Research preprint · Open academic deposit

Rate-level robustness in deterministic spiking networks

When spike-train fidelity overstates the functional fragility actually observed. Under quantisation, individual spikes often diverge — and, on the FlyWire-derived graph, at every scale — and yet firing rates hold. Choosing the wrong level of measurement means concluding a fragility that the network’s behaviour does not show.

Paper: “Rate-Level Robustness in Deterministic Spiking Networks: When Spike-Train Fidelity Overstates Observed Functional Fragility”
Research: Independent · EventCompute
Status: Published · DOI · preprint, not peer-reviewed
Corpus: 18,375 configurations
Max scale: 139,255 neurons · 3.7M edges
Substrate: Q16.16 versus float64
Licence: CC BY 4.0 · DOI 10.5281/zenodo.21750042

Measuring fragility in the right place

To judge whether a quantised network “still works”, its spike trains are usually compared against those of the reference. The criterion is clear-cut: identical, or not.

It is also very pessimistic. A shift of a single time step, on a single spike, on a single neuron, is enough to declare failure — even when the network’s global behaviour is indistinguishable. This work measures three distinct levels of agreement on the same 18,375 configurations, and shows that the choice of level radically changes the conclusion.

Three levels of agreement

Figure 1The same corpus, judged at three levels. Only 83.73% of configurations keep their spikes exact to the time step. But 99.17% keep a rate correlation above 0.99, and 99.76% keep the same final decision. The gap between 83.73% and 99.76% measures how far the strict criterion overstates, on this corpus, the functional fragility observed. The paper gives these values rounded: 83.7%, 99.2% and 99.8%.
source: rate_sweep_summary.json – 18,375 configurations (35 decays × 35 thresholds × 5 seeds × 3 architectures, 5,000 steps each)

83.73%spikes identicalthe strictest criterion

99.17%rate correlation > 0.99population behaviour

99.76%same decisionthe effective output

0.9982mean rate correlationacross the whole corpus

The only valid logical chain

Care is needed not to reverse the reasoning. The only solid implication runs from spikes to rates:

identical spikes ⟹ identical counts ⟹ identical rates

The converse does not hold: identical rates do not imply identical spikes. And decision preservation remains an empirical observation, never a demonstrated consequence of rate preservation.

Scope of the implication

Although strongly correlated on this corpus, the behavioural metrics remain diagnostic indicators and do not, at this stage, constitute a unified guarantee of decision preservation. A rate correlation above 0.99 does not imply that the winning output neuron is the same: the three contracts are not nested as sets. The ordering 83.7% → 99.2% → 99.8% is an empirical fact about the regimes tested, not a law.

Why this hierarchy? Exact identity requires every spike of every neuron at every step to match: a single flip breaks it, hence its link with the minimum margin. The rate is a sum over time: a spike merely shifted by a step (the neuron fires slightly earlier or later, then resynchronises) leaves the count unchanged. Only a lost or added spike moves the rate. The decision adds a second sum, across output neurons, which damps small perturbations further.

What the margin criterion predicts

The margin-to-error ratio, R = m_min / E_accum, is a ranking score: it does not guarantee that spikes are preserved (a closed gate built on it miscertifies 1,898 diverging configurations of this corpus, because it omits the synaptic fan-in term). On the same configurations, I measure what it predicts at each level:

Predictor	Target contract	AUC	Status
Margin criterion R	spikes identical	0.961	ranking score, not a guarantee
Margin criterion R	rate (correlation > 0.99)	0.808	markedly weaker at rate level
1 − CV of margins	rate	0.801	better than chance, not usable as a criterion
Count conservation	rate	0.972	exploratory, post-execution, in-sample diagnostic
Highest a priori predictor found	rate	0.749	an a priori criterion remains an open problem

Reasoning about counts rather than margins exposes an empirical regularity: on this corpus, all 4,009 configurations whose minimum margin exceeds the accumulated error show a rate correlation of 1. This is an observation, not a proved sufficient condition: two of them diverge at spike level and keep their counts only through compensation — the same phenomenon as the 193 configurations whose spike timings differ while counts coincide exactly. The count-conservation diagnostic requires both runs (float64 and Q16.16): it explains the mechanism, it does not select a configuration before running it. It also leaves one failure mode: near saturation, when almost every neuron fires at its maximum, the Pearson correlation becomes ill-conditioned.

What happens at scale

The next question is whether the effect survives the move to scale, or whether it is an artefact of small networks. Four sizes were measured on the FlyWire-derived structural graph, up to the complete reconstruction: 139,255 neurons and 3,732,460 connections.

Figure 2From 1,000 to 139,255 neurons, the rate correlation stays above 0.9993; it decreases slightly with size (by 3.6 × 10⁻⁴ between 1,000 neurons and the complete reconstruction): it remains above 0.999 without being scale-independent. At the same time, spike-train identity is preserved at no scale. And at each scale, a double execution produces an identical fingerprint: the determinism of the implementation is verified by this test up to the complete graph (a fingerprint-equality test, not a proof).
source: fw4_summary.json – four scales, SHA-256 fingerprints verified

See the data

Neurons	Edges	Steps	Rate correlation	Spikes identical	Replay identical
1,000	24,788	5,000	0.999739	no	yes
10,000	505,053	5,000	0.999492	no	yes
50,000	2,121,443	5,000	0.999556	no	yes
139,255	3,732,460	2,700	0.999378	no	yes

On this graph, the weights are synapse counts from the electron-microscopy reconstruction, one to two orders of magnitude weaker than those of the synthetic sweep. The margin criterion flags every neuron as non-robust (no sampled neuron reaches R > 1; at most 0.013), while the rate stays almost untouched: this network lies entirely in the “rate-robust, spike-fragile” quadrant. Calibrated on synthetic sweeps, the criterion therefore appears too conservative for this weight regime. This reading is not extended to mammalian circuits, which are not tested.

The duration confound, declared

Scale constraint

The 139,255-neuron measurement uses 2,700 steps, against 5,000 at the other scales (compute-time ceiling). Averaging over time is precisely what smooths the discrepancies: the cross-scale comparison is therefore descriptive, not duration-controlled, and this confound remains open.

Where the hierarchy strains: a trained network

The hierarchy does not hold unconditionally. On a network trained by gradient descent (SHD, spoken digits, 700 → 256 → 128 → 20, 1,104 neurons, 50 epochs), with the entire datapath in Q16.16 (membrane, synapses, threshold), spike identity is again zero (0 of 2,264 test samples), but the decision no longer follows: only 62.0% of decisions match the float64 reference (1,404 of 2,264), and this figure does not move between Q8, Q12 and Q16.

Agreement with the reference is not accuracy, and the two must be read together: accuracy falls from 77.3% in float64 to 52.74% at Q16.16, a loss of 24.6 points. That is the figure that governs deployability on this benchmark. In this network and protocol, gradient-descent training is associated with margins compressed down to the order of the arithmetic’s resolution. This is an association, not an established cause: one network, one protocol, without the controls (several seeds, several surrogate gradients, quantisation-aware training, untrained or STDP baselines) that would allow a conclusion.

Key point

The rate correlation stays above 0.999 up to 139,255 neurons, while spike identity is preserved at no scale. And the double execution gives the same fingerprint throughout. Declared exception: on a gradient-trained network (SHD), the decision does not follow (62% agreement, −24.6 accuracy points). The useful result is methodological: choosing the wrong level of measurement leads to concluding a fragility that does not affect behaviour. It is a source of error to avoid, not a robustness guarantee to claim.

Scope and limitations

Limitations of the study

No proof and no certificate at the rate level: the regularities observed are empirical and diagnostic. No new theorem is derived.
The count-conservation diagnostic (AUC 0.972) is an in-sample exploratory diagnostic, developed and evaluated on the same grid, and computed after execution. Not validated out of sample.
The margin criterion R is a ranking score (AUC 0.96), not a guarantee that spikes are preserved.
No population inference: the configurations are pseudo-replicated (clustered by architecture and seed).
The entire datapath is in Q16.16, a single format: nothing is extrapolated below the precisions tested.
The SHD counterexample rests on a single training configuration: association, not causation.
The weights used on the FlyWire graph are edge counts derived from reconstruction, not measured biological conductances. RG0 scope: structural graph only, one drive regime; no biological function, no generalisation to living systems.
Determinism (S2) is tested by double execution, not proved.
Replay by double execution was checked with a corrected procedure; the deposited fingerprints are those of this procedure (file fw4_summary.json).
No deployment recommendation. Nothing here measures latency, memory, energy or silicon: conclusions are bounded to simulation.
The duration confound at maximum scale remains open.