# NOVA: Fundamental Limits of Knowledge Discovery Through AI

arXiv: https://arxiv.org/abs/2605.15219 · HTML: https://mlsanity.com/paper/2605.15219/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 12 May 2026.

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

- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse](https://mlsanity.com/paper/2404.05090/) (2024)
- [How good is Good-Turing for Markov samples?](https://mlsanity.com/paper/2102.01938/) (2021)
- [Non-Bayesian Parametric Missing-Mass Estimation](https://mlsanity.com/paper/2101.04329/) (2021)
- [Mean-Squared Accuracy of Good-Turing Estimator](https://mlsanity.com/paper/2104.07029/) (2021)
- [How Much is Unseen Depends Chiefly on Information About the Seen](https://mlsanity.com/paper/2402.05835/) (2024)
- [Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation](https://mlsanity.com/paper/2509.07355/) (2025)
- [Blind-Spot Mass: A Good-Turing Framework for Quantifying Deployment Coverage Risk in Machine Learning Systems](https://mlsanity.com/paper/2604.05057/) (2026)

## Abstract (arXiv)

Can AI systems discover new knowledge through iterative self-improvement, and at what cost? We introduce NOVA, which models the ``generate, verify, accumulate, retrain'' loop as an adaptive sampling process over a knowledge space. We give sufficient conditions for accumulated genuine knowledge to cover a finite domain and show how violations produce contamination, forgetting, exploration failure, and acceptance failure. We then analyze how adaptive generation arises from recursive retraining. In an explicit distribution-level model where accepted artifacts influence the next generator, we identify a recursive-feedback phase transition. Unanchored feedback can lock generation onto early accepted artifacts and leave initially reachable valid artifacts undiscovered with positive probability. Anchoring updates to a persistent base distribution prevents unbounded distortion and guarantees continued exposure. Under imperfect verification, we identify a contamination trap: as easy knowledge is exhausted, even small false-positive rates can admit invalid artifacts faster than genuine discoveries. We show that Good--Turing estimation is a local batch-diversity diagnostic, not an estimator of the historically undiscovered valid mass governing long-term progress. Under a Zipf tail with exponent α>1, the cumulative generation cost of obtaining D distinct genuine discoveries satisfies Rrm cum(D)=Theta(crm genDα). When the valid base distribution has such a tail, anchored retraining preserves the exposure needed for this scaling law. Finally, we show how human guidance, generation, and verification can redirect or expand discovery when autonomous sampling stalls because of repetition, vanishing exposure, or unreliable verification.