Network Specialization to Explain the Performance of Sparse Neural Networks

Recently it has been shown that sparse neural networks perform better than dense networks with similar number of parameters. In addition, large overparameterized networks have been shown to contain sparse networks which, while trained in isolation, reach or exceed the performance of the large model. However, the methods to explain the success of sparse networks are still lacking. In this work I study the performance of sparse networks using network’s activation regions and patterns, concepts from the neural network expressivity literature. I define network specialization, a novel concept that considers how distinctly a feed forward neural network (FFNN) has learned to processes high level features in the data. I propose Minimal Blanket Hypervolume (MBH) algorithm to measure the specialization of a FFNN. It finds parts of the input space that the network associates with some user-defined high level feature, and compares their hypervolume to the hypervolume of the input space. My hypothesis is that sparse networks specialize more to high level features than dense networks with the same number of hidden network parameters. Network specialization and MBH also contribute to the interpretability of deep neural networks (DNNs). The capability to learn representations on several levels of abstraction is at the core of deep learning, and MBH enables numerical evaluation of how specialized a FFNN is w.r.t. any abstract concept (a high level feature) that can be embodied in an input. MBH can be applied to FFNNs in any problem domain, e.g. visual object recognition, natural language processing, or speech recognition. It also enables comparison between FFNNs with different architectures, since the metric is calculated in the common input space. I test different pruning and initialization scenarios on the MNIST Digits and Fashion datasets. I find that sparse networks approximate more complex functions, exploit redundancy in the data, and specialize to high level features better than dense, fully parameterized networks with the same number of hidden network parameters

MaxCorrMGNN: A Multi-Graph Neural Network Framework for Generalized Multimodal Fusion of Medical Data for Outcome Prediction

With the emergence of multimodal electronic health records, the evidence for an outcome may be captured across multiple modalities ranging from clinical to imaging and genomic data. Predicting outcomes effectively requires fusion frameworks capable of modeling fine-grained and multi-faceted complex interactions between modality features within and across patients. We develop an innovative fusion approach called MaxCorr MGNN that models non-linear modality correlations within and across patients through Hirschfeld-Gebelein-Renyi maximal correlation (MaxCorr) embeddings, resulting in a multi-layered graph that preserves the identities of the modalities and patients. We then design, for the first time, a generalized multi-layered graph neural network (MGNN) for task-informed reasoning in multi-layered graphs, that learns the parameters defining patient-modality graph connectivity and message passing in an end-to-end fashion. We evaluate our model an outcome prediction task on a Tuberculosis (TB) dataset consistently outperforming several state-of-the-art neural, graph-based and traditional fusion techniques.Comment: To appear in ML4MHD workshop at ICML 202

A distributed neural network architecture for dynamic sensor selection with application to bandwidth-constrained body-sensor networks

We propose a dynamic sensor selection approach for deep neural networks (DNNs), which is able to derive an optimal sensor subset selection for each specific input sample instead of a fixed selection for the entire dataset. This dynamic selection is jointly learned with the task model in an end-to-end way, using the Gumbel-Softmax trick to allow the discrete decisions to be learned through standard backpropagation. We then show how we can use this dynamic selection to increase the lifetime of a wireless sensor network (WSN) by imposing constraints on how often each node is allowed to transmit. We further improve performance by including a dynamic spatial filter that makes the task-DNN more robust against the fact that it now needs to be able to handle a multitude of possible node subsets. Finally, we explain how the selection of the optimal channels can be distributed across the different nodes in a WSN. We validate this method on a use case in the context of body-sensor networks, where we use real electroencephalography (EEG) sensor data to emulate an EEG sensor network. We analyze the resulting trade-offs between transmission load and task accuracy

Homological Neural Networks: A Sparse Architecture for Multivariate Complexity

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced network-based information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters

On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations

Counterfactual explanations (CEs) are a powerful means for understanding how decisions made by algorithms can be changed. Researchers have proposed a number of desiderata that CEs should meet to be practically useful, such as requiring minimal effort to enact, or complying with causal models. We consider a further aspect to improve the usability of CEs: robustness to adverse perturbations, which may naturally happen due to unfortunate circumstances. Since CEs typically prescribe a sparse form of intervention (i.e., only a subset of the features should be changed), we study the effect of addressing robustness separately for the features that are recommended to be changed and those that are not. Our definitions are workable in that they can be incorporated as penalty terms in the loss functions that are used for discovering CEs. To experiment with robustness, we create and release code where five data sets (commonly used in the field of fair and explainable machine learning) have been enriched with feature-specific annotations that can be used to sample meaningful perturbations. Our experiments show that CEs are often not robust and, if adverse perturbations take place (even if not worst-case), the intervention they prescribe may require a much larger cost than anticipated, or even become impossible. However, accounting for robustness in the search process, which can be done rather easily, allows discovering robust CEs systematically. Robust CEs make additional intervention to contrast perturbations much less costly than non-robust CEs. We also find that robustness is easier to achieve for the features to change, posing an important point of consideration for the choice of what counterfactual explanation is best for the user. Our code is available at: https://github.com/marcovirgolin/robust-counterfactuals

Generalization and Estimation Error Bounds for Model-based Neural Networks

Model-based neural networks provide unparalleled performance for various tasks, such as sparse coding and compressed sensing problems. Due to the strong connection with the sensing model, these networks are interpretable and inherit prior structure of the problem. In practice, model-based neural networks exhibit higher generalization capability compared to ReLU neural networks. However, this phenomenon was not addressed theoretically. Here, we leverage complexity measures including the global and local Rademacher complexities, in order to provide upper bounds on the generalization and estimation errors of model-based networks. We show that the generalization abilities of model-based networks for sparse recovery outperform those of regular ReLU networks, and derive practical design rules that allow to construct model-based networks with guaranteed high generalization. We demonstrate through a series of experiments that our theoretical insights shed light on a few behaviours experienced in practice, including the fact that ISTA and ADMM networks exhibit higher generalization abilities (especially for small number of training samples), compared to ReLU networks

Identifying Interpretable Visual Features in Artificial and Biological Neural Systems

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A recent hypothesis proposes that features in deep networks may be represented in $\textit{superposition}$, i.e., on non-orthogonal axes by multiple neurons, since the number of possible interpretable features in natural data is generally larger than the number of neurons in a given network. Accordingly, we should be able to find meaningful directions in activation space that are not aligned with individual neurons. Here, we propose (1) an automated method for quantifying visual interpretability that is validated against a large database of human psychophysics judgments of neuron interpretability, and (2) an approach for finding meaningful directions in network activation space. We leverage these methods to discover directions in convolutional neural networks that are more intuitively meaningful than individual neurons, as we confirm and investigate in a series of analyses. Moreover, we apply the same method to three recent datasets of visual neural responses in the brain and find that our conclusions largely transfer to real neural data, suggesting that superposition might be deployed by the brain. This also provides a link with disentanglement and raises fundamental questions about robust, efficient and factorized representations in both artificial and biological neural systems