learned step size quantization

Accuracy improved with higher precision, and at 4-bit exceeded baseline full precision accuracy on ResNet-18 (+0.4 top-1) and on ResNet-34 (+0.3 top-1) and nearly matched full precision accuracy on ResNet-50 (0.2 top-1). To use this online calculator for Quantization step size, enter Max Voltage (Xmax), Min voltage (Xmin) & Number of bits (n) and hit the calculate button. We performed a similar sweep for the activation step size learning rate scale with 2-bit weights and full precision activations. The approach itself is simple, requiring a single additional parameter per weight or activation layer. We implemented and tested LSQ in PyTorch. Our approach falls in the school of directly learning quantization parameters through backpropagation, which has the appealing feature that it seeks a quantization that directly improves the metric of interest, the training loss. However, consider that if v is just less than 0.5s, a very small decrease in s will cause the corresponding ^v to change from 0 to s, suggesting that the gradient in this region should be non zero. Choi, J., Chuang, P. Imagenet classification with deep convolutional neural networks. neural networks. The essence of our approach is to learn the step size parameter . Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline . Resiliency of deep neural networks under quantization. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. computing. As demonstrated on the ImageNet Following this we look at the distribution of quantized data, examine quantization error, then compare LSQ to existing quantization methods across several network architectures. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline . That i noticed after my researches about quantization step size, that this last can be small or large. [Papers with Code](/images/pwc_icon.svg) 7 community implementations](https://paperswithcode.com/paper/?openreview=rkgO66VKDS), deep learning, low precision, classification, quantization. The primary differences of our approach from previous work using backpropagation to learn the quantization mapping are the use of a different approximation to the quantizer gradient, described in detail in Section 2.1, and the application of a scaling factor to the learning rate of the parameters controlling quantization. Karpathy, A., Khosla, A., Bernstein, M., etal. Digital Communication - Quantization, The digitization of analog signals involves the rounding off of the values which are approximately equal to the analog values. code [3] MXNet(Gluon-CV) re-implementation of LQ-Nets. Open Publishing. >> We use high precision input activations and weights for the first and last layers, as this standard practice for quantized neural networks has been demonstrated to make a large impact on performance. Esser, S.K., Merolla, P.A., Arthur, J.V., Cassidy, A.S., Appuswamy, R., We present here Learned Step Size Quantization, a method for training deep networks such that they can run at inference time using low precision integer matrix multipliers, which offer power and space advantages over high precision alternatives. These have included quantizers where the mapping from inputs to discrete values is i) fixed based on user settings, ii) tuned using statistics from the data, iii) tuned by solving a quantizer error minimization problem during training, or iv) learned using backpropagation to train parameters controlling the quantization process. of a uniform quantizer by backpropagation of the training loss, applying a Bates, S., Bhatia, S., Boden, N., Borchers, A., etal. datasets. D.S. Convolutional networks for fast, energy-efficient neuromorphic Based on this, for all further training we used an activation step size learning rate scale of 101 and a weight step size learning rate scale of 104. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. Scale-Adjusted Training ICLR2020 reject paper; LLSQ: Learned Symmetric Quantization of Neural Networks for Low-precision Integer Hardware. here, we present a method for training such networks, learned step size quantization, that achieves the highest accuracy to date on the imagenet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline Uo?@YOt!Va&$a:X82sue&3|U9C_f;n/w #Qcfg7:Jr"(Af:E6Cmg=pdKyEs@.R {OaQ. alternatives. To prevent this imbalance from leading to instability in learning, we introduce a step size learning rate scalehyperparameter that is simply a multiplier on the learning rate used for s. Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., The PyTorch implementation of Learned Step size Quantization (LSQ) in ICLR2020 (unofficial) - GitHub - hustzxd/LSQuantization: The PyTorch implementation of Learned Step size Quantization (LSQ) in ICLR2020 (unofficial) by ignoring the discontinuity present in the quantizer. Choi, J., Wang, Z., Venkataramani, S., Chuang, P. McKinstry, J.L., Esser, S.K., Appuswamy, R., Bablani, D., Arthur, J.V., Learned Step Size Quantization (LSQ), that improves on prior efforts with two key contributions. This is an implementation of YOLO using LSQ network quantization method. This is an unofficial implementation of LSQ-Net, a deep neural network quantization framework. All results in this paper use the standard ImageNet training and validation sets, except where it is explicitly noted that they use train-v and train-t. All networks were trained using stochastic gradient descent optimization with a momentum of 0.9, using a softmax cross entropy loss function and cosine learning rate decay, , all with an initial learning rates 10 times lower the full precision networks and the same batch size as the full precision controls. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Prior approaches that use backpropagation to learn parameters controlling quantization (Choi etal., 2018b, a; Jung etal., 2018) create a gradient approximation by beginning with the forward function for the quantizer, removing the round function from this equation, then differentiating the remaining operations. networks. networks. For activations, this difference was 0.46 for mean absolute error, 0.83 for mean square error, and 0.60 for Kullback-Leibler divergence, Rastegari, M., Ordonez, V., Redmon, J., and Farhadi, A. Xnor-net: Imagenet classification using binary convolutional neural For simplicity, we use a single such hyperparameter for all weight layers, and a single such hyperparameter for all activation layers. For inference, we envision computing equation 1 for weights (w) offline, for activations (x) online, and using the resulting w and x values as input to low precision integer matrix multiplication units underlying convolution or fully connected layers. Deep residual learning for image recognition. For example if an ADC has a step size of 1 Volt an input of 1 volt will produce an output, in a 4 bit converter, of 0001. This provides a coarser approximation of this gradient, one drawback of which is that ^v/s=0 if ^v=0. law is a compression algorithm used for non-uniform quantization. The following figure shows the resultant quantized signal which is the digital form . We used LSQ to train several ResNet variants where activations and weights both use 2, 3 or 4 bits of precision, and compared our results to published results of other approaches for training quantized networks. Here is how the Quantization step size calculation can be explained with given input values -> 0.472441 = (80-20)/ ( (2^7)-1). /Filter /FlateDecode The gradient with respect to s at this location provides the first term in equation 5 when |v/s|

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