{"ID":2871161,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21340","arxiv_id":"2509.21340","title":"Cycle is All You Need: More Is Different","abstract":"We propose an information-topological framework in which cycle closure is the fundamental mechanism of memory and consciousness. Memory is not a static store but the ability to re-enter latent cycles in neural state space, with invariant cycles serving as carriers of meaning by filtering order-specific noise and preserving what persists across contexts. The dot-cycle dichotomy captures this: transient dots scaffold exploration, while nontrivial cycles encode low-entropy content invariants that stabilize memory. Biologically, polychronous neural groups realize 1-cycles through delay-locked spiking reinforced by STDP, nested within theta-gamma rhythms that enforce boundary cancellation. These micro-cycles compose hierarchically, extending navigation loops into general memory and cognition. The perception-action cycle introduces high-order invariance: closure holds even across sense-act alternations, generalizing ancestral homing behavior. Sheaf-cosheaf duality formalizes this process: sheaves glue perceptual fragments into global sections, cosheaves decompose global plans into actions and closure aligns top-down predictions with bottom-up cycles. Consciousness then arises as the persistence of high-order invariants that integrate (unity) yet differentiate (richness) across contexts. We conclude that cycle is all you need: persistent invariants enable generalization in non-ergodic environments with long-term coherence at minimal energetic cost.","short_abstract":"We propose an information-topological framework in which cycle closure is the fundamental mechanism of memory and consciousness. Memory is not a static store but the ability to re-enter latent cycles in neural state space, with invariant cycles serving as carriers of meaning by filtering order-specific noise and preser...","url_abs":"https://arxiv.org/abs/2509.21340","url_pdf":"https://arxiv.org/pdf/2509.21340v1","authors":"[\"Xin Li\"]","published":"2025-09-15T21:48:30Z","proceeding":"cs.NE","tasks":"[\"cs.NE\",\"cs.AI\",\"cs.LG\",\"q-bio.NC\"]","methods":"[\"LoRA\"]","has_code":false}