042 — Perturbations: gamma gates rates not just mean inhibition

Abstract

nb025’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.

Methods

Pure inference on the trained nb025 PING baseline (seed 42, $\theta_u =$ off). For each batch the I-population spike tensor $\mathbf{s}^I_\text{base} \in \{0,1\}^{T \times B \times N_I}$ is recorded from a baseline forward pass, then an override tensor replaces it in a second pass via the nb037 hidden-perturbation hook. The E-population experiences only the override I-stream through $W^{IE}$; the readout consumes the perturbed E spikes. Mean per-cell I rate is matched to the baseline to four decimals across every perturbation.

Four perturbation families:

1. Baseline — no override; trained PING dynamics.
2. Cycle-coherent jitter — partition the trial into blocks of length $1/f_\gamma$ ($\approx 28$ ms at the trained operating point from nb041). For each (trial, block), draw a single Gaussian offset $\Delta \sim \mathcal{N}(0, \sigma^2)$ and shift every I-spike in that block by $\Delta$. Within-burst cross-cell synchrony preserved exactly; only the placement of each burst is perturbed. Sweep $\sigma \in \{0, 1, 3, 7, 14, 21, 28, 42, 60, 100\}$ ms.
3. Phase-shuffle — per-trial permutation $\pi_b$ of the time axis applied to all I-cells together: $\mathbf{s}^I_\text{shuf}[t, b, n] = \mathbf{s}^I_\text{base}[\pi_b(t), b, n]$. Preserves cross-cell co-firing within a timestep; destroys all phase structure.
4. Rate-matched Poisson — per-(trial, cell) Bernoulli with $p = \text{count}_{b,n} / T$. Destroys both temporal and cross-cell structure; tests the $g_i$ variance limit.

Test split from nb025 at medium tier (400 samples, $T = 200$ ms, $\Delta t = 0.1$ ms, batch 64).

Results

The argument is built in two stages, each identifying a separate architectural variable that holds the rate floor. (1) Cycle-coherent jitter sweeps the burst placement axis and finds the operative timescale is $1/f_\gamma$. (2) Per-I-cell jitter sweeps the within-burst synchrony axis and finds destroying synchrony silences E (rather than releasing it), with a much sharper sub-millisecond transition. Each sweep absorbs the corresponding categorical endpoint: full phase-shuffle is the $\sigma \to \infty$ limit of cycle-coherent jitter; rate-matched Poisson is the $\sigma \to \infty$ limit of per-cell jitter.

1. Cycle-coherent jitter — the sweep identifies the operative timescale

Take the trained PING network and apply cycle-coherent jitter to the I-stream at inference: partition the trial into blocks of one gamma cycle, draw a single Gaussian offset $\Delta \sim \mathcal{N}(0, \sigma^2)$ per block, and shift every I-spike in that block by $\Delta$. Within-burst synchrony is preserved exactly — bursts move bodily, they do not smear — and the mean I rate is unchanged. At $\sigma = 0$ this is the baseline; as $\sigma$ grows, bursts are displaced from their phase-locked slots until their placement is decoupled from the gamma cycle. If the operative variable is temporal phase relative to the gamma cycle, the relevant timescale is the cycle period $1/f_\gamma$. At the trained operating point ($\tau_\text{GABA} = 9$ ms), nb041 gives $f_\gamma \approx 36$ Hz, predicting the transition at $\sigma \approx 28$ ms.

Figure 1. Cycle-coherent jitter sweep — E rate vs σ

Figure 2. Single-trial rasters across the jitter sweep

The curve matches the prediction. The rate is flat for $\sigma \le 1$ ms ($\approx 8$ Hz, baseline). The transition is centred between $\sigma = 7$ ms and $\sigma = 28$ ms, crossing the phase-shuffle ceiling ($\approx 29$ Hz) between $\sigma = 14$ and $\sigma = 21$ ms — just below the predicted inflection. At $\sigma = 100$ ms the rate has reached $\approx 49$ Hz, above the phase-shuffle level because cycle-coherent jitter at very large $\sigma$ opens gaps in the I-stream wide enough for E to fire densely with no inhibition at all. Accuracy holds at 79–86% throughout — the rate release is not paid in classification.

What this gets us, beyond the binary “rhythm matters”:

1. Identifies the operative timescale. If a different process — refractory dynamics ($\sim 3$ ms), membrane time constant ($\sim 20$ ms), AMPA decay ($\sim 2$ ms) — were the operative clock, the inflection would be elsewhere. It is at $1/f_\gamma$.
2. The dependence is graded, not knife-edge. The I-loop tolerates sub-cycle jitter and degrades smoothly past it.
3. Full phase-shuffle is the $\sigma \to \infty$ asymptote of the jitter sweep, modulo within-burst structure (which is why the $\sigma = 100$ ms jitter rate slightly exceeds the phase-shuffle ceiling line — at very large $\sigma$ cycle-coherent jitter opens gaps in the I-stream wide enough for E to fire densely with no inhibition at all).
4. The transition timescale is a quantitative prediction. $1/f_\gamma$ is set by nb041’s law. The same architecture trained at a different $\tau_\text{GABA}$ would give a different $f_\gamma$, and the jitter inflection should track it accordingly.

2. Per-I-cell jitter — within-burst synchrony is a separate axis

The cycle-coherent sweep moves bursts as whole units, preserving within-burst synchrony exactly. The complementary perturbation is per-spike (per-I-cell) jitter: draw an independent Gaussian offset $\Delta_s \sim \mathcal{N}(0, \sigma^2)$ for every I-spike. Mean per-cell I rate is preserved exactly, burst placement is preserved on average, but the burst itself smears across a window of width ≈ $\sigma$. This tests whether the sharpness of each inhibitory pulse matters, separately from where it lands.

Prediction: if synchrony also matters, the transition should be at $\sigma \approx \tau_\text{GABA} \approx 9$ ms — the smearing width at which the integrated $g_i$ profile starts looking continuous, the same way a rate-matched Poisson I-stream keeps E silent because $g_i$ never drops low enough for $V$ to recover.

Figure 3. Per-I-cell jitter sweep — E rate and accuracy vs σ

Figure 4. Per-I-cell jitter rasters — bursts smearing into a continuous shunt

The clean reading: the two jitter regimes test two different things, and the rate floor depends on both.

• Burst placement (cycle-coherent jitter): bursts must land in phase with E activity, with precision ≈ $1/f_\gamma$. Destroying placement releases E toward COBA territory.
• Burst sharpness (per-cell jitter): bursts must be sharp enough that $g_i$ has clear troughs between them, with smear width $\ll \tau_\text{GABA}$. Destroying sharpness silences E because $g_i$ never drops low enough.

Discussion

The rate floor is held by two independent properties of the I-stream, each tied to a separate transition timescale:

• Burst placement on the gamma cycle, with precision $\sigma \approx 1/f_\gamma \approx 28$ ms. Destroying placement releases E toward COBA territory (cycle-coherent jitter sweep; full phase-shuffle is the $\sigma \to \infty$ asymptote).
• Within-burst synchrony / burst sharpness, with precision $\sigma \ll \tau_\text{GABA} \approx 9$ ms — in practice the transition is at $\sigma \approx 0.5$ ms. Destroying sharpness silences E because $g_i$ becomes a continuous shunt with no recovery troughs (per-I-cell jitter sweep; rate-matched Poisson is the $\sigma \to \infty$ asymptote).

Mean inhibition is not the operative variable along either axis. Cycle-coherent jitter at $\sigma = 100$ ms releases E to ≈ 49 Hz; per-cell jitter at $\sigma = 50$ ms silences E entirely — at identical mean I rates. The “rhythm matters” claim resolves into two more precise claims: bursts must land on phase, and bursts must be sharp.

This integrates with nb041 in a clean way. nb041 retrains PING at different $\tau_\text{GABA}$ and finds $r_E = a + p \cdot f_\gamma$. nb042 (jitter sweep) is the inference-time analogue: keep the trained network, degrade the temporal precision of its I-stream, and watch the rate rise. The transition timescale $1/f_\gamma$ is set by the same architectural variable that sets the slope of the affine law. Two perturbations through different doors give the same answer: the gamma cycle is the operative clock.

Open question

The jitter sweep’s $\sigma = 100$ ms endpoint ($\approx 49$ Hz) exceeds the phase-shuffle ceiling ($\approx 29$ Hz) and approaches COBA-territory firing. The mechanism (gaps in the I-stream let E fire densely) is mechanistically clear, but the quantitative match between $\sigma = \infty$ jitter and trained-COBA rates would require comparing matched-rate operating points. Worth probing if the architecture-equivalence claim from nb038 is to be tightened.

Next steps

For ar010: the jitter sweep is now the load-bearing perturbation result. The categorical bar chart becomes a supporting endpoint comparison. A follow-up worth doing — but not on ar010’s critical path — is to retrain PING at a different $\tau_\text{GABA}$ (say 4.5 ms, giving $f_\gamma \approx 54$ Hz) and re-run the jitter sweep; the predicted transition should now sit at $\sigma \approx 18$ ms. If the inflection tracks $1/f_\gamma$ as $\tau_\text{GABA}$ varies, the quantitative law is independently confirmed by the inference-time experiment.