Firing Rate Across the Timestep Sweep

#exp044 · Gamma-gated sparsity · data v36.0.0
Created
Updated

Abstract

We asked how integration timestep affects the activity and accuracy of PING classifiers. We compared separately trained networks at matched training and evaluation timesteps, with fixed physical refractory periods, and evaluated their MNIST performance.

Excitatory firing and accuracy varied across the sweep, showing that the timestep is part of the learned operating regime rather than a neutral solver setting. The comparison tests pipelines rather than holding weights fixed; the rasters do not establish invariance relative to the gamma period.

Results

Timestep rate and accuracy

Mean test accuracy ranged from 88.37% to 89.63%, spanning 1.27 percentage points. Mean E rate ranged from 14.27 to 17.02 Hz. Accuracy persisted across the tested resolutions, while firing remained timestep-dependent (Figure 1).

Hidden excitatory firing rate and test accuracy against integration timestep, with uncertainty across training seeds.
Figure 1: Hidden E rate (black) and test accuracy (red) across the twelvefold timestep sweep. Markers show means over 3 seeds; bars show ±1 standard error of the mean. Each network was evaluated on 1000 official-test images at its training timestep.

Timestep spike rasters

Single-trial excitatory and inhibitory spike rasters at five integration timesteps, plotted against physical time.
Figure 2: E (black) and I (red) rasters for the same official-test image, seed 42, at timesteps (A–E) 0.05, 0.1, 0.2, 0.3 and 0.6 ms, respectively. Panels display 200 E and 64 I neurons over the first 100 ms. These illustrative probes support visual cadence inspection, not a population estimate of gamma-period invariance.

Training-timestep response

Per-network validation accuracy and excitatory firing rate versus epoch, coloured by integration timestep.
Figure 3: Recorded training histories: (A) validation accuracy and (B) E rate, one line per timestep and seed. Each epoch averaged 3 encoder draws per validation image. The final-epoch comparison is a finite-training snapshot, not an established fixed-point ceiling.

Methods

The audit reused separately trained networks and their learning histories, then measured endpoint dynamics at matched training and inference timesteps.

  1. Reuse the trained population. One PING network was trained per Δ𝑡sim∈{0.05,0.1,0.2,0.3,0.6} ms and seed ∈{42,43,44}, giving fifteen networks. Each had 784 inputs, 1024 excitatory neurons, 256 inhibitory neurons and 10 class outputs. Network geometry, synaptic settings, readout and optimisation settings were checked for agreement across the comparison. E/I refractory holds were fixed at 1.2/0.6 ms: 24/12, 12/6, 6/3, 4/2 and 2/1 steps, respectively. Twelve networks were newly trained for this design; three 0.1-ms networks were reused unchanged after execution-equivalence checks.

  2. Keep data and nominal duration fixed. The 7000-image MNIST training pool contained 6300 optimisation images and 700 validation images; the official test partition was excluded from training. The nominal presentation duration was 200 ms; whole-step rounding gave 4,000, 2,000, 1,000, 666 and 333 steps. Realised 𝑇present was 199.8 ms at 0.3/0.6 ms and 200 ms otherwise. Image intensities drove Poisson input with peak rate 25 Hz.

  1. Use the training endpoint. Networks underwent 50 epochs of surrogate-gradient training [1], with batch size 256 and learning rate 0.0004. Class scores used the mean-membrane readout, and validation histories averaged 3 encoder draws per image. The audit used the final epoch for rates, accuracy and rasters, rather than selecting the best validation epoch.
  1. Measure held-out performance. Each network was evaluated on the fixed 1000-image subset of the official MNIST test partition, without retraining. Accuracy was the percentage of correctly classified images; population firing rate was total spikes divided by the number of evaluated images, population size and realised trial duration in seconds. Excitatory and inhibitory rates were recorded separately.

Parameter summary

ParameterValue
Integration timestep Δ𝑡sim0.05–0.6 ms (swept)
Presentation duration 𝑇present200 ms nominal; 199.8 ms at 0.3/0.6 ms
Refractory hold, E/I1.2/0.6 ms at every timestep
MNIST training pool7000 images: 6300 optimisation / 700 validation
Official-test evaluation1000 images per network
Epochs50

Dataset

References

  1. E. O. Neftci, H. Mostafa, and F. Zenke. “Surrogate Gradient Learning in Spiking Neural Networks.” IEEE Signal Processing Magazine 36(6), 51–63 (2019). doi:10.1109/MSP.2019.2931595