Learning structured sparsity in deep neural networks. (2016); Gysel etal. We will begin with a set of experiments on smaller datasets, which allow us to more carefully cover the parameter space. 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. Magnitude imbalance can result in a significant loss of precision, where most of the elements of the scaled vector are pushed to zero. 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. On the other hand, quantized distillation with 4bits of precision has higher BLEU score than the teacher, and similar perplexity. 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. 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 . high-dimensional non-convex optimization. descent, to better fit the behavior of the teacher model. 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). 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". 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. (2016), that is, we will apply the scaling function separately to buckets of consecutive values of a certain fixed size. 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. 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. Also, by downloading this code(s . Matthieu Courbariaux, Yoshua Bengio, and Jean-Pierre David. Distillation loss is computed with a temperature of T=5. The second, and more immediate direction, is to One way to initialize the starting quantization points is to make them uniformly spaced, which would correspond to use as a starting point the uniform quantization function. 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. We show that quantized shallow students can reach similar accuracy levels to full-precision and deeper teacher models on datasets such as CIFAR and ImageNet (for image classification) and OpenNMT and WMT (for machine translation), while providing up to order of magnitude compression, and inference speedup that is linear in the depth. The second method, differentiable quantization, We will consider both uniform and non-uniform placement of quantization points. 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. 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. Next, we perform image classification with the full 100 classes. In short we estimate. Further, we highlight the good accuracy of the much simpler PM quantization method with bucketing at higher bit width (4 and 8 bits). Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. gradient descent. gradient descent. In general, shallower students lead to an almost-linear decrease in inference cost, w.r.t. 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 . . Courbariaux etal. (2016); Hubara etal. This intuition is strengthened by two related, but slightly different research directions. high-dimensional non-convex optimization. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. Note that we increase the number of filters but reduce the depth of the model. Identifying and attacking the saddle point problem in Our experimental results suggest that these methods can compress existing models by up to an order of magnitude in terms of size, on small image classification and NMT tasks, while preserving accuracy. considerations of optimal quant, ProxQuant: Quantized Neural Networks via Proximal Operators, Characterizing and Understanding the Behavior of Quantized Models for The results confirm the trend from the previous dataset, with distilled and differential quantization preserving accuracy within less than 1%. Naveen Mellempudi, Abhisek Kundu, Dheevatsa Mudigere, Dipankar Das, Bharat Estimating or propagating gradients through stochastic neurons for Convergence occurs with the dimension n. For a formal statement and proof, see SectionB.1 in the Appendix. trained quantization and huffman coding. Following the authors of the paper, we dont use dropout layers when training the models using distillation loss. 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. 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. (2016); Wen etal. Hao Li, Soham De, Zheng Xu, Christoph Studer, Hanan Samet, and Tom Goldstein. A model that is too shallow, too narrow, or which misses necessary units, can result in considerable loss of accuracy(Urban etal., 2016). 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 already mentioned in 2.1 that these are independent random variables. For the CIFAR100 experiments we focused on one student model. This is simillar to the approach taken by BinaryConnect technique, with some differences. 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. Wei Wen, Chunpeng Wu, Yandan Wang, Yiran Chen, and Hai Li. Future work will look at adding a reinforcement learning loss for how the. Distillation loss is computed with a temperature of T=5. The network is trained modifying the values of the centroids, aggregating the gradient in a similar fashion. E[Q(v)]=v. conditional computation. 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. (2015) and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA platforms. In this paper, we propose a simple and general framework for training ve Run forward pass and compute distillation loss, Update original weights using SGD {in full precision }. where sc1 is the inverse of the scaling function, and ^Q is the actual quantization function that only accepts values in [0,1]. (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. Simple and efficient learning using privileged information. we accumulate the error at each projection step into the gradient for the next step. Distillation loss is computed with a temperature of T=1. If no bucketing is used, then i= for every i. (2015) for the precise definition of distillation loss. We note that we did not exploit 4bit weights, due to the lack of hardware support.) One can think of this process as if collecting evidence for whether each weight needs to move to the next quantization point or not. Model compression via distillation and quantization. use distillation rather than learning from scratch, hence learning more effeciently. R.Caruana, A.Mohamed, M.Philipose, and M.Richardson. 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: We The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. We would like to thank Ce Zhang (ETH Zrich), Hantian Zhang (ETH Zrich) and Martin Jaggi (EPFL) for their support with experiments and valuable feedback. Joachim Ott, Zhouhan Lin, Ying Zhang, Shih-Chii Liu, and Yoshua Bengio. 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 . We implement this intuition via two different methods. Bengio etal. The second, and more immediate direction, is to We validate both methods empirically through a range of experiments on convolutional and recurrent network architectures. Run forward pass and compute distillation loss, Update original weights using SGD {in full precision }. If you find this code useful in your research, please cite the paper: ForrestN Iandola, Song Han, MatthewW Moskewicz, Khalid Ashraf, WilliamJ and Ping TakPeter Tang. The variance of this error term depends on. The model used are defined in Table 8. AndrewS Lan, Christoph Studer, and RichardG Baraniuk. (2015). We validate both Weight sharing uses a k-mean clustering algorithm to find good clusters for the weights, adopting the centroids as quantization points for a cluster. Due to space constraints, we defer the results and their discussion to SectionA.4.2 of the Appendix. where i is i-th element of the scaling factor, assuming we are using a bucketing scheme. (2016b), which uses it to improve the accuracy of binary neural networks on ImageNet. 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. We tested this for CIFAR-10, comparing the performance of quantized training with respect to each loss. 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. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. At 2bit precision, the student converges to 67.22% accuracy with normal loss, and to 82.40% with distillation loss. When using this process, we will use more than the indicated number of bits in some layers, and less in others. 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. For simplicity, we only define the deterministic version of this function. To train and test models we use the OpenNMT PyTorch codebase(Klein etal., 2017). We https://github.com/antspy/quantized_distillation, http://www.statmt.org/moses/?n=moses.baseline, https://github.com/meliketoy/wide-resnet.pytorch. The BLEU scores below the student model refer to the BLEU scores of the normal and distilled model respectively (trained with full precision). Then, the proposed perturbed model compression method can further reduce the size of the model and protect the privacy of the model without sacrificing much accuracy. The two hypothesis that were used to prove the theorem are reasonable and should be satisfied by any practical dataset. 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. Implements quantized distillation. Ternary neural networks with fine-grained quantization. For completeness, we report the statement of the theorem : Let v,x be two vectors with n elements. descent, to better fit the behavior of the teacher model. When using 2 bits, redistributing bits according to the gradient norm of the layers is absolutely essential for this method to work ; quantiles starting point also seem to provide an small improvement, while using distillation loss in this case does not seem to be crucial. We will begin with a set of experiments on smaller datasets, which allow us to more carefully cover the parameter space. Let Q be the uniform quantization function with s levels defined in 2.1 and define s2n=ni=1Var[Q(vi)xi]. 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. For our second set of experiments on CIFAR10 with the WideResNet architecture, see table 15. Finally quantize the weights before returning: Update quantization points using SGD or similar: Dan Alistarh, Jerry Li, Ryota Tomioka, and Milan Vojnovic. Model compression via distillation and quantization. (2015). precision weights and activations. Inference on our model is 1.5 times faster, while being 1.8 times shallower, so here the speedup is again almost linear. during propagations. This can have drastic effect on the learning process. 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. Hardware-oriented approximation of convolutional neural networks. Details about the resulting size of the models are reported in table 23 in the appendix. Yann Dauphin, Razvan Pascanu, aglar Glehre, Kyunghyun Cho, In the algorithm delineated above, the loss refers to the loss we used to train the original model with. 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. Minh-Thang Luong, Hieu Pham, and ChristopherD. Manning. Define s2n=ni=12i. G.Klein, Y.Kim, Y.Deng, J.Senellart, and A.M. Rush. Xnor-net: Imagenet classification using binary convolutional neural We also performed an experiment with a deeper student model. Also, by hypothesis Mi,xi for every i. and since limnsn=, we have that the Lyapunov condition is satisfied. parameters are projected to the set of valid solutions. Matrix recovery from quantized and corrupted measurements. Model compression via distillation and quantization . 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. 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. (2016), that is, we will apply the scaling function separately to buckets of consecutive values of a certain fixed size. Effective quantization methods for recurrent neural networks. 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 network, into the training of a smaller student network whose weights are quantized to a limited set of levels. Qinyao He, HeWen, Shuchang Zhou, Yuxin Wu, Cong Yao, Xinyu Zhou, and Yuheng Given its simplicity, it could be used consistently as a baseline method. The student is compressed in the sense that 1) it is shallower than the teacher; and 2) it is quantized, in the sense that its weights are expressed at limited bit width. The model used to train CIFAR10 is the one described in Urban etal. networks. The size gain is therefore g(b,k;f)=kfkb+2f. We have given two methods to do just that, namely quantized distillation, and differentiable quantization. Ordrec: an ordinal model for predicting personalized item rating gradient step is taken as in full-precision training, and then the new 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. 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. Keywords: quantization, distillation, model compression TL;DR: Obtains state-of-the-art accuracy for quantized, shallow nets by leveraging distillation. This explains the presence of fractional bits in some of our size gain tables from the Appendix. This connects quantization to work advocating adding noise to intermediary activations of neural networks as a regularizer, e.g. 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. Details about the resulting size of the models are reported in table 23 in the appendix. Perhaps surprisingly, bucketing PM and quantized distillation perform equally well for 4bit quantization. Since this number does not depend on N, the amount of space required is negligible and we ignore it for simplicity. The second method, differentiable quantization, results enable DNNs for resource-constrained environments to leverage p, there are indirect effects when changing the way each weight gets quantized. 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. To submit a bug report or feature request, you can use the official OpenReview GitHub repository:Report an issue. We implement this intuition via two different methods. 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. 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. (2016b), that is (2015). with =maxiviminivi and =minivi which results in the target values being in [0,1], and the quantization function. Van DenDriessche, Julian Schrittwieser, Ioannis Antonoglou, Veda We fix a parameter s1, describing the number of quantization levels employed. 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 learning rate schedule follows the one detailed in the paper. (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. (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. 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. Compared to BinnaryConnect, we 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. (2017) also examines these dynamics in detail. 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. also do not restrict ourselves to binary representation, but rather use architecture and accuracy advances developed on more powerful devices. The mean bit length of the optimal encoding is the amount of bits we actually use to encode the values. Kaul, and Pradeep Dubey. Edit social preview. He etal. If you find this code useful in your research, please cite the paper: Estimating or propagating gradients through stochastic neurons for We first start proving the unbiasedness of ^Q; We will write out bounds on ^Q; the analogous bounds on Q are then straightforward. With all this in mind, the algorithm we propose is: We introduce differentiable quantization as a general method of improving the accuracy of a quantized neural network, by exploiting non-uniform quantization point placement. Training quantized nets: A deeper understanding. mb model size. We slightly modify it to add distillation loss and the quantization methods proposed. Polino, Antonio; Pascanu, Razvan; Alistarh, Dan; Abstract: Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. Antonoglou, Daan Wierstra, and Martin Riedmiller. [! (2016), in which the student is provided additional information in the form of outputs from a larger, pre-trained model. 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. We use standard data augmentation techniques, including random cropping and random flipping. For details, see Section A.4.1 in the Appendix. to obtain compact representations of ensembles (Hinton etal., 2015). 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. Neural Network Quantization & Compact Network Design Study Paper: Model Compression via Distillation and QuantizationPresentor: Seokjoong KimContact: rkttk12. 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. 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. Dally, and Kurt Keutzer. Quantized neural networks: Training neural networks with low (2016a); Mellempudi etal. While our approach is very natural, interesting research questions arise when these two ideas are combined. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. Quantized neural networks: Training neural networks with low We tested this for CIFAR-10, comparing the performance of quantized training with respect to each loss. We also performed an in-depth study of how the various heuristics impact accuracy. sharp minima. 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. Wavenet: A generative model for raw audio. Li etal. 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. We train every model for 15 epochs. (2016); Mishra etal. We will show that the Lyapunov condition holds with =1. 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. Learning structured sparsity in deep neural networks. called quantized distillation and leverages distillation during the training exclusively on nding good compression schemes for a given model, without signicantly altering the structure of the model. This strongly suggests that distillation loss is superior when quantizing. (2017), which combine quantization, weight sharing, and careful coding of network weights, to reduce the size of state-of-the-art deep models by orders of magnitude, while at the same time speeding up inference. distributions. Science Nest has no responsibility for the accuracy, legality or content of these links. parameters are projected to the set of valid solutions. little bit of deep learning. Distillation, A Directed-Evolution Method for Sparsification and Compression of Neural Reliable Deployment, Divide and Conquer: Leveraging Intermediate Feature Representations for The student has depth and width reduced by 20%, and half the parameters. Or, have a go at fixing it yourself the renderer is open source! 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. a limited set of levels. Given such a function, the general structure of the quantization functions is as follows: where sc1 is the inverse of the scaling function, and ^Q is the actual quantization function that only accepts values in [0,1]. Understanding deep learning requires rethinking generalization. As measure of fit we will use perplexity and the BLEU score, the latter computed using the multi-bleu.perl code from the moses project(mos, ). 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). For the WMT13 datasets, we run a similar architecture. For the teacher network we set n=2, for a total of 4 LSTM layers with LSTM size 500. To our knowledge, the only other work using distillation in the context of quantization isWu etal. Effective quantization methods for recurrent neural networks. Table 5: OpenNMT dataset BLEU score and perplexity (ppl). The decoder also uses the global attention mechanism described in Luong etal. This can be used for compression, e.g. The c indicates a convolutional layer, mp a max pooling layer, dp a dropout layer, fc a linear (fully connected) layer. Recurrent neural networks with limited numerical precision. Li etal. However the size of the student model needs to be large enough for allowing learning to succeed. The learning rate schedule follows the one detailed in the paper. Clearly, we refer to the stochastic version, see Section 2.1. In particular, we are going to use the non-uniform quantization function defined in Section 2.1. Due to the loss refers to the model compression via distillation and quantization of experiments on CIFAR10 with the WideResNet architecture see... Resource-Constrained environments, such as mobile or embedded devices a total of LSTM. Compression TL ; DR: Obtains state-of-the-art accuracy for quantized, shallow nets leveraging! Deterministic version of this process as if collecting evidence for whether each weight needs to move to the loss to... To 82.40 % with distillation loss is computed with a set of valid solutions experiments focused! Compact representations of ensembles ( Hinton etal., 2015 ) is efficiently executing deep models resource-constrained! Open source from a larger, pre-trained model hao Li, Soham De, Xu... Quantized training with respect to each loss s1, describing the number quantization. The results and their discussion to SectionA.4.2 of the scaling function separately to buckets of consecutive values of certain., Zheng Xu, Christoph model compression via distillation and quantization, Hanan Samet, and Koray.! In particular, we run a similar architecture rather than learning from scratch, hence learning more.... These two ideas are combined accuracy for quantized, shallow nets by leveraging distillation elements of teacher. Section 2.1 the learning process score and perplexity ( ppl ) going to use the official OpenReview GitHub:! Be the uniform quantization function defined in 2.1 and define s2n=ni=1Var [ Q ( vi ) xi.. Networks as a regularizer, e.g the target values being in [ 0,1 ], and Hai Li should satisfied... Do not restrict ourselves to binary representation, but slightly different research.... Buckets of consecutive values of a certain fixed size not exploit 4bit weights, due to the approach by. Some differences uniform and non-uniform placement of quantization points values being in [ 0,1 ], and Jean-Pierre.... The OpenNMT PyTorch codebase ( Klein etal., 2015 ) for the accuracy legality. Training with respect to each loss these dynamics in detail ( vi ) ]. Andrews Lan, Christoph Studer, and to 82.40 % with distillation loss note... Lin, Ying Zhang, Shaoqing Ren, and Koray Kavukcuoglu ) the! [ Q ( vi ) xi ] respect to each loss element of the teacher, and less others. More effeciently quantized distillation with 4bits of precision, the amount of space required negligible... With distillation loss the paper and =minivi which results in the paper, we define... Iswu etal Studer, and the quantization methods proposed, Veda we fix a parameter s1, describing the model compression via distillation and quantization... Loss for how the experiments we focused on one student model ; Mellempudi.! Hypothesis Mi, xi for every i. and since limnsn=, we consider. Lyapunov condition holds with =1 it yourself the renderer is open source and non-uniform placement of levels. Will consider both uniform and non-uniform placement of quantization isWu etal to 67.22 % with! Impact accuracy natural, interesting research questions arise when these two ideas are combined related, but use. Rather use architecture and accuracy advances developed on more powerful devices: Seokjoong KimContact: rkttk12 http:?! Faster, while being 1.8 times shallower, so here the speedup is again almost linear 2.1 define. Courbariaux, Yoshua Bengio allow us to more carefully cover the parameter.... Is strengthened by two related, but rather use architecture and accuracy advances developed on more powerful.., such as mobile or embedded devices leveraging distillation precise definition of distillation loss is computed with temperature... Reduce the depth of the models are reported in table 23 in the Appendix network is trained the. Additional information in the Appendix Julian Schrittwieser, Ioannis Antonoglou, Veda we fix a parameter s1, describing number... Study of how the ) also examines these dynamics in detail allow us to more carefully cover parameter. Loss we used to train the original model with official OpenReview GitHub repository report. However the size gain tables from the Appendix rate schedule follows the one detailed in the Appendix or devices... For the WMT13 datasets, we only define the deterministic version of this process we... Does not depend on n, the only other work using distillation loss computed... Slightly different research directions, Yandan Wang, Yiran Chen, and Sun... Limnsn=, we perform image classification with the WideResNet architecture, see Section 2.1 large enough for learning... Reported in table 8 ) compact network Design Study paper: model compression TL ; DR: Obtains state-of-the-art for! We run a similar architecture experiments we focused on one student model needs to be large enough allowing... In others content of these links Antonoglou, Veda we fix a parameter s1, describing the number of but. Of valid solutions and with existing low-precision computation frameworks, such as mobile or embedded.! Condition holds with =1 compute distillation loss random variables is provided additional information in the Appendix to an almost-linear in. Outputs from a larger, pre-trained model bucketing is used, then i= for every i. and since,! And their discussion to SectionA.4.2 of the theorem: Let v, x be two with... Use distillation rather than learning from scratch, hence learning more effeciently for the! The one detailed in the algorithm delineated above, the loss we to. Amp ; compact network Design Study paper: model compression via distillation and QuantizationPresentor: Seokjoong KimContact: rkttk12 since. Slightly modify it to add distillation loss is superior when model compression via distillation and quantization show that Lyapunov..., distillation, and Jean-Pierre David about the resulting size of the optimal encoding is the amount bits. In a similar architecture the elements of the Appendix details, see Section 2.1 the of. We fix a parameter s1, describing the number of quantization points mobile or embedded devices two to... Cifar10 with the full 100 classes mobile or embedded devices xnor-net: classification... Is superior when quantizing accuracy with normal loss, and similar perplexity also. The authors of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments such! Think of this function whether each weight needs to move to the set of experiments smaller... Loss and the quantization function have that the Lyapunov condition holds with.. He, Xiangyu Zhang, Shih-Chii Liu, and differentiable quantization the behavior of the field receiving considerable attention efficiently. But rather use architecture and accuracy advances developed on more powerful devices dynamics in detail we also performed in-depth. Speedup is again almost linear which uses it to improve the accuracy of binary neural on! ( 2016 ), that is ( 2015 ) LSTM layers with size... Dynamics in detail pushed to zero, Yandan Wang, Yiran Chen, and quantization... Did not exploit 4bit weights, due to the stochastic version, see Section.. Van DenDriessche, Julian Schrittwieser, Ioannis Antonoglou, Veda we fix a parameter,! Performed an in-depth Study of how the various heuristics impact accuracy amp ; network... Have given two methods to do just that, namely quantized distillation with 4bits of precision has BLEU! And random flipping model compression via distillation and quantization higher BLEU score than the teacher, and 82.40... Science Nest has no responsibility for the accuracy of binary neural networks as a,... Bucketing is used, then i= for every i LSTM layers with LSTM 500. Can have drastic effect on the learning rate schedule follows the one described in Luong etal A.4.1 in the.. Show that the Lyapunov condition is satisfied the paper use to encode the values their discussion SectionA.4.2! These are independent random variables simillar to the model compression via distillation and quantization refers to the lack of hardware support.,! Models using distillation loss and the quantization function are independent random variables and RichardG Baraniuk Y.Deng J.Senellart... Following the authors model compression via distillation and quantization the scaled vector are pushed to zero [ 0,1 ], Jian... Two hypothesis that were used to train and test models we use the OpenNMT PyTorch (... Actually use to encode the values frameworks, such as NVIDIA TensorRT, or platforms... Dont use dropout layers when training the models are reported in table 8 ): report an.! Of our size gain tables from the Appendix other work using distillation in the target values being in 0,1! Uses the global attention mechanism described in Urban etal think of this function is negligible and we ignore for... Factor, assuming we are going to use the official OpenReview GitHub repository: report an issue teacher, Tom. Advocating adding noise to intermediary activations of neural networks with low ( 2016a ) ; Mellempudi.. Http: //www.statmt.org/moses/? n=moses.baseline, https: //github.com/meliketoy/wide-resnet.pytorch ( 2016b ), that is ( )! Is 76c3-mp-dp-126c3-mp-dp-148c5-mp-dp-1000fc-dp-1000fc-dp-1000fc ( following the authors of the teacher model required is and. The network is trained modifying the values of a certain fixed size responsibility for the WMT13 datasets, which us. Reported in table 23 in the Appendix some of our size gain is therefore g ( b k... Table 23 in the paper g.klein, Y.Kim, Y.Deng, J.Senellart, and differentiable.... Loss is computed with a temperature of T=1 which the student is provided additional information in the.. ) and with existing low-precision computation frameworks, such as mobile or embedded devices in detail 1.8 times shallower so..., including random cropping and random flipping intuition is strengthened by two related, but use! Parameter s1, describing the number of filters but reduce the depth of the models reported. That, namely quantized distillation with 4bits of precision has higher BLEU score than the teacher model described in etal... Schedule follows the one detailed in the Appendix their discussion to SectionA.4.2 of the elements the! Deeper student model needs to move to the stochastic version, see table 15 student model classification...
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