GrAMME: Semi-Supervised Learning using Multi-layered Graph Attention Models

Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to succinctly represent all interactions, and hence multi-layered graphs have become popular. Though this leads to richer representations, extending solutions from the single-graph case is not straightforward. Consequently, there is a strong need for novel solutions to solve classical problems, such as node classification, in the multi-layered case. In this paper, we consider the problem of semi-supervised learning with multi-layered graphs. Though deep network embeddings, e.g. DeepWalk, are widely adopted for community discovery, we argue that feature learning with random node attributes, using graph neural networks, can be more effective. To this end, we propose to use attention models for effective feature learning, and develop two novel architectures, GrAMME-SG and GrAMME-Fusion, that exploit the inter-layer dependencies for building multi-layered graph embeddings. Using empirical studies on several benchmark datasets, we evaluate the proposed approaches and demonstrate significant performance improvements in comparison to state-of-the-art network embedding strategies. The results also show that using simple random features is an effective choice, even in cases where explicit node attributes are not available

Multi-Layered Gradient Boosting Decision Trees

Multi-layered representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical representations by stacking several layers of regression GBDTs as its building block. The model can be jointly trained by a variant of target propagation across layers, without the need to derive back-propagation nor differentiability. Experiments and visualizations confirmed the effectiveness of the model in terms of performance and representation learning ability

Nested LSTMs

We propose Nested LSTMs (NLSTM), a novel RNN architecture with multiple levels of memory. Nested LSTMs add depth to LSTMs via nesting as opposed to stacking. The value of a memory cell in an NLSTM is computed by an LSTM cell, which has its own inner memory cell. Specifically, instead of computing the value of the (outer) memory cell as $c^{outer}_t = f_t \odot c_{t-1} + i_t \odot g_t$, NLSTM memory cells use the concatenation $(f_t \odot c_{t-1}, i_t \odot g_t)$ as input to an inner LSTM (or NLSTM) memory cell, and set $c^{outer}_t$ = $h^{inner}_t$. Nested LSTMs outperform both stacked and single-layer LSTMs with similar numbers of parameters in our experiments on various character-level language modeling tasks, and the inner memories of an LSTM learn longer term dependencies compared with the higher-level units of a stacked LSTM.Comment: Accepted at ACML 201

Modular Representation of Layered Neural Networks

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret knowledge from the inference provided by a layered neural network, since its internal representation has many nonlinear and complex parameters embedded in hierarchical layers. Therefore, it becomes important to establish a new methodology by which layered neural networks can be understood. In this paper, we propose a new method for extracting a global and simplified structure from a layered neural network. Based on network analysis, the proposed method detects communities or clusters of units with similar connection patterns. We show its effectiveness by applying it to three use cases. (1) Network decomposition: it can decompose a trained neural network into multiple small independent networks thus dividing the problem and reducing the computation time. (2) Training assessment: the appropriateness of a trained result with a given hyperparameter or randomly chosen initial parameters can be evaluated by using a modularity index. And (3) data analysis: in practical data it reveals the community structure in the input, hidden, and output layers, which serves as a clue for discovering knowledge from a trained neural network

Probabilistic Discriminative Learning with Layered Graphical Models

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close analogy to neural networks (NNs), that is, they have deep hierarchical structures and convolutional or local connections between layers. Equipped with tensorized truncated variational inference, our LGMs can be efficiently trained via backpropagation on mainstream deep learning frameworks such as PyTorch. To deal with continuous valued inputs, we use a simple yet effective soft-clamping strategy for efficient inference. Through extensive experiments on image classification over MNIST and FashionMNIST datasets, we demonstrate that LGMs are capable of achieving competitive results comparable to NNs of similar architectures, while preserving transparent probabilistic modeling

Deep Echo State Network (DeepESN): A Brief Survey

The study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN) model opened the way to an extremely efficient approach for designing deep neural networks for temporal data. At the same time, the study of DeepESNs allowed to shed light on the intrinsic properties of state dynamics developed by hierarchical compositions of recurrent layers, i.e. on the bias of depth in RNNs architectural design. In this paper, we summarize the advancements in the development, analysis and applications of DeepESNs

Convolutional Neural Networks Analyzed via Convolutional Sparse Coding

Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within the wide field of sparse approximation, Convolutional Sparse Coding (CSC) has gained increasing attention in recent years. A theoretical study of this model was recently conducted, establishing it as a reliable and stable alternative to the commonly practiced patch-based processing. Herein, we propose a novel multi-layer model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers. This is shown to be tightly connected to CNN, so much so that the forward pass of the CNN is in fact the thresholding pursuit serving the ML-CSC model. This connection brings a fresh view to CNN, as we are able to attribute to this architecture theoretical claims such as uniqueness of the representations throughout the network, and their stable estimation, all guaranteed under simple local sparsity conditions. Lastly, identifying the weaknesses in the above pursuit scheme, we propose an alternative to the forward pass, which is connected to deconvolutional, recurrent and residual networks, and has better theoretical guarantees

Knowledge Discovery from Layered Neural Networks based on Non-negative Task Decomposition

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achieve input-output mappings with a given data set. In this paper, we propose the non-negative task decomposition method, which applies non-negative matrix factorization to a trained layered neural network. This enables us to decompose the inference mechanism of a trained layered neural network into multiple principal tasks of input-output mapping, and reveal the roles of hidden units in terms of their contribution to each principal task

Limiting Network Size within Finite Bounds for Optimization

Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the literature the VC Dimension has only been used to approximate the generalization error bounds on different Neural Network architectures. VC Dimension has not yet been implicitly or explicitly stated to fix the network size which is important as the wrong configuration could lead to high computation effort in training and leads to over fitting. So there is a need to bound these units so that task can be computed with only sufficient number of parameters. For binary classification tasks shallow networks are used as they have universal approximation property and it is enough to size the hidden layer width for such networks. The paper brings out a theoretical justification on required attribute size and its corresponding hidden layer dimension for a given sample set that gives an optimal binary classification results with minimum training complexity in a single layered feed forward network framework. The paper also establishes proof on the existence of bounds on the width of the hidden layer and its range subjected to certain conditions. Findings in this paper are experimentally analyzed on three different dataset using Mathlab 2018 (b) software

Soft-Deep Boltzmann Machines

We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs over RBMs has not ever been validated in a theoretical fashion. In this paper, we provide both theoretical and empirical evidences that the representational power of DBMs can be actually rather limited in taking advantages of distributed representations. We propose an approximate measure for the representational power of a BM regarding to the efficiency of a distributed representation. With this measure, we show a surprising fact that DBMs can make inefficient use of distributed representations. Based on these observations, we propose an alternative BM architecture, which we dub soft-deep BMs (sDBMs). We show that sDBMs can more efficiently exploit the distributed representations in terms of the measure. Experiments demonstrate that sDBMs outperform several state-of-the-art models, including DBMs, in generative tasks on binarized MNIST and Caltech-101 silhouettes.Comment: Major revision after bug fixe