RepNN: Tackling spectral bias in deep neural networks via parameter reparameterization

Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors. In this study, we investigate this limitation by examining the failure of shallow ReLU neural networks in fitting high-frequency functions. This observation identifies two important factors in resolving rapid oscillations: the initial slope scale and the distribution of partition points induced by the networks. Motivated by this analysis, we propose RepNN, a reparameterized neural network model with activation ReLU or tanh designed for high-frequency and multiscale problems. The key idea is to reparameterize the weights and biases in the first hidden layer, which enables effective control of the initial slope scale and provides an appropriate distribution of the initial partition points. Furthermore, treating the reparameterized weights and biases as trainable parameters allows the DNN to achieve adaptive frequency scaling during training. In addition, we derive quantitative estimates for the output and slope magnitudes of the reparameterized DNN to guide the initialization of the proposed method. Numerical experiments, including multiscale one- and four-dimensional function approximations, forward and inverse PDE problems in combination with physics-informed neural networks (PINNs), and operator learning for an earthquake problem using real data, demonstrate that RepNN improves the predicted accuracy of vanilla DNNs in capturing highly oscillatory features with slightly additional computational cost. These results indicate that RepNN provides an effective and flexible approach for overcoming spectral bias and applying DNNs to multiscale problems.

Beyond Visual Cues: CoT-Enhanced Reasoning for Semi-supervised Medical Image Segmentation

Semi-supervised medical image segmentation has emerged as a dominant research problem in medical image analysis, mitigating annotation scarcity by leveraging consistency regularization on unlabeled data. However, existing approaches operate predominantly via visual pattern matching, relying heavily on pixel-level similarities. This visual-centric dependency often falters in clinical scenarios characterized by the visual-semantic mismatch, where visually similar lesions warrant distinct diagnostic conclusions, thus failing to capture the underlying diagnostic logic used by experts. To address this, we move beyond visual cues and propose CERS (CoT-Enhanced Reasoning Segmentation), a framework that integrates Chain-of-Thought (CoT) reasoning to distinguish pathologically distinct cases. Specifically, we construct a knowledge pool enriched with linguistic reasoning descriptions generated by large language models (LLMs). A semantic-aware reference selection strategy is introduced to identify historical evidence, filtering candidates first by morphology, and then refining them via CoT consistency to eliminate hard negatives. Furthermore, a multi-scale coordinate attention module (MCAM) is designed to effectively fuse this reasoning-derived context into the decoding process. Extensive experiments demonstrate the superiority of CERS against state-of-the-art approaches, particularly in resolving boundary ambiguities and semantic inconsistencies. The code is available at https://github.com/cymasuna/CERS.

Propagating Structural Guidance: Synthesizing Fluorescein Angiography from Fundus Images and Sparse OCT Scans

Fundus fluorescein angiography (FFA) is critical for assessing retinal vascular abnormalities, but its acquisition is invasive and not always feasible. In contrast, color fundus photography (CFP) is non-invasive and widely accessible, which has motivated studies on CFP-to-FFA synthesis. However, prior works rely solely on CFP surface texture, fundamentally limiting the ability to reconstruct functional vascular information and subtle pathological changes. To address this, we propose a novel framework that synthesizes FFA from CFP with structural guidance provided by optical coherence tomography (OCT). We construct a multi-modal retinal imaging dataset with paired CFP, FFA, and OCT from 3,676 patient eyes--the first tri-modally aligned dataset in retinal imaging. To bridge the spatial gap between OCT and fundus modalities, we propose a Spatially Aligned Cross-Modal Fusion (SACMF) module that projects depth-resolved OCT features onto the fundus plane and injects them into the CFP encoder via adaptive layer normalization. Beyond feature fusion, we further introduce Token-wise Cross-Modality Alignment (TCMA), a token-level contrastive learning strategy that explicitly aligns CFP and FFA representations at corresponding spatial positions. Our method achieves superior synthesis performance compared to state-of-the-art methods. Moreover, extensive experiments demonstrate that the FFA images synthesized by our approach bring greater improvements in downstream disease diagnosis performance than existing methods, highlighting the clinical potential of our approach as a non-invasive decision-support tool in routine workflows. The code is available at https://github.com/while-plus/OCT-guide-FFA-Syn.

Text-Driven Fusion for Infrared and Visible Images: Achieving Image Scene Adaptation on Hyperbolic Space

Infrared and visible image fusion aims to integrate complementary modalities, while existing Euclidean methods impose rigid distance metrics that distort multi-modal interactions and parent-to-child semantic hierarchies. To overcome these limitations, we introduce a text-driven fusion framework empowered by hyperbolic manifold learning. During training, BLIP-extracted text prompts serve as topological anchors within the hyperbolic space, guiding vision-attribute alignment through hyperbolic embeddings that naturally accommodate varying semantic granularities. By exploiting the exponential volume growth dictated by the Poincaré ball's negative curvature, this approach seamlessly embeds hierarchical trees to encode coarse-to-fine semantics without metric saturation, while the vast peripheral space prevents texture distortion during cross-modal fusion. At inference, the fusion process autonomously adapts to input content using the learned text-attribute priors, completely eliminating the need for textual input. Experimental results show our method outperforms state-of-the-art approaches on benchmark datasets, with code available at https://github.com/Shaoyun2023/TEDFusion.

Operator learning for solving Fokker-Planck equations with various initial conditions

The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently approximating the solution operator of the FPE for a whole range of initial conditions. Leveraging the Chapman-Kolmogorov equation for Markovian stochastic processes, the problem is reformulated into approximating a transition PDF starting at initial time from a Dirac mass centered at an arbitrary point. The PDF of an associated linearized stochastic differential equation (SDE) is employed as the base distribution for the normalizing flow, providing a good approximation of the target PDF, especially for small times, and thereby avoiding the singularity of the map associated with the Dirac delta initial distribution. Furthermore, a time-weighted loss function is introduced to mitigate numerical instabilities arising at small times, achieving a balance between causality and training difficulty as time progresses. A variety of numerical experiments are presented to illustrate the effectiveness and robustness of the proposed method.

How Much MRI Preprocessing Is Enough? A Cost-Utility Study for Brain MRI Foundation Models

MRI preprocessing defines the input distribution seen by brain MRI foundation models, yet it is usually treated as routine data cleaning rather than a modeling choice. We ask how much preprocessing is worth its computational cost for self-supervised 3D MRI pretraining. Keeping the corpus, 3D ViT backbone, masking protocol, and downstream evaluations fixed, we compare a graded P0-P7 preprocessing spectrum for masked autoencoding (MAE) and joint-embedding predictive learning (JEPA) on 20,000 heterogeneous brain MRI volumes, then transfer the encoders to IDH prediction, MCI classification, brain age regression, and GLI/PED tumor segmentation. The results do not support a simple "more is better" rule. P0/P1 are numerically unstable, making P2 the lowest-cost feasible level; beyond P2, choosing the best feasible preprocessing level improves aggregate utility by only 3.4 percentage points for MAE and 1.8 percentage points for JEPA, with most paired gains statistically unresolved. Stronger preprocessing is beneficial only in selected regimes: IDH improves modestly, AGE and GLI/PED are often near or best at P2, and MCI shows the clearest empirical P7 gain. Cross-level MCI transfer further shows that much of the P7 advantage can be recovered by applying stronger preprocessing downstream, without requiring P7 throughout pretraining. These findings recast MRI preprocessing as a downstream-aware cost-utility decision rather than a default escalation pipeline. Code is available at https://github.com/PangJiangShuan/PreBrain.

Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a deep adaptive dimension-reduction Bayesian inference framework based on the Variational Flow (VF) model. Since standard normalizing flows are restricted by bijective mappings and cannot directly reduce dimensions, VF overcomes this limitation by integrating VAE-based nonlinear dimension reduction with dual normalizing flows for the latent prior and encoder. This design provides a strictly higher evidence lower bound than VAE and allows more flexible approximation of complex posterior distributions. We further introduce an iterative prior updating strategy that gradually moves the prior mean toward high-probability posterior regions, avoiding manual prior tuning. These components form a closed adaptive loop together with an adaptively fine-tuned Fourier Neural Operator (FNO) surrogate: VF generates posterior-concentrated samples to refine the surrogate, while the updated surrogate further improves posterior inference. Numerical experiments on a 100-dimensional Rosenbrock problem and three standard PDE-governed inverse problems show that our method delivers competitive or superior accuracy compared with MCMC, UKI, and SVGD baselines across all tested configurations, with the most pronounced advantages emerging in challenging scenarios such as high-noise observations and high-dimensional parameter spaces.

Quantifying and Mitigating Self-Preference Bias of LLM Judges

LLM-as-a-Judge has become a dominant approach in automated evaluation systems, playing critical roles in model alignment, leaderboard construction, quality control, and so on. However, the scalability and trustworthiness of this approach can be substantially distorted by Self-Preference Bias (SPB), which is a directional evaluative deviation in which LLMs systematically favor or disfavor their own generated outputs during evaluation. Existing measurements rely on costly human annotations and conflate generative capability with evaluative stance, and thus are impractical for large-scale deployment in real-world systems. To address this issue, we introduce a fully automated framework to quantifying and mitigating SPB, which constructs equal-quality pairs of responses with negligible quality differences, enabling statistical disentanglement of discriminability from bias propensity without human gold standards. Empirical analysis across 20 mainstream LLMs reveals that advanced capabilities are often uncorrelated, or even negatively correlated, with low SPB. To mitigate this bias, we propose a structured multi-dimensional evaluation strategy grounded in cognitive load decomposition, which reduces SPB by 31.5\% on average.

SemiGDA: Generative Dual-distribution Alignment for Semi-Supervised Medical Image Segmentation

Semi-supervised learning addresses label scarcity and high annotation costs in medical image segmentation by exploiting the latent information in unlabeled data to enhance model performance. Traditional discriminative segmentation relies on segmentation masks, neglecting feature-level distribution constraints. This limits robust semantic representation learning and adaptive modeling of unlabeled data in scenarios with few labels. To address these limitations, we propose SemiGDA, a novel Generative Dual-distribution Alignment framework for semi-supervised medical image segmentation. Our SemiGDA overcomes the reliance of discriminative methods on large labeled datasets by aligning feature and semantic distributions to boost semantic learning and scene adaptability. Specifically, we propose a Dual-distribution Alignment Module (DAM), which employs two structurally distinct encoders to model image and mask feature distributions. It enforces their alignment in the latent space via distributional constraints, establishing structured feature consistency. Moreover, we design a Consistency-Driven Skip Adapter (CDSA) strategy, which introduces dual skip adapters (Image and Mask) to fuse multi-scale features via skip connections. Using a consistency loss, CDSA enhances cross-branch semantic alignment and reinforces fine-grained semantic consistency. Experimental results on diverse medical datasets show that our method outperforms other state-of-the-art semi-supervised segmentation methods. Code is released at: https://github.com/taozh2017/SemiGDA.

Amortized Filtering and Smoothing with Conditional Normalizing Flows

Bayesian filtering and smoothing for high-dimensional nonlinear dynamical systems are fundamental yet challenging problems in many areas of science and engineering. In this work, we propose AFSF, a unified amortized framework for filtering and smoothing with conditional normalizing flows. The core idea is to encode each observation history into a fixed-dimensional summary statistic and use this shared representation to learn both a forward flow for the filtering distribution and a backward flow for the backward transition kernel. Specifically, a recurrent encoder maps each observation history to a fixed-dimensional summary statistic whose dimension does not depend on the length of the time series. Conditioned on this shared summary statistic, the forward flow approximates the filtering distribution, while the backward flow approximates the backward transition kernel. The smoothing distribution over an entire trajectory is then recovered by combining the terminal filtering distribution with the learned backward flow through the standard backward recursion. By learning the underlying temporal evolution structure, AFSF also supports extrapolation beyond the training horizon. Moreover, by coupling the two flows through shared summary statistics, AFSF induces an implicit regularization across latent state trajectories and improves trajectory-level smoothing. In addition, we develop a flow-based particle filtering variant that provides an alternative filtering procedure and enables ESS-based diagnostics when explicit model factors are available. Numerical experiments demonstrate that AFSF provides accurate approximations of both filtering distributions and smoothing paths.