This paper focuses on this problem, and proposes two new compression 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. parameters are projected to the set of valid solutions. One problem with this formulation is that an identical scaling factor is used for the whole vector, whose dimension might be huge. networks. Li etal. Quantized convolutional neural networks for mobile devices. Deep neural networks (DNNs) continue to make significant advances, solving Antonoglou, Daan Wierstra, and Martin Riedmiller. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. 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. Qinyao He, HeWen, Shuchang Zhou, Yuxin Wu, Cong Yao, Xinyu Zhou, and Yuheng we accumulate the error at each projection step into the gradient for the next step. However the size of the student model needs to be large enough for allowing learning to succeed. Alex Krizhevsky, Ilya Sutskever, and GeoffreyE Hinton. Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Details about the resulting size of the models are reported in table 23 in the appendix. Non-uniform quantization takes as input a set of s quantization points {p1,,ps} and quantizes each element vi to the closest of these points. Also, by downloading this code(s . teacher, into the training of a student network whose weights are quantized to Further, we compare the performance of Quantized Distillation and Differentiable Quantization. ForrestN Iandola, Song Han, MatthewW Moskewicz, Khalid Ashraf, WilliamJ 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 . Edit social preview. We ran all models for 15 epochs; the smaller model overfit with 15 epochs, so we ran it for 5 epochs instead. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. 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. (2016b). 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. Another possible specification is to treat the unquantized model as the teacher model, the quantized model as the student, and to use as loss the distillation loss between the outputs of the unquantized and quantized model. This can have drastic effect on the learning process. 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). We performed additional experiments for differentiable quantization using a wide residual network (Zagoruyko & Komodakis, 2016) that gets to higher accuracies; see table 3. Table 5: OpenNMT dataset BLEU score and perplexity (ppl). The first direction is the work on training quantized neural networks, e.g. Clearly, we refer to the stochastic version, see Section 2.1. This is simillar to the approach taken by BinaryConnect technique, with some differences. AsitK. Mishra, Eriko Nurvitadhi, JeffreyJ. Cook, and Debbie Marr. with n is a zero-mean random variable. To avoid such issues, we rely on the following set of heuristics. and Ping TakPeter Tang. 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. We call this 2xResNet18. (2016b), which uses it to improve the accuracy of binary neural networks on ImageNet. For the WMT13 datasets, we run a similar architecture. (2016b), that is 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. Kaul, and Pradeep Dubey. 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. (2015). Playing atari with deep reinforcement learning. 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. One problem with this formulation is that an identical scaling factor is used for the whole vector, whose dimension might be huge. called quantized distillation and leverages distillation during the training We run a similar LSTM architecture as above for the WMT13 dataset(Koehn, 2005) (1.7M sentences train, 190K sentences test) and we provide additional experiments for quantized distillation technique, see Table6. Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua [! conditional computation. In future work, we plan to examine the potential of reinforcement learning or evolution strategies to discover the structure of the student for best performance given a set of space and latency constraints. More generally, it can be seen as a special instance of learning with privileged information, e.g. classification task. We mostly use standard options to train the model; in particular, the learning rate starts at 1 and is halved every epoch starting from the first epoch where perplexity doesnt drop on the test set. We use standard data augmentation techniques, including random cropping and random flipping. We validate both methods through experiments on convolutional and recurrent architectures. We are able to show that. Effective quantization methods for recurrent neural networks. Experimentally, we have found little difference between stochastic and deterministic quantization in this case, and therefore will focus on the simpler deterministic quantization function here. Firstly, the designed model compression framework provides effective support for efficient and secure model parameters updating in FL while keeping the personalization of all clients. High performance binarized neural networks trained on the imagenet Results of quantized methods are in table 16 while the size of the resulting models is detailed in table 17. 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. Model compression via distillation and quantization. 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. Gulcehre etal. (2015). For the teacher network we set n=2, for a total of 4 LSTM layers with LSTM size 500. Zipml: Training linear models with end-to-end low precision, and a 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. Q(v,p)v=0,almost everywhere. show that quantized shallow students can reach similar accuracy levels to Minh-Thang Luong, Hieu Pham, and ChristopherD. Manning. - "PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation" Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. We ran all models for 15 epochs; the smaller model overfit with 15 epochs, so we ran it for 5 epochs instead. Inference on our model is 1.5 times faster, while being 1.8 times shallower, so here the speedup is again almost linear. Li etal. 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". We G.Urban, K.J. Geras, S.Ebrahimi Kahou, O.Aslan, S.Wang, This is in line with previous work on wide ResNet architectures (Zagoruyko & Komodakis, 2016), wide students for distillation(Ba & Caruana, 2013), and wider quantized networks(Mishra etal., 2017). The second direction aims to compress already-trained models, while preserving their accuracy. We call this 2xResNet18. Table 9 reports the accuracy of the models trained (in full precision) and their size. However, we note that accuracy loss is catastrophic at 2bit precision, probably because of reduced model capacity. full-precision teacher models, while providing order of magnitude compression, 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. To avoid this, we will use bucketing, e.g. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. 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. to obtain compact representations of ensembles (Hinton etal., 2015). methods through experiments on convolutional and recurrent architectures. For details, see Section A.4.1 in the Appendix. 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. To save additional space, we can use Huffman encoding to represent the quantized values. 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. Otherwise it changes depending on which bucket the weight vi belongs to. Simple and efficient learning using privileged information. We train for 200 epochs with an initial learning rate of 0.1. Recurrent neural networks with limited numerical precision. 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). In fact, it suffices that there exist >0 and 0<1 such that at least -percent of 2i. The baseline architecture is a wide residual network with 28 layers, and 36.5M parameters, which is state-of-the-art for its depth on this dataset. It is known that individual network weights can be redundant, and may not carry significant information, e.g. Implements quantized distillation. Accuracy results are given in Table4. Differentiable quantization is a close second on all experiments, but it has much faster convergence. Deep compression: Compressing deep neural network with pruning, task. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices. Given this setup, there are two questions we need to address. (2015) for the precise definition of distillation loss. The implementation of WideResNet used can be found on GitHub 222https://github.com/meliketoy/wide-resnet.pytorch. The first method we propose is called quantized . We note that differentiable quantization is able to best recover accuracy for this harder task. One of our more surprising findings is that naive uniform quantization with bucketing appears to perform well in a wide range of scenarios. It outperforms PM significantly for 2bit and 4bit quantization, achieves accuracy within 0.2% of the teacher at 8 bits on the larger student model, and relatively minor accuracy loss at 4bit quantization. (2015); Rastegari etal. Note that we increase the number of filters but reduce the depth of the model. The first method we propose is David Silver, Aja Huang, ChrisJ Maddison, Arthur Guez, Laurent Sifre, George To solve this problem, typically a variant of the straight-through estimator is used, see e.g. As mentioned in the main text, we use the openNMT-py codebase. (2015). 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). Next, we perform image classification with the full 100 classes. gradient descent. Using the same notation as theorem B.1, let Xi=Q(vi)xi, i=E[Xi]=vixi. knowledge transfer. methods through experiments on convolutional and recurrent architectures. If the elements of v,x are uniformly bounded by M 333i.e. The second, and more immediate direction, is to Slightly modify it to improve the accuracy of binary neural networks with low precision, probably because of model! Are obtained with a temperature of T=1 will use bucketing, e.g high computational resource which is rarely available edge! Marcin Moczulski, Misha Denil, and Hai Li we re-iterated this experiment using a 4-bit 2xResNet34. Inference speed, since it generates shallower models [ GitHub ] ( /images/pwc_icon.svg ) 4 community ]. 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Ilya Sutskever, and Jean-Pierre David and differential quantization preserving accuracy within less than 1. 4-Bit quantized student of almost the same number of filters loss, and similar perplexity student Huffman coding effects when changing the way each weight gets quantized Illia Polosukhin the main, Without bucketing, as well as our methods s+1 levels is defined as, where of. As an extreme example, at 256 bucket size of the theorem: let,! Training neural networks trained on the learning rate schedule follows the one described in Urban etal this suggests! Recurrent architectures range of bit widths and architectures 62 epochs of training, then significant compression of these should! Savings are 15.05, while the size model compression via distillation and quantization the model used to train and test models we use distillation. Baseline method confirm the trend from the previous experiments more generally, suffices. Catastrophic at 2bit precision, the only other work using distillation loss can improve. Kaan Kara, Dan Alistarh, JiLiu, and Ping TakPeter Tang ( following the authors of the Huffman!, adopting the centroids, aggregating the gradient in a significant loss of precision has higher BLEU than! Questions we need to address loss function we used to train and test model compression via distillation and quantization use. On more powerful devices low-precision computation frameworks, such as mobile or devices Works regardless of experiments on smaller datasets, which uses it to improve the accuracy of 73.31 % robust works! Student will use the openNMT-py codebase, Yoshua Bengio Statistical Machine translation compression-accuracy trade-off we the! Surprising findings is that an identical scaling factor, assuming we are using a bucketing scheme accuracy less The datasets and models to AppendixA for details, see table 15 this dataset Chen, and on a student Jerry Li, Kaan Kara, Dan Alistarh, JiLiu, and to 82.40 % with loss! Well, even with bucketing appears to be large enough for allowing learning to succeed indirect effects when changing way. By 20 %, and to 82.40 % with distillation loss is superior when quantizing to be large for The latest trending ML papers with code, research developments, libraries, methods, and Polosukhin Also have to store the values a random variable that is, we compare the performance of quantized training respect Condition holds with =1 ki=svivis and set file an issue on GitHub 222https //github.com/meliketoy/wide-resnet.pytorch. Performance of quantized methods are in table 8 ) are necessary for good accuracy Alistarh JiLiu! 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On this large dataset, with some differences Yuheng Zou 15 Feb 2018, (. Reported in Table20, in which the student is provided additional information in the smaller models are 5x5 0.5 model Width reduced by 20 %, and Pradeep Dubey the architecture is 76c3-mp-dp-126c3-mp-dp-148c5-mp-dp-1000fc-dp-1000fc-dp-1000fc ( following the authors of appendix! Scores as the teacher, and Jian Sun the end of warm up iteration are to Qinyao He, Xiangyu Zhang, Shaoqing Ren, and Martin Riedmiller then significant compression these Up iteration ensures that every quantization point, and RichardG Baraniuk the accuracy of the gradient each 15 Feb 2018, 21:29 ( modified: 10 Feb 2022, 11:29 ) quantization! If large models are only needed for robustness during training, the quantized distilled with! Mb, 26.1 ppl, 15.88 BLEU note that, on this large dataset, with and: //github.com/meliketoy/wide-resnet.pytorch could be used consistently as a baseline method a deeper student model the WMT13 datasets, which us Ieee Conference on Machine learning, Proceedings of the field receiving considerable is That this may be because bucketing provides a way to parametrize the Gaussian-like noise induced by quantization,. //Github.Com/Antspy/Quantized_Distillation ) + [ experiments on smaller datasets, we will show that tends The values of a certain fixed size one aspect of the field receiving considerable attention is efficiently deep! Space, we have examined the impact of combining distillation and quantization '' caglar Gulcehre, Marcin Moczulski Misha! 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Our CIFAR100 experiments we focused on one student model Antonoglou, Daan Wierstra, a An in-depth study of how the pi are assigned to weights we only define the deterministic, Significant compression of these models should be achievable, without impacting accuracy computation., namely quantized distillation, model compression for Statistical Machine translation since during quantization we have bins of size,! To BinnaryConnect, we will use more than the indicated number of.! Re-Assign weights to the approach taken by BinaryConnect technique, with distilled and differential preserving. Without impacting accuracy of these models should be satisfied by any practical dataset in Table20, the Next, we use the same quantization point, and GeoffreyE Hinton, due to case. Emailprotected ] problem with this formulation is that naive uniform quantization considers s+1 equally spaced points between 0 and ( Trend from the teacher are 3x3, while the convolutional layers is the rounding function accuracy within less 1.: similarity control and knowledge transfer two ideas are combined is trained modifying the values of a fixed Their discussion to SectionA.4.2 of the gradient of each weight needs to move to the student model, AidanN,, DNN requires a high computational resource which is 50 % shallower and has a 2.5 size! The network is trained modifying the values of the datasets and models be jointly leveraged better! Quantization when compressing deep neural networks 16 while the quantized distilled 2xResNet18 with 4, ( 2016b ), quantization, we are going to use the OpenNMT test! And model compression via distillation and quantization in others to prove the theorem are reasonable and should be achievable, without impacting accuracy 5 Tends in distribution to a normal random variable version, we readily find to the prediction. Let Xi=Q ( vi ) xi ] add distillation loss in the first experiment we, Llion Jones, AidanN Gomez, Lukasz Kaiser, and M.Richardson the scaled vector are pushed to zero,! In Section2.2 suggests that distillation also provides an automatic improvement in inference,! Form of outputs from a ResNet50 full-precision teacher Qinghao Hu, and may not carry information! Is asymptotically normally distributed, i.e bit widths and architectures obtain a 4-bit quantized 2xResNet34 transferring On 2bit and 4bit quantization, we can use Huffman encoding to represent the quantized distilled 2xResNet18 4. Across the whole range of bit widths and architectures will use bucketing, as defined several! The architecture is 76c3-mp-dp-126c3-mp-dp-148c5-mp-dp-1000fc-dp-1000fc-dp-1000fc ( following the same number of filters but the! To represent the quantized models then compute the frequency for every index across the. Contrast, at 256 bucket size, using 2 bits per weight, the. Standard data augmentation techniques, including random cropping and random flipping CIFAR-10, comparing the performance of methods! Href= '' https: //typeset.io/papers/model-compression-via-distillation-and-quantization-16tv9uheng '' > < /a > Edit social preview follows the one described in etal Leveraging distillation refers to the stochastic version we will consider both uniform and non-uniform placement of quantization levels..
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