Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the dynamics of learning and the design of autoencoders, a special type of deep learning architectures that resembles a communication channel. By generalizing the information plane to any cost function, and inspecting the roles and dynamics of different layers using layer-wise information quantities, we emphasize the role that mutual information plays in quantifying learning from data. We further suggest and also experimentally validate, for mean square error training, three fundamental properties regarding the layer-wise flow of information and intrinsic dimensionality of the bottleneck layer, using respectively the data processing inequality and the identification of a bifurcation point in the information plane that is controlled by the given data. Our observations have a direct impact on the optimal design of autoencoders, the design of alternative feedforward training methods, and even in the problem of generalization.
There are some other works concentrating on hidden codes visualization, aiming at giving insights on the function of hidden layers. For examples, the authors in @cite_18 use deconvolutional network (deconvnet) @cite_41 to visualize features in higher layers of convolutional neural networks (CNNs), whereas the authors in @cite_21 suggested understanding CNN features by inverting them to measure how many information is retained in these features from a image reconstruction perspective. Other related works include @cite_9 , @cite_62 , etc., and the trend is to explore the hidden mechanism of different layers using an explanatory graph @cite_14 . However, these methods are typically only applicable for CNNs and fail to unveil the intrinsic properties of DNNs in the training phase.
@cite_18 @cite_62 @cite_14 @cite_41 @cite_9 @cite_21
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We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron. This paper learns a graphical model, namely an explanatory graph, which reveals the knowledge hierarchy hidden inside a pre-trained CNN. Considering that each filter in a conv-layer of a pre-trained CNN usually represents a mixture of object parts, we propose a simple yet efficient method to automatically disentangles different part patterns from each filter, and construct an explanatory graph. In the explanatory graph, each node represents a part pattern, and each edge encodes co-activation relationships and spatial relationships between patterns. More importantly, we learn the explanatory graph for a pre-trained CNN in an unsupervised manner, i.e., without a need of annotating object parts. Experiments show that each graph node consistently represents the same object part through different images. We transfer part patterns in the explanatory graph to the task of part localization, and our method significantly outperforms other approaches. We present a hierarchical model that learns image decompositions via alternating layers of convolutional sparse coding and max pooling. When trained on natural images, the layers of our model capture image information in a variety of forms: low-level edges, mid-level edge junctions, high-level object parts and complete objects. To build our model we rely on a novel inference scheme that ensures each layer reconstructs the input, rather than just the output of the layer directly beneath, as is common with existing hierarchical approaches. This makes it possible to learn multiple layers of representation and we show models with 4 layers, trained on images from the Caltech-101 and 256 datasets. When combined with a standard classifier, features extracted from these models outperform SIFT, as well as representations from other feature learning methods. Recent years have produced great advances in training large, deep neural networks (DNNs), including notable successes in training convolutional neural networks (convnets) to recognize natural images. However, our understanding of how these models work, especially what computations they perform at intermediate layers, has lagged behind. Progress in the field will be further accelerated by the development of better tools for visualizing and interpreting neural nets. We introduce two such tools here. The first is a tool that visualizes the activations produced on each layer of a trained convnet as it processes an image or video (e.g. a live webcam stream). We have found that looking at live activations that change in response to user input helps build valuable intuitions about how convnets work. The second tool enables visualizing features at each layer of a DNN via regularized optimization in image space. Because previous versions of this idea produced less recognizable images, here we introduce several new regularization methods that combine to produce qualitatively clearer, more interpretable visualizations. Both tools are open source and work on a pre-trained convnet with minimal setup. Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we conduct a direct analysis of the visual information contained in representations by asking the following question: given an encoding of an image, to which extent is it possible to reconstruct the image itself? To answer this question we contribute a general framework to invert representations. We show that this method can invert representations such as HOG and SIFT more accurately than recent alternatives while being applicable to CNNs too. We then use this technique to study the inverse of recent state-of-the-art CNN image representations for the first time. Among our findings, we show that several layers in CNNs retain photographically accurate information about the image, with different degrees of geometric and photometric invariance.