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In this paper, we compress convolutional neural network (CNN) weights post-training via transform quantization. Previous CNN quantization techniques tend to ignore the joint statistics of weights and activations, producing sub-optimal CNN performance at a given quantization bit-rate, or consider their joint statistics during training only and do not facilitate efficient compression of already trained CNN models. We optimally transform (decorrelate) and quantize the weights post-training using a rate-distortion framework to improve compression at any given quantization bit-rate. Transform quantization unifies quantization and dimensionality reduction (decorrelation) techniques in a single framework to facilitate low bit-rate compression of CNNs and efficient inference in the transform domain. We first introduce a theory of rate and distortion for CNN quantization, and pose optimum quantization as a rate-distortion optimization problem. We then show that this problem can be solved using optimal bit-depth allocation following decorrelation by the optimal End-to-end Learned Transform (ELT) we derive in this paper. Experiments demonstrate that transform quantization advances the state of the art in CNN compression in both retrained and non-retrained quantization scenarios. In particular, we find that transform quantization with retraining is able to compress CNN models such as AlexNet, ResNet and DenseNet to very low bit-rates (1-2 bits).

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在深度學習中,卷積神經網絡(CNN或ConvNet)是一類深度神經網絡,最常用于分析視覺圖像。基于它們的共享權重架構和平移不變性特征,它們也被稱為位移不變或空間不變的人工神經網絡(SIANN)。它們在圖像和視頻識別,推薦系統,圖像分類,醫學圖像分析,自然語言處理,和財務時間序列中都有應用。

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Recently, Learning-based image compression has reached comparable performance with traditional image codecs(such as JPEG, BPG, WebP). However, computational complexity and rate flexibility are still two major challenges for its practical deployment. To tackle these problems, this paper proposes two universal modules named Energy-based Channel Gating(ECG) and Bit-rate Modulator(BM), which can be directly embedded into existing end-to-end image compression models. ECG uses dynamic pruning to reduce FLOPs for more than 50\% in convolution layers, and a BM pair can modulate the latent representation to control the bit-rate in a channel-wise manner. By implementing these two modules, existing learning-based image codecs can obtain ability to output arbitrary bit-rate with a single model and reduced computation.

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