# Let CSP Be Your ANCHOR: Adaptive Crystal Search over Frozen Structure Priors

arXiv: https://arxiv.org/abs/2609.33407 · HTML: https://mlsanity.com/paper/2609.33407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 51 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Unifying Count-Based Exploration and Intrinsic Motivation](https://mlsanity.com/paper/1606.01868/) (2016)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Episodic Curiosity through Reachability](https://mlsanity.com/paper/1810.02274/) (2018)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Reinforcement Learning for Molecular Design Guided by Quantum Mechanics](https://mlsanity.com/paper/2002.07717/) (2020)
- [Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materials](https://mlsanity.com/paper/1911.05020/) (2019)
- [Open Materials Generation with Stochastic Interpolants](https://mlsanity.com/paper/2502.02582/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [Guiding Generative Models to Uncover Diverse and Novel Crystals via Reinforcement Learning](https://mlsanity.com/paper/2511.07158/) (2025)
- [Deep Reinforcement Learning for Inverse Inorganic Materials Design](https://mlsanity.com/paper/2210.11931/) (2022)
- [Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Models](https://mlsanity.com/paper/2605.10759/) (2026)
- [Curiosity in exploring chemical space: Intrinsic rewards for deep molecular reinforcement learning](https://mlsanity.com/paper/2012.11293/) (2020)
- [Crystalite: A Lightweight Transformer for Efficient Crystal Modeling](https://mlsanity.com/paper/2604.02270/) (2026)
- [Kinetic Langevin Diffusion for Crystalline Materials Generation](https://mlsanity.com/paper/2507.03602/) (2025)
- [Open Materials Generation with Inference-Time Reinforcement Learning](https://mlsanity.com/paper/2602.00424/) (2026)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [Atomistic structure learning](https://mlsanity.com/paper/1902.10501/) (2019)
- [CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Models](https://mlsanity.com/paper/2605.08960/) (2026)
- [Reinforcement Learning for Chemical Ordering in Alloy Nanoparticles](https://mlsanity.com/paper/2511.12260/) (2025)

## Abstract (arXiv)

De novo crystal generation (DNG) models decide where to search in composition space and how to generate structures with one set of weights. We argue that discovery is better served by separating the two. A crystal structure prediction (CSP) model is a physical prior that should be improved by likelihood training, while rewards, including novelty measured against the search's own history, should act on a search over compositions. We introduce ANCHOR, a GRPO composition policy trained with multi-objective rewards around a frozen CSP model, and continuous adaptive novelty (CAN), a graded novelty score against known structures and a growing discovery history. Using the frozen CSP model as a fixed ruler under one evaluator, we test where adaptation should act. Replacing DNG compositions with ANCHOR's policy on the same CSP backbone raises MSUN from 11.4% to 47.6% and SUN from 1.1% to 22.1% at 99.9% formula uniqueness. Fine-tuning DNG models directly on the same rewards instead moves their composition marginal without raising their on-hull fraction. We show that KL-regularized fine-tuning of a DNG model can only reweight chemistry the pretrained model already supports by a bounded factor, while unregularized DNG fine-tunes move toward known or less stable chemistry. Even a stability-only reward routed into ANCHOR's CSP backbone roughly halves SUN relative to the frozen backbone, whereas likelihood training on structures found during search can improve a CSP backbone. Under MatterGen's evaluation pipeline, ANCHOR raises state-of-the-art MSUN from 29.2% to 41.3%, transfers without retraining to two further CSP backbones, and reaches 47.1% after distillation into Crystalite-CSP. As with any model optimised against a potential, its on-hull rate depends on that potential.