Balanced Networks, Chaos, and Input-Driven Dynamics
Stub. Balanced excitation/inhibition networks as a biologically-motivated regime of random recurrent networks; the onset of chaos in such networks once coupling strength crosses a critical point (and why it looks like irregular, seemingly-random single-neuron activity); the reliability of a chaotic network's response to repeated input; and how a strong enough input can suppress intrinsic chaos.
Corresponds to the second half of the “High-dimensional and random neural networks” unit (weeks 7–10) — no lecture dates posted yet; update once lectures are posted. Balanced networks (strong excitation and strong inhibition nearly canceling on average) are the standard model for why cortical activity looks irregular rather than synchronized despite dense connectivity. Applying the dynamic-mean-field machinery of the previous note to such a network reveals a sharp transition: below a critical coupling strength the network settles to a fixed point, and above it the dynamics become chaotic (in the same sense as a low-dimensional chaotic flow, just realized by thousands of coupled neurons instead of three coupled variables) — which is one explanation for why single-neuron activity in a deterministic network can look statistically indistinguishable from noise. Reliability asks whether a chaotic network nonetheless produces the same response to the same repeated input (it generally doesn’t, without help), and input-driven dynamics covers how a strong enough external input can suppress the network’s intrinsic chaos, restoring reliable, input-locked responses.
Outline (TODO — flesh out each)
- Balanced excitation/inhibition networks
- The onset of chaos in random recurrent networks
- Reliability of chaotic network responses
- Input-driven suppression of chaos