# Discovery under Hypothesis Redundancy: A Geometric Theory of Discovery Bottlenecks

arXiv: https://arxiv.org/abs/2606.14386 · HTML: https://mlsanity.com/paper/2606.14386/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Alpha-GPT: Human-AI Interactive Alpha Mining for Quantitative Investment](https://mlsanity.com/paper/2308.00016/) (2023)
- [Chain-of-Alpha: Unleashing the Power of Large Language Models for Alpha Mining in Quantitative Trading](https://mlsanity.com/paper/2508.06312/) (2025)
- [Iterative Hypothesis Generation for Scientific Discovery with Monte Carlo Nash Equilibrium Self-Refining Trees](https://mlsanity.com/paper/2503.19309/) (2025)

## Abstract (arXiv)

Scientific discovery saturates when new hypotheses cease to provide independent information, even if the nominal hypothesis space remains large. We study hybrid discovery systems that combine structured local search with LLM-generated non-local proposals and pose the Search Compression Hypothesis: non-local exploration helps only when three geometric conditions co-occur: spectral compression, orthogonal escape from the explored span, and residual signal alignment with the target. We formalize these conditions, derive necessary conditions for hybrid advantage, and test the mechanism in controlled synthetic environments, large-scale A-share factor discovery, and symbolic-regression benchmarks; a public tabular operational sanity check tests the associated budget-allocation implication. Signal-planting and directed-versus-random experiments show that novelty alone is insufficient: random orthogonal jumps expand coverage but do not improve yield without predictive alignment. Across compression sweeps, real factor archives, and LLM-SRBench tasks, hybrid gains concentrate in weakly represented but target-bearing directions and vanish as the hypothesis space approaches full rank. The framework turns LLM-guided discovery from generic novelty search into a diagnostic procedure for deciding when directed non-local exploration is warranted.