SNT-LIFE: From Worm to LLM — A Seven-Operator Theory of Learning and Memory

Learning in both biological and artificial systems involves a sequence of interacting processes: stochastic exploration of the state space, evaluation of outcomes against an adaptive threshold, consolidation of relevant experience into long-term memory, retrieval of previously stored associations, and selective forgetting of low-utility representations. We introduce SNT-LIFE, an operator-based framework that approximates these five functional roles using a compact set of seven structured operators: the Fluctuating operator () for stochastic exploration; the Cyclic Reset operator () for baseline restoration; the Phase Nexter operator () for rapid associative retrieval; the Phase Reverser operator () for error-driven behavioral reversal; the Liminal operator () for homeostatic decision thresholding; the Irreversible Loss operator () for pruning of low-utility memories; and the Subspace Mapping operator () for experience-to-memory consolidation. The operators are formulated as completely positive trace-preserving (CPTP) mappings, or structured approximations thereof, acting on a finite-dimensional density operator state. In a linearized regime near a fixed point, we observe numerical closure of the seven-element operator basis under the Frobenius projection, with residual εclosure ≤ 4.82 × 10⁻¹⁵ on the empirical C.~elegans connectome~{Cook2019}. We further introduce a Soft-Clamp homeostatic threshold adaptation mechanism, for which we provide a fixed-point convergence analysis under a monotonicity assumption. We evaluate the framework in two settings. First, we show that the operator composition is empirically consistent with neural dynamics in the C.~elegans connectome, reproducing key statistical features of whole-brain calcium imaging data~{Kato2015}: PC1 variance~42.3% (observed~43.8%), variance-spectrum correlation $r = 0.986$, and cross-worm generalization $r > 0.95$ on all five recordings. Second, we implement the framework as a memory management layer (SNT-MEM) for Llama-3-8B, suggesting 63.3%± 2.1% memory reduction and 3.8×± 0.3× retrieval speedup on the LongBench benchmark~{LongBench2023}. Ablation studies are consistent with the hypothesis that consolidation and selective forgetting contribute substantially to sustained learning performance; further experimental validation is required to establish generality.