SNT-LIFE: A Minimal Operator Framework for Learning and Memory Across Biological and Artificial Systems

Learning in both biological and artificial systems involves a sequence of processes including exploration, evaluation, consolidation, retrieval, and forgetting. We introduce an operator-based framework in which these processes are represented by a compact set of seven operators: fluctuation, cyclic reset, phase nexter, phase reverser, liminal thresholding, irreversible loss, and subspace mapping — a set we find sufficient in the studied settings. Unlike existing approaches that rely on large parameterized models, the proposed framework emphasizes structural minimality and composability. The operators are formulated as operator mappings, with several components satisfying completely positive trace-preserving (CPTP) conditions, acting on a finite-dimensional state space. In a linearized regime, we observe numerical closure under the Frobenius projection (residual 4. 82 10^-15). We further introduce a homeostatic threshold adaptation mechanism (Soft-Clamp) that stabilizes learning dynamics without manual parameter tuning. We evaluate the framework in two settings. First, we show that the operator composition provides a consistent interpretation of neural dynamics in the C. elegans connectome, reproducing key statistical features observed in calcium imaging data, achieving a variance spectrum correlation of r = 0. 986 with only seven global parameters — an 86 reduction compared to Wilson-Cowan models. Second, we implement the framework as a memory management layer (SNT-MEM) in a large language model (Llama-3-8B), achieving 63. 3\% 2. 1\% memory reduction and 3. 8 0. 3 retrieval speedup on the LongBench benchmark. Ablation studies indicate that consolidation and selective forgetting mechanisms are necessary for sustained learning performance in our experiments. These results provide evidence that operator-structured learning dynamics can serve as a compact and transferable description of learning across biological and artificial systems, while further validation is required to establish generality.