Optimal Neural Network Repair: Achieving Theoretical Limits in Fragment Recovery via Component Fusion
This repository contains the code, data, and experiments for the research paper "Optimal Neural Network Repair: Achieving Theoretical Limits in Fragment Recovery via Component Fusion".
The project establishes and empirically validates the theoretical limit for neural network repair: the minimum number of connections required to restore structural integrity is exactly equal to the number of fragmented components. Our findings are validated on a large-scale network (850 neurons) under severe damage (85% random pruning) and confirmed with a robust statistical analysis of 100 independent replicas.
Statistical analysis of repair strategies across 100 independent replicas under 85% random pruning, demonstrating the perfect consistency and superiority of Component Fusion.
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- 🔬 Validated Theoretical Limit: We demonstrate that the minimum connections for a complete repair equals the number of fragments (
$C_{\text{min}} = F$ ).¹ - 💯 Deterministic Reliability: Our method (Component Fusion) achieved a 100% success rate across 100 replicas, while baselines achieved only 1% and 0%.¹
- 💡 Resource Optimality: We achieved perfect repair using 50% fewer connections than baseline strategies, which were given double the budget and still failed.¹
- ⚙️ Statistical Rigor: All findings were validated under severe stress conditions (85% random pruning on an 850-neuron network) to ensure robustness.¹
This repository is designed for open science and full reproducibility. You can run the complete pipeline, from network generation to statistical analysis and results visualization, in the following Google Colab notebook.
Complete Validation Pipeline Run the large-scale experiment and the 100-replica robustness test to validate the paper's findings.
Component_Fusion_Experiment.ipynb: The interactive Colab notebook with all experiments./data: Contains the .csv files with the detailed results from the 100 replicas./figures: Contains the high-quality figures generated for the paper.LICENSE: The project's MIT License.README.md: This file.
This work was conducted completely independently, without institutional or corporate funding, demonstrating that cutting-edge research can also emerge from open and accessible environments. This project is the practical application and empirical validation of the principles explored in the Topological Reinforcement Operator project.
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BibTeX Snippet
José Ignacio Peinador Sala. Optimal Neural Network Repair: A Principled Approach to Achieving the Theoretical Limits of Structural Restoration, 23 October 2025, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-7926139/v1]