EruDiff: Refactoring Knowledge in Diffusion Models for Advanced Text-to-Image Synthesis

Text-to-image diffusion models have achieved remarkable fidelity in synthesizing images from explicit text prompts, yet exhibit a critical deficiency in processing implicit prompts that require deep-level world knowledge, ranging from natural sciences to cultural commonsense, resulting in counter-factual synthesis. This paper traces the root of this limitation to a fundamental dislocation of the underlying knowledge structures, manifesting as a chaotic organization of implicit prompts compared to their explicit counterparts. In this paper, we propose EruDiff, which aims to refactor the knowledge within diffusion models. Specifically, we develop the Diffusion Knowledge Distribution Matching (DK-DM) to register the knowledge distribution of intractable implicit prompts with that of well-defined explicit anchors. Furthermore, to rectify the inherent biases in explicit prompt rendering, we employ the Negative-Only Reinforcement Learning (NO-RL) strategy for fine-grained correction. Rigorous empirical evaluations demonstrate that our method significantly enhances the performance of leading diffusion models, including FLUX and Qwen-Image, across both the scientific knowledge benchmark (i.e., Science-T2I) and the world knowledge benchmark (i.e., WISE), underscoring the effectiveness and generalizability. Our code is available at https://github.com/xiefan-guo/erudiff.

Fast Beam-Brainstorm: Few-Step Generative Site-Specific Beamforming with Flexible Probing

A novel generative site-specific beamforming (GenSSBF) approach, termed fast beam-brainstorm (F-BBS), is proposed to address the practical bottlenecks of slow beam generation and fixed channel probing lengths in existing GenSSBF. To accelerate beam generation, F-BBS utilizes a two-stage distillation strategy that learns an average velocity field, instead of an instantaneous one, to guide the beam generative process. This strategy enables larger generation steps, realizing few-step or even one-step beam generation. Furthermore, to accommodate flexible channel probing lengths, a stochastic masking mechanism and a beam index-aware masked condition encoder are proposed, enabling a single trained model to operate with variable-length channel probing observations without retraining. Therefore, FBBS achieves the fast generation of high-fidelity communication beams from coarse and variable-length channel probing feedback, i.e., reference signal received power (RSRP), from user equipments. Simulation results on accurate ray-tracing datasets show that 1) F-BBS achieves comparable performance while reducing the beam generation cost by over 90% compared with diffusion-based GenSSBF solutions, 2) F-BBS realizes robust performance across variable channel probing length, and 3) FBBS offers a desirable trade-off between beamforming gain and beam probing overhead.

Beyond Benchmarks of IUGC: Rethinking Requirements of Deep Learning Methods for Intrapartum Ultrasound Biometry from Fetal Ultrasound Videos

A substantial proportion (45\%) of maternal deaths, neonatal deaths, and stillbirths occur during the intrapartum phase, with a particularly high burden in low- and middle-income countries. Intrapartum biometry plays a critical role in monitoring labor progression; however, the routine use of ultrasound in resource-limited settings is hindered by a shortage of trained sonographers. To address this challenge, the Intrapartum Ultrasound Grand Challenge (IUGC), co-hosted with MICCAI 2024, was launched. The IUGC introduces a clinically oriented multi-task automatic measurement framework that integrates standard plane classification, fetal head-pubic symphysis segmentation, and biometry, enabling algorithms to exploit complementary task information for more accurate estimation. Furthermore, the challenge releases the largest multi-center intrapartum ultrasound video dataset to date, comprising 774 videos (68,106 frames) collected from three hospitals, providing a robust foundation for model training and evaluation. In this study, we present a comprehensive overview of the challenge design, review the submissions from eight participating teams, and analyze their methods from five perspectives: preprocessing, data augmentation, learning strategy, model architecture, and post-processing. In addition, we perform a systematic analysis of the benchmark results to identify key bottlenecks, explore potential solutions, and highlight open challenges for future research. Although encouraging performance has been achieved, our findings indicate that the field remains at an early stage, and further in-depth investigation is required before large-scale clinical deployment. All benchmark solutions and the complete dataset have been publicly released to facilitate reproducible research and promote continued advances in automatic intrapartum ultrasound biometry.

FUGC: Benchmarking Semi-Supervised Learning Methods for Cervical Segmentation

Accurate segmentation of cervical structures in transvaginal ultrasound (TVS) is critical for assessing the risk of spontaneous preterm birth (PTB), yet the scarcity of labeled data limits the performance of supervised learning approaches. This paper introduces the Fetal Ultrasound Grand Challenge (FUGC), the first benchmark for semi-supervised learning in cervical segmentation, hosted at ISBI 2025. FUGC provides a dataset of 890 TVS images, including 500 training images, 90 validation images, and 300 test images. Methods were evaluated using the Dice Similarity Coefficient (DSC), Hausdorff Distance (HD), and runtime (RT), with a weighted combination of 0.4/0.4/0.2. The challenge attracted 10 teams with 82 participants submitting innovative solutions. The best-performing methods for each individual metric achieved 90.26\% mDSC, 38.88 mHD, and 32.85 ms RT, respectively. FUGC establishes a standardized benchmark for cervical segmentation, demonstrates the efficacy of semi-supervised methods with limited labeled data, and provides a foundation for AI-assisted clinical PTB risk assessment.

Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics

Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely on task-specific pipelines and trained formal provers, limiting their flexibility and reproducibility. In this paper, we propose the paradigm that directly uses a general coding agent as a formal math reasoner. This paradigm is motivated by (1) A general coding agent provides a natural interface for diverse reasoning tasks beyond proving, (2) Performance can be improved by simply replacing the underlying base model, without training, and (3) MCP enables flexible extension and autonomous calling of specialized tools, avoiding complex design. Based on this paradigm, we introduce Numina-Lean-Agent, which combines Claude Code with Numina-Lean-MCP to enable autonomous interaction with Lean, retrieval of relevant theorems, informal proving and auxiliary reasoning tools. Using Claude Opus 4.5 as the base model, Numina-Lean-Agent solves all problems in Putnam 2025 (12 / 12), matching the best closed-source system. Beyond benchmark evaluation, we further demonstrate its generality by interacting with mathematicians to successfully formalize the Brascamp-Lieb theorem. We release Numina-Lean-Agent and all solutions at https://github.com/project-numina/numina-lean-agent.

Beam-Brainstorm: A Generative Site-Specific Beamforming Approach

Accurately understanding the propagation environment is a fundamental challenge in site-specific beamforming (SSBF). This paper proposes a novel generative SSBF (GenSSBF) solution, which represents a paradigm shift from conventional unstructured prediction to joint-structure modeling. First, considering the fundamental differences between beam generation and conventional image synthesis, a unified GenSSBF framework is proposed, which includes a site profile, a wireless prompting module, and a generator. Second, a beam-brainstorm (BBS) solution is proposed as an instantiation of this GenSSBF framework. Specifically, the site profile is configured by transforming channel data from spatial domain to a reversible latent space via discrete Fourier transform (DFT). To facilitate practical deployment, the wireless prompt is constructed from the reference signal received power (RSRP) measured using a small number of DFT-beams. Finally, the generator is developed using a customized conditional diffusion model. Rather than relying on a meticulously designed global codebook, BBS directly generates diverse and high-fidelity user-specific beams guided by the wireless prompts. Simulation results on accurate ray-tracing datasets demonstrate that BBS can achieve near-optimal beamforming gain while drastically reducing the beam sweeping overhead, even in low signal-to-noise ratio (SNR) environments.

FairGFL: Privacy-Preserving Fairness-Aware Federated Learning with Overlapping Subgraphs

Graph federated learning enables the collaborative extraction of high-order information from distributed subgraphs while preserving the privacy of raw data. However, graph data often exhibits overlap among different clients. Previous research has demonstrated certain benefits of overlapping data in mitigating data heterogeneity. However, the negative effects have not been explored, particularly in cases where the overlaps are imbalanced across clients. In this paper, we uncover the unfairness issue arising from imbalanced overlapping subgraphs through both empirical observations and theoretical reasoning. To address this issue, we propose FairGFL (FAIRness-aware subGraph Federated Learning), a novel algorithm that enhances cross-client fairness while maintaining model utility in a privacy-preserving manner. Specifically, FairGFL incorporates an interpretable weighted aggregation approach to enhance fairness across clients, leveraging privacy-preserving estimation of their overlapping ratios. Furthermore, FairGFL improves the tradeoff between model utility and fairness by integrating a carefully crafted regularizer into the federated composite loss function. Through extensive experiments on four benchmark graph datasets, we demonstrate that FairGFL outperforms four representative baseline algorithms in terms of both model utility and fairness.

Can MLLMs Absorb Math Reasoning Abilities from LLMs as Free Lunch?

Math reasoning has been one crucial ability of large language models (LLMs), where significant advancements have been achieved in recent years. However, most efforts focus on LLMs by curating high-quality annotation data and intricate training (or inference) paradigms, while the math reasoning performance of multi-modal LLMs (MLLMs) remains lagging behind. Since the MLLM typically consists of an LLM and a vision block, we wonder: Can MLLMs directly absorb math reasoning abilities from off-the-shelf math LLMs without tuning? Recent model-merging approaches may offer insights into this question. However, they overlook the alignment between the MLLM and LLM, where we find that there is a large gap between their parameter spaces, resulting in lower performance. Our empirical evidence reveals two key factors behind this issue: the identification of crucial reasoning-associated layers in the model and the mitigation of the gaps in parameter space. Based on the empirical insights, we propose IP-Merging that first identifies the reasoning-associated parameters in both MLLM and Math LLM, then projects them into the subspace of MLLM, aiming to maintain the alignment, and finally merges parameters in this subspace. IP-Merging is a tuning-free approach since parameters are directly adjusted. Extensive experiments demonstrate that our IP-Merging method can enhance the math reasoning ability of MLLMs directly from Math LLMs without compromising their other capabilities.

GeoSDF: Plane Geometry Diagram Synthesis via Signed Distance Field

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on computer tools (e.g., Matplotlib and GeoGebra) to manually generate precise diagrams, but it usually requires huge, complicated calculations cost. Recently, researchers start to work on learning-based methods (e.g., Stable Diffusion and GPT4) to automatically generate diagrams, saving operational cost but usually suffering from limited realism and insufficient accuracy. In this paper, we propose a novel framework GeoSDF to automatically generate diagrams efficiently and accurately with Signed Distance Field (SDF). Specifically, we first represent geometric elements in the SDF, then construct a series of constraint functions to represent geometric relationships, next we optimize such constraint functions to get an optimized field of both elements and constraints, finally by rendering the optimized field, we can obtain the synthesized diagram. In our GeoSDF, we define a symbolic language to easily represent geometric elements and those constraints, and our synthesized geometry diagrams can be self-verified in the SDF, ensuring both mathematical accuracy and visual plausibility. In experiments, our GeoSDF synthesized both normal high-school level and IMO-level geometry diagrams. Through both qualitative and quantitative analysis, we can see that synthesized diagrams are realistic and accurate, and our synthesizing process is simple and efficient. Furthermore, we obtain a very high accuracy of solving geometry problems (over 95\% while the current SOTA accuracy is around 75%) by leveraging our self-verification property. All of these demonstrate the advantage of GeoSDF, paving the way for more sophisticated, accurate, and flexible generation of geometric diagrams for a wide array of applications.

Review of Mathematical Optimization in Federated Learning

Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed datasets while satisfying a variety of privacy and system constraints.Different from conventional distributed optimization methods, FL needs to address several specific issues (e.g., non-i.i.d. data distributions and differential private noises), which pose a set of new challenges in the problem formulation, algorithm design, and convergence analysis. In this paper, we will systematically review existing FL optimization research including their assumptions, formulations, methods, and theoretical results. Potential future directions are also discussed.