Dynamical stability in biologically plausible attractor neural networks

Uri Cohen examines how stable memories can emerge in recurrent networks without imposing specially engineered dynamics such as a Lyapunov gradient. The analysis concerns discrete fixed points in networks with graded activity and noise. Random matrix methods characterize both the bulk and outlier eigenvalues of the local Jacobians. This yields a stability threshold: either all fixed points are stable or all are unstable, depending on their number. That threshold differs from the usual storage capacity, which counts achievable fixed points irrespective of stability. Relating the stability threshold to measurable pattern statistics and activation functions predicts advantages for sparse-like memories and threshold-linear responses. The talk connects these predictions to hippocampal CA3, a proposed auto-associative memory circuit. An assembled dataset of in-vivo patch-clamp recordings from CA3 pyramidal cells in behaving mice provides preliminary support for the predicted threshold-linear activation.