arXiv subjects

Albert J. Wakhloo

Publications and source records attributed to Albert J. Wakhloo.

3 recordsLinked to original sources

arXiv2026

Solution of a chaotic neural network at fixed connectivity

We calculate the moments and response functions of a nonlinear random recurrent neural network in the large-$N$ limit using a diagrammatic technique. Our approach does not require averaging over synaptic weights and gives the first nontrivial term in a $1/\sqrt{N}$ expansion of general intensive-order correlation functions, proving a recent conjecture by Shen and Hu as a special case. Our results provide an analytical link between synaptic connectivity, correlations in spontaneous activity, and the response of a network to small perturbations.

cond-mat.dis-nn↗

arXiv2024

Neural population geometry and optimal coding of tasks with shared latent structure

Humans and animals can recognize latent structures in their environment and apply this information to efficiently navigate the world. However, it remains unclear what aspects of neural activity contribute to these computational capabilities. Here, we develop an analytical theory linking the geometry of a neural population's activity to the generalization performance of a linear readout on a set of tasks that depend on a common latent structure. We show that four geometric measures of the activity determine performance across tasks. Using this theory, we find that experimentally observed disentangled representations naturally emerge as an optimal solution to the multi-task learning problem. When data is scarce, these optimal neural codes compress less informative latent variables, and when data is abundant, they expand these variables in the state space. We validate our theory using macaque ventral stream recordings. Our results therefore tie population geometry to multi-task learning.

q-bio.NC↗

arXiv2023

Linear Classification of Neural Manifolds with Correlated Variability

Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.

q-bio.NC↗