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Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
A bump attractor network is a model that implements a competitive neuronal process emerging from a spike pattern related to an input source. Since the bump network could behave in many ways, this paper explores some critical limits of the…
Monte Carlo approaches have recently been proposed to quantify connectivity in neuronal networks. The key problem is to sample from the conditional distribution of a single neuronal spike train, given the activity of the other neurons in…
This work discusses the implementation of Markov Chain Monte Carlo (MCMC) sampling from an arbitrary Gaussian mixture model (GMM) within SRAM. We show a novel architecture of SRAM by embedding it with random number generators (RNGs),…
Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to…
Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in a wide variety of applications including image classification and speech recognition. Inference and learning in these algorithms uses a Markov Chain Monte…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
Mechanisms underlying the emergence of orientation selectivity in the primary visual cortex are highly debated. Here we study the contribution of inhibition-dominated random recurrent networks to orientation selectivity, and more generally…
Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to…
Sampling problems are widely regarded as the task for which quantum computers can most readily provide a quantum advantage. Leveraging this feature, the quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287…
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…
We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. Generative autoencoders are those which are trained to softly enforce a prior on the…
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
We present a geometrically enhanced Markov chain Monte Carlo sampler for networks based on a discrete curvature measure defined on graphs. Specifically, we incorporate the concept of graph Forman curvature into sampling procedures on both…
We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behaviour, we propose that adaption…