Related papers: A Wasserstein Geometric Framework for Hebbian Plas…
An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…
Robust perception in brains is often attributed to high-dimensional population activity together with local plasticity mechanisms that reinforce recurring structure. In contrast, most modern image recognition systems are trained by error…
In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
Hebbian plasticity in winner-take-all (WTA) networks is highly attractive for neuromorphic on-chip learning, owing to its efficient, local, unsupervised, and on-line nature. Moreover, its biological plausibility may help overcome important…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of $f$-divergences. Wasserstein-1 proximal operators regularize…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…
Synaptic plasticity is widely accepted to be the mechanism behind learning in the brain's neural networks. A central question is how synapses, with access to only local information about the network, can still organize collectively and…
A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation,…
We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…
Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. While existing synaptic plasticity models reproduce some of the observed receptive-field properties, a major obstacle is the…
Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…
This study aims to better understand the functional geometry of the motor cortex, starting from different sources of experimental evidence. Recent studies have proved that cells of the primary motor cortex (M1) are sensitive to short hand…
Artificial neural networks have successfully tackled a large variety of problems by training extremely deep networks via back-propagation. A direct application of back-propagation to spiking neural networks contains biologically implausible…
Image inpainting is a restoration method that reconstructs missing image parts. However, a carefully selected mask of known pixels that yield a high quality inpainting can also act as a sparse image representation. This challenging spatial…
The Wasserstein barycenter extends the Euclidean mean to the space of probability measures by minimizing the weighted sum of squared 2-Wasserstein distances. We develop a free-support algorithm for computing Wasserstein barycenters that…
Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and explore a new objective function,…