Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not conform to the norms are an indication that the rules of science governing the data are incomplete, and something new needs to be present to explain these unexpected outliers. The challenge of finding anomalies can be confounding since it requires codifying a complete knowledge of the known scientific behaviors and then projecting these known behaviors on the data to look for deviations. When utilizing machine learning, this presents a particular challenge since we require that the model not only understands scientific data perfectly but also recognizes when the data is inconsistent and out of the scope of its trained behavior. In this paper, we present three datasets aimed at developing machine learning-based anomaly detection for disparate scientific domains covering astrophysics, genomics, and polar science. We present the different datasets along with a scheme to make machine learning challenges around the three datasets findable, accessible, interoperable, and reusable (FAIR). Furthermore, we present an approach that generalizes to future machine learning challenges, enabling the possibility of large, more compute-intensive challenges that can ultimately lead to scientific discovery.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) for domain-specific question-answering (QA) tasks by leveraging external knowledge sources. However, traditional RAG systems primarily focus on relevance-based retrieval and often struggle with redundancy, especially when reasoning requires connecting information from multiple sources. This paper introduces Vendi-RAG, a framework based on an iterative process that jointly optimizes retrieval diversity and answer quality. This joint optimization leads to significantly higher accuracy for multi-hop QA tasks. Vendi-RAG leverages the Vendi Score (VS), a flexible similarity-based diversity metric, to promote semantic diversity in document retrieval. It then uses an LLM judge that evaluates candidate answers, generated after a reasoning step, and outputs a score that the retriever uses to balance relevance and diversity among the retrieved documents during each iteration. Experiments on three challenging datasets -- HotpotQA, MuSiQue, and 2WikiMultiHopQA -- demonstrate Vendi-RAG's effectiveness in multi-hop reasoning tasks. The framework achieves significant accuracy improvements over traditional single-step and multi-step RAG approaches, with accuracy increases reaching up to +4.2% on HotpotQA, +4.1% on 2WikiMultiHopQA, and +1.3% on MuSiQue compared to Adaptive-RAG, the current best baseline. The benefits of Vendi-RAG are even more pronounced as the number of retrieved documents increases. Finally, we evaluated Vendi-RAG across different LLM backbones, including GPT-3.5, GPT-4, and GPT-4o-mini, and observed consistent improvements, demonstrating that the framework's advantages are model-agnostic.

The evolution of microscopy, beginning with its invention in the late 16th century, has continuously enhanced our ability to explore and understand the microscopic world, enabling increasingly detailed observations of structures and phenomena. In parallel, the rise of data-driven science has underscored the need for sophisticated methods to explore and understand the composition of complex data collections. This paper introduces the Vendiscope, the first algorithmic microscope designed to extend traditional microscopy to computational analysis. The Vendiscope leverages the Vendi scores -- a family of differentiable diversity metrics rooted in ecology and quantum mechanics -- and assigns weights to data points based on their contribution to the overall diversity of the collection. These weights enable high-resolution data analysis at scale. We demonstrate this across biology, materials science, and machine learning (ML). We analyzed the $250$ million protein sequences in the protein universe, discovering that over $200$ million are near-duplicates and that AlphaFold fails on proteins with Gene Ontology (GO) functions that contribute most to diversity. Applying the Vendiscope to the Materials Project database led to similar findings: more than $85\%$ of the crystals with formation energy data are near-duplicates and ML models perform poorly on materials that enhance diversity. Additionally, the Vendiscope can be used to study phenomena such as memorization in generative models. We used the Vendiscope to identify memorized training samples from $13$ different generative models and found that the best-performing ones often memorize the training samples that contribute least to diversity. Our findings demonstrate that the Vendiscope can serve as a powerful tool for data-driven science.

Current state-of-the-art dynamical models, such as Mamba, assume the same level of noisiness for all elements of a given sequence, which limits their performance on noisy temporal data. In this paper, we introduce the $\alpha$-Alternator, a novel generative model for time-dependent data that dynamically adapts to the complexity introduced by varying noise levels in sequences. The $\alpha$-Alternator leverages the Vendi Score (VS), a flexible similarity-based diversity metric, to adjust, at each time step $t$, the influence of the sequence element at time $t$ and the latent representation of the dynamics up to that time step on the predicted future dynamics. This influence is captured by a parameter that is learned and shared across all sequences in a given dataset. The sign of this parameter determines the direction of influence. A negative value indicates a noisy dataset, where a sequence element that increases the VS is considered noisy, and the model relies more on the latent history when processing that element. Conversely, when the parameter is positive, a sequence element that increases the VS is considered informative, and the $\alpha$-Alternator relies more on this new input than on the latent history when updating its predicted latent dynamics. The $\alpha$-Alternator is trained using a combination of observation masking and Alternator loss minimization. Masking simulates varying noise levels in sequences, enabling the model to be more robust to these fluctuations and improving its performance in trajectory prediction, imputation, and forecasting. Our experimental results demonstrate that the $\alpha$-Alternator outperforms both Alternators and state-of-the-art state-space models across neural decoding and time-series forecasting benchmarks.

Large language models (LLMs) are increasingly being used in materials science. However, little attention has been given to benchmarking and standardized evaluation for LLM-based materials property prediction, which hinders progress. We present LLM4Mat-Bench, the largest benchmark to date for evaluating the performance of LLMs in predicting the properties of crystalline materials. LLM4Mat-Bench contains about 1.9M crystal structures in total, collected from 10 publicly available materials data sources, and 45 distinct properties. LLM4Mat-Bench features different input modalities: crystal composition, CIF, and crystal text description, with 4.7M, 615.5M, and 3.1B tokens in total for each modality, respectively. We use LLM4Mat-Bench to fine-tune models with different sizes, including LLM-Prop and MatBERT, and provide zero-shot and few-shot prompts to evaluate the property prediction capabilities of LLM-chat-like models, including Llama, Gemma, and Mistral. The results highlight the challenges of general-purpose LLMs in materials science and the need for task-specific predictive models and task-specific instruction-tuned LLMs in materials property prediction.

From pedestrians to Kuramoto oscillators, interactions between agents govern how a multitude of dynamical systems evolve in space and time. Discovering how these agents relate to each other can improve our understanding of the often complex dynamics that underlie these systems. Recent works learn to categorize relationships between agents based on observations of their physical behavior. These approaches are limited in that the relationship categories are modelled as independent and mutually exclusive, when in real world systems categories are often interacting. In this work, we introduce a level of abstraction between the physical behavior of agents and the categories that define their behavior. To do this, we learn a mapping from the agents' states to their affinities for each category in a graph neural network. We integrate the physical proximity of agents and their affinities in a nonlinear opinion dynamics model which provides a mechanism to identify mutually exclusive categories, predict an agent's evolution in time, and control an agent's behavior. We demonstrate the utility of our model for learning interpretable categories for mechanical systems, and demonstrate its efficacy on several long-horizon trajectory prediction benchmarks where we consistently out perform existing methods.

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint violations such as unmet goals or collisions. This paper presents a novel constraint-aware diffusion model for trajectory optimization. We introduce a novel hybrid loss function for training that minimizes the constraint violation of diffusion samples compared to the groundtruth while recovering the original data distribution. Our model is demonstrated on tabletop manipulation and two-car reach-avoid problems, outperforming traditional diffusion models in minimizing constraint violations while generating samples close to locally optimal solutions.

Motivated by the need to solve open-loop optimal control problems with computational efficiency and reliable constraint satisfaction, we introduce a general framework that combines diffusion models and numerical optimization solvers. Optimal control problems are rarely solvable in closed form, hence they are often transcribed into numerical trajectory optimization problems, which then require initial guesses. These initial guesses are supplied in our framework by diffusion models. To mitigate the effect of samples that violate the problem constraints, we develop a novel constrained diffusion model to approximate the true distribution of locally optimal solutions with an additional constraint violation loss in training. To further enhance the robustness, the diffusion samples as initial guesses are fed to the numerical solver to refine and derive final optimal (and hence feasible) solutions. Experimental evaluations on three tasks verify the improved constraint satisfaction and computational efficiency with 4$\times$ to 30$\times$ acceleration using our proposed framework, which generalizes across trajectory optimization problems and scales well with problem complexity.

This paper introduces alternators, a novel family of non-Markovian dynamical models for sequences. An alternator features two neural networks: the observation trajectory network (OTN) and the feature trajectory network (FTN). The OTN and the FTN work in conjunction, alternating between outputting samples in the observation space and some feature space, respectively, over a cycle. The parameters of the OTN and the FTN are not time-dependent and are learned via a minimum cross-entropy criterion over the trajectories. Alternators are versatile. They can be used as dynamical latent-variable generative models or as sequence-to-sequence predictors. When alternators are used as generative models, the FTN produces interpretable low-dimensional latent variables that capture the dynamics governing the observations. When alternators are used as sequence-to-sequence predictors, the FTN learns to predict the observed features. In both cases, the OTN learns to produce sequences that match the data. Alternators can uncover the latent dynamics underlying complex sequential data, accurately forecast and impute missing data, and sample new trajectories. We showcase the capabilities of alternators in three applications. We first used alternators to model the Lorenz equations, often used to describe chaotic behavior. We then applied alternators to Neuroscience, to map brain activity to physical activity. Finally, we applied alternators to Climate Science, focusing on sea-surface temperature forecasting. In all our experiments, we found alternators are stable to train, fast to sample from, yield high-quality generated samples and latent variables, and outperform strong baselines such as neural ODEs and diffusion models in the domains we studied.

Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search space, which causes them to get stuck in local optima. This ``collapse" problem prevents experimental design algorithms from yielding diverse high-quality data. In this paper, we extend the Vendi scores -- a family of interpretable similarity-based diversity metrics -- to account for quality. We then leverage these quality-weighted Vendi scores to tackle experimental design problems across various applications, including drug discovery, materials discovery, and reinforcement learning. We found that quality-weighted Vendi scores allow us to construct policies for experimental design that flexibly balance quality and diversity, and ultimately assemble rich and diverse sets of high-performing data points. Our algorithms led to a 70%-170% increase in the number of effective discoveries compared to baselines.