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Register a new userQuantized Proximal Averaging Network for Analysis Sparse Coding
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Kartheek Kumar Reddy Nareddy
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the iterative algorithm into a trainable network that facilitates learning the sparsity prior. We also consider quantization of the network weights. Quantization makes neural networks efficient both in terms of memory and computation during inference, and also renders them compatible for low-precision hardware deployment. Our learning algorithm is based on a variant of the ADAM optimizer in which the quantizer is part of the forward pass and the gradients of the loss function are evaluated corresponding to the quantized weights while doing a book-keeping of the high-precision weights. We demonstrate applications to compressed image recovery and magnetic resonance image reconstruction. The proposed approach offers superior reconstruction accuracy and quality than state-of-the-art unfolding techniques and the performance degradation is minimal even when the weights are subjected to extreme quantization.
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It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets, factored RBMs, mcRBMs, convolutional RBMs, sparse autoencoders and several others. Moreover, these triangle or soft threshold encodings are ex- tremely efficient to compute. Several intuitive arguments have been put forward to explain this remarkable performance, yet no mathematical justification has been offered. The main result of this report is to show that these features are realized as an approximate solution to the a non-negative sparse coding problem. Using this connection we describe several variants of the soft threshold features and demonstrate their effectiveness on two image classification benchmark tasks.
We present PrecisionBatching, a quantized inference algorithm for speeding up neural network execution on traditional hardware platforms at low bitwidths without the need for retraining or recalibration. PrecisionBatching decomposes a neural network into individual bitlayers and accumulates them using fast 1-bit operations while maintaining activations in full precision. PrecisionBatching not only facilitates quantized inference at low bitwidths (< 8 bits) without the need for retraining/recalibration, but also 1) enables traditional hardware platforms the ability to realize inference speedups at a finer granularity of quantization (e.g: 1-16 bit execution) and 2) allows accuracy and speedup tradeoffs at runtime by exposing the number of bitlayers to accumulate as a tunable parameter. Across a variety of applications (MNIST, language modeling, natural language inference) and neural network architectures (fully connected, RNN, LSTM), PrecisionBatching yields end-to-end speedups of over 8x on a GPU within a < 1% error margin of the full precision baseline, outperforming traditional 8-bit quantized inference by over 1.5x-2x at the same error tolerance.
In Dictionary Learning one tries to recover incoherent matrices $A^* in mathbb{R}^{n times h}$ (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors $x^* in mathbb{R}^h$ with a small support of size $h^p$ for some $0 <p < 1$ while having access to observations $y in mathbb{R}^n$ where $y = A^*x^*$. In this work we undertake a rigorous analysis of whether gradient descent on the squared loss of an autoencoder can solve the dictionary learning problem. The Autoencoder architecture we consider is a $mathbb{R}^n rightarrow mathbb{R}^n$ mapping with a single ReLU activation layer of size $h$. Under very mild distributional assumptions on $x^*$, we prove that the norm of the expected gradient of the standard squared loss function is asymptotically (in sparse code dimension) negligible for all points in a small neighborhood of $A^*$. This is supported with experimental evidence using synthetic data. We also conduct experiments to suggest that $A^*$ is a local minimum. Along the way we prove that a layer of ReLU gates can be set up to automatically recover the support of the sparse codes. This property holds independent of the loss function. We believe that it could be of independent interest.
Recovering an underlying image from under-sampled measurements, Compressive Sensing Imaging (CSI) is a challenging problem and has many practical applications. Recently, deep neural networks have been applied to this problem with promising results, owing to its implicitly learned prior to alleviate the ill-poseness of CSI. However, existing neural network approaches require separate models for each imaging parameter like sampling ratios, leading to training difficulties and overfitting to specific settings. In this paper, we present a dynamic proximal unrolling network (dubbed DPUNet), which can handle a variety of measurement matrices via one single model without retraining. Specifically, DPUNet can exploit both embedded physical model via gradient descent and imposing image prior with learned dynamic proximal mapping leading to joint reconstruction. A key component of DPUNet is a dynamic proximal mapping module, whose parameters can be dynamically adjusted at inference stage and make it adapt to any given imaging setting. Experimental results demonstrate that the proposed DPUNet can effectively handle multiple CSI modalities under varying sampling ratios and noise levels with only one model, and outperform the state-of-the-art approaches.
Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our method attains linear convergence. In practice, extensive empirical results verify the advantages of our method.
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