# Intuition emerges in Maximum Caliber models at criticality

arXiv: https://arxiv.org/abs/2508.06477 · HTML: https://mlsanity.com/paper/2508.06477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 53 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (2020)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [The Debate Over Understanding in AI's Large Language Models](https://mlsanity.com/paper/2210.13966/) (2022)
- [Statistical physics of inference: Thresholds and algorithms](https://mlsanity.com/paper/1511.02476/) (2015)
- [Superhuman performance of a large language model on the reasoning tasks of a physician](https://mlsanity.com/paper/2412.10849/) (2024)
- [Designing Ecosystems of Intelligence from First Principles](https://mlsanity.com/paper/2212.01354/) (2022)
- [Intelligence at the Edge of Chaos](https://mlsanity.com/paper/2410.02536/) (2024)
- [Parameter Symmetry Potentially Unifies Deep Learning Theory](https://mlsanity.com/paper/2502.05300/) (2025)
- [Collective behavior from surprise minimization](https://mlsanity.com/paper/2307.14804/) (2023)
- [Neural Thermodynamics: Entropic Forces in Deep and Universal Representation Learning](https://mlsanity.com/paper/2505.12387/) (2025)
- [Complex behavior from intrinsic motivation to occupy action-state path space](https://mlsanity.com/paper/2205.10316/) (2022)
- [An effective theory of collective deep learning](https://mlsanity.com/paper/2310.12802/) (2023)
- [Leveraging chaotic transients in the training of artificial neural networks](https://mlsanity.com/paper/2506.08523/) (2025)
- [Intrinsic motivation as constrained entropy maximization](https://mlsanity.com/paper/2502.02962/) (2025)
- [The Missing Reward: Active Inference in the Era of Experience](https://mlsanity.com/paper/2508.05619/) (2025)

## Abstract (arXiv)

Whether large predictive models merely parrot their training data or produce genuine insight lacks a physical explanation. This work reports a primitive form of intuition that emerges as a metastable phase of learning that critically balances next-token prediction against future path-entropy. The intuition mechanism is discovered via mind-tuning, the minimal principle that imposes Maximum Caliber in predictive models with a control temperature-like parameter λ. Training on random walks in deterministic mazes reveals a rich phase diagram: imitation (low λ), rule-breaking hallucination (high λ), and a fragile in-between window exhibiting strong protocol-dependence (hysteresis) and multistability, where models spontaneously discover novel goal-directed strategies. These results are captured by an effective low-dimensional theory and frame intuition as an emergent property at the critical balance between memorizing what is and wondering what could be.