Deep Log-Likelihood Ratio Quantization

In this work, a deep learning-based method for log-likelihood ratio (LLR) lossy compression and quantization is proposed, with emphasis on a single-input single-output uncorrelated fading communication setting. A deep autoencoder network is trained to compress, quantize and reconstruct the bit log-likelihood ratios corresponding to a single transmitted symbol. Specifically, the encoder maps to a latent space with dimension equal to the number of sufficient statistics required to recover the inputs - equal to three in this case - while the decoder aims to reconstruct a noisy version of the latent representation with the purpose of modeling quantization effects in a differentiable way. Simulation results show that, when applied to a standard rate-1/2 low-density parity-check (LDPC) code, a finite precision compression factor of nearly three times is achieved when storing an entire codeword, with an incurred loss of performance lower than 0.1 dB compared to straightforward scalar quantization of the log-likelihood ratios.Comment: Accepted for publication at EUSIPCO 2019. Camera-ready versio

Deep Learning-Based Quantization of L-Values for Gray-Coded Modulation

In this work, a deep learning-based quantization scheme for log-likelihood ratio (L-value) storage is introduced. We analyze the dependency between the average magnitude of different L-values from the same quadrature amplitude modulation (QAM) symbol and show they follow a consistent ordering. Based on this we design a deep autoencoder that jointly compresses and separately reconstructs each L-value, allowing the use of a weighted loss function that aims to more accurately reconstructs low magnitude inputs. Our method is shown to be competitive with state-of-the-art maximum mutual information quantization schemes, reducing the required memory footprint by a ratio of up to two and a loss of performance smaller than 0.1 dB with less than two effective bits per L-value or smaller than 0.04 dB with 2.25 effective bits. We experimentally show that our proposed method is a universal compression scheme in the sense that after training on an LDPC-coded Rayleigh fading scenario we can reuse the same network without further training on other channel models and codes while preserving the same performance benefits.Comment: Submitted to IEEE Globecom 201

Reducing the Model Order of Deep Neural Networks Using Information Theory

Deep neural networks are typically represented by a much larger number of parameters than shallow models, making them prohibitive for small footprint devices. Recent research shows that there is considerable redundancy in the parameter space of deep neural networks. In this paper, we propose a method to compress deep neural networks by using the Fisher Information metric, which we estimate through a stochastic optimization method that keeps track of second-order information in the network. We first remove unimportant parameters and then use non-uniform fixed point quantization to assign more bits to parameters with higher Fisher Information estimates. We evaluate our method on a classification task with a convolutional neural network trained on the MNIST data set. Experimental results show that our method outperforms existing methods for both network pruning and quantization.Comment: To appear in ISVLSI 2016 special sessio

BitNet: Bit-Regularized Deep Neural Networks

We present a novel optimization strategy for training neural networks which we call "BitNet". The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over all real values. Our key idea is to limit the expressive power of the network by dynamically controlling the range and set of values that the parameters can take. We formulate this idea using a novel end-to-end approach that circumvents the discrete parameter space by optimizing a relaxed continuous and differentiable upper bound of the typical classification loss function. The approach can be interpreted as a regularization inspired by the Minimum Description Length (MDL) principle. For each layer of the network, our approach optimizes real-valued translation and scaling factors and arbitrary precision integer-valued parameters (weights). We empirically compare BitNet to an equivalent unregularized model on the MNIST and CIFAR-10 datasets. We show that BitNet converges faster to a superior quality solution. Additionally, the resulting model has significant savings in memory due to the use of integer-valued parameters

Learning Hash Codes via Hamming Distance Targets

We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an accurate approximation for the probability that two inputs fall within a Hamming distance target. Our novel training scheme obtains a good estimate of the true gradient by better sampling inputs and evaluating loss terms between all pairs of inputs in each minibatch. To fully leverage the resulting hashes, we use multi-indexing. We demonstrate that these techniques provide large improvements to a similarity search tasks. We report the best results to date on competitive information retrieval tasks for ImageNet and SIFT 1M, improving MAP from 73% to 84% and reducing query cost by a factor of 2-8, respectively.Comment: 8 pages, overhaul of our previous submission Convolutional Hashing for Automated Scene Matchin

2PFPCE: Two-Phase Filter Pruning Based on Conditional Entropy

Deep Convolutional Neural Networks~(CNNs) offer remarkable performance of classifications and regressions in many high-dimensional problems and have been widely utilized in real-word cognitive applications. However, high computational cost of CNNs greatly hinder their deployment in resource-constrained applications, real-time systems and edge computing platforms. To overcome this challenge, we propose a novel filter-pruning framework, two-phase filter pruning based on conditional entropy, namely \textit{2PFPCE}, to compress the CNN models and reduce the inference time with marginal performance degradation. In our proposed method, we formulate filter pruning process as an optimization problem and propose a novel filter selection criteria measured by conditional entropy. Based on the assumption that the representation of neurons shall be evenly distributed, we also develop a maximum-entropy filter freeze technique that can reduce over fitting. Two filter pruning strategies -- global and layer-wise strategies, are compared. Our experiment result shows that combining these two strategies can achieve a higher neural network compression ratio than applying only one of them under the same accuracy drop threshold. Two-phase pruning, that is, combining both global and layer-wise strategies, achieves 10 X FLOPs reduction and 46% inference time reduction on VGG-16, with 2% accuracy drop.Comment: 8 pages, 6 figure

Discretely Relaxing Continuous Variables for tractable Variational Inference

We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed "DIRECT" approach has several advantages over its predecessors; (i) it can exactly compute ELBO gradients (i.e. unbiased, zero-variance gradient estimates), eliminating the need for high-variance stochastic gradient estimators and enabling the use of quasi-Newton optimization methods; (ii) its training complexity is independent of the number of training points, permitting inference on large datasets; and (iii) its posterior samples consist of sparse and low-precision quantized integers which permit fast inference on hardware limited devices. In addition, our DIRECT models can exactly compute statistical moments of the parameterized predictive posterior without relying on Monte Carlo sampling. The DIRECT approach is not practical for all likelihoods, however, we identify a popular model structure which is practical, and demonstrate accurate inference using latent variables discretized as extremely low-precision 4-bit quantized integers. While the ELBO computations considered in the numerical studies require over $10^{2352}$ log-likelihood evaluations, we train on datasets with over two-million points in just seconds.Comment: Appears in the proceedings of the Advances in Neural Information Processing Systems (NeurIPS), 2018. Full code is available at https://github.com/treforevans/direc

Entropy-Constrained Training of Deep Neural Networks

We propose a general framework for neural network compression that is motivated by the Minimum Description Length (MDL) principle. For that we first derive an expression for the entropy of a neural network, which measures its complexity explicitly in terms of its bit-size. Then, we formalize the problem of neural network compression as an entropy-constrained optimization objective. This objective generalizes many of the compression techniques proposed in the literature, in that pruning or reducing the cardinality of the weight elements of the network can be seen special cases of entropy-minimization techniques. Furthermore, we derive a continuous relaxation of the objective, which allows us to minimize it using gradient based optimization techniques. Finally, we show that we can reach state-of-the-art compression results on different network architectures and data sets, e.g. achieving x71 compression gains on a VGG-like architecture.Comment: 8 pages, 6 figure

Structured Probabilistic Pruning for Convolutional Neural Network Acceleration

In this paper, we propose a novel progressive parameter pruning method for Convolutional Neural Network acceleration, named Structured Probabilistic Pruning (SPP), which effectively prunes weights of convolutional layers in a probabilistic manner. Unlike existing deterministic pruning approaches, where unimportant weights are permanently eliminated, SPP introduces a pruning probability for each weight, and pruning is guided by sampling from the pruning probabilities. A mechanism is designed to increase and decrease pruning probabilities based on importance criteria in the training process. Experiments show that, with 4x speedup, SPP can accelerate AlexNet with only 0.3% loss of top-5 accuracy and VGG-16 with 0.8% loss of top-5 accuracy in ImageNet classification. Moreover, SPP can be directly applied to accelerate multi-branch CNN networks, such as ResNet, without specific adaptations. Our 2x speedup ResNet-50 only suffers 0.8% loss of top-5 accuracy on ImageNet. We further show the effectiveness of SPP on transfer learning tasks.Comment: CNN model acceleration, 13 pages, 6 figures, accepted by Proceedings of the British Machine Vision Conference (BMVC), 2018 ora

Local Feature Detectors, Descriptors, and Image Representations: A Survey

With the advances in both stable interest region detectors and robust and distinctive descriptors, local feature-based image or object retrieval has become a popular research topic. %All of the local feature-based image retrieval system involves two important processes: local feature extraction and image representation. The other key technology for image retrieval systems is image representation such as the bag-of-visual words (BoVW), Fisher vector, or Vector of Locally Aggregated Descriptors (VLAD) framework. In this paper, we review local features and image representations for image retrieval. Because many and many methods are proposed in this area, these methods are grouped into several classes and summarized. In addition, recent deep learning-based approaches for image retrieval are briefly reviewed.Comment: 20 page