Cognitive Substrate Map

A brain-scoped, directed, signed regulatory network of cognition — used to ask which gene up/down-regulations move the brain toward a learning-optimal state at minimal systemic cost.

→ Read the detailed math write-up

The math

1 · Substrate → signed operator

Each edge carries a direction and a sign ($+1$ activation / $-1$ inhibition), oriented so influence flows source → target:

Column-normalize by each regulator's out-strength — the Personalized-PageRank transition. This hub-damps promiscuous regulators and bounds the spectrum, so the propagation below converges:

2 · Propagation to steady state (APPNP)

Perturb a gene with source vector $p$ and solve the fixed point that re-injects the source (weight $\alpha$) and diffuses the rest — the steady state under the 200-node feedback loop:

The $(1-\alpha)^k$ decay damps deep hops (the over-smoothing guard); $x^{*}$ is each node's deviation from baseline.

3 · Scoring — closeness to the target state

Benefit rewards movement toward each target $d_i$ (overshoot flips negative — the inverted-U); cost prices intervention effort + systemic collateral:

4 · Uncertainty band

Sample the uncertain inputs (confidence weights, sign-only magnitudes) $M$ times → a coverage band, not a point. Sobol indices $S_{T_i}$ say which input drives the band.

5 · Optimization

Trace the benefit-vs-cost Pareto front by ε-constraint (exact, since the system is small):

Results

The result

The optimizer is restricted to pushing un-defended upstream drivers — not defended hubs like BDNF (which are moved indirectly, since their many regulators fight a direct push). Under that constraint, CAMK2B is the standout single lever (#1 in 100% of uncertainty draws), with a small optimal set and steep diminishing returns rather than a synergistic stack. All $2^7-1=127$ subsets are searched exhaustively, so the 6-point front is provably optimal within the constraint; the benefit is modest, and it survives a nonlinear cross-check. That is a statement about this graph under this objective — not about a brain. Full write-up →

Substrate

280 nodes in four layers — 70 intervention (knobs), 15 input, 6 readout, 2 trap, 187 bounded expansion — wired by 3,912 directed edges, 2,871 signed (2,253 activating, 618 inhibitory). Fully connected, with a 200-node strongly-connected feedback core.

Controllability

All 280 nodes are reachable from the druggable set. Arbitrary-state control would need 81 independent drivers (~35 druggable) — but you don't need arbitrary control, only control of the scored targets. Formally: $\operatorname{rank}[\,CB, C\hat{W}B, C\hat{W}^2B, \dots] = 72$ of $|S|=78$, so the seven un-defended drivers span 92% of the target space. Dropping the defended hubs from the push set costs just one dimension (92% vs 94% unconstrained) — the constraint is nearly free.

Propagation — verified against the raw edge signs

Perturb one gene $+1$, solve $x^{*}$, check against signs read straight from the edge table (not the model). At $\alpha=0.15$, $\rho(\hat{W})=0.544$: