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This would prevent the requantization step but may require fine-tuning. Variational network quantization. In the first experiment, we quantize the weights to 4-bits and keep the activations in 8-bits. EfficientDet-D1 remains more difficult to quantize than the other networks in this group. Whereas per-channel quantization of weights is increasingly becoming common practice, not all commercial hardware supports it. However, there is a trade-off: with quantization, we can lose significant accuracy. In this section, we introduce the basic principles of neural network quantization and of fixed-point accelerators on which quantized networks run on. 4 bits) in the PTQ. The quantizer block implements the quantization function of equation (7) and each quantizer is defined by a set of quantization parameters (scale factor, zero-point, bit-width). Influence of the initial activation range setting on the QAT training behavior of ResNet18. Agreement NNX16AC86A, Is ADS down? where V denotes the tensor to be quantized. In neural network quantization, the weights and activation tensors are stored in lower bit precision than the 16 or 32-bit precision they are usually trained in. In table 9 we compare the effect of other PTQ improvements such as CLE and bias correction. In earlier QAT work the quantization ranges for weights and activations were updated at each iteration most commonly using the min-max range (Krishnamoorthi, 2018). This could be due to the regularizing effect of training with quantization noise or due to the additional fine-tuning during QAT. 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%. 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. AdaRound provides a theoretically sound, computationally fast weight rounding method. (PDF) A White Paper on Neural Network Quantization (2021) | Markus Several papers (Nagel et al., 2019; Meller et al., 2019; Finkelstein et al., 2019) noted this issue and introduce methods to correct for the expected shift in distribution. The static folding re-parametrization is also valid for per-channel quantization. Reducing the power and latency of neural network . In conclusion, a better initialization can lead to better QAT results, but the gain is usually small and vanishes the longer the training lasts. (2020) showed that rounding-to-nearest is not optimal in terms of the task loss when quantizing weights in the post-training regime. b) Simulation of quantized inference for general-purpose floating-point hardware. If not, we may have to resort to other methods, such as quantization-aware training (QAT), which is discussed in section 4. Table 5 from A White Paper on Neural Network Quantization | Semantic A. Garcia, S. Tiedemann, T. Kemp, and A. Nakamura (2020), Mixed precision dnns: all you need is a good parametrization, International Conference on Learning Representations, M. van Baalen, C. Louizos, M. Nagel, R. A. Amjad, Y. Wang, T. Blankevoort, and M. Welling (2020), Bayesian bits: unifying quantization and pruning, Advances in Neural Information Processing Systems, H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (Eds. In this section, we first explain the fundamentals of this simulation process and then discuss techniques that help to reduce the difference between the simulated and the actual on-device performance. Quantization-aware training models the quantization noise during training through simulated quantization operations. (2019) uses =6 so that only large outliers are clipped. In this section we define the quantization scheme that we will use in this paper. Notice, Smithsonian Terms of Applying CLE brings us back within 2% of FP32 performance, close to the performance of per-channel quantization. Range setting for activation quantizers often requires some calibration data. If batch normalization is applied right after a linear layer y=BatchNorm(Wx), we can rewrite the terms such that the batch normalization operation is fused with the linear layer itself. 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. 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. This can have a big impact on the accuracy of quantized model. In these cases, we resort to quantization-aware training (QAT). The next debugging step is to identify how activation or weight quantization impact the performance independently. Unfortunately, in some cases, the difference in magnitude between them is so large that even for moderate quantization (e.g., INT8), we cannot find a suitable trade-off. While it is clear that starting from an FP32 model is beneficial, the effect of the quantization initialization on the final QAT result is less studied. Higher is better in all cases. Learning the quantization parameters directly, rather than updating them at every epoch, leads to higher performance especially when dealing with low-bit quantization. Before diving into the technical details, we first explore the hardware background of quantization and how it enables efficient inference on device. Despite their abun-dance, current quantization approaches are lacking in two respects when it comes to trading off latency with accuracy. Increasing the granularity of the groups generally improves accuracy at the cost of some extra overhead. Ablation study with various PTQ initialization. W(2)=W(2)S, . 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. Per (output) channel weight ranges of the first depthwise-separable layer inMobileNetV2 after BN folding. White Paper: Convolutional Neural Network with INT4 Optimization on Xilinx Devices A full-process hardware-friendly quantization solution for 4A4W that can achieve comparable accuracy compared to full-precision models. ), A. Wang, A. Singh, J. Michael, F. Hill, O. blog/paper-of-quantization.md at master hustzxd/blog GitHub In this section, we present a best-practice pipeline for QAT based on relevant literature and extensive experimentation. Higher is better in all cases. Incremental network quantization: Towards cnns with low-precision weights. 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. This process is. To move from floating-point to the efficient fixed-point operations, we need a scheme for converting floating-point vectors to integers. where ^x is the layers input with all preceding layers quantized and \mathnormalfa is the activation function. Most existing fixed-point accelerators do not currently support such logic and for this reason, we will not consider them in this work. As a result, the choice of signed or unsigned integer grid matters: Unsigned symmetric quantization is well suited for one-tailed distributions, such as ReLU activations (see figure 3). ai study 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. b(1)=S1b(1). We also propose a debugging workflow to identify and address common issues when quantizing a new model. Previously, we saw how matrix-vector multiplication is calculated in dedicated fixed-point hardware. We use the MSE based criteria for most of the layers, which requires a small calibration set to find the minimum MSE loss. 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 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. Assuming input values are normally distributied, the effect of ReLU on the distribution can be modeled using the clipped normal distribution. Several papers (Krishnamoorthi, 2018; Nagel et al., 2019; Sheng et al., 2018) noted that efficient models with depth-wise separable convolutions, such asMobileNetV1(Howard et al., 2017) andMobileNetV2(Sandler et al., 2018), show a significant drop for PTQ or even result in random performance. 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. In addition, we introduce a debugging workflow to effectively identify and fix problems that might occur when quantizing new networks. Besides reducing the computational overhead of the additional scaling and offset, this prevents extra data movement and the quantization of the layers output. PTQ requires no re-training or labelled data and is thus a lightweight push-button approach to quantization. There are many other types of layers being used in neural networks. QAT requires fine-tuning and access to labeled training data but enables lower bit quantization with competitive results. Figure 10 shows a simple computational graph for the forward and backward pass used in quantization-aware training. During quantization-aware training, we want to simulate inference behavior closely, which is why we have to account for BN-folding during training. However, per-channel quantization provides additional flexibility as it allows us to absorb the batch normalization scaling operation into the per-channel scale-factor. If the problem is fixed and the accuracy recovers, we continue to the next quantizer. MAC operations and data transfer consume the bulk of the energy spent during neural network inference. The observations from weight range initialization hold here as well. In all cases, we observe that 8-bit quantization of weights and activation (W8A8) leads to only marginal loss of accuracy compared to floating-point (within 0.7%) for all models. . The trivial solution c=0 holds for all x. 2018; A white-paper: . Whereas 8-bit quantization incurs close to no accuracy drop, quantizing weights to 4 bits leads to a larger drop, e.g. Apply bias correction or AdaRound if calibration data is available. Correlation between the cost in equation(, Impact of various approximations and assumptions made in section. Astrophysical Observatory. However, determining parameters for activation quantization often requires a few batches of calibration data. 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. This corresponds to re-parametrization of the weights and effectively removes the batch normalization operation from the network entirely. ImageNet validation accuracy (%) averaged over 3 runs. 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. (2020) is, where is annealed during the course of optimization to initially allow free movement of \mathnormalh(Vi,j) and later to force them to converge to 0 or 1. For ResNet18/50 and InceptionV3 the accuracy drop is still within 1% of floating-point for both per-tensor and per-channel quantization. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. We describe a series of recent advances in PTQ and introduce a PTQ pipeline that leads to near floating-point accuracy results for a wide range of models and machine learning tasks. Neural networks are commonly trained using FP32 weights and activations. Together, they achieve near FP32 performance without using any data. Post-training quantization techniques take a pre-trained FP32 networks and convert it into a fixed-point network without the need for the original training pipeline. This can lead to significant overhead in both latency and power, as it is equivalent to adding an extra channel. For the task of semantic segmentation, we evaluate DeepLabV3 (with a MobileNetV2 backbone) (Chen et al., 2017) on Pascal VOC and for object detection, EfficientDet (Tan et al., 2020) on COCO 2017. In this white This provides flexibility and reduces the quantization error (more in section 2.2). This alleviates the need for performance evaluation for each new rounding choice during the optimization. Together, CLE and bias absorption followed by per-tensor quantization yield better results than per-channel quantization. Quantization is the process to convert a floating point model to a quantized model. quantization noise on the network's performance while maintaining low-bit 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 the global solutions have not restored accuracy to acceptable levels, we consider each quantizer individually. Per-channel quantization of activations is much harder to implement because we cannot factor the scale factor out of the summation and would, therefore, require rescaling the accumulator for each input channel. In this section, we start by discussing various common methods used in practice to find good quantization parameters. Depending on the model, some steps might not be required, or other choices could lead to equal or better performance. However, using learnable quantizers requires special care when setting up the optimizer for the task. Average ImageNet validation accuracy (%) over 3 runs. We aim to approximate fixed-point operations using floating-point hardware. 2. The two fundamental components of this NN accelerator are the processing elements Cn,m and the accumulators An. - "A White Paper on Neural Network Quantization" Table 5: Impact of various approximations and assumptions made in section 3.4 on the ImageNet validation accuracy (%) for ResNet18 averaged over 5 runs. However, in practice, we often have a non-linearity directly following the linear operation. Blue boxes represent required steps and the turquoise boxes recommended choices. However, this approach is sensitive to outliers as strong outliers may cause excessive rounding errors. As we saw in table 9, this step is necessary for models that suffer from imbalanced weight distributions, such as MobileNet architectures. In section 2.3.2, we discuss in more detail when it is appropriate to position the quantizer after the non-linearity. In this section, we will explore the effect of initialization for QAT. W(1)=S1W(1) and Before training we have to initialize all quantization parameters. 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. 2018; A white-paper: Quantizing deep convolutional networks for efficient inference. Note that in some QAT literature, the BN-folding effect is ignored. Starting from a real-valued vector x we first map it to the unsigned integer grid {0,,2b1}: where is the round-to-nearest operator and clamping is defined as: To approximate the real-valued input x we perfrom a de-quantization step: Combining the two steps above we can provide a general definition for the quantization function, q(), as: Through the de-quantization step, we can also define the quantization grid limits (qmin,qmax) where qmin=sz and qmax=s(2b1z). Neural network weights are usually quantized by projecting each FP32 value to the nearest quantization grid point, as indicated by in equation (4) for a uniform quantization grid. Our toy example in figure 1 has 16 processing elements arranged in a square grid and 4 accumulators. If these ranges do not match, extra care is needed to make addition work as intended. In figure3(a), we generalize this process for a convolutional layer, but we also include an activation function to make it more realistic. To this end, we consider two main classes of quantization algorithms: Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). 2018 google; ACIQ: analytical clipping for integer quantization of neural networks. The overhead is associated with accumulators handling sums of values with varying scale factors. This is known as per-channel quantization and its implications are discussed in more detailed in section 2.4.2. After completing the above steps, the last step is to quantize the complete model to the desired bit-width. We evaluate all models on the respective validation sets. A White Paper on Neural Network Quantization. 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. Neural Network Quantization Research Review | by Prabhu - Medium As with element-wise addition, it is possible to optimize your network to have shared quantization parameters for the branches being concatenated. Therefore, they propose a procedure to, if possible, absorb high biases into the next layer. 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? Additionally, having almost no hyperparameter tuning makes them usable via a single API call as a black-box method to quantize a pretrained neural network in a computationally efficient manner. This will address the issue of uneven per-channel weight distribution. weight networks (TWN [22]), Binary Neural Networks (BNN [14]), XNOR-net [27], and more [8 ,21 26 33 34 35], is the focus of our investigation. This step can show the relative contribution of activations and weight quantization to the overall performance drop and point us towards the appropriate solution. Or, have a go at fixing it yourself the renderer is open source! Some common solutions involve custom range setting for this quantizer or allowing a higher bit-width for problematic quantizer, e.g., BERT-base from table6. The cross-layer equalization (CLE) procedure (Nagel et al., 2019) achieves this by equalizing dynamic ranges across consecutive layers. PDF A White Paper on Neural Network Quantization - ResearchGate Similar toKrishnamoorthi (2018), we observe that model performance is close to random when quantizingMobileNetV2 to INT8. the scale-factor: Originally, we restricted the zero-point to be an integer. For certain layers, all values in the tensor being quantized may not be equally important. However, at lower bit-widths the MSE approach clearly outperforms the min-max. Alternatively, we can use the BN based range setting to have a fully data-free pipeline. 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 see similar effects for EfficientDet-D1 and DeeplabV3 which both uses depth-wise separable convolutions in their backbone. W4A8 stays within 1% of the original GLUE score, indicating that low bit weight quantization is not a problem for transformer models. In figure 11 we show the full training curve of this experiment. A White Paper on Neural Network Quantization - Semantic Scholar In our example, we use INT8 arithmetic, but this could be any quantization format for the sake of this discussion. However, as research in this area grows, more hardware support for these methods can be expected in the future. Error is the difference between floating-point and quantized model accuracy.
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