This paper presents a method to explain how input information is discarded through intermediate layers of a neural network during the forward propagation, in order to quantify and diagnose knowledge representations of pre-trained deep neural networks. We define two types of entropy-based metrics, i.e., the strict information discarding and the reconstruction uncertainty, which measure input information of a specific layer from two perspectives. We develop a method to enable efficient computation of such entropy-based metrics. Our method can be broadly applied to various neural networks and enable comprehensive comparisons between different layers of different networks. Preliminary experiments have shown the effectiveness of our metrics in analyzing benchmark networks and explaining existing deep-learning techniques.
However, previous studies were usually developed based on heuristic assumptions, which hurt their generality and coherency. For example, many visualization methods assumed gradients on features reflected the importance of the feature, which had been disputed by @cite_22 . The LIME @cite_16 and SHAP @cite_22 assumed a linear attribution for DNNs. In comparison, our research aims to develop generic metrics to quantify the input information hidden in different layers and enable comprehensive comparisons of the representation capacity through different layers of different DNNs.
@cite_16 @cite_22
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Understanding the flow of information in Deep Neural Networks (DNNs) is a challenging problem that has gain increasing attention over the last few years. While several methods have been proposed to explain network predictions, there have been only a few attempts to compare them from a theoretical perspective. What is more, no exhaustive empirical comparison has been performed in the past. In this work, we analyze four gradient-based attribution methods and formally prove conditions of equivalence and approximation between them. By reformulating two of these methods, we construct a unified framework which enables a direct comparison, as well as an easier implementation. Finally, we propose a novel evaluation metric, called Sensitivity-n and test the gradient-based attribution methods alongside with a simple perturbation-based attribution method on several datasets in the domains of image and text classification, using various network architectures. Understanding the flow of information in Deep Neural Networks (DNNs) is a challenging problem that has gain increasing attention over the last few years. While several methods have been proposed to explain network predictions, there have been only a few attempts to compare them from a theoretical perspective. What is more, no exhaustive empirical comparison has been performed in the past. In this work we analyze four gradient-based attribution methods and formally prove conditions of equivalence and approximation between them. By reformulating two of these methods, we construct a unified framework which enables a direct comparison, as well as an easier implementation. Finally, we propose a novel evaluation metric, called Sensitivity-n and test the gradient-based attribution methods alongside with a simple perturbation-based attribution method on several datasets in the domains of image and text classification, using various network architectures. Recent advances in Deep convolutional Neural Networks (DNNs) have enabled unprecedentedly accurate computational models of brain representations, and present an exciting opportunity to model diverse cognitive functions. State-of-the-art DNNs achieve human-level performance on object categorisation, but it is unclear how well they capture human behaviour on complex cognitive tasks. Recent reports suggest that DNNs can explain significant variance in one such task, judging object similarity. Here, we extend these findings by replicating them for a rich set of object images, comparing performance across layers within two DNNs of different depths, and examining how the DNNs’ performance compares to that of non-computational “conceptual” models. Human observers performed similarity judgements for a set of 92 images of real-world objects. Representations of the same images were obtained in each of the layers of two DNNs of different depths (8-layer AlexNet and 16-layer VGG-16). To create conceptual models, other human observers generated visual-feature labels (e.g. “eye”) and category labels (e.g. “animal”) for the same image set. Feature labels were divided into parts, colours, textures and contours, while category labels were divided into subordinate, basic and superordinate categories. We fitted models derived from the features, categories, and from each layer of each DNN to the similarity judgements, using representational similarity analysis to evaluate model performance. In both DNNs, similarity within the last layer explains most of the explainable variance in human similarity judgements. The last layer outperforms almost all feature-based models. Late and mid-level layers outperform some but not all feature-based models. Importantly, categorical models predict similarity judgements significantly better than any DNN layer. Our results provide further evidence for commonalities between DNNs and brain representations. Models derived from visual features other than object parts perform relatively poorly, perhaps because DNNs more comprehensively capture the colours, textures and contours which matter to human object perception. However, categorical models outperform DNNs, suggesting that further work may be needed to bring high-level semantic representations in DNNs closer to those extracted by humans. Modern DNNs explain similarity judgements remarkably well considering they were not trained on this task, and are promising models for many aspects of human cognition. Despite the state-of-the-art accuracy of Deep Neural Networks (DNN) in various classification problems, their deployment onto resource constrained edge computing devices remains challenging, due to their large size and complexity. Several recent studies have reported remarkable results in reducing this complexity through quantization of DNN models. However, these studies usually do not consider the change in loss when performing quantization, nor do they take the disparate importance of DNN connections to the accuracy into account. We address these issues in this paper by proposing a new method, called adaptive quantization, which simplifies a trained DNN model by finding a unique, optimal precision for each connection weight such that the increase in loss is minimized. The optimization problem at the core of this method iteratively uses the loss function gradient to determine an error margin for each weight and assign it a precision accordingly. Since this problem uses linear functions, it is computationally cheap and, as we will show, has a closed-form approximate solution. Experiments on MNIST, CIFAR, and SVHN datasets showed that the proposed method can achieve near or better than state-of-the-art reduction in model size with similar error rate. Furthermore, it can achieve compressions close to floating-point model compression methods without loss of accuracy.