We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schrödinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks.

Recent advancements in optimization-based text-to-3D generation heavily rely on distilling knowledge from pre-trained text-to-image diffusion models using techniques like Score Distillation Sampling (SDS), which often introduce artifacts such as over-saturation and over-smoothing into the generated 3D assets. In this paper, we address this essential problem by formulating the generation process as learning an optimal, direct transport trajectory between the distribution of the current rendering and the desired target distribution, thereby enabling high-quality generation with smaller Classifier-free Guidance (CFG) values. At first, we theoretically establish SDS as a simplified instance of the Schrödinger Bridge framework. We prove that SDS employs the reverse process of an Schrödinger Bridge, which, under specific conditions (e.g., a Gaussian noise as one end), collapses to SDS's score function of the pre-trained diffusion model. Based upon this, we introduce Trajectory-Centric Distillation (TraCe), a novel text-to-3D generation framework, which reformulates the mathematically trackable framework of Schrödinger Bridge to explicitly construct a diffusion bridge from the current rendering to its text-conditioned, denoised target, and trains a LoRA-adapted model on this trajectory's score dynamics for robust 3D optimization. Comprehensive experiments demonstrate that TraCe consistently achieves superior quality and fidelity to state-of-the-art techniques.

Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual entities is often impossible. Such trajectory inference is vital for unraveling the mechanisms of dynamic processes. While Schrödinger Bridge (SB) offer a potent framework, their traditional application to pairwise time points can be insufficient for systems defined by multiple intermediate snapshots. This paper introduces Multi-Marginal Schrödinger Bridge Matching (MSBM), a novel algorithm specifically designed for the multi-marginal SB problem. MSBM extends iterative Markovian fitting (IMF) to effectively handle multiple marginal constraints. This technique ensures robust enforcement of all intermediate marginals while preserving the continuity of the learned global dynamics across the entire trajectory. Empirical validations on synthetic data and real-world single-cell RNA sequencing datasets demonstrate the competitive or superior performance of MSBM in capturing complex trajectories and respecting intermediate distributions, all with notable computational efficiency. Code is available at https://github.com/bw-park/MSBM.

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schrödinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks.

We study the problem of Inverse Reinforcement Learning (IRL) with an average-reward criterion.

This study explores how virtual environments and artificial intelligence can enhance university students' learning experiences, with particular attention to the digital preferences of Generation Z. An experiment was conducted at the Faculty of Pedagogy, Humanities, and Social Sciences at University of Gyor, where Walter's Cube technology and a trained AI mediator were integrated into the instruction of ten philosophical topics. The curriculum was aligned with the official syllabus and enriched with visual content, quotations, and explanatory texts related to iconic figures in philosophy. A total of 77 first-year undergraduate students from full-time humanities and social sciences programs participated in the study. Following their end-of-semester offline written examination, students voluntarily completed a paper-based, anonymous ten-question test and provided feedback on the method's effectiveness. No sensitive personal data were collected, and the research was conducted with formal approval from the Faculty Dean. Descriptive statistics and inferential tests were applied to evaluate the impact of the virtual environment and AI mediation on learning outcomes. Results indicate that 80 percent of participants achieved good or excellent final exam grades, and the majority rated the virtual material as highly effective. Qualitative feedback emphasized increased motivation and deeper engagement, attributed to the immersive 3D presentation and interactive AI support. This research contributes to the advancement of digital pedagogy and suggests new directions for applying virtual and AI-based methods in higher education, particularly in disciplines where abstract reasoning and conceptual understanding are central.

Large language models (LLMs) have demonstrated strong performance in natural language generation but remain limited in knowle- dge-intensive tasks due to outdated or incomplete internal knowledge. Retrieval-Augmented Generation (RAG) addresses this by incorporating external retrieval, with GraphRAG further enhancing performance through structured knowledge graphs and multi-hop reasoning. However, existing GraphRAG methods largely ignore the temporal dynamics of knowledge, leading to issues such as temporal ambiguity, time-insensitive retrieval, and semantic redundancy. To overcome these limitations, we propose Temporal GraphRAG (T-GRAG), a dynamic, temporally-aware RAG framework that models the evolution of knowledge over time. T-GRAG consists of five key components: (1) a Temporal Knowledge Graph Generator that creates time-stamped, evolving graph structures; (2) a Temporal Query Decomposition mechanism that breaks complex temporal queries into manageable sub-queries; (3) a Three-layer Interactive Retriever that progressively filters and refines retrieval across temporal subgraphs; (4) a Source Text Extractor to mitigate noise; and (5) a LLM-based Generator that synthesizes contextually and temporally accurate responses. We also introduce Time-LongQA, a novel benchmark dataset based on real-world corporate annual reports, designed to test temporal reasoning across evolving knowledge. Extensive experiments show that T-GRAG significantly outperforms prior RAG and GraphRAG baselines in both retrieval accuracy and response relevance under temporal constraints, highlighting the necessity of modeling knowledge evolution for robust long-text question answering. Our code is publicly available on the T-GRAG

Controlling autonomous vehicles at their handling limits is a significant challenge, particularly for electric vehicles with active four wheel drive (A4WD) systems offering independent wheel torque control. While traditional Vehicle Dynamics Control (VDC) methods use complex physics-based models, this study explores Deep Reinforcement Learning (DRL) to develop a unified, high-performance controller. We employ the Proximal Policy Optimization (PPO) algorithm to train an agent for optimal lap times in a simulated racecar (TORCS) at the tire grip limit. Critically, the agent learns an end-to-end policy that directly maps vehicle states, like velocities, accelerations, and yaw rate, to a steering angle command and independent torque commands for each of the four wheels. This formulation bypasses conventional pedal inputs and explicit torque vectoring algorithms, allowing the agent to implicitly learn the A4WD control logic needed for maximizing performance and stability. Simulation results demonstrate the RL agent learns sophisticated strategies, dynamically optimizing wheel torque distribution corner-by-corner to enhance handling and mitigate the vehicle's inherent understeer. The learned behaviors mimic and, in aspects of grip utilization, potentially surpass traditional physics-based A4WD controllers while achieving competitive lap times. This research underscores DRL's potential to create adaptive control systems for complex vehicle dynamics, suggesting RL is a potent alternative for advancing autonomous driving in demanding, grip-limited scenarios for racing and road safety.

Diffusion models achieve strong generative performance but often rely on large datasets that may include sensitive content. This challenge is compounded by the models' tendency to memorize training data, raising privacy concerns. SFBD (Lu et al., 2025) addresses this by training on corrupted data and using limited clean samples to capture local structure and improve convergence. However, its iterative denoising and fine-tuning loop requires manual coordination, making it burdensome to implement. We reinterpret SFBD as an alternating projection algorithm and introduce a continuous variant, SFBD flow, that removes the need for alternating steps. We further show its connection to consistency constraint-based methods, and demonstrate that its practical instantiation, Online SFBD, consistently outperforms strong baselines across benchmarks.