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Traditionally, quantization is designed to minimize the reconstruction error of a data source. When considering downstream classification tasks, other measures of distortion can be of interest; such as the 0-1 classification loss. Furthermore, it is desirable that the performance of these quantizers not deteriorate once they are deployed into production, as relearning the scheme online is not always possible. In this work, we present a class of algorithms that learn distributed quantization schemes for binary classification tasks. Our method performs well on unseen data, and is faster than previous methods proportional to a quadratic term of the dataset size. It works by regularizing the 0-1 loss with the reconstruction error. We present experiments on synthetic mixture and bivariate Gaussian data and compare training, testing, and generalization errors with a family of benchmark quantization schemes from the literature. Our method is called Regularized Classification-Aware Quantization.
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In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reduc- ing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradi- ent descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.
Neural network quantization enables the deployment of large models on resource-constrained devices. Current post-training quantization methods fall short in terms of accuracy for INT4 (or lower) but provide reasonable accuracy for INT8 (or above). In this work, we study the effect of quantization on the structure of the loss landscape. Additionally, we show that the structure is flat and separable for mild quantization, enabling straightforward post-training quantization methods to achieve good results. We show that with more aggressive quantization, the loss landscape becomes highly non-separable with steep curvature, making the selection of quantization parameters more challenging. Armed with this understanding, we design a method that quantizes the layer parameters jointly, enabling significant accuracy improvement over current post-training quantization methods. Reference implementation is available at https://github.com/ynahshan/nn-quantization-pytorch/tree/master/lapq
Quantization is a technique used in deep neural networks (DNNs) to increase execution performance and hardware efficiency. Uniform post-training quantization (PTQ) methods are common, since they can be implemented efficiently in hardware and do not require extensive hardware resources or a training set. Mapping FP32 models to INT8 using uniform PTQ yields models with negligible accuracy degradation; however, reducing precision below 8 bits with PTQ is challenging, as accuracy degradation becomes noticeable, due to the increase in quantization noise. In this paper, we propose a sparsity-aware quantization (SPARQ) method, in which the unstructured and dynamic activation sparsity is leveraged in different representation granularities. 4-bit quantization, for example, is employed by dynamically examining the bits of 8-bit values and choosing a window of 4 bits, while first skipping zero-value bits. Moreover, instead of quantizing activation-by-activation to 4 bits, we focus on pairs of 8-bit activations and examine whether one of the two is equal to zero. If one is equal to zero, the second can opportunistically use the others 4-bit budget; if both do not equal zero, then each is dynamically quantized to 4 bits, as described. SPARQ achieves minor accuracy degradation, 2x speedup over widely used hardware architectures, and a practical hardware implementation. The code is available at https://github.com/gilshm/sparq.
The Residual Quantization (RQ) framework is revisited where the quantization distortion is being successively reduced in multi-layers. Inspired by the reverse-water-filling paradigm in rate-distortion theory, an efficient regularization on the variances of the codewords is introduced which allows to extend the RQ for very large numbers of layers and also for high dimensional data, without getting over-trained. The proposed Regularized Residual Quantization (RRQ) results in multi-layer dictionaries which are additionally sparse, thanks to the soft-thresholding nature of the regularization when applied to variance-decaying data which can arise from de-correlating transformations applied to correlated data. Furthermore, we also propose a general-purpose pre-processing for natural images which makes them suitable for such quantization. The RRQ framework is first tested on synthetic variance-decaying data to show its efficiency in quantization of high-dimensional data. Next, we use the RRQ in super-resolution of a database of facial images where it is shown that low-resolution facial images from the test set quantized with codebooks trained on high-resolution images from the training set show relevant high-frequency content when reconstructed with those codebooks.
Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to minimize risk due to misclassification under uncertainty in real life. Unlike Bayesian neural nets indirectly infering uncertainty through weight uncertainties, evidential neural networks (ENNs) have been recently proposed to support explicit modeling of the uncertainty of class probabilities. It treats predictions of an NN as subjective opinions and learns the function by collecting the evidence leading to these opinions by a deterministic NN from data. However, an ENN is trained as a black box without explicitly considering different types of inherent data uncertainty, such as vacuity (uncertainty due to a lack of evidence) or dissonance (uncertainty due to conflicting evidence). This paper presents a new approach, called a {em regularized ENN}, that learns an ENN based on regularizations related to different characteristics of inherent data uncertainty. Via the experiments with both synthetic and real-world datasets, we demonstrate that the proposed regularized ENN can better learn of an ENN modeling different types of uncertainty in the class probabilities for classification tasks.
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