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This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…

We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle yields a fundamental identification between the inverse…

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson [36], is known to support stationary and travelling bumps of localised…

We develop a new neural network architecture that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

Graph Neural Networks (GNNs) are highly vulnerable to adversarial perturbations in both topology and features, making the learning of robust representations a critical challenge. In this work, we bridge GNNs with control theory to introduce…

Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…

Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…

Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…

This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…

We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative…

We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…