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Register a new userNorm-based generalisation bounds for multi-class convolutional neural networks
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We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the $L^2$-norm of the weight matrices, where previous bounds exhibit at least a square-root dependence on the number of classes. (2) We adapt the classic Rademacher analysis of DNNs to incorporate weight sharing -- a task of fundamental theoretical importance which was previously attempted only under very restrictive assumptions. In our results, each convolutional filter contributes only once to the bound, regardless of how many times it is applied. Further improvements exploiting pooling and sparse connections are provided. The presented bounds scale as the norms of the parameter matrices, rather than the number of parameters. In particular, contrary to bounds based on parameter counting, they are asymptotically tight (up to log factors) when the weights approach initialisation, making them suitable as a basic ingredient in bounds sensitive to the optimisation procedure. We also show how to adapt the recent technique of loss function augmentation to our situation to replace spectral norms by empirical analogues whilst maintaining the advantages of our approach.
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Discrete event sequences are ubiquitous, such as an ordered event series of process interactions in Information and Communication Technology systems. Recent years have witnessed increasing efforts in detecting anomalies with discrete-event sequences. However, it still remains an extremely difficult task due to several intrinsic challenges including data imbalance issues, the discrete property of the events, and sequential nature of the data. To address these challenges, in this paper, we propose OC4Seq, a multi-scale one-class recurrent neural network for detecting anomalies in discrete event sequences. Specifically, OC4Seq integrates the anomaly detection objective with recurrent neural networks (RNNs) to embed the discrete event sequences into latent spaces, where anomalies can be easily detected. In addition, given that an anomalous sequence could be caused by either individual events, subsequences of events, or the whole sequence, we design a multi-scale RNN framework to capture different levels of sequential patterns simultaneously. Experimental results on three benchmark datasets show that OC4Seq consistently outperforms various representative baselines by a large margin. Moreover, through both quantitative and qualitative analysis, the importance of capturing multi-scale sequential patterns for event anomaly detection is verified.
Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing similar sparse enforcing penalties at different representation layers in a symbiotic relation between synthesis and analysis sparse priors. We explore different iterative methods to solve this new problem in practice, and we propose a new Multi-Layer Iterative Soft Thresholding Algorithm (ML-ISTA), as well as a fast version (ML-FISTA). We show that these nested first order algorithms converge, in the sense that the function value of near-fixed points can get arbitrarily close to the solution of the original problem. We further show how these algorithms effectively implement particular recurrent convolutional neural networks (CNNs) that generalize feed-forward ones without introducing any parameters. We present and analyze different architectures resulting unfolding the iterations of the proposed pursuit algorithms, including a new Learned ML-ISTA, providing a principled way to construct deep recurrent CNNs. Unlike other similar constructions, these architectures unfold a global pursuit holistically for the entire network. We demonstrate the emerging constructions in a supervised learning setting, consistently improving the performance of classical CNNs while maintaining the number of parameters constant.
Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCN operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the Pubmed dataset.
We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.
Artificial neural networks (ANNs) are commonly labelled as black-boxes, lacking interpretability. This hinders human understanding of ANNs behaviors. A need exists to generate a meaningful sequential logic for the production of a specific output. Decision trees exhibit better interpretability and expressive power due to their representation language and the existence of efficient algorithms to generate rules. Growing a decision tree based on the available data could produce larger than necessary trees or trees that do not generalise well. In this paper, we introduce two novel multivariate decision tree (MDT) algorithms for rule extraction from an ANN: an Exact-Convertible Decision Tree (EC-DT) and an Extended C-Net algorithm to transform a neural network with Rectified Linear Unit activation functions into a representative tree which can be used to extract multivariate rules for reasoning. While the EC-DT translates the ANN in a layer-wise manner to represent exactly the decision boundaries implicitlylearned by the hidden layers of the network, the Extended C-Net inherits the decompositional approach from EC-DT and combines with a C5 tree learning algorithm to construct the decision rules. The results suggest that while EC-DT is superior in preserving the structure and the accuracy of ANN, Extended C-Net generates the most compact and highly effective trees from ANN. Both proposed MDT algorithms generate rules including combinations of multiple attributes for precise interpretation of decision-making processes.
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