Networks with Application to Object Identification and Segmentation and To solve this problem, typically a variant of the straight-through estimator is used, see e.g. use distillation rather than learning from scratch, hence learning more effeciently. 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. (2015). 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. Hantian Zhang, Jerry Li, Kaan Kara, Dan Alistarh, JiLiu, and CeZhang. On the other hand, recent parallel work (Ba & Caruana, 2013; Hinton et al., 2015) introduces the process of distillation, which can be used for transferring the behaviour of a given model to any other structure. sc(v)=v, The decoder also uses the global attention mechanism described in Luong etal. All the results are obtained with a bucket size of 256, which we found to empirically provide a good compression-accuracy trade-off. We tested this for CIFAR-10, comparing the performance of quantized training with respect to each loss. 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 c indicates a convolutional layer, mp a max pooling layer, dp a dropout layer, fc a linear (fully connected) layer. We note that, on this large dataset, PM quantization does not perform well, even with bucketing. Want to hear about new tools we're making? In particular, medium and large-sized students are able to essentially recover the same scores as the teacher model on this dataset. [2106.14681] PQK: Model Compression via Pruning, Quantization, and We re-iterated this experiment using a 4-bit quantized 2xResNet34 student transferring from a ResNet50 full-precision teacher. To submit a bug report or feature request, you can use the official OpenReview GitHub repository:Report an issue. The basic idea is that quantized models can leverage distillation loss(Hinton etal., 2015), the weighted average between the correct targets (represented by the labels) and soft targets (represented by the teachers outputs). - "PQK: Model Compression via Pruning, Quantization, and Knowledge Distillation" PQK has two phases. Minh-Thang Luong, Hieu Pham, and ChristopherD. Manning. gradient step is taken as in full-precision training, and then the new If you find this code useful in your research, please cite the paper: (We use b bits per weight, plus the scaling factors and for every bucket). Hence. 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. We validate both 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. Ternary neural networks with fine-grained quantization. Details about the resulting size of the models are reported in table 23 in the appendix. As mentioned in the main text, we use the openNMT-py codebase. Magnitude imbalance can result in a significant loss of precision, where most of the elements of the scaled vector are pushed to zero. Overall, quantized distillation appears to be the method with best accuracy across the whole range of bit widths and architectures. We use the same teacher as in the previous experiments. the depth reduction. Table 9 reports the accuracy of the models trained (in full precision) and their size. If you find this code useful in your research, please cite the paper: Model compression via distillation and quantization . task. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. Notice that distillation loss can significantly improve the accuracy of the quantized models. Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. 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. It is known that individual network weights can be redundant, and may not carry significant information, e.g. knowledge transfer. The second, and more immediate direction, is to 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. While our approach is very natural, interesting research questions arise when these two ideas are combined. Add a The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. One key question we are interested in is whether distillation loss is a consistently better metric when quantizing, compared to standard loss. We fix a parameter s1, describing the number of quantization levels employed. The second method, which we call differentiable quantization, takes a different approach, by attempting to converge to the optimal location of quantization points through stochastic gradient descent. The first method we propose is called quantized . devices. 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. 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. Accuracy results are given in Table4. However, we note that accuracy loss is catastrophic at 2bit precision, probably because of reduced model capacity. The variance of this error term depends on. Distilling the Knowledge in a Neural Network. Surya Ganguli, and Yoshua Bengio. PQK: Model Compression via Pruning, Quantization, and Knowledge One The implementation of WideResNet used can be found on GitHub 222https://github.com/meliketoy/wide-resnet.pytorch. Compression of Generative Pre-trained Language Models via Quantization 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. Table1 contains the results for full-precision training, PM quantization with and without bucketing, as well as our methods. 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. called quantized distillation and leverages distillation during the training methods through experiments on convolutional and recurrent architectures. 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. Hardware-oriented approximation of convolutional neural networks. (2015) and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA platforms. We show that quantized shallow students can reach similar accuracy levels to state-of-the-art full-precision teacher models, while providing up to order of magnitude compression, and inference speedup that is almost linear in the depth reduction. This code has been written to experiment with quantized distillation and differentiable quantization, techniques developed in our paper "Model compression via distillation and quantization". little bit of deep learning. We will show that the Lyapunov condition holds with =1. (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. The second, and more immediate direction, is to For the WMT13 datasets, we run a similar architecture. Details about the resulting size of the models are reported in table 23 in the appendix. Deep compression: Compressing deep neural network with pruning, The wide factor is a multiplicative factor controlling the amount of filters in each layer; for more details please refer to the original paper Zagoruyko & Komodakis (2016). Deep residual learning for image recognition. (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. 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. One can think of this process as if collecting evidence for whether each weight needs to move to the next quantization point or not. If large models are only needed for robustness during training, then significant compression of these models should be achievable, without impacting accuracy. Model compression via distillation and quantization Authors: Antonio Polino Razvan Pascanu Universit de Montral Dan Alistarh Microsoft Request full-text Abstract Deep neural networks (DNNs). At the same time, we note that distillation also provides an automatic improvement in inference speed, since it generates shallower models. The learning rate schedule follows the one detailed in the paper. (2016a). and Ping TakPeter Tang. (2015) for the precise definition of distillation loss. All convolutional layers of the teacher are 3x3, while the convolutional layers in the smaller models are 5x5. Teacher model: 84.8M param, 340 MB, 26.1 ppl, 15.88 BLEU. We will consider both uniform and non-uniform placement of quantization points. As usual, to obtain the best results one should experiment with hyperparameters optimization, and different variants of gradient descent. Therefore, the scalar product of the quantized weights and the inputs is an important quantity: We already know from section B that the quantization function is unbiased; hence we know that. Magnitude imbalance can result in a significant loss of precision, where most of the elements of the scaled vector are pushed to zero. 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. 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