Elliptic cortical networks: A mathematically constrained architecture for biologically-inspired intelligence

Cortical columns form the brain’s computational backbone, yet artificial networks fail to capture their sophisticated organization. This work introduces Elliptic Cortical Networks (ECN), which model each of six cortical layers using multiple elliptic curves—between two and seven per layer. The Weierstrass equation y 2 = x 3 + a x + b ( mod p ) constrains computations to valid curve points, preventing hallucination without explicit regularization. Layer-specific field sizes reflect biological roles: small fields in Layer I enable rapid modulation, while large fields in Layer IV preserve sensory precision. Inter-curve projections implement synaptic connectivity through feature extraction, transformation, and remapping operations. Temporal dynamics follow Hierarchical Temporal Memory (HTM) principles via curve point evolution. Comprehensive experimental validation across six dimensions demonstrates: 1980-fold memory compression for neural state representation, 374 forward passes per second throughput, 100 % accuracy on XOR learning tasks, and 12.3 % ± 6.4 % improvement in predictive learning but with perfect mathematical constraint satisfaction (100 %). The architecture demonstrates that mathematical constraints can enhance rather than limit computational power, offering a path toward more reliable artificial intelligence systems.