S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning

TL;DR

S-AI-Recursive is a bio-inspired, energy-efficient AI architecture that uses hormonal feedback loops for iterative reasoning, formalized as a dynamical system with proven stability and tested on symbolic benchmarks.

Contribution

It introduces a novel recursive reasoning cycle driven by two hormones, formalizes the framework mathematically, and demonstrates competitive performance with fewer parameters.

Findings

Achieves stable iterative reasoning with fewer than ten million parameters.

Proves Lyapunov stability and entropic contraction of the reasoning cycle.

Demonstrates competitive reasoning performance on symbolic benchmarks.

Abstract

This article introduces S-AI-Recursive, a bio-inspired Sparse Artificial Intelligence architecture in which reasoning is operationalized as a hormonal closed-loop iteration rather than a single feed-forward pass. Building upon the S-AI foundational framework [1], the hormonal-probabilistic unification doctrine [2], and the formal mathematical methodology established in S-AI-IoT [3], the present work formalizes the Recursive Reasoning Cycle (RRC) as a dynamical system governed by two novel hormones: Clarifine, a convergence signal, and Confusionin, an uncertainty detector, whose antagonistic regulation drives iterative state refinement toward a stable cognitive equilibrium. The complete mathematical framework is developed, including recursive state dynamics, Lyapunov stability proof, entropic contraction theorem, hormonal stopping criterion with finite-time termination guarantee, Euler-Maruyama discretization with projection, primal-dual agent selection under iteration budget, and recursive engram memory with warm-start acceleration. Experimental validation on the SAI-UT+ testbench demonstrates that S-AI-Recursive achieves competitive reasoning performance on abstract and symbolic benchmarks with fewer than ten million parameters, confirming the central principle of temporal parsimony: iterative cognitive depth substitutes for architectural width.