Switching On the Inhibitory Loop

Abstract

We asked what happens when reciprocal inhibition is enabled after feedforward training. We held the learned input and readout weights fixed and varied bidirectional E↔I coupling in three MNIST classifiers. At full loop strength, mean E rate fell from 86 to 7 Hz, while test accuracy fell by 47 percentage points. This demonstrates post-training rate suppression under these conditions, without isolating a benefit of gamma timing or testing whether retraining could recover accuracy.

Results

Loop-strength rates and accuracy

At full loop strength, E rate fell from approximately 86 to 7 Hz, I rate reached 40 Hz, and accuracy fell by 47 percentage points. Because both coupling directions varied, lower activity alone does not identify a causal benefit of rhythm (Fig. 1).

Loop-strength PING rasters

Burst grouping increased across the sampled loop strengths. These illustrative panels do not estimate gamma frequency or establish a continuous transition (Fig. 2).

Methods

We reused networks from the exp022 — MNIST and reanalysed recorded inference observations. No new training or simulation was performed for this account.

1. 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.

2. Enable the loop after training. Three feedforward controls, seeds 42–44, had no activity penalty or recurrent coupling during training. Dimensionless strength $s$ took eleven values from 0 to 1 in steps of 0.1; it set E→I and I→E initializer means to $s$ and $2 s$, 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.

3. 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:

   $$r_{P} = \frac{1}{N_{\text{eval}} N_{P} T_{\text{present}}} \sum_{b = 1}^{N_{\text{eval}}} \sum_{n \in P} n_{\text{spike} ( b , n )} . \tag{1}$$

   Here $P$ denotes E or I, $N_{P}$ its neuron count, $N_{\text{eval}}$ the number of presentations, $T_{\text{present}}$ their duration in seconds, and $n_{\text{spike} ( b , n )}$ neuron $n$’s spike count during presentation $b$; $r_{P}$ is in hertz. Curves show means and sample standard deviations across the three networks; single-image rasters are illustrative.

4. Probe input drive. Auxiliary probes reused seed-42 classifiers trained with and without the loop. Uniform independent Poisson inputs covered 26 rates between 0 and 100 Hz, with 32 trials per rate; a separate trained-loop probe used one test image at ten maximum pixel rates from 0 to approximately 23.08 Hz. These recorded firing curves complement the exp023 — Turning the PING Loop On they are not additional loop-transfer accuracy evaluations.