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Register a new userLearning Structures for Deep Neural Networks
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Jinhui Yuan
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper, we focus on the unsupervised setting for structure learning of deep neural networks and propose to adopt the efficient coding principle, rooted in information theory and developed in computational neuroscience, to guide the procedure of structure learning without label information. This principle suggests that a good network structure should maximize the mutual information between inputs and outputs, or equivalently maximize the entropy of outputs under mild assumptions. We further establish connections between this principle and the theory of Bayesian optimal classification, and empirically verify that larger entropy of the outputs of a deep neural network indeed corresponds to a better classification accuracy. Then as an implementation of the principle, we show that sparse coding can effectively maximize the entropy of the output signals, and accordingly design an algorithm based on global group sparse coding to automatically learn the inter-layer connection and determine the depth of a neural network. Our experiments on a public image classification dataset demonstrate that using the structure learned from scratch by our proposed algorithm, one can achieve a classification accuracy comparable to the best expert-designed structure (i.e., convolutional neural networks (CNN)). In addition, our proposed algorithm successfully discovers the local connectivity (corresponding to local receptive fields in CNN) and invariance structure (corresponding to pulling in CNN), as well as achieves a good tradeoff between marginal performance gain and network depth.
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Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
Graph neural networks (GNNs) integrate deep architectures and topological structure modeling in an effective way. However, the performance of existing GNNs would decrease significantly when they stack many layers, because of the over-smoothing issue. Node embeddings tend to converge to similar vectors when GNNs keep recursively aggregating the representations of neighbors. To enable deep GNNs, several methods have been explored recently. But they are developed from either techniques in convolutional neural networks or heuristic strategies. There is no generalizable and theoretical principle to guide the design of deep GNNs. To this end, we analyze the bottleneck of deep GNNs by leveraging the Dirichlet energy of node embeddings, and propose a generalizable principle to guide the training of deep GNNs. Based on it, a novel deep GNN framework -- EGNN is designed. It could provide lower and upper constraints in terms of Dirichlet energy at each layer to avoid over-smoothing. Experimental results demonstrate that EGNN achieves state-of-the-art performance by using deep layers.
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $mathcal{M}$ using principal bundles with structure group $K$ and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces $mathcal{M}=G/K$, which are instead equivariant with respect to the global symmetry $G$ on $mathcal{M}$. Group equivariant layers can be interpreted as intertwiners between induced representations of $G$, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case $mathcal{M}=S^2=mathrm{SO}(3)/mathrm{SO}(2)$. Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch-Gordan coefficients for $G=mathrm{SO}(3)$, illustrating the power of representation theory for deep learning.
Training deep neural models in the presence of corrupted supervision is challenging as the corrupted data points may significantly impact the generalization performance. To alleviate this problem, we present an efficient robust algorithm that achieves strong guarantees without any assumption on the type of corruption and provides a unified framework for both classification and regression problems. Unlike many existing approaches that quantify the quality of the data points (e.g., based on their individual loss values), and filter them accordingly, the proposed algorithm focuses on controlling the collective impact of data points on the average gradient. Even when a corrupted data point failed to be excluded by our algorithm, the data point will have a very limited impact on the overall loss, as compared with state-of-the-art filtering methods based on loss values. Extensive experiments on multiple benchmark datasets have demonstrated the robustness of our algorithm under different types of corruption.
Todays deep learning models are primarily trained on CPUs and GPUs. Although these models tend to have low error, they consume high power and utilize large amount of memory owing to double precision floating point learning parameters. Beyond the Moores law, a significant portion of deep learning tasks would run on edge computing systems, which will form an indispensable part of the entire computation fabric. Subsequently, training deep learning models for such systems will have to be tailored and adopted to generate models that have the following desirable characteristics: low error, low memory, and low power. We believe that deep neural networks (DNNs), where learning parameters are constrained to have a set of finite discrete values, running on neuromorphic computing systems would be instrumental for intelligent edge computing systems having these desirable characteristics. To this extent, we propose the Combinatorial Neural Network Training Algorithm (CoNNTrA), that leverages a coordinate gradient descent-based approach for training deep learning models with finite discrete learning parameters. Next, we elaborate on the theoretical underpinnings and evaluate the computational complexity of CoNNTrA. As a proof of concept, we use CoNNTrA to train deep learning models with ternary learning parameters on the MNIST, Iris and ImageNet data sets and compare their performance to the same models trained using Backpropagation. We use following performance metrics for the comparison: (i) Training error; (ii) Validation error; (iii) Memory usage; and (iv) Training time. Our results indicate that CoNNTrA models use 32x less memory and have errors at par with the Backpropagation models.
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