PING: Leak and Capacitance

Results

We applied paired interventions to the trained PING (pyramidal–interneuron gamma) circuit used in exp123, with checkpoint weights from exp022. Excitatory ($E$) and inhibitory ($I$) populations changed together within each sweep. The figures describe 37,000 presentations from one checkpoint: 100 test images, ten per digit, with ten paired encodings each. They do not establish variation across trained networks or classification performance.

The historical presentation exp134-r004-present was derived from exp134-r002-analyse and exp134-r001-compute. It used SNNLab 0.18.0 and 100 images. The current recipe defaults to 500 images and the current SNNLab API; those changes have not produced the displayed evidence.

Leak conductance

From ×0.5 to ×2, total E firing rose from 14,898 to 20,524 spikes/s, and cycle participation from 19.4% to 28.7%. Spectral peaks shifted from 58.9 to 64.7 Hz with local reversals; rhythm contrast decreased. Greater participation therefore did not imply greater rhythm contrast.

Membrane capacitance

Total E firing rose from 14,463 to 20,177 spikes/s, and participation from 20.6% to 27.1%. The endpoint spectral peaks were 58.5 and 67.1 Hz, with local reversals between them. Rhythm contrast increased overall.

Methods

1. Paired inputs and frozen weights. We sampled ten images per digit without replacement from exp123’s balanced 500-image official MNIST test bank, using selection seed 134. Pixel intensities in [0, 1] scaled Poisson encoding rates up to 25 Hz. Encoding identifiers 42–51 used generator seeds $1000k+s$, where $k$ is the original image index and $s$ the encoding identifier. Each 200 ms presentation started from fresh state at a 0.1 ms timestep. All conditions reused the encodings and final-epoch checkpoint weights.
2. Separate membrane sweeps (Figures 1–2). The dimensionless multiplier $m_j=0.5\times4^{j/18}$, with setting index $j=0,\ldots,18$, scaled either leak conductances $(g_{L,E},g_{L,I})=m_j(0.05,0.10)$ µS or capacitances $(C_{m,E},C_{m,I})=m_j(1,0.5)$ nF. The other parameter stayed at its baseline. The passive time constant is $\tau_{m,P}=C_{m,P}/g_{L,P}$ in ms for population $P\in\{E,I\}$. Thus leak scaling gives $(20,5)/m_j$ ms, and capacitance scaling gives $m_j(20,5)$ ms. Both sweeps share the ×1 baseline; inhibitory synaptic decay remains 6 ms. These are interventions in the conductance-based model, not evidence that passive time constants alone determine the response.
3. Frequency and firing (panels A, C). We demeaned full-trial E population spike counts and computed a Hann-window Welch power spectral density (PSD) with one segment spanning the trial. The peak of the mean PSD in 5–150 Hz used parabolic interpolation. Total E spikes/s divides each trial’s total spike count by 0.2 s, then averages trials; it is not a per-neuron rate.
4. Participation (panel B). We smoothed I population counts with a 1 ms Gaussian and detected volleys at least 2 ms apart, requiring prominence of at least one spike and 20% of the smoothed maximum. Midpoints bracketed complete interior cycles. A trial required at least one cycle and mean I participation of at least 50%. E participation is the fraction of E neurons spiking at least once per accepted cycle, averaged over cycles, accepted draws within each image, then eligible images. Every condition accepted all 1,000 trials and all 100 images; rejected trials would be excluded, not zero-filled.
5. Rhythm contrast and diagnostics (panels D–G). SNNLab’s normalized autocorrelogram used 1 ms bins and lags up to 100 ms. Contrast is $(L-T)/(L+T)$, where $L$ is the smoothed central-lobe height before the first trough and $T$ that trough’s height. We averaged finite trial contrasts. Rasters show one diagnostic image and encoding, not an independent evaluation.