One Spike per Gamma Cycle

#exp046 · Gamma-gated sparsity · data v36.0.0
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Abstract

We asked whether the earlier rate–frequency relationship reflects excitatory neurons participating in gamma cycles without repeatedly firing. We reused the inhibitory-timescale sweep and counted each excitatory neuron’s spikes between inhibitory population bursts.

Excitatory neurons were usually silent within a cycle and, when active, overwhelmingly emitted a single spike; the busiest cells tracked that ceiling. This supports the one-spike-per-cycle approximation for this sweep, but does not turn the population relationship into a universal participation law.

Results

Spikes per neuron-cycle

Across 167,178,240 neuron–cycle pairs, E neurons emitted zero spikes in 75.2% of pairs and one spike in 23.6%. Two-or-more events occurred in 1.15% of pairs and three-or-more in 0.10%; pooled over the sweep, 98.9% contained at most one spike (Fig. 1).

Six bar charts, one per τ_GABA, of the probability an E neuron emits 0, 1, 2, or ≥3 spikes in a gamma cycle; every panel is dominated by the 0 and 1 bars.
Figure 1: Distribution of E spike count per gamma cycle per neuron at 𝜏GABA values (A–F) 4.5, 6, 9, 12, 18 and 27 ms, respectively, aggregating three training replicates per condition and 167.2 million neuron–cycle pairs.

Rate versus gamma frequency

The busiest neuron in each network tracked the one-spike-per-cycle ceiling 𝑟=𝑓𝛾 (fit 𝑟=0.97𝑓𝛾, 𝑅fit2=0.88), whereas the median neuron followed the shallower 𝑟≈0.20𝑓𝛾 participation slope from the inhibitory-timescale sweep. Even the most active neuron rarely exceeded one spike per cycle, making the ceiling near-strict in these measurements (Fig. 2).

Per-neuron E rate against measured gamma frequency; the busiest neuron tracks the one-spike-per-cycle line while the median neuron tracks the earlier sweep's shallower slope.
Figure 2: Per-neuron E rate versus measured gamma frequency 𝑓𝛾 across the 𝜏GABA sweep. Curves show the busiest and median neurons in each network, the one-spike-per-cycle reference and the earlier participation slope.

Methods

Cycle statistics were evaluated from the final-epoch checkpoints used by the earlier inhibitory-timescale study, so this experiment audits the same endpoint gamma dynamics. We retained the source training horizon from those checkpoint configurations.

For each of the sweep’s 18 trained networks (6 𝜏GABA × 3 seeds):

  1. Run fixed-trial inference. We ran inference on the fixed 1,000-image subset of the official MNIST test partition; we captured per-trial (𝑇,𝐵,𝑁𝐸) and (𝑇,𝐵,𝑁𝐼) spike tensors.
  1. Detect inhibitory bursts. We detected I-burst times per trial: we smoothed the population I rate with a 1-ms Gaussian, and used scipy peak detection with min-distance set to half the network’s own 1/𝑓𝛾.
  2. Define cycles. Cycle boundaries were the midpoints between consecutive I-burst peaks (the first cycle started at 𝑡=0 and the last ended at trial end).
  3. Count excitatory spikes. For each (neuron, cycle, trial), we counted the number of E spikes within the cycle window.
  1. Aggregate displayed counts. We bucketed counts globally into {0,1,2,≥3} and aggregated by 𝜏GABA.

The cycle anchor is the I-burst: this is the right anchor because the cycle is operationally defined as “the time between one inhibitory blanket and the next”, not as the time between E bursts (which can be silent on a given cycle).

Dataset