We asked whether surrogate-gradient training preserves PING rhythmicity when recurrent excitatory–inhibitory conductances can change. We compared trainable recurrent loops across initializations with a control whose recurrent PING weights remained frozen.
Recurrent training weakened rhythmicity early and did not recover the rhythmic control, while activity and accuracy changed by condition. This constrains these learning recipes, but does not show that recurrent learning must always destroy gamma or that the compared conditions are accuracy-equivalent.
Training from standard and 10%-standard recurrence drove most E→I weights to zero, while most I→E weights remained positive and their total mean grew. Both conditions ended with lower reference-image contrast and higher E rates than frozen recurrence. Zero-initialized recurrence remained zero (Fig. 1). These observations do not isolate pruning as the cause of reduced contrast or establish equivalent accuracy.
The unsmoothed trainable contrast averaged 0.05 after epoch 1 and ended at 0.018–0.111. Because there is no epoch-0 observation, these histories cannot resolve the intervening transition (Fig. 2).
We reused networks from the exp022 — Training Runs and reanalysed recorded observations. No new training or simulation was performed.
Compare recurrent trainability. Twelve conductance-based leaky-integrate-and-fire classifiers had 784 Poisson input channels, 1,024 excitatory (E), 256 inhibitory (I) and 10 output neurons. Three seeds per condition compared frozen canonical recurrence with trainable canonical, zero and 10%-canonical E→I/I→E conductances; E→E and I→I coupling stayed zero. Canonical initializer means were and , respectively, with standard deviations one tenth of each mean and negative draws clamped to zero.
Train on a held-out split. The 7,000-image subset contained 6,300 optimizer-training and 700 validation images from the official MNIST training partition. Input and readout weights trained for 50 epochs with AdamW, learning rate , zero weight decay, batch size 256, surrogate slope 1, voltage-gradient damping 1,000, gradient-norm clipping at 1 and no firing-rate penalty. Class scores were mean pre-reset output voltages; each 200 ms presentation used 0.1 ms steps and pixel-dependent input rates up to 25 Hz.
Constrain conductance signs. Trainable recurrent magnitudes were projected onto the non-negative cone after each optimizer step. Inhibition arose through , where is inhibitory conductance, mV its reversal potential, and membrane voltage: a positive I→E weight need not become negative to inhibit. Input zeros remained trainable and could regrow.
Evaluate final networks. All endpoint tests and weight comparisons used epoch 50, not validation-selected weights. Accuracy and whole-population mean E/I rates used the same 1000 official-test images per network; per-epoch validation metrics averaged three fixed Poisson encoding draws. For endpoint spectra, demeaned nonconstant E-population traces received full-trial Welch density estimation; the mean spectrum’s largest bin within 5–150 Hz defined the selected peak, without interpolation.
Measure temporal contrast. After each epoch, the same fixed reference digit’s Poisson spike realization elicited a diagnostic response. E-population counts were binned at 1 ms; their autocorrelation was normalized by lag overlap and squared mean count, over 0–100 ms, then smoothed with weights after replacing the zero-lag entry by its neighbour:
Here is dimensionless contrast, the first local trough from lag 2 ms onward, and the preceding positive-lag maximum of the smoothed autocorrelogram. We reused the recorded scalar; it is neither a test-population rhythm estimate nor a calibrated probability of PING.