Unsupervised Learning for Quadratic Assignment

We introduce PLUME search, a data-driven framework that enhances search efficiency in combinatorial optimization through unsupervised learning. Unlike supervised or reinforcement learning, PLUME search learns directly from problem instances using a permutation-based loss with a non-autoregressive approach. We evaluate its performance on the quadratic assignment problem, a fundamental NP-hard problem that encompasses various combinatorial optimization problems. Experimental results demonstrate that PLUME search consistently improves solution quality. Furthermore, we study the generalization behavior and show that the learned model generalizes across different densities and sizes.

Large Language Models Are Innate Crystal Structure Generators

Crystal structure generation is fundamental to materials discovery, enabling the prediction of novel materials with desired properties. While existing approaches leverage Large Language Models (LLMs) through extensive fine-tuning on materials databases, we show that pre-trained LLMs can inherently generate stable crystal structures without additional training. Our novel framework MatLLMSearch integrates pre-trained LLMs with evolutionary search algorithms, achieving a 78.38% metastable rate validated by machine learning interatomic potentials and 31.7% DFT-verified stability via quantum mechanical calculations, outperforming specialized models such as CrystalTextLLM. Beyond crystal structure generation, we further demonstrate that our framework can be readily adapted to diverse materials design tasks, including crystal structure prediction and multi-objective optimization of properties such as deformation energy and bulk modulus, all without fine-tuning. These results establish pre-trained LLMs as versatile and effective tools for materials discovery, opening up new venues for crystal structure generation with reduced computational overhead and broader accessibility.

PhantomWiki: On-Demand Datasets for Reasoning and Retrieval Evaluation

High-quality benchmarks are essential for evaluating reasoning and retrieval capabilities of large language models (LLMs). However, curating datasets for this purpose is not a permanent solution as they are prone to data leakage and inflated performance results. To address these challenges, we propose PhantomWiki: a pipeline to generate unique, factually consistent document corpora with diverse question-answer pairs. Unlike prior work, PhantomWiki is neither a fixed dataset, nor is it based on any existing data. Instead, a new PhantomWiki instance is generated on demand for each evaluation. We vary the question difficulty and corpus size to disentangle reasoning and retrieval capabilities respectively, and find that PhantomWiki datasets are surprisingly challenging for frontier LLMs. Thus, we contribute a scalable and data leakage-resistant framework for disentangled evaluation of reasoning, retrieval, and tool-use abilities. Our code is available at https://github.com/kilian-group/phantom-wiki.

AlphaNet: Scaling Up Local Frame-based Atomistic Foundation Model

We present AlphaNet, a local frame-based equivariant model designed to achieve both accurate and efficient simulations for atomistic systems. Recently, machine learning force fields (MLFFs) have gained prominence in molecular dynamics simulations due to their advantageous efficiency-accuracy balance compared to classical force fields and quantum mechanical calculations, alongside their transferability across various systems. Despite the advancements in improving model accuracy, the efficiency and scalability of MLFFs remain significant obstacles in practical applications. AlphaNet enhances computational efficiency and accuracy by leveraging the local geometric structures of atomic environments through the construction of equivariant local frames and learnable frame transitions. We substantiate the efficacy of AlphaNet across diverse datasets, including defected graphene, formate decomposition, zeolites, and surface reactions. AlphaNet consistently surpasses well-established models, such as NequIP and DeepPot, in terms of both energy and force prediction accuracy. Notably, AlphaNet offers one of the best trade-offs between computational efficiency and accuracy among existing models. Moreover, AlphaNet exhibits scalability across a broad spectrum of system and dataset sizes, affirming its versatility.

Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling

Rare event sampling in dynamical systems is a fundamental problem arising in the natural sciences, which poses significant computational challenges due to an exponentially large space of trajectories. For settings where the dynamical system of interest follows a Brownian motion with known drift, the question of conditioning the process to reach a given endpoint or desired rare event is definitively answered by Doob's h-transform. However, the naive estimation of this transform is infeasible, as it requires simulating sufficiently many forward trajectories to estimate rare event probabilities. In this work, we propose a variational formulation of Doob's $h$-transform as an optimization problem over trajectories between a given initial point and the desired ending point. To solve this optimization, we propose a simulation-free training objective with a model parameterization that imposes the desired boundary conditions by design. Our approach significantly reduces the search space over trajectories and avoids expensive trajectory simulation and inefficient importance sampling estimators which are required in existing methods. We demonstrate the ability of our method to find feasible transition paths on real-world molecular simulation and protein folding tasks.

On Speeding Up Language Model Evaluation

Large language models (LLMs) currently dominate the field of natural language processing (NLP), representing the state-of-the-art across a diverse array of tasks. Developing a model of this nature, from training to inference, requires making numerous decisions which define a combinatorial search problem. For example, selecting the optimal pre-trained LLM, prompt, or hyperparameters to attain the best performance for a task often requires evaluating multiple candidates on an entire test set. This exhaustive evaluation can be time-consuming and costly, as both inference and metric computation with LLMs are resource-intensive. In this paper, we address the challenge of identifying the best method within a limited budget for evaluating methods on test examples. By leveraging the well-studied multi-armed bandit framework, which sequentially selects the next method-example pair to evaluate, our approach, combining multi-armed bandit algorithms with low-rank factorization, significantly reduces the required resources. Experiments show that our algorithms can identify the top-performing method using only 5-15\% of the typically needed resources, resulting in an 85-95\% reduction in cost.

React-OT: Optimal Transport for Generating Transition State in Chemical Reactions

Transition states (TSs) are transient structures that are key in understanding reaction mechanisms and designing catalysts but challenging to be captured in experiments. Alternatively, many optimization algorithms have been developed to search for TSs computationally. Yet the cost of these algorithms driven by quantum chemistry methods (usually density functional theory) is still high, posing challenges for their applications in building large reaction networks for reaction exploration. Here we developed React-OT, an optimal transport approach for generating unique TS structures from reactants and products. React-OT generates highly accurate TS structures with a median structural root mean square deviation (RMSD) of 0.053{\AA} and median barrier height error of 1.06 kcal/mol requiring only 0.4 second per reaction. The RMSD and barrier height error is further improved by roughly 25% through pretraining React-OT on a large reaction dataset obtained with a lower level of theory, GFN2-xTB. We envision the great accuracy and fast inference of React-OT useful in targeting TSs when exploring chemical reactions with unknown mechanisms.

On Size and Hardness Generalization in Unsupervised Learning for the Travelling Salesman Problem

We study the generalization capability of Unsupervised Learning in solving the Travelling Salesman Problem (TSP). We use a Graph Neural Network (GNN) trained with a surrogate loss function to generate an embedding for each node. We use these embeddings to construct a heat map that indicates the likelihood of each edge being part of the optimal route. We then apply local search to generate our final predictions. Our investigation explores how different training instance sizes, embedding dimensions, and distributions influence the outcomes of Unsupervised Learning methods. Our results show that training with larger instance sizes and increasing embedding dimensions can build a more effective representation, enhancing the model's ability to solve TSP. Furthermore, in evaluating generalization across different distributions, we first determine the hardness of various distributions and explore how different hardnesses affect the final results. Our findings suggest that models trained on harder instances exhibit better generalization capabilities, highlighting the importance of selecting appropriate training instances in solving TSP using Unsupervised Learning.

Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints

Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has focused on scenarios where feasibility constraints are not given explicitly. Overlooking these constraints can lead to spurious solutions that are unrealistic in practice. To deal with such unknown constraints, we propose to perform optimization within the data manifold using diffusion models. To constrain the optimization process to the data manifold, we reformulate the original optimization problem as a sampling problem from the product of the Boltzmann distribution defined by the objective function and the data distribution learned by the diffusion model. To enhance sampling efficiency, we propose a two-stage framework that begins with a guided diffusion process for warm-up, followed by a Langevin dynamics stage for further correction. Theoretical analysis shows that the initial stage results in a distribution focused on feasible solutions, thereby providing a better initialization for the later stage. Comprehensive experiments on a synthetic dataset, six real-world black-box optimization datasets, and a multi-objective optimization dataset show that our method achieves better or comparable performance with previous state-of-the-art baselines.

Probabilistic Phase Labeling and Lattice Refinement for Autonomous Material Research

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.