LegalOne: A Family of Foundation Models for Reliable Legal Reasoning

While Large Language Models (LLMs) have demonstrated impressive general capabilities, their direct application in the legal domain is often hindered by a lack of precise domain knowledge and complexity of performing rigorous multi-step judicial reasoning. To address this gap, we present LegalOne, a family of foundational models specifically tailored for the Chinese legal domain. LegalOne is developed through a comprehensive three-phase pipeline designed to master legal reasoning. First, during mid-training phase, we propose Plasticity-Adjusted Sampling (PAS) to address the challenge of domain adaptation. This perplexity-based scheduler strikes a balance between the acquisition of new knowledge and the retention of original capabilities, effectively establishing a robust legal foundation. Second, during supervised fine-tuning, we employ Legal Agentic CoT Distillation (LEAD) to distill explicit reasoning from raw legal texts. Unlike naive distillation, LEAD utilizes an agentic workflow to convert complex judicial processes into structured reasoning trajectories, thereby enforcing factual grounding and logical rigor. Finally, we implement a Curriculum Reinforcement Learning (RL) strategy. Through a progressive reinforcement process spanning memorization, understanding, and reasoning, LegalOne evolves from simple pattern matching to autonomous and reliable legal reasoning. Experimental results demonstrate that LegalOne achieves state-of-the-art performance across a wide range of legal tasks, surpassing general-purpose LLMs with vastly larger parameter counts through enhanced knowledge density and efficiency. We publicly release the LegalOne weights and the LegalKit evaluation framework to advance the field of Legal AI, paving the way for deploying trustworthy and interpretable foundation models in high-stakes judicial applications.

PLawBench: A Rubric-Based Benchmark for Evaluating LLMs in Real-World Legal Practice

As large language models (LLMs) are increasingly applied to legal domain-specific tasks, evaluating their ability to perform legal work in real-world settings has become essential. However, existing legal benchmarks rely on simplified and highly standardized tasks, failing to capture the ambiguity, complexity, and reasoning demands of real legal practice. Moreover, prior evaluations often adopt coarse, single-dimensional metrics and do not explicitly assess fine-grained legal reasoning. To address these limitations, we introduce PLawBench, a Practical Law Benchmark designed to evaluate LLMs in realistic legal practice scenarios. Grounded in real-world legal workflows, PLawBench models the core processes of legal practitioners through three task categories: public legal consultation, practical case analysis, and legal document generation. These tasks assess a model's ability to identify legal issues and key facts, perform structured legal reasoning, and generate legally coherent documents. PLawBench comprises 850 questions across 13 practical legal scenarios, with each question accompanied by expert-designed evaluation rubrics, resulting in approximately 12,500 rubric items for fine-grained assessment. Using an LLM-based evaluator aligned with human expert judgments, we evaluate 10 state-of-the-art LLMs. Experimental results show that none achieves strong performance on PLawBench, revealing substantial limitations in the fine-grained legal reasoning capabilities of current LLMs and highlighting important directions for future evaluation and development of legal LLMs. Data is available at: https://github.com/skylenage/PLawbench.

PMPBench: A Paired Multi-Modal Pan-Cancer Benchmark for Medical Image Synthesis

Contrast medium plays a pivotal role in radiological imaging, as it amplifies lesion conspicuity and improves detection for the diagnosis of tumor-related diseases. However, depending on the patient's health condition or the medical resources available, the use of contrast medium is not always feasible. Recent work has explored AI-based image translation to synthesize contrast-enhanced images directly from non-contrast scans, aims to reduce side effects and streamlines clinical workflows. Progress in this direction has been constrained by data limitations: (1) existing public datasets focus almost exclusively on brain-related paired MR modalities; (2) other collections include partially paired data but suffer from missing modalities/timestamps and imperfect spatial alignment; (3) explicit labeling of CT vs. CTC or DCE phases is often absent; (4) substantial resources remain private. To bridge this gap, we introduce the first public, fully paired, pan-cancer medical imaging dataset spanning 11 human organs. The MR data include complete dynamic contrast-enhanced (DCE) sequences covering all three phases (DCE1-DCE3), while the CT data provide paired non-contrast and contrast-enhanced acquisitions (CTC). The dataset is curated for anatomical correspondence, enabling rigorous evaluation of 1-to-1, N-to-1, and N-to-N translation settings (e.g., predicting DCE phases from non-contrast inputs). Built upon this resource, we establish a comprehensive benchmark. We report results from representative baselines of contemporary image-to-image translation. We release the dataset and benchmark to catalyze research on safe, effective contrast synthesis, with direct relevance to multi-organ oncology imaging workflows. Our code and dataset are publicly available at https://github.com/YifanChen02/PMPBench.

Adaptive Exponential Integration for Stable Gaussian Mixture Black-Box Variational Inference

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization methods often suffer from instability and inefficiency. We develop a stable and efficient framework that combines three key components: (1) affine-invariant preconditioning via natural gradient formulations, (2) an exponential integrator that unconditionally preserves the positive definiteness of covariance matrices, and (3) adaptive time stepping to ensure stability and to accommodate distinct warm-up and convergence phases. The proposed approach has natural connections to manifold optimization and mirror descent. For Gaussian posteriors, we prove exponential convergence in the noise-free setting and almost-sure convergence under Monte Carlo estimation, rigorously justifying the necessity of adaptive time stepping. Numerical experiments on multimodal distributions, Neal's multiscale funnel, and a PDE-based Bayesian inverse problem for Darcy flow demonstrate the effectiveness of the proposed method.

Learning Patient-Specific Disease Dynamics with Latent Flow Matching for Longitudinal Imaging Generation

Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain: disease dynamics are inherently continuous and monotonic, yet latent representations are often scattered, lacking semantic structure, and diffusion-based models disrupt continuity with random denoising process. In this work, we propose to treat the disease dynamic as a velocity field and leverage Flow Matching (FM) to align the temporal evolution of patient data. Unlike prior methods, it captures the intrinsic dynamic of disease, making the progression more interpretable. However, a key challenge remains: in latent space, Auto-Encoders (AEs) do not guarantee alignment across patients or correlation with clinical-severity indicators (e.g., age and disease conditions). To address this, we propose to learn patient-specific latent alignment, which enforces patient trajectories to lie along a specific axis, with magnitude increasing monotonically with disease severity. This leads to a consistent and semantically meaningful latent space. Together, we present $Δ$-LFM, a framework for modeling patient-specific latent progression with flow matching. Across three longitudinal MRI benchmarks, $Δ$-LFM demonstrates strong empirical performance and, more importantly, offers a new framework for interpreting and visualizing disease dynamics.

A Generative Data Framework with Authentic Supervision for Underwater Image Restoration and Enhancement

Underwater image restoration and enhancement are crucial for correcting color distortion and restoring image details, thereby establishing a fundamental basis for subsequent underwater visual tasks. However, current deep learning methodologies in this area are frequently constrained by the scarcity of high-quality paired datasets. Since it is difficult to obtain pristine reference labels in underwater scenes, existing benchmarks often rely on manually selected results from enhancement algorithms, providing debatable reference images that lack globally consistent color and authentic supervision. This limits the model's capabilities in color restoration, image enhancement, and generalization. To overcome this limitation, we propose using in-air natural images as unambiguous reference targets and translating them into underwater-degraded versions, thereby constructing synthetic datasets that provide authentic supervision signals for model learning. Specifically, we establish a generative data framework based on unpaired image-to-image translation, producing a large-scale dataset that covers 6 representative underwater degradation types. The framework constructs synthetic datasets with precise ground-truth labels, which facilitate the learning of an accurate mapping from degraded underwater images to their pristine scene appearances. Extensive quantitative and qualitative experiments across 6 representative network architectures and 3 independent test sets show that models trained on our synthetic data achieve comparable or superior color restoration and generalization performance to those trained on existing benchmarks. This research provides a reliable and scalable data-driven solution for underwater image restoration and enhancement. The generated dataset is publicly available at: https://github.com/yftian2025/SynUIEDatasets.git.

Rotated Mean-Field Variational Inference and Iterative Gaussianization

We propose to perform mean-field variational inference (MFVI) in a rotated coordinate system that reduces correlations between variables. The rotation is determined by principal component analysis (PCA) of a cross-covariance matrix involving the target's score function. Compared with standard MFVI along the original axes, MFVI in this rotated system often yields substantially more accurate approximations with negligible additional cost. MFVI in a rotated coordinate system defines a rotation and a coordinatewise map that together move the target closer to Gaussian. Iterating this procedure yields a sequence of transformations that progressively transforms the target toward Gaussian. The resulting algorithm provides a computationally efficient way to construct flow-like transport maps: it requires only MFVI subproblems, avoids large-scale optimization, and yields transformations that are easy to invert and evaluate. In Bayesian inference tasks, we demonstrate that the proposed method achieves higher accuracy than standard MFVI, while maintaining much lower computational cost than conventional normalizing flows.

Towards Robust Influence Functions with Flat Validation Minima

The Influence Function (IF) is a widely used technique for assessing the impact of individual training samples on model predictions. However, existing IF methods often fail to provide reliable influence estimates in deep neural networks, particularly when applied to noisy training data. This issue does not stem from inaccuracies in parameter change estimation, which has been the primary focus of prior research, but rather from deficiencies in loss change estimation, specifically due to the sharpness of validation risk. In this work, we establish a theoretical connection between influence estimation error, validation set risk, and its sharpness, underscoring the importance of flat validation minima for accurate influence estimation. Furthermore, we introduce a novel estimation form of Influence Function specifically designed for flat validation minima. Experimental results across various tasks validate the superiority of our approach.

Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening

Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by $k$-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility.

New affine invariant ensemble samplers and their dimensional scaling

We introduce some new affine invariant ensemble samplers that are easy to construct and improve upon existing widely used algorithms, especially for high-dimensional problems. Specifically, we propose a derivative-free ensemble side move sampler that performs favorably compared to popular samplers in the \texttt{emcee} package. Additionally, we develop a class of derivative-based ensemble Hamiltonian Monte Carlo (HMC) samplers with affine invariance, which outperform standard HMC without affine invariance when sampling highly skewed distributions. We provide asymptotic scaling analysis for high-dimensional Gaussian targets to further elucidate the properties of these affine invariant ensemble samplers. In particular, with derivative information, the affine invariant ensemble HMC can scale much better with dimension compared to derivative-free ensemble samplers.