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Deep neural networks are complex and opaque. As they enter application in a variety of important and safety critical domains, users seek methods to explain their output predictions. We develop an approach to explaining deep neural networks…

Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…

We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs…

We propose a geometric model-free causality measurebased on multivariate delay embedding that can efficiently detect linear and nonlinear causal interactions between time series with no prior information. We then exploit the proposed causal…

Learning in neural systems arises from synaptic changes that reshape the representations underlying behavior. While low-rank recurrent neural networks (RNNs) have emerged as a powerful framework for linking connectivity to function, a…

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially…

Encoding models are used for predicting brain activity in response to sensory stimuli with the objective of elucidating how sensory information is represented in the brain. Encoding models typically comprise a nonlinear transformation of…

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…

Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level…

Echo State Networks (ESNs) are known for their fast and precise one-shot learning of time series. But they often need good hyper-parameter tuning for best performance. For this good validation is key, but usually, a single validation split…

Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent biological constraints. Mainstream machine learning, by contrast, predominantly builds models from…

Despite substantial progress in deep learning approaches to time-series reconstruction, no existing methods are designed to uncover local activities with minute signal strength due to their negligible contribution to the optimization loss.…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

Explosive synchronization (ES) is nowadays a hot topic of interest in nonlinear science and complex networks. So far, it is conjectured that ES is rooted in the setting of specific microscopic correlation features between the natural…

The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…

We present a formal, mathematical foundation for modeling and reasoning about the behavior of $synchronous$, $stochastic$ $Spiking$ $Neural$ $Networks$ $(SNNs)$, which have been widely used in studies of neural computation. Our approach…

Evolving Cascade Neural Networks (ECNNs) and a new training algorithm capable of selecting informative features are described. The ECNN initially learns with one input node and then evolves by adding new inputs as well as new hidden…

Although conditional branching between possible behavioural states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem we demonstrate…

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…