The Evidence Layer for Scientific AI

 Long Analysis Plan Copied

Straight answer first: none of the supplied evidence records directly test 'cell-type-specific synaptic motifs generating coupled mean-variability dynamics.' What the records do provide are the theoretical and methodological building blocks for that analysis: (1) an exact large-N path-integral framework linking recurrent coupling statistics to covariance (variability) statistics Path-integral covariance statistics in nonlinear RNNs; (2) a DMFT framework in which a tunable learned-structure parameter (gamma) interpolates between random and structured connectivity and controls single-neuron response statistics, validated against macaque M1/PMd data DMFT of learned vs random structure in task-trained RNNs; and (3) a cautionary simulation showing RNN dynamics can reflect state adaptation rather than the intended cognitive construct RNN dynamics vs in-context state adaptation confound. Your project must therefore be built from first principles, and the mean-variability coupling hypothesis is genuinely novel relative to these records.

Proposed computational analysis plan

Stage 1 — Model definition. Define a heterogeneous RNN with two (or more) neuronal classes (e.g., excitatory/inhibitory analogues) whose recurrent couplings carry class-specific motifs: within-class vs cross-class gain, motif correlation structure, and cell-type-specific noise variances D. Use the stochastic dynamics of the path-integral framework: tau dphi_i/dt = -phi_i + W_ij f(phi_j) + xi_i, with W-statistics parameterized per cell type Stochastic RNN dynamics model.

Stage 2 — Analytic core (mean-variability coupling). Derive class-conditional self-consistent equations G0^(c) = D^(c) + lambda^(c)^2 G0^(c) V(G0^(c)) for each cell type c, where the mean input variance G0 simultaneously sets mean firing (via the activation function) and covariance magnitude. Test analytically whether cell-type-specific motifs generate coupled (rather than independent) mean-variability relationships, using the linear special case G0 = D/(1-lambda^2) as an exact sanity check, then power-law and Pade nonlinearities. Validate with Euler-integrated simulations at N in [100, 800], as done previously Numerical validation protocol for covariance theory.

Stage 3 — Structure-disorder interpolation. Add a gamma-like learned-structure parameter per cell type (as in the DMFT task-trained framework) and sweep the motif-strength grid (g values 0.5-2.5, gamma 0.025-1.75) to map how cell-type-specific restructuring reshapes mean-variability coupling, outlier eigenmodes, and single-neuron response non-Gaussianity Gamma-sweep protocol for structure vs disorder. Code from that study (github.com/davidclark1/RNN-Learning-Theory, PyTorch/JAX) is a reusable scaffold.

Stage 4 — Falsification controls. Pre-register falsification criteria adapted from the records: (a) if the predicted G0 self-consistency fails at large N, the motif-to-variability link is wrong; (b) if mean-variability coupling persists after ablating cell-type-specific motifs (shuffled W-statistics), the motifs are not the cause; (c) guard against the in-context-adaptation confound by testing whether dynamics decode latent state variables rather than motif-driven statistics State-adaptation confound control.

Figure: the exact linear solution (blue) diverges as lambda^2 approaches 1; the dotted curve is a BGPT-illustrative simulation with a weak cubic nonlinearity (not sourced data), showing how nonlinearity partially stabilizes the mean-variability coupling — the quantity your motifs will reshape.

Confidence note: the plan rests on strong theory from the path-integral and DMFT records; the specific claim that cell-type-specific motifs generate coupled mean-variability dynamics is untested in the supplied evidence and is the hypothesis your Stage 2-4 analyses must decide. Evidence that would overturn it: motif ablations leaving mean-variability coupling intact, or violation of the G0 self-consistency in large-N simulation.