# Beyond Action Entropy: Quotient-Space Exploration for Genome-Scale Metabolic Model Repair

arXiv: https://arxiv.org/abs/2610.11627 · HTML: https://mlsanity.com/paper/2610.11627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [SetPO: Set-Level Policy Optimization for Diversity-Preserving LLM Reasoning](https://mlsanity.com/paper/2602.01062/) (2026)
- [Symmetry-Aware GFlowNets](https://mlsanity.com/paper/2506.02685/) (2025)
- [A generalizable framework for unlocking missing reactions in genome-scale metabolic networks using deep learning](https://mlsanity.com/paper/2409.13259/) (2024)
- [GGBound: A Genome-Grounded Agent for Microbial Life-Boundary Prediction](https://mlsanity.com/paper/2605.14442/) (2026)

## Abstract (arXiv)

Repairing scientific models from functional observations differs fundamentally from supervised prediction: feedback may certify a solution without revealing which structural correction is responsible. We study this setting for genome-scale metabolic model (GEM) repair, where multiple reaction edits can explain the same phenotypes and many apparently distinct edits correspond to the same biological mechanism. This many-to-one structure creates a hidden failure mode for conventional exploration: diversity in the output space need not translate into diversity of scientific hypotheses. We introduce QuotientPO, which collapses equivalent repairs into canonical mechanisms and optimizes exploration directly over the resulting quotient space. To make quotient exploration informative under finite rollouts, we derive a kernelized R'enyi estimator that resolves graded crowding among distinct repair cores beyond coarse exact-match counts. On 2,212 held-out GEMs, QuotientPO improves Success@32 from 17.93% to 20.10% (+12.1% relative) while consistently increasing distinct successful-core discovery under the same sampling budget. These results establish quotient-space exploration as a principled approach to mechanism-level discovery under verifier-induced equivalence.