S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910218093330432 |
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| author | Slaoui, Said |
| author_facet | Slaoui, Said |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13872 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning Slaoui, Said Neural and Evolutionary Computing Artificial Intelligence 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. |
| title | S-AI-Recursive: A Bio-Inspired and Temporal Sparse AI Architecture for Iterative, Introspective, and Energy-Frugal Reasoning |
| topic | Neural and Evolutionary Computing Artificial Intelligence |
| url | https://arxiv.org/abs/2605.13872 |