# PRAXIS: Learning Dynamics of Self-Improving Models with Symbolic Archives

arXiv: https://arxiv.org/abs/2610.11803 · HTML: https://mlsanity.com/paper/2610.11803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [AgentSquare: Automatic LLM Agent Search in Modular Design Space](https://mlsanity.com/paper/2410.06153/) (2024)
- [Efficient Reinforcement Finetuning via Adaptive Curriculum Learning](https://mlsanity.com/paper/2504.05520/) (2025)
- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [Nested Learning: The Illusion of Deep Learning Architectures](https://mlsanity.com/paper/2512.24695/) (2025)
- [Guided Self-Evolving LLMs with Minimal Human Supervision](https://mlsanity.com/paper/2512.02472/) (2025)
- [Survey: Multi-Armed Bandits Meet Large Language Models](https://mlsanity.com/paper/2505.13355/) (2025)
- [The Path of Self-Evolving Large Language Models: Achieving Data-Efficient Learning via Intrinsic Feedback](https://mlsanity.com/paper/2510.02752/) (2025)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [SelfAI: A self-directed framework for long-horizon scientific discovery](https://mlsanity.com/paper/2512.00403/) (2025)

## Abstract (arXiv)

Self-improving learning systems adapt data selection, optimization, and auxiliary symbolic components, inducing nonstationary objectives outside standard learning assumptions. We introduce textscPRAXIS, a co-evolutionary framework that models generators, learners, and symbolic archives as interacting dynamical processes. We prove that KL-constrained generator updates and controlled archive-weight movement bound one-step objective drift, that archive updates suppress a program relative to any fixed comparator with a persistent cumulative utility advantage under sub-Gaussian noise, and that stochastic gradient descent achieves an average-stationarity guarantee whose degradation is governed by cumulative objective drift. Experiments across visual robustness, relational graph reasoning, and algorithmic graph reasoning exhibit generator stabilization, decreasing learner loss, and archive concentration consistent with these theoretical mechanisms.