△ Mechanism confirmed, baseline not beaten 2026

Causal E/I Micro-Event Cell

Implementation & benchmark of arXiv:2608.16701 — Order-Sensitive Fast-Synapse Limits in Sparse Excitatory-Inhibitory Threshold-Reset Networks

Usefulness7/10

Difficulty5/10

Novelty7/10

Architecture Accuracy Stability Rnn Training dynamics Dynamical systems Computation

Source paper: Order-Sensitive Fast-Synapse Limits in Sparse Excitatory-Inhibitory Threshold-Reset Networks arXiv:2608.16701 ⓘ · analyzed Sep 1, 2026

AI-generated research hypothesis, automatically tested. Not peer-reviewed.

Idea description

Replace signed-input aggregation in a spiking recurrent cell with a causal micro-event queue that processes excitatory and inhibitory arrivals in timestamp order, applying threshold and reset after each event. This preserves computations that disappear when all events in a timestep are replaced by one net current, particularly near threshold.

Formulas

$$x+a-b<\theta\le x+a$$

$$m(x,a,b,\theta)=\min\{\theta-(x+a-b),\;x+a-\theta\}>0$$

$$\mathbb{E}_{G}\left|F_{N}^{\varepsilon_N,\mathrm{E}}(t_*)-F_{N}^{\varepsilon_N,\mathrm{I}}(t_*)-\frac{1}{2}\right|\longrightarrow 0$$

$$u_i\leftarrow u_i+\Delta_i,\qquad s_i\leftarrow\mathbf{1}[u_i\ge\theta],\qquad u_i\leftarrow(1-s_i)u_i+s_i u_{\mathrm{reset}}$$

Mathematical statement

The local mechanism is the paper's Theorem 2.1. For a node with pre-event state x<theta, total excitatory pulse mass a>=0, total inhibitory pulse magnitude b>=0, and threshold theta, excitatory-first ordering fires while inhibitory-first ordering does not exactly when x+a-b<theta<=x+a. The left inequality says the final net state remains subthreshold; the right inequality says the excitatory pulse alone crosses threshold. A strict perturbation margin is m=min{theta-(x+a-b),x+a-theta}>0. The paper also gives the population-level discrepancy E_G[|F_N^(epsilon_N,E)(t*)-F_N^(epsilon_N,I)(t*)-1/2|] -> 0 for moderately sparse random graphs, where F_N^(epsilon,o)(t) is the population-averaged firing count, q_N -> infinity, q_N/N -> 0, and nonzero edge weights are order 1/q_N. The neural adaptation uses the local inequality to detect when timestep aggregation is unsafe.

Implementation notes

Integrate this at the recurrent update of a leaky integrate-and-fire or adaptive spiking RNN, specifically between synaptic-delay lookup and threshold/reset. For every destination neuron and macro-timestep t, collect incoming events as tuples (tau_j, Delta_j), where tau_j in [0,1) is normalized arrival time and Delta_j is signed pulse mass. Sort by tau_j, using a stable tie-break rule for equal timestamps. Pseudocode: initialize u <- alpha*u_previous; build events from presynaptic spikes, delays, and signed weights; sort events; for each (tau, delta), set u <- u + delta, emit spike s <- indicator(u >= theta), and if s=1 set u <- u_reset; append emitted spikes with time t+tau. Apply refractory masking and the next leak after all events. The first formula is used diagnostically with x equal to the pre-event membrane state, a equal to positive event mass, and b equal to negative event magnitude. Estimate the unsafe fraction by counting neurons satisfying the interval and estimate m from the second formula. Compare this cell with a baseline that computes one signed sum per timestep. First run a small recurrent SNN on synthetic pulse classification or SHD with randomized sub-timestep delays. Measure accuracy, spike-count error, and disagreement between fine-step and coarse-step simulations at matched FLOPs. Success means lower discretization error and improved accuracy when many neurons lie in the order-sensitive interval, without degradation when event order is irrelevant.

Verification

Mechanism confirmed, baseline not beaten

Stage 1 · Toy mechanism gate: Passed ✓

Stage 2 · Mechanism transferred to benchmark: Confirmed ✓

Stage 2 · Practical benchmark result: Significantly worse ✗

Methodology: 8 paired seeds, permutation test (p<0.05) against a learning-rate-tuned baseline. How verification works

Stage 1 — Mechanism check agent confidence 9/10

Built a causal timestamp-ordered E/I micro-event cell and a signed-current aggregation baseline in causal_ei_experiment.py. All three mechanism predictions were confirmed: interval fractions matched analytic values within 0.0019, random-order firing was 0.4983 versus the predicted 0.5, and unsafe-case disagreement was 0.4989 versus 0.5. The mini-experiment found 35.1% unsafe cases and 17.5% overall disagreement, demonstrating the claimed near-threshold mechanism; this is not evidence of trained-task accuracy improvement.

Agent confidence: 9/10

Baseline: Spike rate 0.15002; one signed net-current update per macro-step.
Idea: Micro-event spike rate 0.32525; overall disagreement 0.17523; unsafe fraction 0.35121; unsafe-case disagreement 0.49893 versus predicted 0.5; maximum toy interval-sweep absolute error 0.00184; random-order firing 0.4983 versus predicted 0.5.

Limitations: No trained recurrent SNN or classification accuracy experiment was run, and computational speed/FLOPs were not benchmarked. The mini-experiment uses two events per sample and validates local causal-versus-aggregated behavior rather than the paper's population-level asymptotic theorem.

How to run: python3 causal_ei_experiment.py

Stage 2 — Benchmark vs. tuned baseline (arXiv:2608.16701) Sep 2, 2026

Significantly WORSE than the tuned baseline (+25.4%, p=0.0081, wins 0 / 8 paired seeds).

Benchmark: Dynamics forecasting
Model: rnn_small
Paired seeds: 8
Baseline mean: 0.0301
Idea mean: 0.0377
Effect (Δ): 0.0077 (+25.4%; negative = idea better)
Wins: 0 / 8 paired seeds
p-value: 0.0081 (permutation test, 20 000 shuffles)
Smallest detectable effect: ±7.5%
Mechanism: Confirmed ✓
Practical effect: Hurts
Baseline tuning: swept over 3 configs

Limitations:

Only the registered built-in dynamics track was tested. No larger datasets, longer training, speed/FLOP measurements, spiking classification track, or alternative timestamp distributions were evaluated. The mechanism signature confirms behavioral divergence but does not imply task improvement.

How to run: python3 causal_ei_bench.py

Verdict computed by deterministic test code from paired-seed statistics — not by the language model.

Stage 2 — Benchmark Sep 1, 2026 latest Failed ✗

Agent confidence: 9/10

The causal E/I micro-event cell was implemented as a matched recurrent dynamics system and evaluated end-to-end against signed macro-step aggregation. The mechanism signature was confirmed through nonzero trained-model behavioral differences, but test MSE was significantly worse for the idea: 0.03774771 versus 0.03009093, paired delta +0.00765679, permutation p=0.0081; therefore there is no benchmark win.

Baseline: best_cfg={lr:0.003,epochs:12}; sweep means lr=0.0015: 0.03892234, lr=0.003: 0.03009093, lr=0.006: 0.05556619; full mean=0.03009093, std=0.00407143, per_seed=[0.03666029,0.02726038,0.03030632,0.03209355,0.02480439,0.03368592,0.02425563,0.03166095]
Idea: best_cfg={lr:0.003,epochs:12}; sweep means lr=0.0015: 0.05525698, lr=0.003: 0.03774771, lr=0.006: 0.04161697; mean=0.03774771, std=0.00409269, per_seed=[0.04495187,0.03703208,0.03814383,0.04309968,0.03429987,0.03708112,0.03175383,0.03561943]

Benchmark result