Cycle is All You Need: More Is Different

• URL: http://arxiv.org/abs/2509.21340v1
• Date: Mon, 15 Sep 2025 21:48:30 GMT
• Title: Cycle is All You Need: More Is Different
• Authors: Xin Li,
• Abstract summary: We propose an information-topological framework in which cycle closure is the fundamental mechanism of memory and consciousness.<n>We show that memory is not a static store but the ability to re-enter latent cycles in neural state space.<n>We conclude that cycle is all you need: persistent invariants enable generalization in non-ergodic environments.
• Score: 6.0044467881527614
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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