Beyond Pattern Recognition: A New Paradigm Uniting Symbolicism and Connectionism

This version archives a focused follow-up research package from the Neural Sculpting Paradigm project: the Neural K Framework and Evidence Package.

The framework studies neural-network induction from a training-set-centered, loss-resolved function-space perspective. It proposes and experimentally tests two central principles: (1) a fixed neural architecture, encoding, loss, and parameter measure induce a highly non-uniform prior over functions; and (2) as raw loss on a complete target is tightened, the parameter volumes of different functions and within-function implementations contract at different rates. The resulting architecture-relative, precision-dependent curve is called the Neural K-profile.

The package connects this framework to direct generalization, grokking, overfitting, Minimum Description Length, algorithmic information theory, statistical-mechanical free energy, prediction, agreement, and symbolic rule formation. It also distinguishes static function-space geometry from optimizer reachability and dynamics.

The archive contains the author-reviewed Core Theory, a research narrative, a detailed evidence ledger, E01–E25 experiment documentation and reproduction scripts, references, and a bilingual static website. The Core Theory was reviewed paragraph by paragraph and deeply revised by the author. The specific prose of the remaining materials was organized by AI from the author’s experiments, theoretical judgments, scripts, result packages, and research conversations.

This is a timestamped interim research archive rather than a completed peer-reviewed paper.

Snapshot:
Git commit: acafc97ee8c617d62edc6c59025fdb953fb7e5fd
Repository: https://github.com/ball-lightning6/neural-sculpting-paradigm