We investigate the problem of the robustness of a trained neural network to the perturbation of its input values. More specifically, we examine the interplay between the accuracy of the network, as measured by the mean squared error, and robustness. Accordingly, we present a robustness measure, which, with high probability, suggests an upper bound on the mean squared error of the network, with respect to an input data set, for a given perturbation of the input values of the network. The measure we propose is both simple and efficient to compute, treating the neural network as a black box. We provide experimental results on several real-world data sets showing the efficacy of the proposed method. We also introduce the concept of robustness curves, which allows us to further analyse robustness within and between data sets.
Continuous attractor neural networks (CANNs) are the canonical computational framework for how the brain encodes continuous variables such as spatial position, head direction, and movement direction, and explain the activity of hippocampal place cells, entorhinal grid cells, and…
Oscillatory neural networks (ONNs) have emerged as a promising neuromorphic architecture, leveraging coupled dynamical systems to perform computation and represent information through phase relationships. Their interactions can be designed to support intrinsic energy-minimizing d…
Deploying spiking neural networks (SNNs) on neuromorphic hardware demands aggressive synaptic pruning while preserving temporal computation integrity. Existing strategies either neglect neuronal criticality or rely on convex relaxations of the inherently combinatorial pruning pro…
Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such l…
The flatness hypothesis suggests that flatness of the loss landscape, as measured by the eigenvalues of the loss Hessian, correlates with better neural network generalization. While various algorithms reduce these eigenvalues, most focus on procedural design, leaving it unclear h…
In-context learning (ICL) operates via implicit gradient descent embedded in the forward pass of modern AI architectures -- Transformers, Mamba, state-space models, and MLPs. Capturing this capability in biologically plausible Spiking Neural Networks (SNNs) has remained an open c…