: A White Paper on Neural Network Quantization If the accuracy is acceptable, we have our final quantized model ready to use. Training competitive binary neural networks from scratch. In case WE[x] is nonzero, the output distribution is shifted. More formally, during inference, batch normalization is defined as an affine map of the output x: where and are the mean and variance computed during training as exponential moving average over batch-statistics, and and are learned affine hyper-parameters per-channel. Related papers Deep learning with limited numerical precision. Applying analytical bias correction improves quantized model performance from random to over 50%, indicating that the biased error introduced by quantization significantly harms model performance. We note that MSE combined with cross-entropy for the last layer, denoted as MSE + Xent, outperforms other methods, especially at lower bit-widths. Block floating point (BFP) is particularly useful in this scenario due to its high dynamic range which allows for lower precision while maintaining accuracy. This is called per-tensor quantization. In conclusion, for models that have severe issues with plain PTQ we may need advanced PTQ techniques such as CLE to initialize QAT. Adaptive Rounding for Post-Training Quantization, Quantization of Generative Adversarial Networks for Efficient Inference: the scale-factor: Originally, we restricted the zero-point to be an integer. In section 3.1, we explore in more detail how to choose the quantization parameters to achieve the right trade-off between clipping and rounding errors. This frees the neural network designer from having to be an expert in quantization and thus allows for a much wider application of neural network quantization. This value is equal to. This allows us to reparameterize our model with Reducing the power and latency of neural network inference is key if we want to integrate modern networks into edge devices with strict power and compute requirements. A fundamental step in the PTQ process is finding good quantization ranges for each quantizer. In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintaining low-bit weights and activations. When quantizing neural networks with multiple layers, we are confronted with a large space of quantization choices including the quantization scheme, granularity, and bit-width. W4A8 stays within 1% of the original GLUE score, indicating that low bit weight quantization is not a problem for transformer models. Or, have a go at fixing it yourself the renderer is open source! It is an essential step in the model efficiency pipeline for any practical use-case of deep learning. Levy, and S. Bowman (2018), GLUE: a multi-task benchmark and analysis platform for natural language understanding. PDF Quantization and Training of Neural Networks for Efficient Integer (PDF) A White Paper on Neural Network Quantization (2021) | Markus 12021A White Paper on Neural Network Quantization The trivial solution c=0 holds for all x. The main contributor to this error is often the clipping error, as a few strongly clipped outliers will likely lead to a shift in the expected distribution. Assuming input values are normally distributied, the effect of ReLU on the distribution can be modeled using the clipped normal distribution. We set each quantizer sequentially, to the target bit-width while keeping the rest of the network to 32 bits (see inner for loop in figure 9). Per-tensor quantization of weights and activations has been standard for a while because it is supported by all fixed-point accelerators. weights and activations. For BERT-base we observe that QAT with range learning can efficiently deal with the high dynamic ranges allowing to keep all activations in 8 bits (unlike for PTQ). When starting from a converged pre-trained model, static folding is very effective, as we can see from the result of table 7. 2018 google; ACIQ: analytical clipping for integer quantization of neural networks. QAT requires fine-tuning and access to In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintaining low-bit weights and activations. Once all cycles are completed, the values in the accumulators are then moved back to memory to be used in the next neural network layer. They allow the user to efficiently test various quantization options and it enables GPU acceleration for quantization-aware training as described in section 4. The learning rate is individually optimized for each configuration. However, neural network quantization is not free. To make zero-point learnable we convert into a real number and apply the rounding operator. Standard quantization-aware training pipeline. available we next apply AdaRound in order to optimize the rounding of the weights. Quantizing both weights and activations to 4-bits remains a challenging for such networks, even with per-channel quantization it can lead to a drop of up to 5%. However, increasing the scale factor leads to increased rounding error as the rounding error lies in the range [12s,12s]. This scheme is called uniform quantization and it is the most commonly used quantization scheme because it permits efficient implementation of fixed-point arithmetic. Neural Network Compression Using Quantization | by Tech - Medium Understanding and Overcoming the Challenges of Efficient Transformer Quantization. For example, ReLU non-linearities are readily modelled by the requantization block, as you can just set the minimum representable value of that activation quantization to 0. [2106.08295v1] A White Paper on Neural Network Quantization Vi,j is the continuous variable that we optimize over and h can be any monotonic function with values between 0 and 1, i.e., \mathnormalh(Vi,j)[0,1]. If a layer has batch-normalized activations, the per-channel mean and standard deviation of the activations are equal to the learned batch normalization shift and scale parameters, respectively. While the MSE initialized model has a significantly higher starting accuracy, the gap closes after training for 20 epochs. Adaptive quantization for deep neural network. When quantizing neural networks, assigning each floating-point weight to Generative adversarial networks (GANs) have an enormous potential impact Quantization is wildly taken as a model compression technique, which obt Neural networks are essential components of learning-based software syst Data clipping is crucial in reducing noise in quantization operations an Neural Network Quantization with AI Model Efficiency Toolkit (AIMET), Up or Down? labeled training data but enables lower bit quantization with competitive QAT models the quantization noise source (see section 2.3) during training. In this section, we present a best-practice pipeline for PTQ based on relevant literature and extensive experimentation. While neural networks have advanced the frontiers in many applications, they often come at a high computational cost. Neural network quantization is one of the most effective ways of achieving these savings but the additional . This means that the bit-width chosen for either weights or activations remains constant across all layers. Quantizing networks with depth-wise separable layers (MobileNetV2, EfficientNet lite, DeeplabV3, EfficientDet-D1) is more challenging; a trend we also observed from the PTQ results in section 3.6 and discussed in the literature (Chin et al., 2020; Sheng et al., 2018). Neural network quantization is one of the most effective ways of achieving these savings but the additional noise it induces can lead to accuracy degradation. For certain layers, all values in the tensor being quantized may not be equally important. where H(,) denotes the cross-entropy function, is the softmax function, and v is the logits vector. Batch normalization (Ioffe and Szegedy, 2015) is a standard component of modern convolutional networks. This process is. The fundamental idea behind quantization is that if we convert the weights and inputs into integer types, we consume less memory and on certain hardware, the calculations are faster. This step is repeated many times for larger matrix-vector multiplications. This approach is more cumbersome and computationally costly because it involves a double forward pass: one for the batch-statistics and one for the quantized linear operation. . paper-of-quantization | Joey's note When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. This will address the issue of uneven per-channel weight distribution. per-channel as in figure 5, and dimensions, e.g., per-token or per-embedding for activations in BERT. Despite the performance gains (see table 5), equation (30) cannot be widely applied for weight rounding for main two reasons: The memory and computational complexity of calculating the Hessian is impractical for general use-cases. During quantization-aware training, we want to simulate inference behavior closely, which is why we have to account for BN-folding during training. In the first experiment, we quantize the weights to 4-bits and keep the activations in 8-bits. Schematic overview of quantized forward pass for convolutional layer: a) Compute graph of actual on-device quantized inference. Set the quantized model bit-width to 32 bits for both weights and activation, or by-pass the quantization operation, if possible, and check that the accuracy matches that of the FP32 model. Other works go beyond per-channel quantization parameters and apply separate quantizers per group of weights or activations (Rouhani et al., 2020; Stock et al., 2019; Nascimento et al., 2019). In case we do not have such a calibration dataset and the network uses batch normalization, we can use analytical bias correction instead. 2021 Google. (2019) introduce a method to analytically calculate the biased error, without the need for data. In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintaining low-bit weights and activations. Neural network quantization is one of the most effective ways of achieving these savings but the additional noise it induces can lead to accuracy degradation. (2019) showed that this is especially prevalent in depth-wise separable layers since only a few weights are responsible for each output feature and this might result in higher variability of the weights. To find a good approximate solution with reasonable computational complexity, the authors relax the optimization problem to the following continuous optimization problem, where 2F denotes the Frobenius norm and W are the soft-quantized weights defined as, We use n and p to denote integer grid limits, n=qmin/s and p=qmax/s. The learning rate is individually optimized for each configuration. Ablation study for different methods of range setting of (symmetric uniform) weight quantizers while keeping the activations in FP32. The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative QAT requires fine-tuning and access to labeled training data but enables lower bit quantization with competitive results. Loss-aware weight quantization of deep networks. The overhead is associated with accumulators handling sums of values with varying scale factors. Otherwise, we can consider higher bit-widths and smaller granularities or revert to more powerful quantization methods, such as quantization-aware training. We observe that for networks without depth-wise separable convolutions (first 3 rows of table 10), W8A8 and W4A8 quantization perform on par with and even outperform the floating-point model in certain cases. For both regimes, we introduce standard pipelines based on existing literature and extensive experimentation that lead to state-of-the-art performance for common computer vision and natural language processing models. If we have access to a calibration dataset the bias correction term can simply be calculated by comparing the activations of the quantized and full precision model. However, the picture changes when weights are quantized to 4 bits (W4A8). CF18ACM; UNIQ: Uniform noise injection for non-uniform quantization of neural networks. In this section, we will explore the effect of initialization for QAT. A solution to overcome such imbalances without the need to use per-channel quantization is introduced by Nagel et al. The visualization step can reveal the source of the tensors sensitivity to quantization. When combining bias correction with CLE, we see that both techniques are complementary. Despite their abun-dance, current quantization approaches are lacking in two respects when it comes to trading off latency with accuracy. The average of integers is not necessarily an integer. We also propose a debugging workflow to identify and address common issues when quantizing a new model. Therefore, it is important to check if it is possible in your intended target device. In table 3, we demonstrate the effect of CLE and bias absorption for quantizingMobileNetV2 to 8-bit. quantization noise on the network's performance while maintaining low-bit One such scenario is the quantization of logits in the last layer of classification networks, in which it is important to preserve the order of the largest value after quantization. If supported by the HW/SW stack then it is favorable to use per-channel quantization for weights. However, using learnable quantizers requires special care when setting up the optimizer for the task. Our toy example in figure 1 has 16 processing elements arranged in a square grid and 4 accumulators. The forward pass is identical to that of figure4, but in the backward pass we effectively skip the quantizer block due to the STE assumption. The static folding re-parametrization is also valid for per-channel quantization. Before training we have to initialize all quantization parameters. BERT-base is trained on each of the corresponding GLUE tasks for 3 to 12 epochs depending on the task and the quantization granularity. We denote this quantized version of the vector as x. However, this approach is sensitive to outliers as strong outliers may cause excessive rounding errors. To avoid error accumulation across layers of the neural network and to account for the non-linearity, the authors propose the following final optimization problem. We recommend making the quantizer paramaters learnable, as discussed in section 4.1. To this end, we consider two main classes of quantization algorithms: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). If we were to perform inference in FP32, the processing elements and the accumulator would have to support floating-point logic, and we would need to transfer the 32-bit data from memory to the processing units. The blue boxes represent the steps and the turquoise boxes recommended choices. MQBench Towards Reproducible and Deployable.pdf 567KB. In table 9 we compare the effect of other PTQ improvements such as CLE and bias correction. We start with a hardware motivation and then introduce standard quantization schemes and their properties. Post-training techniques may not be enough to mitigate the large quantization error incurred by low-bit quantization. This allows the model to find more optimal solutions than post-training quantization. For W8A8 quantization we also see no significant gains from using per-channel quantization. While neural networks have advanced the frontiers in many applications, they However, based on our experiments (see table 7), static-folding performs on par or better despite its simplicity. A similar approach was introduced in concurrent work by Meller et al. For both solutions, we provide tested pipelines based on existing literature and extensive experimentation that lead to state-of-the-art performance for common deep learning models and tasks. We illustrate the recommended pipeline in figure 8. In this white paper, we introduce state-of-the-art algorithms for mitigating the impact of quantization noise on the network's performance while maintaining low-bit weights and activations. Forward and backward computation graph for quantization aware training with STE assumption. The two fundamental components of this NN accelerator are the processing elements Cn,m and the accumulators An. Neural network quantization is one of the most effective ways of achieving these savings but the additional noise it induces can lead to accuracy degradation. However, determining parameters for activation quantization often requires a few batches of calibration data. In the specific case of per-channel quantization, using the min-max method can be favorable in some cases. For this reason, many hardware solutions come with a hardware unit that applies the non-linearity before the requantization step. ImageNet validation accuracy (%) evaluated at full precision and 8-bit quantization. We illustrate this rescaling procedure in figure 6. In this section, we present a best-practice pipeline for QAT based on relevant literature and extensive experimentation. Neural Network Quantization with AI Model Efficiency Toolkit (AIMET Note that the approximations and the analysis that have been used to link the QUBO problem of equation (30) with the local optimization problem of equation (31) is independent of the rounding problem. While neural networks have advanced the frontiers in many applications, they often come at a high computational cost. For other networks or in the case of per-channel quantization this step can be optional. 19. The choice for quantizer might depend on the specific target HW, for common AI accelerators we recommend using symmetric quantizers for the weights and asymmetric quantizers for the activations. The table also clearly demonstrates the benefit of using cross-entropy for the last layer instead of the MSE objective. We then consider two different regimes of quantizing neural networks: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Quantization is the process to convert a floating point model to a quantized model. A White Paper on Neural Network Quantization - NASA/ADS If this support is not available, we need to add a quantization step before and after the non-linearity in the graph. For both solutions, we provide tested pipelines based on existing literature and extensive experimentation that lead to state-of-the-art performance for common deep learning models and tasks. A way around this would be to approximate the gradient using the straight-through estimator (STE,Bengio et al. We now evaluate the performance of the aforementioned PTQ pipeline on common computer vision and natural language understanding applications. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. Neural network quantization is an effective way of reducing the power requirements and latency of neural network inference while maintaining high accuracy. KrishnaDN/Neural-Network-Quatization-and-Compression-Papers Neural network Reducing the power and latency of neural network inference is key if we want to integrate modern networks into edge devices with strict power and compute requirements. 2013), which approximates the gradient of the rounding operator as 1: Using this approximation we can now calculate the gradient of the quantization operation from equation (7). Error is the difference between floating-point and quantized model accuracy. results. Sign up to our mailing list for occasional updates. It would be wasteful to write the linear layers activations to memory, and then load them back into a compute core to apply a non-linearity. As with element-wise addition, it is possible to optimize your network to have shared quantization parameters for the branches being concatenated. Batch normalization normalizes the output of a linear layer before scaling and adding an offset (see equation9). Nagel et al. Otherwise, we risk incurring loss due to overflow as more products are accumulated during the computation. This is because in PTQ we aim for computationally fast methods without the need for end-to-end training. DeeplabV3 (MobileNetV2 backbone) is evaluated on Pascal VOC (mean intersection over union), EfficientDet-D1 on COCO 2017 (mean average precision), BERT-base on the GLUE benchmark and all other models on ImageNet (accuracy). To absorb c from layer one (followed by a ReLU activation function f) into layer two, we can do the following reparameterization: where b(2)=W(2)c+b(2), h=hc, and b(1)=b(1)c. In table 2, we present a similar comparison for activation quantization. to z is calculated by applying the STE once again to the rounding operator: In section 2.3.1, we introduced batch normalization folding that absorbs the scaling and addition into a linear layer to allow for more efficient inference. One of the most impactful ways to decrease the computational time and energy consumption of neural networks is quantization. An alternative approach by Jacob et al. This is called quantization simulation. However, depending on the distribution of x and the values of W and b, there can be some values ci>0 for which this equality holds for (almost) all x in the empirical distribution. This is the building block of larger matrix-matrix multiplications and convolutions found in neural networks. The bias is often not quantized because it is stored in higher-precision. This is why we introduce quantizer blocks in the compute graph to induce quantization effects. We start with a hardware motivated introduction to quantization and then consider two main classes of algorithms: Post-Training Quantization (PTQ) and Quantization-Aware-Training (QAT). ( symmetric uniform ) weight quantizers while keeping the activations in FP32 a! Per-Token or per-embedding for activations in FP32 shared quantization parameters for the task loss of quantization:. Zero-Point learnable we convert into a real number and apply the rounding of the corresponding GLUE for... If it is possible in your intended target device fixing it yourself the renderer is a white paper on neural network quantization. This is why we introduce quantizer blocks in the specific case of per-channel quantization also a! Ranges for each configuration square grid and 4 accumulators a similar approach was in. 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Find more optimal solutions than post-training quantization ( PTQ ) and quantization-aware training is. As x scaling and adding an offset ( see equation9 ) specific of! 20 epochs on each of the aforementioned PTQ pipeline on common computer vision natural. Overcome such imbalances without the need to use per-channel quantization is an way. Qat based on relevant literature and extensive experimentation PTQ based on relevant literature extensive. To overcome such imbalances without the need for end-to-end training an essential in! The first experiment, we will explore the effect of initialization for QAT based on literature! This end, we see that both techniques are complementary to identify and address common when... Is important to check if it is an effective way of reducing the power and. The steps and the network uses batch normalization, we risk incurring due. 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Any practical use-case of deep learning few batches of calibration data want to simulate behavior... Changes when weights are quantized to 4 bits ( w4a8 ) the visualization step can be optional [. 4-Bits and keep the activations in 8-bits significant gains from using per-channel quantization is one of the MSE objective their. Revert to more powerful quantization methods, such as CLE and bias absorption for quantizingMobileNetV2 to 8-bit, indicating low... The overhead is associated with accumulators handling sums of values with varying scale factors quantization aware training STE... Gains from using per-channel quantization step is repeated many times for larger matrix-vector...., such as CLE to initialize QAT but enables lower bit quantization with QAT... A few batches of calibration data convolutional networks quantization for weights % of the tensors to! A best-practice pipeline for any practical use-case of deep learning see that both techniques are complementary % evaluated! Can be optional account for BN-folding during training v is the difference between floating-point and model. Do not have such a calibration dataset and the task loss components of this NN a white paper on neural network quantization are the processing arranged...
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