# Cycle is All You Need: More Is Different

arXiv: https://arxiv.org/abs/2509.21340 · HTML: https://mlsanity.com/paper/2509.21340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 81 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Cognitive computational neuroscience](https://mlsanity.com/paper/1807.11819/) (2018)
- [Sheaf theory: from deep geometry to deep learning](https://mlsanity.com/paper/2502.15476/) (2025)
- [Internal feedback in the cortical perception-action loop enables fast and accurate behavior](https://mlsanity.com/paper/2211.05922/) (2022)
- [Nonmodular architectures of cognitive systems based on active inference](https://mlsanity.com/paper/1903.09542/) (2019)
- [Inverted Inference and Recursive Bootstrapping: A Primal-Dual Theory of Structured Cognition](https://mlsanity.com/paper/2404.01183/) (2024)
- [Self-orthogonalizing attractor neural networks emerging from the free energy principle](https://mlsanity.com/paper/2505.22749/) (2025)
- [Poincare return maps in neural dynamics: three examples](https://mlsanity.com/paper/2007.05595/) (2020)
- [Computation, Condensation, and the Incompleteness Between Them: A Coupled Foundation of Intelligence](https://mlsanity.com/paper/2303.04203/) (2023)
- [On Broken Symmetry in Cognition](https://mlsanity.com/paper/2303.06047/) (2023)
- [Associative Memory for Non-Stationary Environments: A Self-Sizing Generalization of Hopfield Networks](https://mlsanity.com/paper/2507.10443/) (2025)
- [What should we forget? A computational model of memory consolidation](https://mlsanity.com/paper/2508.11646/) (2025)
- [The Urysohn Machine: A Metric-Topological Model of Computation](https://mlsanity.com/paper/2508.14143/) (2025)

## Abstract (arXiv)

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.