We asked what happens when reciprocal inhibition is added after a feedforward classifier has already been trained. We kept the learned input and readout weights fixed while progressively enabling bidirectional excitatory–inhibitory coupling during inference.
Stronger coupling grouped activity into bursts and sharply suppressed excitatory firing, but also reduced classification accuracy. This demonstrates post-training rate suppression, not a benefit of gamma timing or evidence that retraining would recover the lost accuracy.
At full loop strength, E rate fell from approximately 112 to 8 Hz, I rate reached 45 Hz, and accuracy fell by 48 percentage points. Because both coupling directions varied, lower activity alone does not identify a causal benefit of rhythm (Fig. 1).
Burst grouping increased across the sampled loop strengths. These illustrative panels do not estimate gamma frequency or establish a continuous transition (Fig. 2).
We reused networks from the exp022 — Training Runs and reanalysed recorded inference observations. No new training or simulation was performed for this account.
Reuse trained classifiers. MNIST handwritten digits [1] supplied 6,300 training and 700 validation images from the official training partition. Conductance-based leaky-integrate-and-fire networks had 784 Poisson input channels, 1,024 excitatory (E), 256 inhibitory (I), and 10 output neurons; pixels set rates up to 25 Hz. Input and readout weights trained for 50 epochs; class scores were mean pre-reset output voltages. We selected the minimum mean validation cross-entropy over three fixed encoding draws, breaking ties by accuracy and then earliest epoch, rather than using final-epoch weights.
Enable the loop after training. Three feedforward controls, seeds 42–44, had no activity penalty or recurrent coupling during training. Dimensionless strength took eleven values from 0 to 1 in steps of 0.1; it set E→I and I→E initializer means to and , respectively, with standard deviations one tenth of those means and normalization by source population size. These lower-clamped normal weights replaced the zero recurrent matrices; learned input and readout weights stayed fixed, and E→E and I→I coupling stayed zero. The same network seed was reused across strengths; no optimization followed the intervention.
Evaluate responses. Each strength used the same 1000 images from the official 10000-image test partition, with 200 ms presentations and 0.1 ms steps. Accuracy counted correct classifications; rates included all neurons and all evaluated presentations:
Here denotes E or I, its neuron count, the number of presentations, their duration in seconds, and neuron ’s spike count during presentation ; is in hertz. Curves show means and sample standard deviations across the three networks; single-image rasters are illustrative.
| Parameter | Value |
| Integration timestep | 0.1 ms |
| Trial duration | 200 ms |
| Evaluation corpus | Official MNIST test partition (10000 images) |
| Evaluated images per seed | 1000 |
| Training epochs | 50 |
| Optimizer | AdamW; learning rate ; zero weight decay |
| Batch size; gradient-norm clip | 256; 1 |
| Excitatory / inhibitory synaptic decay | 2 / 6 ms |
The broader activity frontier contains 36 classifiers: two network configurations, three seeds, and six activity conditions (penalty off or ceilings of 25, 10, 5, 2.5 and 1 Hz). Its summaries preserve selected and final-epoch validation accuracy, final-epoch training E rate, and across-seed means and SEM; these are distinct from the inference measurements above. The loop-transfer comparison used only the three unpenalised feedforward classifiers. The exp025 — Accuracy and Firing Rate With and Without Inhibition describes the broader training design.
Feedforward and loop-enabled training used voltage-gradient damping of 1 and 1,000 respectively; this difference affects the auxiliary between-model comparisons, not the within-classifier inference intervention. Dale’s law was enforced, adaptive thresholds were disabled, and membrane time constants were not trained.
Illustrative snapshots use test-image index 0, not selection by digit class. A fixed pseudorandom sample selects 200 E and 64 I neurons for display; reported firing rates use the full populations. Uniform-input E+I overlays add the two population means without weighting by neuron count, and are not a whole-network mean. Neither the transfer rasters nor these firing curves provide a spectral gamma-frequency estimate. The accuracy decline is consistent with changing the trained network’s dynamics, but does not identify the readout as its sole cause or test recovery by retraining.