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Spike Distance Function as a Learning Objective for Spike Prediction
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Proposes a spike distance function (distance to nearest spike) as a regression learning objective for spike prediction, trained with a ConvNext CNN and inferred via an L2 energy-minimization algorithm, outperforming Poisson-objective models on chicken and frog retinal ganglion cell recordings.
Problem
Poisson learning objectives for neuronal spike prediction quantize spikes into fixed summation intervals, limiting millisecond-scale temporal precision and causing training and inference difficulties at short intervals.
Approach
Replace the Poisson spike-count objective with a spike distance function that maps each time point to the temporal distance to the nearest spike, train networks to regress its log via MSE, and infer spike trains by iteratively removing spikes to minimize L2 error against the predicted distance array.
Key results
- The spike distance model outperforms all Poisson models across Van Rossum distance, Schreiber similarity and Pearson correlation over a range of smoothing values on chicken RGCs (IQM with bootstrap CIs over 11 runs).
- The best Poisson model (Poisson-80ms with rounded-mean inference) is outperformed by the spike distance model; with sampling inference Poisson models are outperformed notably in Van Rossum distance.
- The performance gap is narrower on frog RGCs, but the spike distance model remains the most consistently competitive across the three metrics.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Chicken RGC test set | Van Rossum distance | Helped |
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Chicken RGC test set | Schreiber similarity | Helped |
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Chicken RGC test set | Pearson correlation | Helped |
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Frog RGC | Van Rossum distance | Helped |
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Frog RGC | Schreiber similarity | Helped |
| Use the spike distance objective instead of the Poisson objective | neural network spike prediction · Frog RGC | Pearson correlation | Helped |
| Infer Poisson spike counts by rounding the model output rather than sampling (ablation) | Poisson models · Chicken RGC test set | spike-train similarity | Helped |
| Infer Poisson spike counts using the distribution mode rather than the rounded mean (ablation) | Poisson models · Chicken RGC test set | spike-train similarity | Hurt |
| Use stochastic spike placement rather than uniform tiling (ablation) | Poisson spike-count inference · Experiments not reported in main results | spike-train similarity | Hurt |
| Use Poisson-5 ms rather than a longer summation interval with rounded-mean inference (ablation) | Poisson models · Chicken RGC test set | spike-train similarity | Hurt |
| Use Poisson-80 ms with rounded-mean inference rather than other Poisson settings (ablation) | Poisson models · Chicken RGC test set | spike-train similarity | Helped |
| Vary the number of shared-base mid-layers from 0 to 7 (ablation) | Poisson-80 ms · Chicken RGC validation cells | validation loss | No clear effect |
Surprising findings
- Poisson models with short summation intervals (5 ms) using rounded-mean inference perform indistinguishably from an empty spike train.
- Pretraining on synthetic spike distance data and a Van Rossum-like or separate time-to-past/future representation were tried and found harder to infer spikes from, though not pursued.
Limitations
- Comparison limited to a convolutional architecture; interaction with architecture (e.g., translation invariance) not investigated.
- Interpretability of spike distance outputs (vs. GLM stimulus filters) unclear; approach argued only for precise spike timing.
- Inference algorithm is approximate; optimal inference not explored, and models trained per cell rather than jointly.
Experimental setup
Datasets: chicken retinal ganglion cell MEA recording (full-field colour noise, 60 cells) frog (Xenopus) retinal ganglion cell MEA recording (113 cells)
Benchmarks: chicken RGC test set (90 s) frog RGC test set
Metrics: Van Rossum distance Schreiber similarity Pearson correlation
Baselines: Poisson-5ms Poisson-10ms Poisson-20ms Poisson-40ms Poisson-80ms Poisson-160ms
Builds on: ConvNext ConvNextv2 one-cycle learning rate policy signed distance function
Closest papers by meaning
- Timing Is All You Need: SpikeCore, Learnable Delays, and Gain Control for Neuromorphic Classification (NeurIPS 2026 · similarity 0.87)
- P-SPIKESSM: HARNESSING PROBABILISTIC SPIKING STATE SPACE MODELS FOR LONG-RANGE DEPENDENCY TASKS (ICLR 2025 · similarity 0.87)
- Scalable inference of functional neural connectivity at submillisecond timescales (NeurIPS 2025 · similarity 0.85)
- Towards a "Universal Translator" for Neural Dynamics at Single-Cell, Single-Spike Resolution (NeurIPS 2024 · similarity 0.85)
- Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings (ICLR 2024 · similarity 0.84)
- Causal pieces: analysing and improving spiking neural networks piece by piece (NeurIPS 2026 · similarity 0.84)
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