math_model.py

import torch.nn as nn
import torch

def quantize(tensor, scale, zero_point, is_asym=False):
    if is_asym:
        clamp_min, clamp_max = torch.tensor(0.), torch.tensor(255.)
    else:
        clamp_min, clamp_max = torch.tensor(-128.), torch.tensor(127.)
    quant_tensor = torch.clamp(torch.round(tensor/scale + zero_point), clamp_min, clamp_max) 
    return quant_tensor

def dequantize(tensor, scale, zero_point):
    return (tensor - zero_point) * scale


class QuantLinear(nn.Module):
    def __init__(self, in_ch, out_ch, quant_param):
        super().__init__()
        mul_factor = torch.tensor(quant_param['smoothquant_mul']).view(quant_param['smoothquant_mul_shape'])
        self.register_buffer('mul_factor', mul_factor)
        self.linear = nn.Linear(in_ch, out_ch)
        weight_scale = torch.tensor(quant_param['weight_scale']).view(quant_param['weight_scale_shape'])
        weight_zp = torch.tensor(quant_param['weight_zp']).view(quant_param['weight_zp_shape'])
        assert quant_param['weight_zp_dtype'] == 'torch.int8', f"Weight Zero-Point dtype should be 'torch.int8', found: {quant_param['weight_zp_dype']}"
        input_scale = torch.tensor(quant_param['input_scale']).view(quant_param['input_scale_shape'])
        input_zp = torch.tensor(quant_param['input_zp']).view(quant_param['input_zp_shape'])
        assert quant_param['input_zp_dtype'] == 'torch.int8', f"Input Zero-Point dtype should be 'torch.int8', found: {quant_param['input_zp_dype']}"
        self.register_buffer('weight_scale', weight_scale)
        self.register_buffer('weight_zp', weight_zp)
        self.register_buffer('input_scale', input_scale)
        self.register_buffer('input_zp', input_zp)

    # I.e., "fake quantization"
    def qdq_forward(self, x):
        scaled_x = x * self.mul_factor
        weight_zp_uint8 = (self.weight_zp + 128).to(torch.uint8).to(torch.float32)
        quant_weight = quantize(self.linear.weight, self.weight_scale, weight_zp_uint8, is_asym=True)
        quant_input = quantize(scaled_x, self.input_scale, self.input_zp, is_asym=False)
        dequantized_weight = dequantize(quant_weight, self.weight_scale, weight_zp_uint8)
        dequantized_input = dequantize(quant_input, self.input_scale, self.input_zp)
        out = torch.nn.functional.linear(dequantized_input, dequantized_weight, self.linear.bias)
        return out

    # Accelerated version
    def qop_forward(self, x):
        # With an integer linear kernel, if the weight zero point is not zero,
        # A correction term must be calculated to correct the output.
        # The correction term calculated as follows:
        #  - sum the input tensor across the dot-product dimentions: (e.g., `torch.sum(quant_input, dim=-1)`)
        #  - multiply this sum with every weight zero-point (e.g., `torch.sum(quant_input, dim=-1) * self.weight_zp`
        #  - Subtract from previous output (e.g., `quant_output -= torch.sum(quant_input, dim=-1) * self.weight_zp`)
        #  - All other code is just to make sure the broadcasting semantics work correctly
        quant_weight = quantize(self.linear.weight, self.weight_scale, self.weight_zp, is_asym=False).to(torch.int8)
        fused_input_scale = self.input_scale / self.mul_factor # Fuse SmoothQuant and input scales, can be computed offline
        quant_input = quantize(x, fused_input_scale, self.input_zp, is_asym=False).to(torch.int8)
        quant_output = torch.nn.functional.linear(quant_input.to(torch.float32), quant_weight.to(torch.float32), None).to(torch.int32) # Convert inputs to FP32 to avoid F.linear quantizing the output to int8
        correction = torch.sum(quant_input, dim=-1, keepdim=True).to(torch.int32) * self.weight_zp.to(torch.int8).view([1]*(quant_input.ndim-1) + [self.weight_zp.nelement()]) # Correct for weight zero-point
        quant_output = quant_output - correction
        output = dequantize(quant_output, (self.weight_scale * self.input_scale).view([1]*(quant_output.ndim-1) + [(self.weight_scale * self.input_scale).nelement()]), 0.0)
        output += self.linear.bias
        return output

    def forward(self, x, qop=False):
        if qop:
            return self.qop_forward(x)
        else:
            return self.qdq_forward(x)

class QuantConv2d(nn.Module):
    def __init__(self, in_ch, out_ch, kernel_size, quant_param):
        super().__init__()
        mul_factor = torch.tensor(quant_param['smoothquant_mul']).view(quant_param['smoothquant_mul_shape'])
        self.register_buffer('mul_factor', mul_factor)
        self.conv2d = nn.Conv2d(in_ch, out_ch, kernel_size)
        weight_scale = torch.tensor(quant_param['weight_scale']).view(quant_param['weight_scale_shape'])
        weight_zp = torch.tensor(quant_param['weight_zp']).view(quant_param['weight_zp_shape'])
        assert quant_param['weight_zp_dtype'] == 'torch.int8', f"Weight Zero-Point dtype should be 'torch.int8', found: {quant_param['weight_zp_dype']}"
        input_scale = torch.tensor(quant_param['input_scale']).view(quant_param['input_scale_shape'])
        input_zp = torch.tensor(quant_param['input_zp']).view(quant_param['input_zp_shape'])
        assert quant_param['input_zp_dtype'] == 'torch.int8', f"Input Zero-Point dtype should be 'torch.int8', found: {quant_param['input_zp_dype']}"
        self.register_buffer('weight_scale', weight_scale)
        self.register_buffer('weight_zp', weight_zp)
        self.register_buffer('input_scale', input_scale)
        self.register_buffer('input_zp', input_zp)

    # I.e., "fake quantization"
    def qdq_forward(self, x):
        scaled_x = x * self.mul_factor
        weight_zp_uint8 = (self.weight_zp + 128).to(torch.uint8).to(torch.float32)
        quant_weight = quantize(self.conv2d.weight, self.weight_scale, weight_zp_uint8, is_asym=True)
        quant_input = quantize(scaled_x, self.input_scale, self.input_zp, is_asym=False)
        dequantized_weight = dequantize(quant_weight, self.weight_scale, weight_zp_uint8)
        dequantized_input = dequantize(quant_input, self.input_scale, self.input_zp)
        out = torch.nn.functional.conv2d(dequantized_input, dequantized_weight, self.conv2d.bias)
        return out

    # Accelerated version
    def qop_forward(self, x):
        # With an integer conv2d kernel, if the weight zero point is not zero,
        # A correction term must be calculated to correct the output.
        # Conceptually, it's identical to the linear case except that it's difficult
        # to reduce the input across the dot-product dimension. This leaves us with two obvious options:
        #  1. Manually compute the reduction via Im2Col -> `torch.sum`
        #  2. Add an extra _output channel_ to the convolution with a kernel made from all ones (e.g., `torch.ones()`)
        # In this example, I've used option #2.
        # The correction term is then calculated as follows:
        #  - Add an extra output channel to the weight tensor with all values equal to 1 to calculate the sum (e.g., `torch.cat((quant_weight, torch.ones(shape)), dim=0)`)
        #  - Extract the sum from the output tensor (e.g., `sum = quant_output[:,-1,:,:]`)
        #  - multiply this sum with every weight zero-point (e.g., `sum * self.weight_zp`
        #  - Subtract from previous output (e.g., `quant_output -= sum * self.weight_zp`)
        #  - All other code is just to make sure the broadcasting semantics work correctly
        quant_weight = quantize(self.conv2d.weight, self.weight_scale, self.weight_zp, is_asym=False).to(torch.int8)
        b_shape = list(quant_weight.shape) # Used for weight zero-point correction
        b_shape[0] = 1 # Used for weight zero-point correction
        weight_cat = torch.ones((1,1,1,1)).broadcast_to(b_shape).to(torch.int8) # Used for weight zero-point correction
        quant_weight = torch.cat((quant_weight,weight_cat),dim=0).to(torch.int8) # Create extra output channel, used for weight zero-point correction
        fused_input_scale = self.input_scale / self.mul_factor # Fuse SmoothQuant and input scales, can be computed offline
        quant_input = quantize(x, fused_input_scale, self.input_zp, is_asym=False).to(torch.int8)
        quant_output = torch.nn.functional.conv2d(quant_input.to(torch.float32), quant_weight.to(torch.float32), None).to(torch.int32) # Convert inputs to FP32 to avoid F.conv2d quantizing the output to int8
        correction = quant_output[:,-1,:,:] * self.weight_zp.to(torch.int8).view([1, self.weight_zp.nelement()] +  [1]*(quant_output.ndim-2)) # Correct zero-point for weight
        quant_output = quant_output[:,:-1,:,:] - correction
        output = dequantize(quant_output, (self.weight_scale * self.input_scale).view([1, (self.weight_scale * self.input_scale).nelement()] + [1]*(quant_output.ndim-2)), 0.0)
        output += self.conv2d.bias.view([1, self.conv2d.bias.nelement()] + [1]*(quant_output.ndim-2))
        return output

    def forward(self, x, qop=False):
        if qop:
            return self.qop_forward(x)
        else:
            return self.qdq_forward(x)