State-compression ladder · Note M13.5

When faithful isn't useful

A neuron that perfectly reproduces rich biological dynamics is not, for that reason, a better computational primitive. A preregistered negative result — and the deeper question it hands forward.

2026 · whitebox program companion to the M13 paper all stages preregistered

M13 showed that a Hodgkin–Huxley teacher of known dimension can be compactly approximated — a frozen learned vector field plus a one-scalar correction reproduces its spike trains at F1 > 0.9. M13.5 asked the obvious next question, the one the whole program is built around:

If richer local neuron dynamics really are worth their silicon, then a frozen neuron used as a reservoir element should expose more useful temporal computation, per unit hardware, than a far simpler cell.

It does not. Under a preregistered common-clock protocol, the deployed M13 primitive was less useful than the simple controls — and the way it failed is more instructive than a win would have been.

01The measurement, and the failures it caught

Every arm was a frozen cell in one shared recurrent reservoir, driven through an identical affine input path, read out by a single trained linear decoder. The discipline was strict: preregister each step, publish the failures rather than patch them, and never tune the harness until a spiking arm "looked good."

That discipline did its job. A passive information-capacity probe was abandoned when qualification showed it could not be made step-halving stable for a stiff spiking substrate — the spike-timing that carries the nonlinearity is exactly what a common sampling clock scrambles. A task-based reframing recovered far more stability, but the canonical M13 arm still missed the preregistered per-seed convergence bar. So the decisive test was made deliberately fair: select each arm's operating point by validation skill, at equal budget, and require a minimum useful skill before any comparison.

02The result

At its best equal-budget operating point, across the whole grid, the M13 cell reached only about half the memory skill of the controls — and never cleared the minimum-skill threshold at all. There was not enough useful computation to even proceed to the hardware-cost comparison.

min-skill gate · R²=0.20 0.224 trace bank 0.227 LIF 0.110 M13-kc1
Delayed-recall skill (held-out R², short delay) at each arm's skill-selected, equal-budget operating point. The two simple controls clear the preregistered minimum-skill line; the deployed M13 primitive reaches half their skill and falls below it. Parity (the nonlinear task) sat at chance for M13 as well.

03What it actually means

The headline is not "rich neurons lost." It is more specific, and more useful:

  1. Fidelity is not utility. M13 is excellent at what it was trained for — turning input current into HH-like dynamics. Being frozen and asked to expose features to a cheap decoder is a different demand, and it met it worse than a leaky integrator.
  2. More state is not more accessible state. The decoder only ever sees one membrane scalar. Hidden gating variables can do real internal work without producing coordinates a simple readout can use.
  3. Rich dynamics have a shape. HH's richness is tuned for spike initiation, refractoriness, ionic recovery — not for arbitrary delayed recall or parity. M13 faithfully inherited that shape, useful basis and all its irrelevance.
  4. The simplest memory did its job. A boring exponential trace, c ← a·c + b·u, was already a good coordinate for the memory task. No threshold, no gating — just a well-placed timescale.
  5. LIF did well for the same reason: leak + threshold + reset is a cheap, generic basis — memory plus one nonlinearity — and on this evidence a better one than HH-shaped dynamics.
  6. So the founding ratio does not rise. If LIF delivers equal-or-better useful computation while being dramatically cheaper, added neuron complexity is not justified by this measurement.

Substrate complexity is not fungible computational capacity. What matters is whether the dynamics expose useful, robust coordinates to the rest of the system.

04The second result — robustness, for free

Independently of the hardware question, the arc produced a finding worth keeping. At the microscopic level the spike time t_spike is wildly sensitive to numerical refinement. But decoded into a task, the score became 10–40× more stable. Push further — to genuinely relational observables — and the sensitivity nearly vanishes.

0.031 0.102 ms absolute spike time — drifts & accumulates ≈0.0005 · r=0.997 relational (phase / sync) — invariant
Coupled HH network under a halved integration step. Absolute spike-timing disagreement grows across the run; the Kuramoto synchronization order parameter and pairwise phase differences barely move. A global timing shift cancels in a difference. (M14 v0 diagnostic.)

For hardware this matters: real silicon has jitter, mismatch, noise, finite timing resolution. You may not need reproducible spikes if the collective variable is stable.

05The ledger

+P1. The compressed M13 field faithfully preserves the spike-event geometry — which falsifies the hope that compression would regularize away that sensitivity. banked
+P2. Task-level decoding suppresses event-timing sensitivity by 1–2 orders of magnitude — a real, hardware-relevant robustness. banked
+Method. Event-faithful stiff spikers cannot be ranked by passive common-clock capacity probes; a fair, skill-gated task test is needed even to ask the question. banked
Hypothesis. "Richer local dynamics buy more computation per hardware cost" — not supported under this measurement. No claim made. closed

None of this contradicts the M13 paper: M13 was validated as a trained, closed-loop corrector. The negative is precise — as a frozen, passive reservoir cell under a common clock, it does not out-compute a leaky integrator at equal budget.

06Where it points — M14

Every failure in this arc had the same shape: the fragile thing was the individual event; the stable, useful things were relational. So the next question moves the computational object off the single cell and into the relationships between cells — relative timing, phase, synchronization, cluster membership — the natural territory of oscillatory / ONN computing, and quantities the M14 v0 diagnostic above already shows are numerically robust.

The thing worth paying hardware for may not be more state. It may be better coordinates. M13's were biologically meaningful; the trace bank's were temporally useful; M14 asks whether relative phase and synchronization are better still.


Part of the whitebox / MorphoHDL program. Every stage of M13.5 was preregistered before running and its failures recorded in full; the passive-IPC halt, the two-operating-point amendment, and the final skill-gated design were each frozen under external review before execution. Companion to the M13 state-compression paper.