🔬 materials science

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

The paper introduces ANCHOR, a framework that decouples crystal structure generation from composition search by employing a frozen Crystal Structure Prediction (CSP) model as a fixed physical prior while using a GRPO-trained policy with adaptive novelty rewards to optimize composition selection, thereby significantly improving the discovery of unique, stable, and novel crystal structures compared to traditional end-to-end de novo generation approaches.

Original authors: Emma Lei Hovmand, Jonas Elsborg, Melih Kandemir, Arghya Bhowmik

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Emma Lei Hovmand, Jonas Elsborg, Melih Kandemir, Arghya Bhowmik

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The search for new materials is a quest to find the perfect arrangement of atoms. Crystalline solids, the ordered structures that make up everything from computer chips to battery electrodes, hold the key to solving some of humanity's biggest energy and environmental challenges. However, the universe of possible crystal combinations is so vast that finding a stable, useful one is like looking for a needle in a haystack the size of a galaxy. For decades, scientists have relied on two main approaches to solve this puzzle. The first is to predict the structure of a crystal once its chemical recipe is known. The second is to generate entirely new materials from scratch, inventing both the recipe and the structure simultaneously. While modern computer models have become incredibly good at guessing what a crystal looks like once its ingredients are listed, they often struggle to decide which ingredients are worth trying in the first place. They tend to stick to recipes they have seen before, missing the rare, stable combinations that lie just outside their training data.

A team of researchers at the Technical University of Denmark and the University of Southern Denmark has proposed a new way to navigate this vast chemical space. They argue that the computer's ability to guess a structure and its ability to choose a recipe are two different skills that should not be forced to work as a single unit. In their new system, called ANCHOR, they separate these tasks completely. They take a powerful, pre-trained model that acts as a reliable "structural prior"—a fixed, unchanging expert that knows how to build stable crystals for any given set of ingredients. This expert model is frozen in place, meaning it is never altered during the search. Instead, a separate, adaptive "search agent" is trained to decide which chemical recipes to propose to this expert. This agent learns by trial and error, receiving rewards when it suggests a recipe that leads to a stable, unique, and previously unknown crystal.

The researchers found that when they let the search agent guide the process, the results improved dramatically. By keeping the structural expert frozen and only training the agent to choose better recipes, they increased the rate of finding stable, unique, and novel crystals from 11.4% to 47.6%. This is a massive leap in efficiency. In contrast, when they tried to train the entire system at once—letting the model change both its recipe choices and its structural building rules—the system tended to collapse. It would start repeating the same few recipes over and over, or it would drift toward chemical combinations that were easy to score but physically unstable. The study showed that trying to optimize the whole model at once often leads to a loss of diversity, where the computer gets stuck in a loop of rediscovering the same old materials rather than finding new ones.

A key innovation in this work is a new way of measuring "novelty." Traditional methods check if a new crystal looks like anything in a fixed database of known materials. If it doesn't match, it gets a reward. However, this approach has a flaw: if the computer finds a new crystal and then finds it again later, it still gets the same reward, encouraging it to waste time rediscovering what it already knows. The ANCHOR system uses a "continuous adaptive novelty" score. This score checks the new crystal against both the fixed database and the system's own growing history of discoveries. If the system has already found a specific structure, the score drops to zero, effectively telling the search agent, "You have already seen this; try something else." This simple rule prevents the search from getting stuck in loops and forces it to keep exploring new territory.

The researchers also discovered that the way rewards are applied matters as much as the rewards themselves. When they tried to improve the structural model directly by feeding it rewards, the model's ability to find stable crystals actually worsened. The model learned to game the system, producing structures that looked good on paper but were physically unstable. However, when they used the structures found by the search agent to retrain the structural model later, the model improved. This suggests a clear division of labor: the search agent should explore the chemical space to find promising recipes, and the structural model should be refined later using the best examples found during that search.

The results of this approach are significant. Under standard testing conditions used by the field, the ANCHOR system achieved a success rate of 41.3% for finding stable, unique, and novel crystals, surpassing the previous best results of 29.2%. Even more impressively, the system was able to transfer its knowledge to different structural models without needing to be retrained, proving that the search strategy is robust and adaptable. The study concludes that the bottleneck in discovering new materials is not the ability to build a crystal, but the ability to choose the right chemical recipe to build it. By separating the search for recipes from the construction of structures, and by using a smart, history-aware scoring system, the researchers have shown a clear path toward more efficient and effective materials discovery. This work suggests that the future of finding new materials lies not in making bigger, more complex models, but in organizing the search process more intelligently.

Technical Summary: Let CSP Be Your ANCHOR

Problem Statement

De novo crystal generation (DNG) models typically learn a joint distribution $p_0(c, x) = p_0(c)p_0(x|c)$ , where $c$ represents chemical composition and $x$ represents crystal structure. In these models, the composition marginal $p_0(c)$ acts as a chemical prior derived from training data, while the conditional $p_0(x|c)$ addresses the crystal structure prediction (CSP) problem. The authors argue that discovery is hindered when reward-guided fine-tuning adapts the entire joint generator.

When a single model is fine-tuned with rewards (e.g., stability, novelty, uniqueness), the optimization conflates two distinct tasks: deciding where to search in composition space and deciding how to generate structures for a given composition. The paper posits that:

Reward-driven adaptation should primarily alter the composition marginal to explore new chemical spaces, not the structural generator.
Structural priors (CSP models) should remain fixed or be improved via likelihood training on discovered structures, rather than being distorted by reward gradients that may penalize physically plausible structures simply because they have been "seen" before (history-dependent novelty).
History-dependent novelty creates a semantic credit assignment problem: a crystal does not become less physically plausible after discovery, yet optimizing a joint generator against such rewards forces the structural model to adapt to search history rather than physics.

Methodology: ANCHOR

The authors introduce ANCHOR (Adaptive Novelty for Crystals with History-aware Outer-loop Reinforcement), a framework that architecturally separates the composition search from structure generation.

1. Architectural Separation

ANCHOR replaces the likelihood-trained composition marginal of a DNG model with a trainable composition policy ( $\pi_\theta$ ), while keeping the structural prior (a pretrained CSP model) frozen.

Frozen CSP Backbone: A pretrained diffusion model (e.g., KLDM-CSP) acts as a fixed physical prior. It generates structures $x$ given a composition $c$ queried by the policy. This model is never updated via reward gradients.
GRPO Composition Policy: A separate policy $\pi_\theta(c)$ is trained using Group Relative Policy Optimization (GRPO). This policy learns to propose compositions $c$ that maximize rewards when processed by the frozen CSP.

2. Continuous Adaptive Novelty (CAN)

To address the issue of rediscovery and the limitations of fixed-reference novelty, ANCHOR employs Continuous Adaptive Novelty (CAN):

Graded Scoring: Instead of a binary novel/known flag, structures are scored using a k-nearest-neighbour (kNN) Radial Distribution Function (RDF) distance against a reference set.
Adaptive History: The reference set includes both a fixed external database (MP-20) and a growing history ( $Z_{hist}$ ) of structures discovered during the current search.
Mechanism: The novelty score $\nu(x)$ is the minimum of the score against the fixed reference and the score against the agent's own history. Once a structure (or a closely related one) is found, its novelty score drops, preventing the policy from receiving rewards for rediscovering it. This ensures the search continues to explore rather than collapse onto known or previously found compositions.

3. Multi-Objective Reward

The policy is optimized using a multi-objective reward function $r(c)$ that includes:

Stability: Based on energy above the convex hull ( $E_{hull}$ ).
Diversity: Structural and compositional diversity within a rollout group.
Count Bonus: A decaying bonus for visiting new reduced formulas to prevent premature convergence.
Adaptive Novelty: The CAN score described above.

The reward is scalarized using weights sampled from a Dirichlet distribution for each rollout, allowing the policy to learn trade-offs without fixed hyperparameters.

Key Contributions

Separation of Composition and Structure: ANCHOR demonstrates that replacing the composition marginal of a DNG model with a GRPO policy, while freezing the CSP backbone, significantly outperforms fine-tuning the joint generator. This isolates the "search" (composition) from the "generation" (structure).
Continuous Adaptive Novelty (CAN): The authors show that a graded, history-aware novelty score is essential for sustained discovery. Binary novelty flags or fixed-reference novelty alone lead to lower Unique and Novel rates. CAN prevents the search from collapsing onto repeated compositions, raising the Stable, Unique, Novel (SUN) metric from 8.9% (binary flag) to 22.1% under the internal evaluator.
Empirical Validation of Separation: Using the frozen CSP as a "fixed ruler," the authors prove that the composition marginal is the primary bottleneck in DNG discovery. Replacing the DNG composition source with ANCHOR's policy on the same CSP backbone increases MSUN (Metastable, Unique, Novel) from 11.4% to 47.6% and SUN from 1.1% to 22.1% under the internal evaluator.
Distillation vs. Reward Fine-tuning: The paper shows that fine-tuning a DNG model directly with rewards (DDPO) mostly shifts the composition marginal toward "easy" chemistry (often rediscovering known structures) without improving the on-hull fraction. Conversely, likelihood training (distillation) on structures found by the search improves the CSP backbone's ability to generate stable structures.

Results

Under the MatterGen evaluation pipeline and internal protocols:

State-of-the-Art Performance: Under the MatterGen evaluation pipeline, ANCHOR achieves 41.3% MSUN, surpassing the previous best MatterGen result of 29.2% MSUN. Under the internal evaluator using the KLDM backbone, ANCHOR raises MSUN from 11.4% to 47.6% and SUN from 1.1% to 22.1%.
Transferability: The ANCHOR policy transfers without retraining to different CSP backbones (Crystalite-CSP, OMatG-CSP), maintaining high discovery rates (e.g., 46.7% MSUN on Crystalite).
Distillation Gains: Distilling the CSP backbone using structures found by ANCHOR (via likelihood training) further improves performance. Under the MatterGen pipeline, distillation into Crystalite-CSP raises MSUN to 47.1%. Under the internal evaluator, distillation into Crystalite-CSP raises SUN from 20.4% to 26.0%.
Failure of Joint Fine-tuning: Reward fine-tuning of DNG models (Crystalite-DNG, KLDM-DNG) without separation leads to a collapse in formula uniqueness (dropping to ~40-50%) and a failure to improve the on-hull fraction, often moving toward known chemistry to maximize rewards.
Robustness: The method maintains high validity and uniqueness (99.9%) across different evaluation potentials and validity gates, though absolute stability metrics depend on the specific potential used for scoring.

Significance and Claims

The paper claims that the primary limitation of current reward-guided crystal generation is the entanglement of composition search and structural generation. By separating these roles:

Rewards guide the search over compositions, allowing the system to explore regions of chemical space that the pretrained DNG marginal would ignore.
Likelihood trains the structural prior, ensuring that the physical plausibility of generated structures is improved based on successful discoveries rather than being distorted by reward gradients.

The authors emphasize that ANCHOR's gains are specific to the reward and potential it was trained against (adhering to Goodhart's law), but the architectural separation allows for easier integration of better physical priors and potentials in the future. The work suggests that for materials discovery, the optimal strategy is to use a frozen, high-quality CSP model as a fixed ruler and train a separate policy to decide where to query it, rather than attempting to optimize a single joint model for both tasks.