---
title: "Governing Equations of Human Sleep Macro-Structure:Symbolic Discovery from 1,106 Nights"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.00550v1"
permalink: "https://feed.astralor.com/items/itm_8e787a7932f483fe7449fb9c"
published: "2026-10-31T02:19:16.000Z"
score: 57
channel: "ai"
tags: ["Governing Equations","Human Sleep Macro-Structure","Symbolic Discovery","Nights Human","REM","These","Human"]
---

# Governing Equations of Human Sleep Macro-Structure:Symbolic Discovery from 1,106 Nights

## At a glance

Human sleep is organized into a small number of cycles per night: deep sleep dominates early cycles, REM lengthens toward morning, and light sleep clusters at cycle boundaries. These regularities have long been describe…

## Key points

- Human sleep is organized into a small number of cycles per night: deep sleep dominates early cycles, REM lengthens toward morning, and light sleep clusters at cycle boundaries.
- These regularities have long been described qualitatively but never distilled into closed-form laws from large-scale data.
- A total of 1,106 nights (Sleep-EDF 153 + SHHS 953) are segmented into REM-anchored cycles, and four cycle-indexed statistics follow simple closed-form equations: cycle length declines nearly linearly (R^2=0.996), REM du…

## Full text

Human sleep is organized into a small number of cycles per night: deep sleep dominates early cycles, REM lengthens toward morning, and light sleep clusters at cycle boundaries. These regularities have long been described qualitatively but never distilled into closed-form laws from large-scale data. A total of 1,106 nights (Sleep-EDF 153 + SHHS 953) are segmented into REM-anchored cycles, and four cycle-indexed statistics follow simple closed-form equations: cycle length declines nearly linearly (R^2=0.996), REM duration follows an inverted U (R^2=0.873), deep-sleep (N3) run length decays exponentially (R^2=0.987) with a time constant of 2.94 cycles, consistent with the homeostatic Process S of the two-process model, and light-sleep (N1) run length follows a U shape (R^2=0.956), confirming a "long-short-long" pattern across the night. The laws are reproduced by per-night differentiable fitting (142/142 and 773/773 nights converge), by unconstrained symbolic regression (PySR), and by a 500-night generative synthesizer built from them. Their robustness is established against the two main methodological threats: bootstrap CIs computed by resampling whole nights (1,000 replications) exclude zero for every shape term, and a five-level scan of the REM-merge segmentation threshold preserves every qualitative form. These appear to be the first closed-form laws governing the macro-structure of sleep, distilled and tested across an age-mixed sample (healthy young adults and community-based older adults).

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