers for BERT, on top of the savings of the original approach. Last, we extend our method to linearly approximate sub-modules, finding that attention is most tolerant to this change.

We propose a novel interpretation technique to explain the behavior of structured output models, which learn mappings between an input vector to a set of output variables simultaneously. Because of the complex relationship between the computational path of output variables in structured models, a feature can affect the value of output through other ones. We focus on one of the outputs as the target and try to find the most important features utilized by the structured model to decide on the target in each locality of the input space. In this paper, we assume an arbitrary structured output model is available as a black box and argue how considering the correlations between output variables can improve the explanation performance. The goal is to train a function as an interpreter for the target output variable over the input space. We introduce an energy-based training process for the interpreter function, which effectively considers the structural information incorporated into the model to be explained. The effectiveness of the proposed method is confirmed using a variety of simulated and real data sets.

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.

We propose the APTx Neuron, a novel, unified neural computation unit that integrates non-linear activation and linear transformation into a single trainable expression. The APTx Neuron is derived from the APTx activation function, thereby eliminating the need for separate activation layers and making the architecture both computationally efficient and elegant. The proposed neuron follows the functional form y = sum_{i=1}^{n} ((alpha_i + tanh(beta_i x_i)) cdot gamma_i x_i) + delta, where all parameters alpha_i, beta_i, gamma_i, and delta are trainable. We validate our APTx Neuron-based architecture on the MNIST dataset, achieving up to 96.69% test accuracy within 11 epochs using approximately 332K trainable parameters. The results highlight the superior expressiveness and computational efficiency of the APTx Neuron compared to traditional neurons, pointing toward a new paradigm in unified neuron design and the architectures built upon it.

Generative modeling, representation learning, and classification are three core problems in machine learning (ML), yet their state-of-the-art (SoTA) solutions remain largely disjoint. In this paper, we ask: Can a unified principle address all three? Such unification could simplify ML pipelines and foster greater synergy across tasks. We introduce Latent Zoning Network (LZN) as a step toward this goal. At its core, LZN creates a shared Gaussian latent space that encodes information across all tasks. Each data type (e.g., images, text, labels) is equipped with an encoder that maps samples to disjoint latent zones, and a decoder that maps latents back to data. ML tasks are expressed as compositions of these encoders and decoders: for example, label-conditional image generation uses a label encoder and image decoder; image embedding uses an image encoder; classification uses an image encoder and label decoder. We demonstrate the promise of LZN in three increasingly complex scenarios: (1) LZN can enhance existing models (image generation): When combined with the SoTA Rectified Flow model, LZN improves FID on CIFAR10 from 2.76 to 2.59-without modifying the training objective. (2) LZN can solve tasks independently (representation learning): LZN can implement unsupervised representation learning without auxiliary loss functions, outperforming the seminal MoCo and SimCLR methods by 9.3% and 0.2%, respectively, on downstream linear classification on ImageNet. (3) LZN can solve multiple tasks simultaneously (joint generation and classification): With image and label encoders/decoders, LZN performs both tasks jointly by design, improving FID and achieving SoTA classification accuracy on CIFAR10. The code and trained models are available at https://github.com/microsoft/latent-zoning-networks. The project website is at https://zinanlin.me/blogs/latent_zoning_networks.html.

How do reasoning models verify their own answers? We study this question by training a model using DeepSeek R1's recipe on the CountDown task. We leverage the fact that preference tuning leads to mode collapse, yielding a model that always produces highly structured chain-of-thought sequences. With this setup, we do top-down and bottom-up analyses to reverse-engineer how the model verifies its outputs. Top-down, we find Gated Linear Unit (GLU) weights encoding verification-related tokens, such as ``success'' or ``incorrect''. Bottom-up, we find that ``previous-token heads'' are mainly responsible for self-verification in our setup. Our analyses meet in the middle: drawing inspiration from inter-layer communication channels, we use the identified GLU weights to localize as few as three attention heads that can disable self-verification, pointing to a necessary component of a potentially larger verification circuit. Finally, we verify that similar verification components exist in our base model and a general reasoning DeepSeek-R1 model.

Pretrained language models (PLMs) have demonstrated remarkable performance in various natural language processing tasks: Unidirectional PLMs (e.g., GPT) are well known for their superior text generation capabilities; bidirectional PLMs (e.g., BERT) have been the prominent choice for natural language understanding (NLU) tasks. While both types of models have achieved promising few-shot learning performance, their potential for zero-shot learning has been underexplored. In this paper, we present a simple approach that uses both types of PLMs for fully zero-shot learning of NLU tasks without requiring any task-specific data: A unidirectional PLM generates class-conditioned texts guided by prompts, which are used as the training data for fine-tuning a bidirectional PLM. With quality training data selected based on the generation probability and regularization techniques (label smoothing and temporal ensembling) applied to the fine-tuning stage for better generalization and stability, our approach demonstrates strong performance across seven classification tasks of the GLUE benchmark (e.g., 72.3/73.8 on MNLI-m/mm and 92.8 on SST-2), significantly outperforming zero-shot prompting methods and achieving even comparable results to strong few-shot approaches using 32 training samples per class.

We present our transducer model on Librispeech. We study variants to include an external language model (LM) with shallow fusion and subtract an estimated internal LM. This is justified by a Bayesian interpretation where the transducer model prior is given by the estimated internal LM. The subtraction of the internal LM gives us over 14% relative improvement over normal shallow fusion. Our transducer has a separate probability distribution for the non-blank labels which allows for easier combination with the external LM, and easier estimation of the internal LM. We additionally take care of including the end-of-sentence (EOS) probability of the external LM in the last blank probability which further improves the performance. All our code and setups are published.

LLMs are not generally able to adjust the length of their outputs based on strict length requirements, a capability that would improve their usefulness in applications that require adherence to diverse user and system requirements. We present an approach to train LLMs to acquire this capability by augmenting existing data and applying existing fine-tuning techniques, which we compare based on the trained models' adherence to the length requirement and overall response quality relative to the baseline model. Our results demonstrate that these techniques can be successfully applied to train LLMs to adhere to length requirements, with the trained models generating texts which better align to the length requirements. Our results indicate that our method may change the response quality when using training data that was not generated by the baseline model. This allows simultaneous alignment to another training objective in certain scenarios, but is undesirable otherwise. Training on a dataset containing the model's own responses eliminates this issue.

A proper initialization of the weights in a neural network is critical to its convergence. Current insights into weight initialization come primarily from linear activation functions. In this paper, I develop a theory for weight initializations with non-linear activations. First, I derive a general weight initialization strategy for any neural network using activation functions differentiable at 0. Next, I derive the weight initialization strategy for the Rectified Linear Unit (RELU), and provide theoretical insights into why the Xavier initialization is a poor choice with RELU activations. My analysis provides a clear demonstration of the role of non-linearities in determining the proper weight initializations.