Reference-Guided Hebbian Learning with Nesterov Acceleration: Implementation and Convergence Analysis (Jupyter Notebooks)

This repository contains the complete Python implementation and numerical experiments accompanying the manuscript "Reference-Guided Hebbian Learning with Nesterov Acceleration" (Nesterov-Mueller & Koliakova). The code implements a layer-local neural network training algorithm for binary classification that replaces backpropagation with a reference-guided Hebbian update rule, accelerated by Nesterov's inertial method. The algorithm is built on four theoretical pillars: (1) a per-layer convex LogCosh objective whose gradient coincides with the Hebbian update (following Melchior, Schiewer & Wiskott, 2024); (2) the optimal O(1/t^2) convergence rate (Nesterov, 1983); (3) an implicit diagonal Riemannian metric G_l = I (x) diag(1 - a_l^2) under which the Hebbian update is exactly a preconditioned gradient step, yielding structural immunity to the vanishing gradient problem (Theorem 1 of the manuscript); (4) descent of an augmented Lyapunov functional that combines the per-layer losses with a kinetic term in the Nesterov velocities, following Su, Boyd & Candes (2014). Contents: - Hebbian_Nesterov_Complete.ipynb : full implementation of the ContrastiveHebbianNet class, training on the peptide-based disease classification dataset (n = 105, 49 features), all seven figures of the manuscript, ablation studies, and a direct comparison with backpropagation. - Convergence_Comparison.ipynb : per-epoch convergence analysis comparing Hebbian+Nesterov, BP-Adam, and BP-SGD on training accuracy, test accuracy, training metric (class separation vs. cross-entropy loss), and cluster compactness. - Data.xlsx : the peptide measurement dataset (SampleID x PeptideID, median values, disease status labels). The implementation is in pure NumPy + scikit-learn to facilitate reproduction and inspection of every algorithmic step. No deep learning framework is required. Running both notebooks end-to-end takes approximately five minutes on a standard laptop. Reproducibility: all random seeds are fixed (seed = 42). The geometric classification rule, the Nesterov look-ahead update, and the medoid reference selection are implemented exactly as described in Section 3 of the manuscript. If you use this code in academic work, please cite both this Zenodo record and the accompanying manuscript.