# Temperature-driven inversion and nonlinear dynamics in ChatGPT-like AIs

arXiv: https://arxiv.org/abs/2608.00939 · HTML: https://mlsanity.com/paper/2608.00939/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 2 Aug 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Can ChatGPT Forecast Stock Price Movements? Return Predictability and Large Language Models](https://mlsanity.com/paper/2304.07619/) (2023)
- [HalluLens: LLM Hallucination Benchmark](https://mlsanity.com/paper/2504.17550/) (2025)
- [A Theoretical Analysis of the Repetition Problem in Text Generation](https://mlsanity.com/paper/2012.14660/) (2020)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [The Curse of Depth in Large Language Models](https://mlsanity.com/paper/2502.05795/) (2025)
- [Large Language Models Hallucination: A Comprehensive Survey](https://mlsanity.com/paper/2510.06265/) (2025)
- [Repetition Neurons: How Do Language Models Produce Repetitions?](https://mlsanity.com/paper/2410.13497/) (2024)
- [Unveiling Attractor Cycles in Large Language Models: A Dynamical Systems View of Successive Paraphrasing](https://mlsanity.com/paper/2502.15208/) (2025)
- [Phase transition in large language models and the criticality of natural languages](https://mlsanity.com/paper/2406.05335/) (2024)
- [Phase Transitions in Large Language Models and the O(N) Model](https://mlsanity.com/paper/2501.16241/) (2025)
- [From Condensation to Rank Collapse: A Two-Stage Analysis of Transformer Training Dynamics](https://mlsanity.com/paper/2510.06954/) (2025)
- [Shadows in the Attention: Contextual Perturbation and Representation Drift in the Dynamics of Hallucination in LLMs](https://mlsanity.com/paper/2505.16894/) (2025)
- [Phase Transitions in the Output Distribution of Large Language Models](https://mlsanity.com/paper/2405.17088/) (2024)
- [Networkcontrology](https://mlsanity.com/paper/1510.08320/) (2015)
- [States of LLM-generated Texts and Phase Transitions between them](https://mlsanity.com/paper/2503.06330/) (2025)
- [LLMs as High-Dimensional Nonlinear Autoregressive Models with Attention: Training, Alignment and Inference](https://mlsanity.com/paper/2602.00426/) (2026)
- [Generative Criticality in Large Language Model Temperature Scaling](https://mlsanity.com/paper/2606.06238/) (2026)

## Built on by (most cited first, 1 of 1)

- [Interaction Creates Dynamical AI Behavior Absent in Isolation](https://mlsanity.com/paper/2608.07457/) (2026)

## Abstract (arXiv)

Increasing the temperature of an ordinary many-state system increases access to a wider range of states and hence increases its entropy. We find the opposite in ChatGPT-like AIs, even though raising the decoder temperature likewise increases access to a wider range of states (next-token choices). Across 12,000 continuations from 11 AIs, autoregressive feedback drives the long-time output population through an entropy maximum and into population inversion. The transition features frozen states, cycles, intermittency and noise-induced ordering. We present evidence of a hidden coordinate that acts as the state variable of an effective nonlinear map. Its trajectory average strongly predicts output repetition in separate test trajectories. ChatGPT-like AIs therefore behave not as `stochastic parrots', but as a new class of controllable nonlinear physical systems whose internal dynamics can be measured and perturbed.