Ming-Chiang Chang, Sebastian Ament, Maximilian Amsler et al.
X-ray diffraction (XRD) is an essential technique to determine a material's crystal structure in high-throughput experimentation, and has recently been incorporated in artificially intelligent agents in autonomous scientific discovery processes. However, rapid, automated and reliable analysis method of XRD data matching the incoming data rate remains a major challenge. To address these issues, we present CrystalShift, an efficient algorithm for probabilistic XRD phase labeling that employs symmetry-constrained pseudo-refinement optimization, best-first tree search, and Bayesian model comparison to estimate probabilities for phase combinations without requiring phase space information or training. We demonstrate that CrystalShift provides robust probability estimates, outperforming existing methods on synthetic and experimental datasets, and can be readily integrated into high-throughput experimental workflows. In addition to efficient phase-mapping, CrystalShift offers quantitative insights into materials' structural parameters, which facilitate both expert evaluation and AI-based modeling of the phase space, ultimately accelerating materials identification and discovery.
While Large Language Models (LLMs) have demonstrated significant advancements in reasoning and agent-based problem-solving, current evaluation methodologies fail to adequately assess their capabilities: existing benchmarks either rely on closed-ended questions prone to saturation and memorization, or subjective comparisons that lack consistency and rigor. In this work, we introduce HeuriGym, an agentic framework designed for evaluating heuristic algorithms generated by LLMs for combinatorial optimization problems, characterized by clearly defined objectives and expansive solution spaces. HeuriGym empowers LLMs to propose heuristics, receive evaluative feedback via code execution, and iteratively refine their solutions. We evaluate nine state-of-the-art models on nine problems across domains such as computer systems, logistics, and biology, exposing persistent limitations in tool use, planning, and adaptive reasoning. To quantify performance, we propose the Quality-Yield Index (QYI), a metric that captures both solution pass rate and quality. Even top models like GPT-o4-mini-high and Gemini-2.5-Pro attain QYI scores of only 0.6, well below the expert baseline of 1. Our open-source benchmark aims to guide the development of LLMs toward more effective and realistic problem-solving in scientific and engineering domains.
We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the ordering of vertices aligns with the clique structures. By integrating this clique-oriented ordering into branch-and-bound search, we improve search efficiency and reduce the number of computational steps. Our results demonstrate how unsupervised learning of vertex ordering can enhance search efficiency across diverse graph instances. We further study the generalization across different sizes.
We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the model learns to approximate permutation matrices via continuous relaxations. Our unsupervised approach achieves competitive performance against classical heuristics, demonstrating that the inherent structure of the problem can effectively guide combinatorial optimization without sequential decision-making. Our method offers concrete evidence that neural networks can directly capture and exploit combinatorial structure.