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Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…
The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
The coincidence similarity index, based on a combination of the Jaccard and overlap similarity indices, has noticeable properties in comparing and classifying data, including enhanced selectivity and sensitivity, intrinsic normalization,…
We analytically derive the geometrical structure of the weight space in multilayer neural networks (MLN), in terms of the volumes of couplings associated to the internal representations of the training set. Focusing on the parity and…
We consider efficiency in the implementation of deep neural networks. Hardware accelerators are gaining interest as machine learning becomes one of the drivers of high-performance computing. In these accelerators, the directed graph…
Can neural networks systematically capture discrete, compositional task structure despite their continuous, distributed nature? The impressive capabilities of large-scale neural networks suggest that the answer to this question is yes.…
Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random weights. To address this issue, we study the mapping between…
The mental lexicon is a complex cognitive system representing information about the words/concepts that one knows. Decades of psychological experiments have shown that conceptual associations across multiple, interactive cognitive levels…
Single layer feedforward networks with random weights are successful in a variety of classification and regression problems. These networks are known for their non-iterative and fast training algorithms. A major drawback of these networks…
Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
Recent years have been marked with the fast-pace diversification and increasing ubiquity of machine learning applications. Yet, a firm theoretical understanding of the surprising efficiency of neural networks to learn from high-dimensional…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
A Multilayer Network (MN) is a system consisting of several topological levels (i.e., layers) representing the interactions between the system's objects and the related interdependency. Therefore, it may be represented as a set of layers…
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…
This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…
Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…