This week

Neural networks with multiple discrete attractors are a common memory model, previously built under specific connectivity and dynamics assumptions. We analyse local stability of discrete fixed points in a broad class of networks with graded neural activities, and show that all fixed points are stable below a critical load that is distinct from the classical "storage capacity". This critical value depends on the statistics of neural activities in the fixed points as well as the single-neuron activation function. We derive a theory of this stability for the case of dense patterns, expected in the presence of noise, by analysing the bulk and the outliers of the Jacobian spectrum. Our analysis highlights the computational benefits of noisy threshold-linear activation and sparse-like patterns.

Tree-level string theory extends Einstein gravity by an infinite set of massive higher spin particles. From a purely spacetime perspective (if we didn't know about the worldsheet picture) the consistency of string amplitudes would appear truly miraculous. This prompts the question: is string theory the unique framework for a higher spin extension of gravity? We investigate this question by bootstrap methods, focussing on maximal 10D supergravity. We parametrize theory space by the first few EFT coefficients and by the on-shell coupling of the lightest massive state, and impose on these data causality and positivity constraints. While Type II string theory lives strictly inside the allowed region, we uncover a novel extremal solution of the bootstrap problem, which appears to contain a single linear Regge trajectory. We repeat a similar analysis for supergluon scattering.