Locality and weight sharing shape Hebbian principal-component learning in biologically constrained visual models.

Introduction: Biologically motivated artificial visual learning requires local plasticity rules to be evaluated within architectures whose connectivity assumptions remain explicit. Convolutional Hebbian networks demonstrate that competitive local learning can support visual classification, but their performance is coupled to exact weight sharing, a prior that is not anatomically literal. This study asks whether Hebbian principal component analysis (HPCA) can support representations when spatial locality is preserved but exact translational weight sharing is removed. Methods: HPCA was evaluated on CIFAR-10 as the primary benchmark, with MNIST and STL-10 used as controls. We compared fully connected HPCA, position-specific locally connected HPCA with fixed receptive fields, non-shared synaptic weights, and population-wise divisive response normalization, and HPCA substitutions in two shared-kernel convolutional Hebbian benchmarks. Representations were learned without supervised feature-layer targets or BP-based feature-layer fine-tuning, frozen, and evaluated through supervised readouts. Results: Position-specific locally connected HPCA outperformed the fully connected reference. On CIFAR-10, the best locally connected model reached 61.42 ± 0.36%. Shared-kernel HPCA reached 74.51 ± 0.38% in the modular benchmark with common HPCA preprocessing and 76.57 ± 0.55% in the SoftHebb architecture with reference preprocessing. Discussion: The results show that HPCA remains effective across position-specific locally connected and shared-kernel convolutional architectures, but that performance depends strongly on the surrounding architecture and benchmark protocol. The tested shared-kernel configurations achieved higher accuracy, yet useful frozen visual representations still emerged when exact parameter sharing was removed. Locally connected HPCA therefore provides a controlled model for examining how local plasticity interacts with receptive-field structure and convolutional inductive bias in biologically constrained visual learning.