State-compression ladder · Note M14 · Part V
On raw audio, the space↔time transpose recovers full-recurrence accuracy at a fraction of the cost — and reveals a minimum useful local temporal horizon, below which recurrence still clearly matters.
Part IV showed the transpose winning on sequential MNIST, but a fair critic could still call that a quirk of pixels serialized into time. So we took the winning primitive unchanged — short shared-GRU blocks run in parallel, their states concatenated for a cheap readout — to a signal that is genuinely temporal.
First, spoken digits as log-mel frames. There the story was clean but incomplete: the transpose gave the same accuracy ~30× faster with ~28× lower latency, and the spatial tree lost a third time — but the task was too easy to test the accuracy side, because even full recurrence already reached 0.99.
So the real test is raw waveform: feed the 8 kHz samples one at a time. Now a single sample carries almost no class information, and the model must build features from local temporal structure — periodicity, formants, transients. We split each 0.5 s utterance into contiguous blocks and swept the block length from the whole utterance down to a single sample.
The shape is the result, and it is the sharpest one the programme has produced: full temporal ↓, hybrid ↑, fully spatial ↓.
Local temporal computation is necessary — the fully-spatial extreme collapses to chance. Global temporal recurrence is unnecessary — a hybrid matches full recurrence at a fraction of the training time and latency.
The failing extreme is also a clean control. If the wide readout had been quietly exploiting where in the waveform things happened rather than genuine temporal processing, the one-sample-per-lane arm — which hands the readout all the positions and no dynamics — would have scored well. It scored at chance. So the accuracy in the middle is real temporal computation, done locally.
The knee did not land at an arbitrary computational sweet spot but at a physically interpretable short-time acoustic scale. Tens of milliseconds were enough for the local recurrent blocks to extract useful waveform structure; shrinking the block to only a few milliseconds progressively destroyed classification. So the rule the whole arc has been circling is now concrete:
Use recurrence at the timescale where local structure exists; spatialize beyond it.
That single sweep rules out both trivial readings. It is not "just parallelize everything" — as the block shrinks toward one sample, accuracy collapses to chance. And it is not "the whole signal needs one continuous recurrent state" — a ~32–64 ms block already carries essentially all the useful accuracy, and carrying recurrence across the entire utterance buys nothing over it except a 20–30× slower, gradient-starved training path. There is a minimum useful local temporal horizon, and once you preserve it, long-range recurrent depth is optional.
The honest boundary: this establishes that the transpose generalizes to a real temporal signal at an interpretable timescale. It does not claim STT is a better speech architecture than convolutional, state-space or conformer models — those are the next baselines if this direction is pursued. Accuracies here are modest (~0.8) because the primitive is a plain GRU on raw samples with no learned frontend; the finding is the shape, not the state of the art. These curves are single-seed; a three-seed confirmation of the knee points (16 / 32 / 64 ms) is pending — the stronger claim being not that 32 ms wins but that 32–64 ms forms a stable plateau while 16 ms drops, i.e. a robust timescale boundary rather than a lucky hyperparameter.
But the whole line is now clear, and it inverts the programme's starting assumption:
Richer cell — no payoff. Richer relationships — no payoff. Deep spatial credit — no payoff. But short nonlinear temporal computation, replicated in parallel and composed cheaply — yes, clearly, and it generalizes from pixels to a raw acoustic waveform.
The remaining questions are the ones worth building toward: whether cheap local or direct credit between blocks can replace exact backprop (the path to on-chip learning), and which recurrences are expressive enough for the task while composing associatively, so even the within-block steps admit a parallel scan.
Part of the whitebox / MorphoHDL program. Part V of a series with M13.5 (I), M14 (II), Part III, and Part IV. Free Spoken Digit Dataset, 8 kHz mono, peak-normalized, 0.5 s crop/pad; shared GRU, contiguous blocks, transpose readout; per-arm learning-rate calibration; wall-clock as the reported budget. The horizon comes from real audio, not padding.