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Brains have evolved diverse neurons with varying morphologies and dynamics that impact temporal information processing. In contrast, most neural network models use homogeneous units that vary only in spatial parameters (weights and biases).…
A central challenge in the computational modeling of neural dynamics is the trade-off between accuracy and simplicity. At the level of individual neurons, nonlinear dynamics are both experimentally established and essential for neuronal…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
Spectral networks derived from multivariate time series data arise in many domains, from brain science to Earth science. Often, it is of interest to study how these networks change under different conditions. For instance, to better…
Comprehending the interplay between spatial and temporal characteristics of neural dynamics can contribute to our understanding of information processing in the human brain. Graph neural networks (GNNs) provide a new possibility to…
Parameter-space and function-space provide two different duality frames in which to study neural networks. We demonstrate that symmetries of network densities may be determined via dual computations of network correlation functions, even…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
Feature discrimination is a crucial aspect of neural network design, as it directly impacts the network's ability to distinguish between classes and generalize across diverse datasets. The accomplishment of achieving high-quality feature…
We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…
Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries -- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode…
Learning in neural networks critically hinges on the intricate geometry of the loss landscape associated with a given task. Traditionally, most research has focused on finding specific weight configurations that minimize the loss. In this…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
Deep 'Analog Artificial Neural Networks' (ANNs) perform complex classification problems with remarkably high accuracy. However, they rely on humongous amount of power to perform the calculations, veiling the accuracy benefits. The…
Datasets often contain input dimensions that are unnecessary to predict the output label, e.g. background in object recognition, which lead to more trainable parameters. Deep Neural Networks (DNNs) are robust to increasing the number of…
Spiking Neural Networks (SNN) are more closely related to brain-like computation and inspire hardware implementation. This is enabled by small networks that give high performance on standard classification problems. In literature, typical…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…
It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort…
Understanding information processing in the brain requires the ability to determine the functional connectivity between the different regions of the brain. We present a method using transfer entropy to extract this flow of information…