Related papers: A Wasserstein Geometric Framework for Hebbian Plas…

Physical transport processes organize through local interactions that redistribute imbalance while preserving conservation. Classical solvers enforce this organization by applying fixed discrete operators on rigid grids. We introduce the…

Rapidly learning from ongoing experiences and remembering past events with a flexible memory system are two core capacities of biological intelligence. While the underlying neural mechanisms are not fully understood, various evidence…

We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the…

Hebbian and anti-Hebbian plasticity are widely observed in the biological brain, yet their theoretical understanding remains limited. In this work, we find that when a learning method is regularized with L2 weight decay, its learning signal…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Biological neural networks continuously adapt and modify themselves in response to experiences throughout their lifetime - a capability largely absent in artificial neural networks. Hebbian plasticity offers a promising path toward rapid…

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and sub-networks. To a first approximation, this memory can be…

Feedback-rich neural architectures can regenerate earlier representations and inject temporal context, making them a natural setting for strictly local synaptic plasticity. Existing literature raises doubt about whether a minimal,…

The free energy principle casts perception as variational inference, but its biological implementation remains underspecified. In particular, the generalized-coordinate formalism should not be read as a literal claim that neurons compute…

A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the…

When an object moves smoothly across a field of view, the identify of the object is unchanged, but the activation pattern of the photoreceptors on the retina changes drastically. One of the major computational roles of our visual system is…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a…

Hebbian synaptic plasticity inevitably leads to interference and forgetting when different, overlapping memory patterns are sequentially stored in the same network. Recent work on artificial neural networks shows that an…

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…

We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by…

The Hellinger-Kantorovich (HK) space provides a natural geometry for nonnegative measures with varying total mass, but its differential-geometric structure is less well understood than that of the closely related Wasserstein space of…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…