2026 INCTN + TEX meeting at SISSA

Bayesian theory of task adaptation in low-rank recurrent neural networks

Sep 22, 2026, 3:30 PM

2h 30m

Aula Magna “Paolo Budinich” (SISSA)

Poster Poster session

Speaker

Mr Lars Schutzeichel (Juelich Research Centre, Juelich, Germany - International School of Advanced Studies (SISSA), Trieste, Italy)

Description

Low-rank recurrent networks are a mathematically tractable framework for relating connectivity to activity in biological and artificial neural networks. Such networks produce low-dimensional activity, consistent with brain recordings during cognitive tasks, and despite their simplicity can implement a variety of complex computations. How learning shapes their connectivity to do so, however, remains not fully understood.
Here, we build a theory of trained networks that explains how this structure emerges from the imposed task. To this end, we develop a dynamical mean-field theory (DMFT) of task adaptation in low-rank recurrent networks, giving a Bayesian description of how an ensemble of untrained networks (the prior) becomes an ensemble of trained networks (the posterior) [Fischer et al., 2024; Lauditi et al., 2025; Bauer et al., 2026; Clark et al., 2026]. Previous work has shown that the dynamics of low-rank networks can be described by a set of magnetization-like order parameters [Mastrogiuseppe et al., 2018], which measure how strongly the neurons' activities align with the connectivity vectors. In our theory, we recover this description and the corresponding order parameters as the dominant saddle point of an action. Task adaptation then amounts to adding a loss term to the action, shifting this saddle point from 'task-agnostic' to 'task-adapted'. This displacement is characterized by two fields: one field that drives the solution away from the task-agnostic one, and a second field that measures the discrepancy between the network output and the target. Together, they capture how the weights and the neuronal activity are reshaped by task adaptation.
We validate the theory on a variety of tasks, each requiring different structure in the connectivity. Using the two fields, we predict how the distribution of low-rank weights changes with task adaptation, morphing from initial unstructured Gaussians into non-Gaussian distributions whose shape depends on the task.