Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow trajectories, enabling more effective inference. However, existing OT -based methods estimate the OT plan using (mini-)batches of sampled noise and data points, which limits their scalability to large and high-dimensional datasets in FGMs. This paper introduces AlignFlow, a novel approach that leverages Semi-Discrete Optimal Transport (SDOT) to enhance the training of FGMs by establishing an explicit, optimal alignment between noise distribution and data points with guaranteed convergence. SDOT computes a transport map by partitioning the noise space into Laguerre cells, each mapped to a corresponding data point. Experimental results show that Align-Flow improves the performance of a wide range of state-of-the-art FGM algorithms and can be integrated as a plug-and-play component. A generative model in machine learning is designed to produce new data samples that closely resemble those drawn from a given dataset. This task is of fundamental importance and has seen significant advances over the past decades.

In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium.

Pasur is a fishing card game played over six rounds and is played similarly to games such as Cassino and Scopa, and Bastra. This paper introduces a CUDA-accelerated computational framework for simulating Pasur, emphasizing efficient memory management. We use our framework to compute near-Nash equilibria via Counterfactual Regret Minimization (CFR), a well-known algorithm for solving large imperfect-information games. Solving Pasur presents unique challenges due to its intricate rules and the large size of its game tree. We handle rule complexity using PyTorch CUDA tensors and to address the memory-intensive nature of the game, we decompose the game tree into two key components: (1) actual game states, and (2) inherited scores from previous rounds. We construct the Full Game Tree by pairing card states with accumulated scores in the Unfolding Process. This design reduces memory overhead by storing only essential strategy values and node connections. To further manage computational complexity, we apply a round-by-round backward training strategy, starting from the final round and recursively propagating average utilities to earlier stages. Our approach constructs the complete game tree, which on average consists of over $10^9$ nodes. We provide detailed implementation snippets. After computing a near-Nash equilibrium strategy, we train a tree-based model to predict these strategies for use during gameplay. We then estimate the fair value of each deck through large-scale self-play between equilibrium strategies by simulating, for instance, 10,000 games per matchup, executed in parallel using GPU acceleration. Similar frameworks can be extended to other reinforcement learning algorithms where the action tree naturally decomposes into multiple rounds such as turn-based strategy games or sequential trading decisions in financial markets.

In the realm of Artificial Intelligence Generated Content (AIGC), flow-matching models have emerged as a powerhouse, achieving success due to their robust theoretical underpinnings and solid ability for large-scale generative modeling. These models have demonstrated state-of-the-art performance, but their brilliance comes at a cost. The process of sampling from these models is notoriously demanding on computational resources, as it necessitates the use of multi-step numerical ordinary differential equations (ODEs). Against this backdrop, this paper presents a novel solution with theoretical guarantees in the form of Flow Generator Matching (FGM), an innovative approach designed to accelerate the sampling of flow-matching models into a one-step generation, while maintaining the original performance. On the CIFAR10 unconditional generation benchmark, our one-step FGM model achieves a new record Fr\'echet Inception Distance (FID) score of 3.08 among few-step flow-matching-based models, outperforming original 50-step flow-matching models. Furthermore, we use the FGM to distill the Stable Diffusion 3, a leading text-to-image flow-matching model based on the MM-DiT architecture. The resulting MM-DiT-FGM one-step text-to-image model demonstrates outstanding industry-level performance. When evaluated on the GenEval benchmark, MM-DiT-FGM has delivered remarkable generating qualities, rivaling other multi-step models in light of the efficiency of a single generation step.

Expressive large-scale neural networks enable training powerful models for prediction tasks. However, in many engineering and science domains, such models are intended to be used not just for prediction, but for design -- e.g., creating new proteins that serve as effective therapeutics, or creating new materials or chemicals that maximize a downstream performance measure. Thus, researchers have recently grown an interest in building deep learning methods that solve offline \emph{model-based optimization} (MBO) problems, in which design candidates are optimized with respect to surrogate models learned from offline data. However, straightforward application of predictive models that are effective at predicting in-distribution properties of a design are not necessarily the best suited for use in creating new designs. Thus, the most successful algorithms that tackle MBO draw inspiration from reinforcement learning and generative modeling to meet the in-distribution constraints. Meanwhile, recent theoretical works have observed that exploiting the structure of the target black-box function is an effective strategy for solving MBO from offline data. Unfortunately, discovering such structure remains an open problem. In this paper, following first principles, we develop a model that learns the structure of an MBO task and empirically leads to improved designs. To this end, we introduce \emph{Cliqueformer} -- a scalable transformer-based architecture that learns the black-box function's structure in the form of its \emph{functional graphical model} (FGM), thus bypassing the problem of distribution shift, previously tackled by conservative approaches. We evaluate Cliqueformer on various tasks, ranging from high-dimensional black-box functions from MBO literature to real-world tasks of chemical and genetic design, consistently demonstrating its state-of-the-art performance.

An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.

While machine learning models are typically trained to solve prediction problems, we might often want to use them for optimization problems. For example, given a dataset of proteins and their corresponding fluorescence levels, we might want to optimize for a new protein with the highest possible fluorescence. This kind of data-driven optimization (DDO) presents a range of challenges beyond those in standard prediction problems, since we need models that successfully predict the performance of new designs that are better than the best designs seen in the training set. It is not clear theoretically when existing approaches can even perform better than the naive approach that simply selects the best design in the dataset. In this paper, we study how structure can enable sample-efficient data-driven optimization. To formalize the notion of structure, we introduce functional graphical models (FGMs) and show theoretically how they can provide for principled data-driven optimization by decomposing the original high-dimensional optimization problem into smaller sub-problems. This allows us to derive much more practical regret bounds for DDO, and the result implies that DDO with FGMs can achieve nearly optimal designs in situations where naive approaches fail due to insufficient coverage of the offline data. We further present a data-driven optimization algorithm that inferes the FGM structure itself, either over the original input variables or a latent variable representation of the inputs.