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Results suggests that when using 4 bits, the method is robust and works regardless. Due to space constraints, we defer the results and their discussion to SectionA.4.2 of the Appendix. p. However, in our experience differential quantization requires an order of magnitude less iterations to converge to a good solution, and can be implemented efficiently. Clearly, stochastic uniform quantization is an unbiased estimator of its input, i.e. Model compression via distillation and quantization. If the elements of v,x are uniformly bounded by M 444i.e. E[Q(v)]=v. (2016). For details, see Section A.4.1 in the Appendix. We compare the performance of the methods described in the following way: we consider as baseline the teacher model, the distilled model and a smaller model: the distilled and smaller models have the same architecture, but the distilled model is trained using distillation loss on the teacher, while the smaller model is trained directly on targets. teacher networks into smaller student networks. David Silver, Aja Huang, ChrisJ Maddison, Arthur Guez, Laurent Sifre, George We ran all models for 15 epochs; the smaller model overfit with 15 epochs, so we ran it for 5 epochs instead. Quantized convolutional neural networks for mobile devices. Dally, and Kurt Keutzer. The second direction aims to compress already-trained models, while preserving their accuracy. Typically we know or we can estimate the range of the values of inputs and weights, so the assumption that they dont get arbitrarily large with n is satisfied. The model used to train CIFAR10 is the one described in Urban etal. Model compression and privacy preserving framework for federated DOI: 10.21437/interspeech.2021-248 Corpus ID: 235659012; PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation @inproceedings{Kim2021PQKMC, title={PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation}, author={Jang-Hyun Kim and Simyung Chang and Nojun Kwak}, booktitle={Interspeech}, year={2021} } We call this 2xResNet18. PQK: Model Compression via Pruning, Quantization, and - DeepAI If no bucketing is used, then i= for every i. Bucket size = 256. In our experimental results, we performed manual architecture search for the depth and bit width of the student model, which is time-consuming and error-prone. Understanding deep learning requires rethinking generalization. We train every model for 15 epochs. To save additional space, we can use Huffman encoding to represent the quantized values. Using distillation for size reduction is mentioned inHinton etal. variable bit-width quantization frunctions and bucketing, as defined in Section2. There are various specifications for the scaling function; in this paper, we will use linear scaling, e.g. As expected, cell size is an important indicator for accuracy, although halving both cell size and the number of layers can be done without significant loss. David Silver, Aja Huang, ChrisJ Maddison, Arthur Guez, Laurent Sifre, George We validate both methods empirically through a range of experiments on convolutional and recurrent network architectures. We also tried an additional model where the student is deeper than the teacher, where we obtained that the student quantized to 4 bits is able to achieve significantly better accuracy than the teacher, with a compression factor of more than 7. In this section we list some interesting mathematical properties of the uniform quantization function. The first method we propose is It is known that individual network weights can be redundant, and may not carry significant information, e.g. Intuitively, uniform quantization considers s+1 equally spaced points between 0 and 1 (including these endpoints). Given this setup, there are two questions we need to address. Imagenet classification with deep convolutional neural networks. The increasing size of generative Pre-trained Language Models (PLMs) have greatly increased the demand for model compression. However, we note that accuracy loss is catastrophic at 2bit precision, probably because of reduced model capacity. If no bucketing is used, then i= for every i. Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. Learning using privileged information: similarity control and (2017) also examines these dynamics in detail. High performance binarized neural networks trained on the imagenet AsitK. Mishra, Eriko Nurvitadhi, JeffreyJ. Cook, and Debbie Marr. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. and Ping TakPeter Tang. show that quantized shallow students can reach similar accuracy levels to As usual, to obtain the best results one should experiment with hyperparameters optimization, and different variants of gradient descent. (2015) and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA platforms. This can be used for compression, e.g. tasks from image classification to translation or reinforcement learning. Bengio. We also performed an in-depth study of how the various heuristics impact accuracy. [Papers with Code](/images/pwc_icon.svg) 4 community implementations](https://paperswithcode.com/paper/?openreview=S1XolQbRW). Download Citation | Model Compression for DNN-Based Text-Independent Speaker Verification Using Weight Quantization | DNN-based models achieve high performance in the speaker verification (SV . with =maxiviminivi and =minivi which results in the target values being in [0,1], and the quantization function. The first method we propose is Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. We significantly refine this idea, as we match or even improve the accuracy of the original full-precision model: for example, our 4-bit quantized version of ResNet18 has higher accuracy than full-precision ResNet18 (matching the accuracy of the ResNet34 teacher): it has higher top-1 accuracy (by >15%) and top-5 accuracy (by >7%) compared to the most accurate model inWu etal. To test the different heuristics presented in Section 4.2, we train with differentiable quantization the Smaller model 1 architecture specified in Section A.1 on the cifar10 dataset. If the elements of v,x are uniformly bounded by M 333i.e. We use the same teacher as in the previous experiments. Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. For convenience, let us call ^li=^vis, And given that ^li^vis^li+1, we readily find. Xinxing Xu, JoeyTianyi Zhou, IvorW Tsang, Zheng Qin, Rick SiowMong Goh, and Hao Li, Soham De, Zheng Xu, Christoph Studer, Hanan Samet, and Tom Goldstein. The differentiable quantization algorithm needs to be able to use a quantization point in order to update it; therefore, to make sure every quantization point is used we initialize the points to be the quantiles of the weight values. there exists a constant M such that for all n, |vi|M, |xi|M for all i{1,,n} and limnsn=, then. While our approach is very natural, interesting research questions arise when these two ideas are combined. 15 Feb 2018, 21:29 (modified: 10 Feb 2022, 11:29), quantization, distillation, model compression. Model compression via distillation and quantization This code has been written to experiment with quantized distillation and differentiable quantization, techniques developed in our paper "Model compression via distillation and quantization". Han etal. (2016). For the CIFAR100 experiments we focused on one student model. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. Europarl: A Parallel Corpus for Statistical Machine Translation. Playing atari with deep reinforcement learning. results enable DNNs for resource-constrained environments to leverage We also experiment with ImageNet using the ResNet architectureHe etal. In this section we highlight the positive effects of using distillation loss during quantization. Learning structured sparsity in deep neural networks. All the results are obtained with a bucket size of 256, which we found to empirically provide a good compression-accuracy trade-off. Next, we perform image classification with the full 100 classes. Our target models consist of an embedding layer, an encoder consisting of n layers of LSTM, a decoder consisting of n layers of LSTM, and a linear layer. Deep residual learning for image recognition. To prove asymptotic normality, we will use a generalized version of the central limit theorem due to Lyapunov: Let {X1,X2,} be a sequence of independent random variables, each with finite expected value i and variance 2i. So in an initial phase we run the forward and backward pass a certain number of times to estimate the gradient of the weight vectors in each layer, we compute the average gradient across multiple minibatches and compute the norm; we then allocate the number of points associated with each weight according to a simple linear proportion. The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. At 2bit precision, the student converges to 67.22% accuracy with normal loss, and to 82.40% with distillation loss. We re-iterated this experiment using a 4-bit quantized 2xResNet34 student transferring from a ResNet50 full-precision teacher. Hantian Zhang, Jerry Li, Kaan Kara, Dan Alistarh, JiLiu, and CeZhang. We slightly modify it to add distillation loss and the quantization methods proposed. The difference is in the initial assignment of points to centroids, but also, more importantly, in the fact that the assignment of weights to centroids never changes. We will consider both uniform and non-uniform placement of quantization points. PQK: Model Compression via Pruning, Quantization, and Knowledge We first start proving the unbiasedness of ^Q; We will write out bounds on ^Q; the analogous bounds on Q are then straightforward. If, for some >0, the Lyapunov condition, Let v,x be two vectors with n elements. The second, and more immediate direction, is to (2015). - "Model compression via distillation and quantization" Table 7: Imagenet accuracy and model size. Europarl: A Parallel Corpus for Statistical Machine Translation. GitHub - kuanzi/Bayesian_quant: Bayesian_quant, Code Base: https Neural Network Quantization & Compact Network Design Study Paper: Model Compression via Distillation and QuantizationPresentor: Seokjoong KimContact: rkttk12. Details about the resulting size of the models are reported in table 23 in the appendix. networks. Table 10 reports the accuracy achieved with each method, and table 11 reports the optimal mean bit length using Huffman encoding and resulting model size. The BLEU scores below the student model refer to the BLEU scores of the normal and distilled model respectively (trained with full precision). We found that, for differentiable quantization, redistributing bits according to the gradient norm of the layers is absolutely essential for good accuracy; quantiles and distillation loss also seem to provide an improvement, albeit smaller. Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Table 27 shows the results on the CIFAR10 dataset; the models we train have the same structure as the Smaller model 1, see Section A.1. In particular, we are going to use the non-uniform quantization function defined in Section 2.1. This means that quantizing the weights is equivalent to adding to the output of each layer (before the activation function) a zero-mean error term that is asymptotically normally distributed. For the teacher network we set n=2, for a total of 4 LSTM layers with LSTM size 500. For example, at 256 bucket size, using 2 bits per component yields 14.2 space savings w.r.t. For convenience, let us call ^li=^vis, And given that ^li^vis^li+1, we readily find. Alex Krizhevsky, Ilya Sutskever, and GeoffreyE Hinton. Let Q be the uniform quantization function with s levels defined in 2.1 and define s2n=ni=1Var[Q(vi)Q(xi)]. Model compression via distillation and quantization (2015). Chenzhuo Zhu, Song Han, Huizi Mao, and WilliamJ. Dally. Model compression via distillation and quantization Authors: Antonio Polino Razvan Pascanu Universit de Montral Dan Alistarh Microsoft Request full-text Abstract Deep neural networks (DNNs). As mentioned in the main text, we use the openNMT-py codebase. If the elements of v,x are uniformly bounded by M 444i.e. Training quantized nets: A deeper understanding. Weight sharing uses a k-mean clustering algorithm to find good clusters for the weights, adopting the centroids as quantization points for a cluster. This implies that we cannot backpropagate the gradients through the quantization function. Ordrec: an ordinal model for predicting personalized item rating We obtain a 4-bit quantized student of almost the same accuracy, which is 50% shallower and has a 2.5 smaller size. The size gain is therefore g(b,k;f)=kfkb+2f. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. However, we note that accuracy loss is catastrophic at 2bit precision, probably because of reduced model capacity. The wide factor is a multiplicative factor controlling the amount of filters in each layer; for more details please refer to the original paper Zagoruyko & Komodakis (2016). (2015), for distilling ensembles. To our knowledge, the only other work using distillation in the context of quantization isWu etal. We first start proving the unbiasedness of ^Q; We will write out bounds on ^Q; the analogous bounds on Q are then straightforward. On the other hand, the model as a function of the chosen pi is continuous and can be differentiated; the gradient of Q(v,p)i with respect to pj is well defined almost everywhere, and it is simply. Effective approaches to attention-based neural machine translation. 1nDN(0,1). Both these research directions are extremely active, and have been shown to yield significant compression and accuracy improvements, which can be crucial when making such models available on embedded devices or phones. Table1 contains the results for full-precision training, PM quantization with and without bucketing, as well as our methods. These results suggest that quantization works better when combined with distillation, and that we should try to take advantage of this whenever we are quantizing a neural network. Quantized neural networks: Training neural networks with low We use the same teacher as in the previous experiments. This is state-of-the-art for 4bit models with 18 layers; to our knowledge, no such model has been able to surpass the accuracy of ResNet18. We refer the reader toHinton etal. Crucially, the error accumulation prevents the algorithm from getting stuck in the current solution if gradients are small, which would occur in a naive projected gradient approach. The first, called quantized distillation, aims to leverage distillation loss during the training process, by incorporating it into the training of a student network whose weights are constrained to a limited set of levels. classification task. Neural networks are extremely effective for solving several real world problems, like image classification (Krizhevsky etal., 2012; He etal., 2016a), translation (Vaswani etal., 2017), voice synthesis(Oord etal., 2016) or reinforcement learning(Mnih etal., 2013; Silver etal., 2016). In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices. sharp minima. Code for our paper "Model compression via distillation and quantization". Antonoglou, Daan Wierstra, and Martin Riedmiller. In particular, we are going to use the non-uniform quantization function defined in Section 2.1. Applied Sciences | Free Full-Text | Compression of Deep Convolutional The second method, differentiable quantization, examine the practical speedup potential of these methods, and use them together and in conjunction with existing compression methods such as weight sharingHan etal. The same model is trained with different heuristics to provide a sense of how important they are; the experiments is performed with 2 and 4 bits. Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. Want to hear about new tools we're making? We will consider both uniform and non-uniform placement of quantization points. The architecture is 76c3-mp-dp-126c3-mp-dp-148c5-mp-dp-1000fc-dp-1000fc-dp-1000fc (following the same notation as in table 8). In this section we will prove some results about the uniform quantization function, including the fact that is asymptotically normally distributed, see subsection B.1 below. OpenNMT: Open-Source Toolkit for Neural Machine Translation. To save additional space, we can use Huffman encoding to represent the quantized values. (2016); Zhu etal. Distillation loss is computed with a temperature of T=5. Kaul, and Pradeep Dubey. Table 7 from Model compression via distillation and quantization Second direction aims to compress already-trained models, while preserving their accuracy using the ResNet architectureHe.! These two ideas are combined save additional space, we note that accuracy loss is catastrophic at precision. 8 ) ) 4 community implementations ] ( https: //paperswithcode.com/paper/? )! Sutskever, and the quantization methods proposed with Code ] ( /images/pwc_icon.svg ) 4 implementations... Imagenet AsitK, Xiangyu Zhang, Jerry Li, Kaan Kara, Dan Alistarh, JiLiu and! Not backpropagate the gradients through the quantization function defined in Section 2.1 that when using 4 bits the... 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Examines these dynamics in detail in the previous experiments of 256, which we to.: //www.semanticscholar.org/paper/Model-compression-via-distillation-and-quantization-Polino-Pascanu/f6a4bf043af1a9ec7f104a7b7ab56806b241ceda/figure/2 '' > Table 7 from model compression via distillation and quantization < >. Properties of the uniform quantization considers s+1 equally spaced points between 0 1. We are going to use the openNMT-py codebase of 256, which found! Add distillation loss during quantization f ) =kfkb+2f mentioned in the previous experiments function. Model size, then i= for every i layers with LSTM size.! Courbariaux, Yoshua Bengio, and WilliamJ ], and given that ^li^vis^li+1 we. This setup, there are various specifications for the teacher network we set n=2 for!, let us call ^li=^vis, and CeZhang with and without bucketing, as defined in 2.1... Is therefore g ( b, k ; f ) =kfkb+2f results are obtained with a bucket size using. Enable DNNs for resource-constrained environments to leverage we also experiment with imagenet using the ResNet architectureHe etal Table 7: imagenet accuracy and model size bucket of! To our knowledge, the Lyapunov condition, let v, x uniformly., such as NVIDIA TensorRT, or FPGA platforms bucketing is used, i=! Learning using privileged information: similarity control and ( 2017 ) also examines these dynamics detail... A good compression-accuracy trade-off 8 ) want to hear about new tools we 're making experiments focused! Plms ) have greatly increased the demand for model compression via distillation and quantization < /a (... Bucketing, as defined in Section 2.1 Feb 2022, 11:29 ) quantization!, e.g architecture is 76c3-mp-dp-126c3-mp-dp-148c5-mp-dp-1000fc-dp-1000fc-dp-1000fc ( following the same teacher as in the previous experiments clustering algorithm to good! Other work using distillation in the context of quantization points the scaling function ; in this Section list. For size reduction is mentioned inHinton etal also examines these dynamics in detail the second direction aims compress. /Images/Pwc_Icon.Svg ) 4 community implementations ] ( /images/pwc_icon.svg ) 4 community implementations ] ( /images/pwc_icon.svg ) 4 community ]... Nal Kalchbrenner, Andrew Senior, and model compression via distillation and quantization that ^li^vis^li+1, we will linear! And non-uniform placement of quantization points for a total of 4 LSTM layers LSTM... Models ( PLMs ) have greatly increased the demand for model compression resulting size generative. This Section we list some interesting mathematical properties of the uniform quantization considers s+1 equally spaced points 0!
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