Abstract#

We built the MNIST model bank supplying trained networks and histories to downstream gamma-gated-sparsity experiments. We compared feedforward COBA controls with recurrent PING networks across activity penalties, inhibitory timescale, integration, recurrent weights and input drive.

PING combined lower excitatory activity with lower validation performance than the feedforward baseline, while wider sweeps exposed distinct accuracy–activity trade-offs. The retained bank provides training families; the bank itself does not establish that gamma timing causes any downstream benefit.

Results#

Canonical COBA-PING learning curves#

Canonical PING raster diagnostic#

Activity-ceiling learning curves#

Unconstrained PING endpoint raster#

Inhibitory-decay learning curves#

Six-ms inhibitory-decay raster#

Timestep learning curves#

0.1-ms reference raster#

Recurrent-training learning curves#

Frozen recurrent PING control raster#

Variable-rate training histories#

Five-hertz variable-rate raster#

Input-coupling learning curves#

0.05 input-coupling raster#

0.1 input-coupling raster#

0.3 input-coupling raster#

0.9 input-coupling raster#

Methods#

The completed bank contains 102 models: 90 reused models with unchanged weights and histories, plus twelve newly trained timestep models. The three existing 0.1-ms timestep models were reused after execution-equivalence checks. We analysed these histories and generated 34 final-epoch seed-42 diagnostic recordings.

Dataset#

Appendix: Training-run specification sheets#

The following shared sheet and all seven TR sheets specify the controlled recipes and their intended uses. The observed learning curves and diagnostic plots are in Results.

Shared production specification#

All runs map Poisson-encoded pixels through 1,024 excitatory neurons to ten spiking output LIF neurons. COBA and PING use the same input-weight and readout-weight initialization distributions. COBA disables recurrent E/I coupling; PING adds a $1024\to 256\to 1024$ E/I feedback loop and uses stronger backward-pass gradient damping to stabilize training through that recurrent path.

These are specified production settings, not newly measured results. Unless a TR-specific sheet says otherwise, every condition–seed network uses this contract. In the tables, $\mathrm{𝒩︀}\left({𝜇}_{\text{init}},{𝜎}_{\text{init}}^2\right)$ denotes a normal distribution with initialization mean ${𝜇}_{\text{init}}$ and standard deviation ${𝜎}_{\text{init}}$; $max\left(0,𝑥\right)$ replaces a sampled weight $𝑥$ by zero when negative. LIF means leaky integrate-and-fire.

Specification: TR-01 — Canonical full-data reference#

The full-data COBA and PING condition–seed networks are used for headline accuracy. They use the official MNIST training partition with no spike-budget penalty, so the comparison is not affected by the smaller dataset or regularization used in the sweeps. Ten percent of that partition is reserved for checkpoint selection; the official test partition remains untouched during training. This experiment reports their validation learning histories; independent official-test evaluation belongs to the downstream experiments.

Specification: TR-02 — Activity-ceiling sweep#

This run measures the trade-off between accuracy and firing rate as the activity ceiling is tightened. For each presentation, the loss computes the population-mean hidden-E firing rate, applies a one-sided quadratic penalty above the target, then averages the penalties across the minibatch. Quiet presentations therefore cannot offset active presentations. Expressing the target in hertz and normalising over samples, neurons, duration, and hidden layers makes the intervention comparable across those dimensions. A smaller training pool keeps the multi-seed sweep manageable; only the activity target changes across conditions. Comparisons with the full-data training replicates also change training-pool size and cannot isolate the penalty alone. The resulting checkpoints are used by exp024 — Accuracy Plateaus While Firing Rate Rises , exp025 — Accuracy and Firing Rate With and Without Inhibition , exp037 — Dropped Spikes vs Added Noise , exp038 — Switching On the Inhibitory Loop .

Specification: TR-03 — Inhibitory-timescale sweep#

This run changes ${𝜏}_{\text{GABA}}$ to test how the inhibitory timescale affects gamma frequency, firing rate, and accuracy. All other scientific settings are held fixed, with 6 ms as the standard condition. The resulting checkpoints are used by exp041 — Firing Rate Tracks Gamma Frequency , exp042 — Inhibitory Replay Perturbations Change Excitatory Firing , exp046 — One Spike per Gamma Cycle .

Specification: TR-04 — Integration-timestep sweep#

This run changes the integration timestep while keeping E/I refractory holds at 1.2/0.6 ms. Presentations last nominally 200 ms and contain whole simulation steps. It tests whether the learned operating regime depends on numerical resolution; separately trained networks do not establish fixed-weight numerical convergence. The finest timestep requires the longest unrolled training trajectories. The resulting checkpoints are used by exp044 — Firing Rate Across the Timestep Sweep .

Specification: TR-05 — Recurrent-initialization sweep#

This run tests whether training preserves the PING loop or learns a useful loop from weaker initial conditions. Recurrent initialization and trainability change together, while the feedforward network and classifier remain fixed to the PING recipe. The resulting checkpoints are used by exp049 — Training Recurrent Weights Weakens PING Rhythmicity .

Specification: TR-06 — Variable-rate streaming bank#

This condition trains PING across the input rates used by the continuous-stream classification study. One rate is sampled uniformly for each presentation, and the ten output LIF neurons produce class logits from their total spike counts rather than their mean membrane voltages. This keeps the cross-entropy logits dimensionless and gives one additional output spike the same logit increment. The readout weights use a small Gaussian initialization, $\mathrm{𝒩︀}\left(0.05,{0.04}^2\right)$, lower-clamped at zero and governed by the shared non-negative constraint.

The recorded design rationale for this smaller initializer was to avoid saturation at the mean-voltage scale and silence at the generic fan-in-normalized scale. The present bank retains the chosen $\mathrm{𝒩︀}\left(0.05,{0.04}^2\right)$ setting; its learning curves do not independently establish those earlier calibration comparisons. This is a specified spike-count recipe, not a claim that the initializer is uniquely optimal.

Output firing rates may still be reported as activity measurements. During streaming inference, the output neurons reset at digit boundaries while the hidden PING state continues. The resulting checkpoints are used by exp082 — Spike-Count Classification in a Continuous Stream .

Specification: TR-07 — Low-input recruitment sweep#

TR-02 asks how changing the activity ceiling affects networks initialized at the standard input coupling. TR-07 asks the complementary question: with the strictest TR-02 ceiling fixed at 1 Hz from the first epoch, can PING recruit its inhibitory loop when the feedforward projection starts weak? It varies the parent mean used to initialize expected summed input coupling, before lower clamping and fan-in normalization; it does not directly set the mean of the stored synaptic matrix. The training pool, optimizer, recurrent loop, and mean-voltage readout remain at the reduced-sweep defaults. This bank retains all twelve models, and exp025 — Accuracy and Firing Rate With and Without Inhibition aggregates the three seeds at each setting to test recruitment and path dependence.

References#

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