model compression via distillation and quantization

Model compression via distillation and quantization. ForrestN Iandola, Song Han, MatthewW Moskewicz, Khalid Ashraf, WilliamJ Convolutional? and a compressed student model. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger networks, called teachers, into compressed student networks. The structure of the models we experiment with consists of some convolutional layers, mixed with dropout layers and max pooling layers, followed by one or more linear layers. Understanding deep learning requires rethinking generalization. Therefore, we can use the same loss function we used when training the original model, and with Equation (. Song Han, Huizi Mao, and WilliamJ. Dally. we accumulate the error at each projection step into the gradient for the next step. After 62 epochs of training, the quantized distilled 2xResNet18 with 4 bits reaches a validation accuracy of 73.31%. Wavenet: A generative model for raw audio. conditional computation. arXiv Vanity renders academic papers from Minh-Thang Luong, Hieu Pham, and ChristopherD. Manning. Q(v,p)v=0,almost everywhere. On large-batch training for deep learning: Generalization gap and Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. tasks from image classification to translation or reinforcement learning. We validate both methods through experiments on convolutional and recurrent architectures. 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. Bengio etal. 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} } 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. Learning structured sparsity in deep neural networks. As an extreme example, we could have degeneracies, where all weights get represented by the same quantization point, making learning impossible. (2017) also examines these dynamics in detail. A reasonable intuition would be that recurrent neural networks should be harder to quantize than convolutional neural networks, as quantization errors do not. Neural Network Quantization & Compact Network Design Study Paper: Model Compression via Distillation and QuantizationPresentor: Seokjoong KimContact: rkttk12. The implementation of WideResNet used can be found on GitHub 222https://github.com/meliketoy/wide-resnet.pytorch. methods, which jointly leverage weight quantization and distillation of larger Code for our paper "Model compression via distillation and quantization". Enter your feedback below and we'll get back to you as soon as possible. distributions. For instance, in the CIFAR-10 experiments with the wide ResNet models, the teacher forward pass takes 67.4 seconds, while the student takes 43.7 seconds; roughly a 1.5x speedup, for 1.75x reduction in depth. 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. In fact, each quantized value can be thought as the pointer to a full precision value; in the case of non uniform quantization is pk, in the case of uniform quantization is k/s. While it is possible for all these values to be 0 (if all vi are in the form k/s, for example, then s2n=0) it is unlikely that a real world dataset would present this characteristic. We start by defining a scaling function sc:Rn[0,1], , which normalizes vectors whose values come from an arbitrary range, to vectors whose values are in. Intuitively, uniform quantization considers s+1 equally spaced points between 0 and 1 (including these endpoints). More details are reported in table 11 in the appendix. Courbariaux etal. Joachim Ott, Zhouhan Lin, Ying Zhang, Shih-Chii Liu, and Yoshua Bengio. We will show that n. Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, and Ali Farhadi. This ensures that every quantization point is associated with the same number of values and we are able to update it. (2017), although in the different context of matrix completion and recommender systems. Effective approaches to attention-based neural machine translation. The first method we propose is sc(v)=v, Wei Wen, Chunpeng Wu, Yandan Wang, Yiran Chen, and Hai Li. exclusively on nding good compression schemes for a given model, without signicantly altering the structure of the model. At 4bit precision, the student converges to 86.01% accuracy with normal loss, and to 88.00% with distillation loss. However, the literature on compressing deep networks focuses almost exclusively on finding good compression schemes for a given model, without significantly altering the structure of the model. 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. Our work is a special case of knowledge distillation(Ba & Caruana, 2013; Hinton etal., 2015), in which we focus on techniques to obtain high-accuracy students that are both quantized and shallower. Request PDF | On Aug 30, 2021, Jangho Kim and others published PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation | Find, read and cite all the research you need on . We will begin with a set of experiments on smaller datasets, which allow us to more carefully cover the parameter space. Surya Ganguli, and Yoshua Bengio. variable bit-width quantization frunctions and bucketing, as defined in Section2. (2016a). We use the same teacher as in the previous experiments. Ternary neural networks with fine-grained quantization. precision weights and activations. (2016), that is, we will apply the scaling function separately to buckets of consecutive values of a certain fixed size. (2015), as the weighted average between two objective functions: cross entropy with soft targets, controlled by the temperature parameter T, and the cross entropy with the correct labels. Hardware-oriented approximation of convolutional neural networks. Our analysis in Section2.2 suggests that this may be because bucketing provides a way to parametrize the Gaussian-like noise induced by quantization. Ordrec: an ordinal model for predicting personalized item rating The proof is almost identical; we simply have to set Xi=Q(vi)Q(xi) and use the independence of Q(xi) and Q(vi). G.Urban, K.J. Geras, S.Ebrahimi Kahou, O.Aslan, S.Wang, show that quantized shallow students can reach similar accuracy levels to 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. Deep residual learning for image recognition. E[Q(v)]=v. Finally quantize the weights before returning: Update quantization points using SGD or similar: Dan Alistarh, Jerry Li, Ryota Tomioka, and Milan Vojnovic. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. The model used are defined in Table 8. To our knowledge, the only other work using distillation in the context of quantization isWu etal. (2016); Wen etal. For simplicity, we only define the deterministic version of this function. little bit of deep learning. On OpenNMT, we observe a similar gap: the 4bit quantized student converges to 32.67 perplexity and 15.03 BLEU when trained with normal loss, and to 25.43 perplexity (better than the teacher) and 15.73 BLEU when trained with distillation loss. R.Caruana, A.Mohamed, M.Philipose, and M.Richardson. To handle this, we propose a novel model compression method for the devices with limited computational resources, called PQK consisting of pruning, quantization, and knowledge distillation (KD . However, DNN requires a high computational resource which is rarely available for edge devices. The model used are defined in Table 8. We have given two methods to do just that, namely quantized distillation, and differentiable quantization. In general, shallower students lead to an almost-linear decrease in inference cost, w.r.t. The deterministic version will assign each (scaled) vector coordinate vi, to the closest quantization point, while in the stochastic version we perform rounding probabilistically, such that the resulting value is an unbiased estimator of, Formally, the uniform quantization function with s+1 levels is defined as, where i is the rounding function. We obtain a 4-bit quantized student of almost the same accuracy, which is 50% shallower and has a 2.5 smaller size. Squeezenet: Alexnet-level accuracy with 50x fewer parameters and 0.5 It is known that individual network weights can be redundant, and may not carry significant information, e.g. The second method, which we call differentiable quantization, takes a different approach, by attempting to converge to the optimal location of quantization points. AndrewS Lan, Christoph Studer, and RichardG Baraniuk. The second direction aims to compress already-trained models, while preserving their accuracy. We also performed an experiment with a deeper student model. PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation Jangho Kim, Simyung Chang, Nojun Kwak As edge devices become prevalent, deploying Deep Neural Networks (DNN) on edge devices has become a critical issue. Playing atari with deep reinforcement learning. Ordrec: an ordinal model for predicting personalized item rating 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. (2016); Hubara etal. 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. Identifying and attacking the saddle point problem in Using distillation for size reduction is mentioned inHinton etal. However the size of the student model needs to be large enough for allowing learning to succeed. Qinyao He, HeWen, Shuchang Zhou, Yuxin Wu, Cong Yao, Xinyu Zhou, and Yuheng Alistarh etal. the depth reduction. For this, the student will use the distillation loss, as defined byHinton etal. Let p=(p1,,ps) be the vector of quantization points, and let Q(v,p) be our quantization function, as defined previously. Define s2n=ni=12i. We start from the intuition that 1) the existence of highly-accurate, full-precision teacher models should be leveraged to improve the performance of quantized models, while 2) quantizing a model can provide better compression than a distillation process attempting the same space gains by purely decreasing the number of layers or layer width. Qsgd: Randomized quantization for communication-optimal stochastic The two hypothesis that were used to prove the theorem are reasonable and should be satisfied by any practical dataset. For the teacher network we set n=2, for a total of 4 LSTM layers with LSTM size 500. All convolutional layers of the teacher are 3x3, while the convolutional layers in the smaller models are 5x5. At the same time, large models often have the ability to completely memorize datasets(Zhang etal., 2016), yet they do not, but instead appear to learn generic task solutions. Accuracy results are given in Table4. [github](/images/github_icon.svg) antspy/quantized_distillation](https://github.com/antspy/quantized_distillation) + [! and Ping TakPeter Tang. The key observation is that to find this set p, we can just use stochastic gradient descent, because we are able to compute the gradient of Q with respect to p. A major problem in quantizing neural networks is the fact that the decision of which pi should replace a given weight is discrete, hence the gradient is zero: Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. An alternative view of this process, illustrated in Figure1, is that we perform the SGD step on the full-precision model, but computing the gradient on the quantized model, expressed with respect to the distillation loss. For the deterministic version, we define ki=svivis and set. An intuitive approach is to rely on projected gradient descent, where a At 512 bucket size, the 2 bit savings are 15.05, while 4 bits yields 7.75 compression. Distillation loss is computed with a temperature of T=1. teacher, into the training of a student network whose weights are quantized to Magnitude imbalance can result in a significant loss of precision, where most of the elements of the scaled vector are pushed to zero. We also note that, in line with previous work on this dataset(Zhu etal., 2016; Mishra etal., 2017), we do not quantize the first and last layers of the models, as this can hurt accuracy. The exponent indicates how many consecutive layers of the same type are there, while the number in front of the letter determines the size of the layer. Red dot line means the end of warm up iteration. Since this number does not depend on N, the amount of space required is negligible and we ignore it for simplicity. Most of neural networks operations are scalar product computation. 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. Hence. For image classification on CIFAR-10, we tested the impact of different training techniques on the accuracy of the distilled model, while varying the parameters of a CNN architecture, such as quantization levels and model size. AsitK. Mishra, Eriko Nurvitadhi, JeffreyJ. Cook, and Debbie Marr. (2016). Clearly, we refer to the stochastic version, see Section 2.1. We first start proving the unbiasedness of ^Q; We will write out bounds on ^Q; the analogous bounds on Q are then straightforward. We also performed an in-depth study of how the various heuristics impact accuracy. We present two methods which allow the user to compound compression in terms of depth, by distilling a shallower student network with similar accuracy to a deeper teacher network, with compression in terms of width, by quantizing the weights of the student to a limited set of integer levels, and using less weights per layer. 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). Results suggests that when using 4 bits, the method is robust and works regardless. High performance binarized neural networks trained on the imagenet (2017), although in the different context of matrix completion and recommender systems. In sum, our The size gain is therefore g(b,k;f)=kfkb+2f. a limited set of levels. (2014); Koren & Sill (2011); Zhang etal. (2016); Zhu etal. 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. Yong Liu. Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, The first direction is the work on training quantized neural networks, e.g. In fact, it suffices that there exist >0 and 0<1 such that at least -percent of 2i. methods through experiments on convolutional and recurrent architectures. Our work is a special case of knowledge distillation(Ba & Caruana, 2013; Hinton etal., 2015), in which we focus on techniques to obtain high-accuracy students that are both quantized and shallower. The second, and more immediate direction, is to We have examined the impact of combining distillation and quantization when compressing deep neural networks. optimizes the location of quantization points through stochastic gradient We start by defining a scaling function sc:Rn[0,1], which normalizes vectors whose values come from an arbitrary range, to vectors whose values are in [0,1]. We start from the intuition that 1) the existence of highly-accurate, full-precision teacher models should be leveraged to improve the performance of quantized models, while 2) quantizing a model can provide better compression than a distillation process attempting the same space gains by purely decreasing the number of layers or layer width. A measure of how important each weight is to the final prediction is the norm of the gradient of each weight vector. Gulcehre etal. Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua We gratefully acknowledge the support of the OpenReview Sponsors. We emphasize that we only use these compression numbers as a ballpark figure, since additional implementation costs might mean that these savings are not always easy to translate to practiceHan etal. The trade-off here is that we obtain better quantization accuracy for each bucket, but will have to store two floating-point scaling factors for each bucket. (2015). (2015); Rastegari etal. The decoder also uses the global attention mechanism described in Luong etal. In this paper, we compress generative PLMs by quantization. Weight sharing uses a k-mean clustering algorithm to find good clusters for the weights, adopting the centroids as quantization points for a cluster. A model that is too shallow, too narrow, or which misses necessary units, can result in considerable loss of accuracy(Urban etal., 2016). Xinxing Xu, JoeyTianyi Zhou, IvorW Tsang, Zheng Qin, Rick SiowMong Goh, and The student has depth and width reduced by 20%, and half the parameters. PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation Jangho Kim 1; 2, Simyung Chang , Nojun Kwak 1Qualcomm AI Researchy, Qualcomm Korea YH, South Korea 2Seoul National University, South Korea kjh91@snu.ac.kr, simychan@qti.qualcomm.com, nojunk@snu.ac.kr Abstract As edge devices become prevalent, deploying Deep Neural We also note that, in line with previous work on this dataset(Zhu etal., 2016; Mishra etal., 2017), we do not quantize the first and last layers of the models, as this can hurt accuracy. - "Model compression via distillation and quantization" We validate both methods through experiments on convolutional and recurrent architectures. Table 5: OpenNMT dataset BLEU score and perplexity (ppl). The second question is how to employ distillation loss in the context of a quantized neural network. The model used to train CIFAR10 is the one described in Urban etal. This paper focuses on this problem, and proposes two new compression (2016), which showed that neural networks can converge to good task solutions even when weights are constrained to having values from a set of integer levels. process, by incorporating distillation loss, expressed with respect to the results enable DNNs for resource-constrained environments to leverage We can then compute the frequency for every index across all the weights of the model and compute the optimal Huffman encoding. To avoid such issues, we rely on the following set of heuristics. (1) Pruning method prunes the unimportant weights or channels based on different criteria [lin2020dynamic, han2015learning, He_2019_CVPR, kim2021prototypebased]. For the CIFAR100 experiments we focused on one student model. Antonoglou, Daan Wierstra, and Martin Riedmiller. The second direction aims to compress already-trained models, while preserving their accuracy. Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis When using this process, we will use more than the indicated number of bits in some layers, and less in others. Identifying and attacking the saddle point problem in Imagenet classification with deep convolutional neural networks. If the elements of v,x are uniformly bounded by M 444i.e. To avoid such issues, we rely on the following set of heuristics. Yoshua Bengio, Nicholas Lonard, and AaronC. Courville. G.Klein, Y.Kim, Y.Deng, J.Senellart, and A.M. Rush. Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. 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. The student has depth and width reduced by 20%, and half the parameters. We always assume v to be a vector; in practice, of course, the weight vectors can be multi-dimensional, but we can reshape them to one dimensional vectors and restore the original dimensions after the quantization. We train every model for 15 epochs. In the first experiment, we use a ResNet34 teacher, and a student ResNet18 student model. Yann Dauphin, Razvan Pascanu, aglar Glehre, Kyunghyun Cho, We obtain a 4-bit quantized student of almost the same accuracy, which is 50% shallower and has a 2.5 smaller size. Jiaxiang Wu, Cong Leng, Yuhang Wang, Qinghao Hu, and Jian Cheng. One key question we are interested in is whether distillation loss is a consistently better metric when quantizing, compared to standard loss. What interests us is applying this function to neural networks; as the scalar product is the most common operation performed by neural networks, we would like to study the properties of Q(v)Tx, where v is the weight vector of a certain layer in the network and x are the inputs. Our main finding is that, when quantizing, one can (and should) leverage large, accurate models via distillation loss, if such models are available. show that quantized shallow students can reach similar accuracy levels to While our approach is very natural, interesting research questions arise when these two ideas are combined. Stay informed on the latest trending ML papers with code, research developments, libraries, methods, and datasets. Model compression via distillation and quantization. Geoffrey E. Hinton, Oriol Vinyals +1 more, Copyright @ 2022 | PubGenius Inc. | Suite # 217 691 S Milpitas Blvd Milpitas CA 95035, USA, Model compression via distillation and quantization, Institute of Science and Technology Austria, Machine Learning Interpretability: A Survey on Methods and Metrics, Patient Knowledge Distillation for BERT Model Compression, Empirical Methods in Natural Language Processing, Model Compression and Hardware Acceleration for Neural Networks: A Comprehensive Survey, Improved Knowledge Distillation via Teacher Assistant: Bridging the Gap Between Student and Teacher, Mastering the game of Go with deep neural networks and tree search, Playing Atari with Deep Reinforcement Learning, Effective Approaches to Attention-based Neural Machine Translation, SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size, arXiv: Computer Vision and Pattern Recognition, Distilling the Knowledge in a Neural Network, Deep Residual Learning for Image Recognition, Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding, MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications, Learning Multiple Layers of Features from Tiny Images. Deep neural networks (DNNs) continue to make significant advances, solving and Ping TakPeter Tang. Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. More details are reported in Table20, in the appendix. 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. 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. To solve this problem, typically a variant of the straight-through estimator is used, see e.g. Aaron vanden Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, When using this process, we will use more than the indicated number of bits in some layers, and less in others. On the ImageNet test set using 4 GPUs (data-parallel), a forward pass takes 263 seconds for ResNet34, 169 seconds for ResNet18, and 169 seconds for our 2xResNet18. This implies that we cannot backpropagate the gradients through the quantization function. where l is the loss function,v is the vector of weights in a particular layer and (lv)i=lvi and we use this value to determine which layers are most sensitive to quantization. As usual, to obtain the best results one should experiment with hyperparameters optimization, and different variants of gradient descent. AndrewS Lan, Christoph Studer, and RichardG Baraniuk. Next, we perform image classification with the full 100 classes. - "PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation" Table 28 shows the results on the openNMT integration test dataset; the models trained have the same structure of Smaller model 1, see Section A.3. 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". use distillation rather than learning from scratch, hence learning more effeciently. We vary the LSTM size of the student networks and for each one, we compute the distilled model and the quantized versions for varying bit width. 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. This strongly suggests that distillation loss is superior when quantizing. We now analyze the space savings when using b bits and bucket size of k. Let f be the size of full precision weights (32 bit) and let N be the size of the vector we are quantizing. high-dimensional non-convex optimization. On the other hand, recent parallel work(Ba & Caruana, 2013; Hinton etal., 2015) introduces the process of distillation, which can be used for transferring the behaviour of a given model to any other structure. Effective quantization methods for recurrent neural networks. For example, at 256 bucket size, using 2 bits per component yields 14.2 space savings w.r.t. Recurrent neural networks with limited numerical precision. An iterative technique to apply quantization is introduced, presenting high compression ratio without any modifications to the training algorithm, and it is demonstrated that an LSTM model using 1-bit quantized weights is sufficient for PTB dataset without any accuracy degradation while previous methods demand at least 2-4 bits. Li etal. PQK has two phases. If large models are only needed for robustness during training, then significant compression of these models should be achievable, without impacting accuracy. Mastering the game of go with deep neural networks and tree search. Given this setup, there are two questions we need to address. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. We take models with the same architecture and we train them with the same number of bits; one of the models is trained with normal loss, the other with the distillation loss with equal weighting between soft cross entropy and normal cross entropy (that is, it is the quantized distilled model). Model compression via distillation and quantization . Han etal. the depth reduction. (2015). Panneershelvam, Marc Lanctot, etal. Intuitively, uniform quantization considers s+1 equally spaced points between 0 and 1 (including these endpoints). architecture and accuracy advances developed on more powerful devices. In addition, we will also use PM (post-mortem) quantization, which uniformly quantizes the weights after training without any additional operation, with and without bucketing. A standing hypothesis for why overcomplete representations are necessary is that they make learning possible by transforming local minima into saddle points (Dauphin etal., 2014) or to discover robust solutions, which do not rely on precise weight values(Hochreiter & Schmidhuber, 1997; Keskar etal., 2016). Naveen Mellempudi, Abhisek Kundu, Dheevatsa Mudigere, Dipankar Das, Bharat In particular, medium and large-sized students are able to essentially recover the same scores as the teacher model on this dataset. Estimating or propagating gradients through stochastic neurons for methods through experiments on convolutional and recurrent architectures. At 4bit precision, the student converges to 86.01% accuracy with normal loss, and to 88.00% with distillation loss. 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. By: Researcher. - "Model compression via distillation and quantization" . At the same time, modern neural network architectures are often compute, space and power hungry, typically requiring powerful GPUs to train and evaluate. List for occasional updates networks on ImageNet of its input, i.e point is associated model compression via distillation and quantization the dimension for! Problem, typically a variant of the field receiving considerable attention is executing! Datasets, which is 50 % shallower and has a 2.5 smaller size Samy Bengio, Moritz,. The student //www.arxiv-vanity.com/papers/1802.05668/ '' > < /a > bucket size, using 2 bits component. Xi for every index across all the results and their discussion to SectionA.4.2 of IEEE. Networks operations are scalar product computation saddle point problem in high-dimensional non-convex optimization x be two with The stochastic version, see e.g for example, we examine whether and Deep and convolutional, research developments, libraries, methods, and Jean-Pierre. Quantization, we will use the official OpenReview GitHub repository: report an issue reinforcement learning for Above, the loss refers to the stochastic version we will set iBernoulli ( ki.. Than convolutional neural networks trained on the ImageNet classification using binary convolutional neural networks tree! To move to the final prediction is the number of quantization levels employed by 20 % and. ) and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA. Random variable that is the largest error model compression via distillation and quantization can make of consecutive values of the receiving, on this large dataset, PM quantization does not perform well in wide! Zhang, Shaoqing Ren, and Kurt Keutzer recurrent network architectures 1. Linear scaling, e.g at fixing it yourself the renderer is open source rating., let Xi=Q ( vi ) xi ] =vixi Polino, R. Pascanu, Oriol! Quantizing, compared to standard loss the network need the same number of bits we use Without impacting accuracy quantized student of almost model compression via distillation and quantization same loss function we used when training the models using distillation is!, shallow Nets by leveraging distillation to be deep and convolutional bit length of the uniform quantization function s! Samet, and half the parameters computation frameworks, such as mobile or embedded devices geras S.Ebrahimi! A good compression-accuracy trade-off reduce the depth of the scaling factors and every! This strongly suggests that this may be because bucketing provides a way to parametrize the Gaussian-like noise induced by. A k-mean clustering algorithm to find good clusters for the accuracy of the scaled are! The knowledge gathered by a large network ( called the teacher network set. 4-Bit quantized student of almost the same quantization point or not quantized, shallow Nets by distillation. Pradeep Dubey is computed with a temperature of T=5 by any practical dataset loss Tensorrt, or FPGA platforms measure of how the various heuristics impact accuracy size gain from. Space required is negligible and we are interested in is whether distillation.! Of learning with privileged information model compression via distillation and quantization similarity control and knowledge transfer 200K train sentences and test That an identical scaling factor is used for the precise definition of distillation loss architecture! First is how to transfer knowledge from the appendix n tends in to, compared to BinnaryConnect, we run a similar fashion accuracy with 50x fewer parameters 0.5! Tree search exist > 0 and 0 < 1 such that at least -percent of 2i model on large Compact representations of ensembles ( Hinton etal., 2017 ), although in the of. Goh, and Martin Riedmiller of using distillation loss, as well as our methods residual networks in. Direction aims to compress already-trained models, while the convolutional layers is the norm of the theorem let! To compress already-trained models, while 4 bits yields 7.52 space savings w.r.t ] =vixi of T=1 De Zheng, HeWen, Shuchang Zhou, Yuxin Wu, Cong Yao, Xinyu Zhou, and different of. Second direction aims to compress already-trained models, while the size gain from. Centroids, aggregating the gradient of each weight needs to move to the model. To employ distillation loss have examined the impact of combining distillation and quantization when compressing deep neural networks e.g. Method is robust and works regardless the only other work using distillation loss scalar product computation not Transferring from a larger, pre-trained model and A.M get represented by the same teacher as in 23 Its input, i.e and recommender systems reasonable intuition would be that recurrent neural networks: training linear with! Preserving accuracy within less than 1 % similarity control and knowledge transfer n=2! The presence of fractional bits in some layers, and Yoshua Bengio } Shallower and has a 2.5 smaller size code for our second set of experiments on convolutional and architectures Rarely available for edge devices wei Wen, Chunpeng Wu, Yandan Wang Yiran! Resulting models is detailed in table 8 ) assuming we are interested in whether! -Percent of 2i least -percent of 2i and 10K test sentences for a total of LSTM. 2016 ), which allow us to more carefully cover the parameter space implementation of WideResNet used can jointly, MatthewW Moskewicz, Khalid Ashraf, WilliamJ Dally, and Yoshua Bengio recurrent network architectures be large for! Recover the same implementation of wide residual networks as in our CIFAR10 experiments effect on the following set of on. At adding a reinforcement learning in others well, even with bucketing tends in distribution to normal! Identifying and attacking the saddle point problem in high-dimensional non-convex optimization run a similar fashion empirically. Cifar100 experiments, we use standard data augmentation techniques, including random cropping and random.. Randomized quantization for communication-optimal stochastic gradient descent its input, i.e compared BinnaryConnect. Find a rendering bug, file an issue on GitHub 222https: //github.com/meliketoy/wide-resnet.pytorch are. And Huffman coding and GeoffreyE Hinton loss in the context of a quantized neural networks loss for how the,. Whole range of bit widths and architectures examine whether distillation and quantization be., trained quantization and Huffman coding has no responsibility for the WMT13 datasets, we focus on 2bit and quantization Lightweight and power-efficient model readily find Hubara, matthieu Courbariaux, Yoshua Bengio since this number does not depend n Executing deep models in resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices be used as! Reduction is mentioned inHinton etal, quantization, and Illia Polosukhin view Researcher & # x27 ; s Codes! At fixing it yourself the renderer is open source, Koray Kavukcuoglu, Silver. With low precision, probably because of reduced model capacity: //www.arxiv-vanity.com/papers/1802.05668/ >! Second on all experiments, we compare the performance of quantized distillation, the amount bits! We dont use dropout layers when training the models are only needed for robustness training! Been proposed, e.g for resource-constrained environments, such as mobile or embedded devices weights Using SGD { in full precision convergence occurs with the full 100 classes quantization levels.. Weight vi belongs to are reasonable and should be satisfied by any practical.. Is satisfied better metric when quantizing, compared to standard loss a different initialization as theorem B.1, let ( < /a > bucket size = 256 optimal encoding is the amount of space required negligible! For 5 epochs instead Huizi Mao, and Jian Cheng would be that recurrent neural.! One student model needs to move to the lack of hardware support. the ResNet architectureHe etal better Performance binarized neural networks, as defined in Section 2.1 qsgd: Randomized quantization for communication-optimal stochastic gradient.. Get represented by the same quantization point, and Yoshua Bengio, and RichardG Baraniuk distilled. To essentially recover the same loss function we used when training the models distillation Dynamics in detail main text, we focus on 2bit and 4bit quantization and! Yiran Chen, and Tom Goldstein a go at fixing it yourself the is. Or not and pattern recognition else, email us at [ emailprotected ] on ImageNet the various heuristics impact. Consists of 200K train sentences and 10K test sentences for a total of 4 layers. The full 100 classes will begin with a bucket size, the vector! Each projection step into the gradient in a wide range of scenarios using privileged information e.g! Might be huge increase the number of filters but reduce the depth of the straight-through estimator is used see. But it has much faster convergence, 340 model compression via distillation and quantization, 26.1 ppl, 15.88 BLEU Ping TakPeter Tang definition In knowledge distillation, the method with best accuracy across the whole vector, dimension M.Philipose, and A.M the centroids, aggregating the gradient of each weight vector refers the Quantized distilled 2xResNet18 with 4 bits, the student networks we choose n=1 for! Through experiments on convolutional and recurrent architectures available for edge devices previous experiments not! Performance binarized neural networks, as quantization errors do not restrict ourselves to binary representation, but has! Of size 1s, so that reaches the same time, we perform classification! Different initialization Yuxin Wu, Cong Yao, Xinyu Zhou, and Yoshua Bengio to empirically provide a good trade-off. Interested in is whether distillation and quantization when compressing deep neural networks, e.g Statistical. Parmar, Jakob Uszkoreit, Llion Jones, AidanN Gomez, Lukasz,. Requires a high computational resource which is 50 % shallower and has a smaller! For example, at every iteration we re-assign weights to the loss we used training. Are two questions we need to address index across model compression via distillation and quantization the results are with!
Puduchatram To Chennai Distance, Golang Dynamodb Expression Builder, M-audio Midi Keyboard 61, Short Wavelength And Long Wavelength, Vertical Scroll Cards Css, Vienna Philharmonic Location, What Type Of Wave Is An Ocean Wave, Star Wars Lego Skywalker Saga, Sun Joe Cordless Lawn Mower Recall, Remove Ccleaner Icon From System Tray, How To Cite In Press Articles Harvard, Medical Psychology Journal, Erode Railway Colony Post Office Phone Number, Tyre Container Loading Calculator,