Continuous Time Scikit Digits

Abstract

We compared frozen conductance-based leaky integrate-and-fire (COBA-LIF) digit classifiers with and without pyramidal–interneuron gamma (PING) inhibitory feedback, using one training image and identical 100 Hz maximum-rate pixel input. Across discrete timesteps from 0.1 to 0.0125 ms and adaptive continuous-time inference, both selected digit 0. Median hidden excitatory voltage error relative to continuous time changed from 1.62 to 0.2 mV for COBA and from 4.05 to 4.35 mV for PING. Continuous refinement preserved all neuronal and class counts. This single training-image diagnostic does not estimate held-out accuracy or establish trajectory equivalence.

Results

One image, one shared input

We compared discrete and continuous-time inference using the frozen scikit-learn digits classifiers from exp141, frozen at their minimum-validation-loss checkpoints. Original image 0 has label 0 and belongs to the training split. Only one training seed and one diagnostic image were tested. We increased the maximum input rate from 25 to 100 Hz per fully bright pixel, scaling darker pixels linearly.

SNNLab generated one encoding with seed 0 on a fixed 0.2 ms grid. All 14 comparison executions replayed its 390 saved spikes (Figure 1). Every arrival is exactly representable at all four timesteps; the input audit found zero timing shifts. The weights stayed frozen at their original 25 Hz training values.

COBA

COBA’s median E-neuron voltage difference outside spike windows fell from 1.62 to 0.2 mV between 0.1 and 0.0125 ms (Figure 2E). The continuous network emitted 3923 hidden E spikes. COBA has no inhibitory population.

PING

PING’s median E-neuron voltage difference changed from 4.05 to 4.35 mV (Figure 3E); refinement of the discrete timestep did not reduce this error. At the finest timestep, the median I-neuron difference was 1.67 mV. The continuous network emitted 879 E/I spikes.

Classification with matching output dynamics

Each discrete COBA-LIF output layer used its own network’s timestep: 0.1, 0.05, 0.025 or 0.0125 ms. In the continuous case, the output neurons evolved continuously alongside E/I. The saved native graph snapshots verify each discrete output clock; the continuous solver retains output threshold roots.

Both models selected the true digit in every condition (Figure 4). Continuous COBA predicted 0; continuous PING predicted 0. Class counts and ranks changed even though the winning digit did not. Total output spikes remain exp141’s trained class score.

Two separate 25 Hz source controls reproduced every saved exp141 spike and class score exactly. They are retained as validation evidence; all conditions in Figure 4, including the native 0.2 ms cases, use 100 Hz. Continuous refinement preserved every neuron’s count and all ten class counts; the largest root shift was 2.59e-11 ms. This is one training image, not a test-accuracy estimate or evidence of equivalent trajectories.

Methods

1. Select and verify the source (Figure 1). Pin exp141-r012-compute by its payload digest. Load its native best-validation simulation-start parameter snapshots, rather than final-epoch weights. Replay the original saved 25 Hz input in separate controls and verify every hidden, inhibitory and output spike and score against the saved original. Encode the same image once at 100 Hz with the native SNNLab rate encoder.
2. Match physical arrivals (Figures 2–4). Use a 0.1, 0.05, 0.025 and 0.0125 ms sweep. Replay the same saved integer-nanosecond arrivals without rounding or resampling, including each graph’s spiking output layer at that same timestep. Preserve a physical 0.2 ms E–I delay and zero additional E-to-output delay. Retain native 0.2 ms inference separately because its slot timing differs.
3. Integrate continuous dynamics (Figures 2–4). Integrate every continuous COBA-LIF voltage adaptively, with analytic receptor decay, full-weight arrivals, upward threshold roots, hard resets and exact refractory clamps. Retain all unrounded spikes and common 0.1 ms samples. Native-clock inference remains at 0.2 ms and uses the same 100 Hz input. See Appendix A for recording and arrival-clock conventions.
4. Check numerical refinement (Figure 4). Tighten the tolerances and halve the maximum integration step. Require equal per-neuron and class counts, maximum root shift below 0.001 ms and maximum per-neuron guarded voltage MAE below 0.001 mV. Both models passed.

The input image, trained weights and spike-count scoring come from exp141. Inference uses a 100 Hz maximum pixel rate without retraining. Output dynamics follow the discrete or continuous condition being compared.

Continuous membrane equation

For membrane voltage $V$ in millivolts and time $t$ in milliseconds, all hidden, inhibitory and output neurons follow

$C$ is capacitance in nanofarads; $g_L$, $g_A$ and $g_G$ are leak, AMPA and GABA conductances in microsiemens. Their reversal potentials $E_L$, $E_A$ and $E_G$ are in millivolts. Receptors decay exponentially between arrivals. Each arrival adds its frozen weight to the appropriate conductance. Upward threshold crossings emit spikes, reset voltage and begin a physical refractory clamp; conductances keep evolving. Output neurons receive AMPA only and have the hidden E-cell physics. DOP853 integrates voltage between arrivals and threshold events. The parameter table records nominal and refined tolerances and step limits; recording times are independent of adaptive integration steps.