Diffusion model (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2021b; Kingma et al., 2021) is a class of generative model that adds noise to real data to train the score network and sequentially approximate the time-reversed process (Föllmer and Wakolbinger, 1986; Anderson, 1982) to generate samples from the true data distribution. This model has shown remarkable empirical success in numerous domains such as image generation (Song et al., 2021b,a), video generation (Luo et al., 2023), medical data processing (Song et al., 2022; Chung and Ye, 2022; Akrout et al., 2023), and audio generation (Kong et al., 2020). However, "classical" diffusion models formulated on finite-dimensional Euclidean spaces limit their applicability to function generation problems as they can only generate function values realized on a fixed discretization of the function's domain (Li et al., 2020) and cannot capture functional properties of a data such as integrability or smoothness (Kerrigan et al., 2023). Motivated by such a limitation of finite-dimensional models, there has been a line of works extending the finite-dimensional diffusion model to infinite-dimensional Hilbert spaces; for instance, Hagemann et al. (2023); Kerrigan et al. (2023); Lim et al. (2023a,b); Pidstrigach et al. (2023); Phillips et al. (2022); Baldassari et al. (2023). Kerrigan et al. (2023) proposes a discrete-time model that serves as an analog of Ho et al. (2020) in infinite-dimensional space, and Hagemann et al. (2023) introduces a finite-dimensional approximation of an infinite-dimensional SDEs and utilizes the time-reversal formula in finite-dimensional spaces. Lim et al. (2023a); Franzese et al. (2023); Pidstrigach et al. (2023) propose continuous-time models by extending the SDE framework of Song et al. (2021b) to infinite dimensions based on semigroup theory (ref. Da Prato and Zabczyk (2014)); however, their consideration is limited to a relatively simple class of SDEs, such as Langevin type SDE or SDEs with constant-time diffusion coefficients. Later, Lim et al. (2023b) proved a general form of time-reversal formula which encompasses various choices of SDEs such as VPSDE, VESDE, sub-VPSDE (Song et al., 2021b) and variance scheduling (Nichol and

Recent advancements in AI have revolutionized property prediction in materials science and accelerating material discovery. Graph neural networks (GNNs) stand out due to their ability to represent crystal structures as graphs, effectively capturing local interactions and delivering superior predictions. However, these methods often lose critical global information, such as crystal systems and repetitive unit connectivity. To address this, we propose CAST, a cross-attention-based multimodal fusion model that integrates graph and text modalities to preserve essential material information. CAST combines node- and token-level features using cross-attention mechanisms, surpassing previous approaches reliant on material-level embeddings like graph mean-pooling or [CLS] tokens. A masked node prediction pretraining strategy further enhances atomic-level information integration. Our method achieved up to 22.9\% improvement in property prediction across four crystal properties including band gap compared to methods like CrysMMNet and MultiMat. Pretraining was key to aligning node and text embeddings, with attention maps confirming its effectiveness in capturing relationships between nodes and tokens. This study highlights the potential of multimodal learning in materials science, paving the way for more robust predictive models that incorporate both local and global information.

Recent advances in Large Language Models (LLMs) have motivated the development of general LLMs for molecular tasks. While several studies have demonstrated that fine-tuned LLMs can achieve impressive benchmark performances, they are far from genuine generalist molecular LLMs due to a lack of fundamental understanding of molecular structure. Specifically, when given molecular task instructions, LLMs trained with naive next-token prediction training assign similar likelihood scores to both original and negatively corrupted molecules, revealing their lack of molecular structure understanding that is crucial for reliable and general molecular LLMs. To overcome this limitation and obtain a true generalist molecular LLM, we introduce a novel multi-modal training method based on a thorough multi-modal instruction tuning as well as a molecular structure preference optimization between chosen and rejected graphs. On various molecular benchmarks, the proposed generalist molecular LLM, called Mol-LLM, achieves state-of-the-art performances among generalist LLMs on most tasks, at the same time, surpassing or comparable to state-of-the-art specialist LLMs. Moreover, Mol-LLM also shows superior generalization performances in reaction prediction tasks, demonstrating the effect of the molecular structure understanding for generalization perspective.

Molecules have a number of distinct properties whose importance and application vary. Often, in reality, labels for some properties are hard to achieve despite their practical importance. A common solution to such data scarcity is to use models of good generalization with transfer learning. This involves domain experts for designing source and target tasks whose features are shared. However, this approach has limitations: i). Difficulty in accurate design of source-target task pairs due to the large number of tasks, and ii). corresponding computational burden verifying many trials and errors of transfer learning design, thereby iii). constraining the potential of foundation modeling of multi-task molecular property prediction. We address the limitations of the manual design of transfer learning via data-driven bi-level optimization. The proposed method enables scalable multi-task transfer learning for molecular property prediction by automatically obtaining the optimal transfer ratios. Empirically, the proposed method improved the prediction performance of 40 molecular properties and accelerated training convergence.

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob's $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: (1) learning bridges between two infinite-dimensional distributions and (2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

Scaling laws have allowed Pre-trained Language Models (PLMs) into the field of causal reasoning. Causal reasoning of PLM relies solely on text-based descriptions, in contrast to causal discovery which aims to determine the causal relationships between variables utilizing data. Recently, there has been current research regarding a method that mimics causal discovery by aggregating the outcomes of repetitive causal reasoning, achieved through specifically designed prompts. It highlights the usefulness of PLMs in discovering cause and effect, which is often limited by a lack of data, especially when dealing with multiple variables. Conversely, the characteristics of PLMs which are that PLMs do not analyze data and they are highly dependent on prompt design leads to a crucial limitation for directly using PLMs in causal discovery. Accordingly, PLM-based causal reasoning deeply depends on the prompt design and carries out the risk of overconfidence and false predictions in determining causal relationships. In this paper, we empirically demonstrate the aforementioned limitations of PLM-based causal reasoning through experiments on physics-inspired synthetic data. Then, we propose a new framework that integrates prior knowledge obtained from PLM with a causal discovery algorithm. This is accomplished by initializing an adjacency matrix for causal discovery and incorporating regularization using prior knowledge. Our proposed framework not only demonstrates improved performance through the integration of PLM and causal discovery but also suggests how to leverage PLM-extracted prior knowledge with existing causal discovery algorithms.

Finding a high-quality feasible solution to a combinatorial optimization (CO) problem in a limited time is challenging due to its discrete nature. Recently, there has been an increasing number of machine learning (ML) methods for addressing CO problems. Neural diving (ND) is one of the learning-based approaches to generating partial discrete variable assignments in Mixed Integer Programs (MIP), a framework for modeling CO problems. However, a major drawback of ND is a large discrepancy between the ML and MIP objectives, i.e., variable value classification accuracy over primal bound. Our study investigates that a specific range of variable assignment rates (coverage) yields high-quality feasible solutions, where we suggest optimizing the coverage bridges the gap between the learning and MIP objectives. Consequently, we introduce a post-hoc method and a learning-based approach for optimizing the coverage. A key idea of our approach is to jointly learn to restrict the coverage search space and to predict the coverage in the learned search space. Experimental results demonstrate that learning a deep neural network to estimate the coverage for finding high-quality feasible solutions achieves state-of-the-art performance in NeurIPS ML4CO datasets. In particular, our method shows outstanding performance in the workload apportionment dataset, achieving the optimality gap of 0.45%, a ten-fold improvement over SCIP within the one-minute time limit.

While pre-trained language models (PLMs) have become a de-facto standard promoting the accuracy of text classification tasks, recent studies find that PLMs often predict over-confidently. Although various calibration methods have been proposed, such as ensemble learning and data augmentation, most of the methods have been verified in computer vision benchmarks rather than in PLM-based text classification tasks. In this paper, we present an empirical study on confidence calibration for PLMs, addressing three categories, including confidence penalty losses, data augmentations, and ensemble methods. We find that the ensemble model overfitted to the training set shows sub-par calibration performance and also observe that PLMs trained with confidence penalty loss have a trade-off between calibration and accuracy. Building on these observations, we propose the Calibrated PLM (CALL), a combination of calibration techniques. The CALL complements the drawbacks that may occur when utilizing a calibration method individually and boosts both classification and calibration accuracy. Design choices in CALL's training procedures are extensively studied, and we provide a detailed analysis of how calibration techniques affect the calibration performance of PLMs.

Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination -- a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose an attention encoder-LSTM decoder hybrid model, in which the decoder's hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for coordinated routing of multiple vehicles than the attention-based model.

In this paper, we consider stochastic multi-armed bandits (MABs) with heavy-tailed rewards, whose $p$-th moment is bounded by a constant $\nu_{p}$ for $1