# Causal E/I Micro-Event Cell

- ID: 2411
- Canonical URL: https://synthcore.org/idea/2411/causal-e-i-micro-event-cell
- API JSON: https://synthcore.org/api/idea/2411.json
- API Markdown: https://synthcore.org/api/idea/2411.md
- Verification status: mech_ok_no_baseline
- Source: [arXiv:2608.16701](https://arxiv.org/abs/2608.16701)
- Category: architecture
- Solves: accuracy, stability
- ML areas: rnn, training-dynamics
- Math tags: dynamical-systems, computation
- Ratings: usefulness 7/10; difficulty 5/10; novelty 7/10

## 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.

## 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.

## Key formulas

- $$x+a-b<\theta\le x+a$$
- $$m(x,a,b,\theta)=\min\{\theta-(x+a-b),\;x+a-\theta\}>0$$
- $$\mathbb{E}_{G}\left|F_{N}^{\varepsilon_N,\mathrm{E}}(t_*)-F_{N}^{\varepsilon_N,\mathrm{I}}(t_*)-\frac{1}{2}\right|\longrightarrow 0$$
- $$u_i\leftarrow u_i+\Delta_i,\qquad s_i\leftarrow\mathbf{1}[u_i\ge\theta],\qquad u_i\leftarrow(1-s_i)u_i+s_i u_{\mathrm{reset}}$$

## 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

- Status: mech_ok_no_baseline
- Mechanism evidence: yes
- Mechanism confirmed: yes
- Practical verdict: harms
- Verdict: 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.

### Mechanism check

- Verdict: 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.
- Confidence: 9/10
- 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.

### Practical benchmark

- Paired seeds: 8
- Baseline mean: 0
- Idea mean: 0
- p-value: 0.0081
- Paired wins: 0/8
- Benchmark verdict: idea worse (significant)

## Artifacts

- [bench_report.json](https://synthcore.org/code/942/bench_report.json)
- [causal_ei_bench.py](https://synthcore.org/code/942/causal_ei_bench.py)
- [causal_ei_experiment.py](https://synthcore.org/code/942/causal_ei_experiment.py)
- [report.md](https://synthcore.org/code/942/report.md)
- [report_bench_2026-09-01T161842.md](https://synthcore.org/code/942/report_bench_2026-09-01T161842.md)
- [results.json](https://synthcore.org/code/942/results.json)
- [Download all files as ZIP](https://synthcore.org/download/942)

## Disclaimer

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 Not peer-reviewed.