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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). [ABSTRACT FROM AUTHOR]

Recently, many fast implementations of the bilateral and the nonlocal filters were proposed based on lattice and vector quantization, e.g. clustering, in higher dimensions. However, these approaches can still be inefficient owing to the complexities in the resampling process or in filtering the high-dimensional resampled signal. In contrast, simply scalar resampling the high-dimensional signal after decorrelation presents the opportunity to filter signals using multi-rate signal processing techniques. This work proposes the Gaussian lifting framework for efficient and accurate bilateral and nonlocal means filtering, appealing to the similarities between separable wavelet transforms and Gaussian pyramids. Accurately implementing the filter is important not only for image processing applications, but also for a number of recently proposed bilateral-regularized inverse problems, where the accuracy of the solutions depends ultimately on accurate filter implementations. We show that our Gaussian lifting approach filters images more accurately and efficiently across many filter scales. Adaptive lifting schemes for bilateral and nonlocal means filtering are also explored. [ABSTRACT FROM AUTHOR]