exp025′s rate gap admits a cheap reading: PING fires less because the I-loop delivers more inhibition. This entry forecloses that reading and identifies what about the I-stream is doing the suppressing: qualitatively (rhythm vs mean), and quantitatively (which temporal precision is required). Scaffolded by ar009 §Leg 1 item 2.
Pure inference on the trained exp025 PING baseline (seed 42, off). For each batch the I-population spike tensor is recorded from a baseline forward pass, then an override tensor replaces it in a second pass via the exp037 hidden-perturbation hook. The E-population experiences only the override I-stream through ; the readout consumes the perturbed E spikes.
Every perturbation only moves spikes in time (or, for Poisson, redraws at the matched count) — none adds or removes them — so the mean per-cell I rate is matched to baseline by construction: exactly for phase-shuffle, and to within ≈ 3% for the jitter families across the range where each result is read. The one exception is cycle-coherent jitter at the largest : a Gaussian block offset with ms displaces part of each burst past the ends of the fixed presentation window, where it is clamped and lost, so the realised I rate falls to 40.5 Hz (24% below the 53.2 Hz baseline). Realised I is therefore plotted on every sweep, and the strict same-mean-inhibition comparison (the compound figure below) is anchored at ms, where realised I is still within 3% of baseline on both arms.
Five perturbation families:
Baseline: no override; trained PING dynamics.
Cycle-coherent jitter: partition the trial into blocks of length (≈ 22.8 ms at the trained operating point from exp041). For each (trial, block), draw a single Gaussian offset and shift every I-spike in that block by . Within-burst cross-cell synchrony is preserved exactly; only the placement of each burst is perturbed. Sweep ms.
Per-I-cell jitter: draw an independent Gaussian offset for every I-spike and shift each spike by its own offset. Destroys within-burst cross-cell synchrony while keeping the mean per-cell rate; the within-burst counterpart of cycle-coherent jitter. Sweep ms.
Phase-shuffle: per-trial permutation of the time axis applied to all I-cells together: . Preserves cross-cell co-firing within a timestep; destroys all phase structure.
Rate-matched Poisson: per-(trial, cell) Bernoulli with . Destroys both temporal and cross-cell structure; tests the variance limit.
Figure 1:Two inference-time perturbations of the trained-PING I-stream, both holding the mean per-cell I rate fixed at ≈ 53.2 Hz, push the E rate in opposite directions, which a mean-inhibition account cannot produce. Both columns use the same jitter magnitude, σ = 14 ms — only the kind of jitter differs. Left column, smear the bursts: per-I-cell jitter (realised I 52.5 Hz) scatters the spikes within each burst, destroying synchrony while leaving the mean untouched; the burst dissolves into a continuous shunt, the E rate falls to zero, and accuracy collapses toward chance (9.9% at the Poisson limit). Right column, move the bursts: cycle-coherent jitter (realised I 51.7 Hz — within 3% of the left column) displaces each gamma burst bodily but keeps its within-burst synchrony; the I-stream opens gaps and the E rate rises from 9.1 Hz at baseline to 35.8 Hz, accuracy holding near 84.9%. Same jitter magnitude, same mean inhibition (both ≈ 53.2 Hz), opposite outcome: what gates the E rate is the timing of inhibition, the rhythm, not its average level. The cycle-coherent rise continues past the full phase-shuffle level to 66.3 Hz by σ = 100 ms (bottom-right sweep), but there the finite trial window truncates the most-displaced bursts and realised I falls 24%, so the strict rate-matched reading is taken at σ = 14 ms; see Methods.
Figure 2:Per-I-cell jitter sweep, three seeds. Each spike receives an independent Gaussian offset; mean per-cell I rate is preserved exactly. E rate (black diamonds, left axis) falls monotonically from baseline (9.1 Hz), already more than halved to 4.3 Hz by ms and essentially zero (0 Hz) by ms, below ms. Accuracy (red squares, right axis) holds at ≈ 89.2% up to ms, then collapses through 83.4% (σ = 1), 65.4% (σ = 2) and 17.7% (σ = 5), bottoming at chance (10.6%) by ms. The grey trace is the realised mean I rate, held flat near 53.2 Hz across the sweep: the E collapse happens under matched inhibition. The asymptote is the rate-matched Poisson regime: E silent, accuracy at chance.Figure 3:Single trial replayed at five per-cell jitter levels. At the I-bursts are crisp vertical bands. At ms the bursts visibly smear into a few-ms-wide cluster and E firing already collapses to the low single digits (per-trial E annotated on each panel; sweep mean 1.7 Hz). At ms the I-stream looks indistinguishable from a continuous low-variance shunt, and E is silenced. Per-cell jitter doesn’t release E; it destroys the bursty structure that gave E its recovery troughs in the first place.
Figure 4:E rate (black diamonds) and accuracy (red squares) vs cycle-coherent jitter , three seeds. As grows the displaced bursts open wider gaps and the E rate climbs from baseline (9.1 Hz) past the full phase-shuffle level (25.9 Hz, the reference with within-burst structure destroyed) to 66.3 Hz by ms, with the sharpest rise near the predicted transition timescale ≈ 22.8 ms; accuracy declines only gently, holding near 81.7%. The grey trace is the realised mean I rate: it holds within 3% of baseline through ms — where the E rate has already risen to 35.8 Hz — then droops to 40.5 Hz (24% below baseline) by ms, as the finite trial window truncates the most-displaced bursts. The strict same-mean-inhibition comparison is read at the smaller , where the rate is matched and the E rise is already unambiguous.Figure 5:Single trial replayed at five jitter levels ( ms; seed 42, MNIST digit 0 sample 0). Per-trial E rate annotated on each panel. The I-bands stay vertical and crisp at every : within-burst synchrony is preserved exactly. What changes is where each burst lands: at larger the bursts are displaced bodily from their phase-locked positions, opening longer gaps in the I-stream that E fires through, and the E rate climbs accordingly.
Toroidal (wrapped) jitter, to extend the rate-matched range and disentangle release from truncation. The strict same-mean-inhibition claim is now anchored at ms, where realised I holds within 3% of baseline on both arms and the E rate has already risen to 35.8 Hz — the qualitative result stands on rate-matched ground. Beyond ms, though, the cycle-coherent E-rate rise and the realised-I droop become confounded: some of the extra E firing is genuine gap-opening, and some is simply less inhibition delivered, because the finite window clamps and loses the most-displaced bursts. Wrapping each block offset modulo the trial length would restore exact spike-count preservation at every and separate the two, at the cost of re-injecting a wrapped burst at the opposite trial edge — a phase artifact of its own, so the wrapped sweep is a robustness check, not a replacement. The prediction: if the wrapped E rate still climbs past the phase-shuffle level (25.9 Hz), the release at large is real; if it flattens there, part of the 66.3 Hz overshoot at ms was the truncation. Either way the anchored rhythm-vs-mean conclusion is unaffected.
