TL;DR
This work builds, directly from head-direction cell data, recurrent networks that behave as quasicontinuous attractors, and recovers the ingredients of classical ring attractors, namely, Mexican hat interactions and a spontaneously broken symmetry producing bump states.
This work introduces a new class of equivariant recurrent neural networks, where the connectivity is based on group convolution, and reduces such networks to low-rank models using the group Fourier transform.
Analysis of the Lyapunov spectrum and participation-ratio dimension show that motif structure changes the geometry of chaotic activity, reducing entropy production and attractor dimensionality even when the effective spectral edge is held fixed.
Modern Hopfield networks provide a unifying framework for associative memory, transformer attention, diffusion-based generative models, and biological attractor dynamics, linking these systems through a common energy-based dynamics in which states are updated toward weighted combinations of stored patterns. Across thes...
This work developed a task-optimized three-layer recurrent neural network with a place-field-like readout (RNNPF) for path integration and compared it with a variant using a Cartesian-coordinate readout.
We develop a dynamical mean-field theory for nonreciprocal associative networks that store an extensive number of dynamical attractors, from limit cycles to strange attractors. Using a path integral calculation under quenched disorder, we derive self-consistent dynamical mean-field equations for pattern overlaps, autoc...
Recurrent attractor networks are widely thought to form the basis of working memory1-3, but how they can be rapidly switched on and off is unclear4-7. Here we investigate stability and switching in a recurrent circuit of the fly navigation centre8. h∆K and PFG neurons are recurrently connected in a ring structure and e...
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