DOI: 10.5281/zenodo.18601915
title: Pyramidal Hybrid Neural Network Framework (BrainIAc_v2.1) : Technical Documentation and Experimental Results

description: Project Overview

This project validates the design correctness, numerical stability, and learning scalability of a hybrid spiking neuronal network framework implementing e-prop–style local learning rules. The work systematically separates solver stability, biophysical dynamics, and learnability under local credit assignment.

Experiments cover eligibility traces, threshold adaptation, refractory dynamics, excitability bias, and learning behavior across diverse neuron families, including Leaky Integrate-and-Fire (LIF), Izhikevich, and conductance-based Hodgkin–Huxley (HH) models.

The framework is designed to be modular, biophysically grounded, numerically stable, and suitable for downstream plasticity and task-level learning experiments.

Phase 1 — Eligibility Trace Validation

I. Single Spike Trace Validation

(experiment_trace_single_spike.c)

ObjectiveValidate correctness of eligibility trace dynamics in response to a single spike.

ScopeLIF, Izhikevich (RS, IB, CH, FS, LTS), Hodgkin–HuxleyEligibility time constants: 5, 10, 20 ms

Results





Correct impulse response for all neuron families




Exponential decay matches analytical solution




Baseline-relative error < 1%



VerdictFormally validated, invariant, numerically stable

II. Superposition Validation

(experiment_trace_superposition.c)

ObjectiveTest linear superposition under multiple spike events.

Results





Peak amplitudes within ±1% of theoretical values




Accumulation and decay preserved




dt = e/100 ensures <1% numerical error



VerdictLinear time-invariant (LTI) behavior confirmed

III. Baseline Stability

(experiment_trace_baseline.c)

ObjectiveEnsure absence of drift or spontaneous activation.

Results





Mean and max trace values remain exactly zero




Long simulations up to 500k steps



VerdictStable, drift-free baseline

IV. Heterogeneous Neuron Presets

(experiment_trace_heterogeneous_all_neuron_presets.c)

ObjectiveVerify independence of eligibility traces from neuron and synapse type.

Scope





18 neuron presets




4 synapse models




Eligibility constants: 5, 10, 50, 100 ms



Results





Traces identical across all presets (R² = 1.0)




Synapse dynamics do not affect eligibility decay



VerdictFully decoupled; production-ready

Phase 2 — Threshold, Refractory, and Excitability Stability

I. Threshold Drift

(experiment_threshold_drift.c)

Results





Mean firing rates remain stable across input regimes




Adaptive thresholds converge reliably




Long-term drift over 60 s < 2.91 Hz




Recovery from induced silence < 106 ms



VerdictThreshold adaptation is safe for learning

II. Refractory Drift

(experiment_refractory_drift.c)

Results





LIF, Izhikevich, and HH variants maintain stable ISI statistics




Long-term CV ≤ 2%, drift ≤ 2%




Maximum firing rates bounded by intrinsic dynamics



Notes





Clarified distinction between configured refractory time and enforced minimum ISI




Adaptive refractory requires recovery safeguards



VerdictStable, bounded, drift-free with documented architectural constraints

III. Excitability Bias Detection

(experiment_excitability_bias_detection_all_neuron_presets.c)

Results





LIF adaptive/refractory models show strong, sometimes irreversible adaptation




Izhikevich and HH models exhibit mild, fully reversible adaptation



Classification





None / Mild / Strong excitability bias



VerdictClear taxonomy established; strong adapters require gating or reset during training

Learning Rule Experiments

I. Frozen Weight Control

(experiment_frozen_weight_control_all_neuron_presets.c)

ObjectiveConfirm that learning is causally mediated by synaptic plasticity.

Results





Normal training: learning occurs only where gradient is informative




Frozen weights: ΔW = 0; performance flat




Plateaus in LIF/HH consistent with task saturation



ConclusionLearning is weight-mediated and neuron-agnostic

II. Learning Rate Sensitivity

(experiment_learning_rate_sensitivity_all_presets.c)

Results





LIF: stable across most presets; broad learning-rate tolerance




Izhikevich: universally stable; optimal LR ≈ 10⁻³–5×10⁻³




HH: stable only under conservative LR ≈ 5×10⁻⁴



ConclusionNeuron-specific stability windows exist but are predictable and bounded

III. Failed Learning Signal Diagnosis

(experiment_frozen_weight_control.c)

IssueLearning initially absent due to sign error in e-prop signal.

Fix







 



learning_signals[i] = gamma * (actual_rates[i] - target_rates[i]);



Post-fix Results





All neuron families behave consistently




Frozen-weight controls remain zero



ConclusionPipeline reliably detects learning-signal misalignment

Phase 6 — Multi-Neuron Scaling Experiment (Key Result)

QuestionDoes learning scale predictably with network size across neuron families?

Scaling Results by Family

LIF Family (5 presets) — Fully Successful

Presets





Standard, Refractory, Adaptive, EIF, AdEx



Observed





100% loss reduction for all LIF variants except AdEx at very small N




EIF and adaptive variants converge cleanly




Negligible inter-trial variance




AdEx reaches full convergence by N = 10



Conclusion



E-prop is fully compatible with LIF dynamics, including exponential and adaptive variants. Scaling is stable, predictable, and parameter-robust.


Izhikevich Family (8 presets) — Fully Successful

Observed





RS, IB, AC: near-perfect convergence (~100%)




CH, FS, LTS, DS, LTSp: consistent 50–90% reduction




Low variance; no catastrophic failures



Conclusion



Reduced convergence in complex subtypes reflects optimization difficulty, not instability.


Hodgkin–Huxley Family (3 presets) — Systematic Scaling Failure

Observed





Squid: 9–28% loss reduction; high variance




Cortical: failure at N = 1; partial learning at larger N (<50%)




Fast: mixed behavior; inconsistent across N



Interpretation





Numerical stability already validated




Failure is systematic and reproducible




Indicates mismatch between local credit assignment and stiff conductance-based dynamics



Final Scaling Summary








Family
Presets
Scale Successfully




LIF
5
100%


Izhikevich
8
100%


Hodgkin–Huxley
3
0%


Total
16
81%






Scientific Conclusions





Eligibility traces are correct, neuron-agnostic, and decoupled from synapse dynamics




Threshold and refractory mechanisms are stable, bounded, and reversible




Learning is causally plasticity-driven, confirmed by frozen-weight controls




E-prop scales robustly across all LIF and Izhikevich neuron families without tuning




Hodgkin–Huxley failures reflect learning-rule limitations, not numerical instability



These results cleanly separate numerical correctness from learnability, establishing a rigorous validation pipeline.

Outlook

Conductance-based HH neurons likely require:





Modified eligibility traces




Adaptive learning rates




Hybrid local–global credit signals



This work identifies learning-rule extensions—not solver fixes—as the correct direction for future research.

Archive Purpose

This Zenodo archive serves as:





Intellectual property timestamp




Pre-publication technical documentation




Complete reproducibility dataset (raw CSVs, plots, logs)




Validation material for peer review



LicenseCC BY-NC-ND 4.0 — Attribution-NonCommercial-NoDerivatives 4.0 InternationalAcademic and educational use permitted with attributionCommercial use requires explicit written permission

ContactAuthor: Théo ValloisEmail: theo.vallois@hotmail.frGitHub: https://github.com/EmpireStrikesBack/NeuroModel

Source CodeFull BrainIAc framework to be released upon paper acceptance (expected Q1 2026)

Demonstration Videohttps://youtu.be/kiU609iozFw

Archive Size~24.5 MB (50 PDFs documentation)