State-compression ladder · Note M14 · companion to M13.5
If richer individual neurons don't buy accessible computation, perhaps it lives in the relationships between dynamical units. A preregistered arc of increasingly realistic tests — and where the optimism went.
M13.5 closed on a specific negative: a faithfully compressed neuron, frozen and used as a reservoir element, exposed less useful stable computation than a leaky integrator. Its parting thought was that the fragile thing had been the individual event, t_spike, while the stable, useful quantities looked relational. M14 took that seriously.
The opening result was encouraging. In a coupled oscillator network under constant drive, halving the integration step scrambled the absolute spike times — drift accumulating from 0.03 to 0.10 ms across a run — yet the relational structure barely moved: pairwise phase differences and the synchronization order parameter agreed to ≈0.0005, correlation 0.997. A global timing shift cancels in a difference. It looked like exactly the robust coordinate M13.5 was missing.
The bet: computation that lives in relationships between units — relative phase, synchronization, cluster membership — is both useful and numerically robust where absolute timing is not.
Each more realistic test removed a little more of it. Every stage was preregistered, with a convergence gate that had to pass before any performance number was read.
It is tempting to conclude that temporal dynamical computation is inherently discretization-fragile. That is broader than the experiments support. The defensible statement is narrower, and better:
Under the tested discretized interfaces, computations whose useful representation stayed tied to event timing did not yield a stable advantage — and neither richer local dynamics nor a relational transformation removed that sensitivity.
The two negatives even fail in slightly different places. In M13.5, a continuous spiking substrate → threshold/event assignment → unstable observable and task skill. In M14, an event stream → a continuously perturbed oscillator trajectory → unstable phase and relational representation. Exp-2b showed that locking and averaging are together insufficient under event drive, which strongly implicates continuous input perturbation. But we did not run the isolating control — the same event sequence under analytically exact versus timestep-assigned integration — so the input interface is the best-supported cause, not a proven one.
Which leaves a conclusion much sharper than "neural sensors didn't work":
Dynamical richness is useful only if it creates coordinates that are both task-accessible and robust at the system interface. You can spend gates on ionic state, learned fields, oscillators and synchronization — but if the useful coordinate is mediated through a timing-sensitive interface, downstream cleverness need not recover the expected advantage.
The interface can dominate the substrate.
That is a worthwhile warning for anyone proposing analog, neuromorphic or physical dynamical computing — and it was reached by preregistering every step and publishing the failures rather than the hopes.
One question is deliberately left unresolved rather than rescued. Is the failure characteristic of temporal dynamical computation itself, or specifically of event-mediated interfaces? A frame-defined predictive task — moving digits under clean fixed update boundaries, where temporal evolution is still essential (the system must represent velocity) but event-assignment ambiguity is removed — is the natural test that would separate them.
And the programme's founding intuition — that one physical state through many times is dual to many physical states at one instant — has a crisp next form. Backpropagation is just reverse-mode differentiation through an unrolled graph; time is only one axis to unroll. So the sharp question is not "can we backpropagate through space" (we can) but whether a temporal computation can be transposed into a spatial, relational representation — measured as an accuracy curve over the factorizations 1×64 … 8×8 … 64×1 at fixed effective state. That would turn "how much computation should live in space versus time?" into an engineering curve.
Both are filed as new questions, not continuations. This arc closes with a falsified hypothesis and a sharper one to ask next — which is the better place to stop.
Part of the whitebox / MorphoHDL program. Companion to "When faithful isn't useful" (M13.5). Every stage of M14 was preregistered before running, with a convergence gate ahead of every performance number; the N-MNIST relational bridge was closed by its own pre-committed stop rule after two attempts, with no further rescue.