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Applications · Chemistry, Physics, and Earth Sciences

Lingshi MENG, Haosen Shi, Sinno Jialin Pan

Physics-Informed Neural Networks (PINNs) represent a significant advancement in computational methods for solving partial differential equations (PDEs). However, the adoption of deeper neural network architectures presents significant challenges, as they struggle to address differential-related complications that arise during the computation of derivatives over the input of PINNs. These complications extend beyond traditional vanishing and exploding gradients to include vanishing and exploding differentials, with both phenomena becoming more severe as networks grow deeper. By examining the computation graph of derivatives in deep neural networks, we identify key bottlenecks causing numerical instabilities in deep architectures. In response, we introduce a novel approach that utilizes Coupling Layers with carefully regulated spectral norms of Jacobian matrices to stabilize and facilitate deep PINN training, effectively addressing differential-related challenges and improving model stability. Our proposed architecture successfully mitigates the fundamental constraints of deeper PINNs while maximizing their capabilities through consistent differential propagation. Comprehensive evaluations show that our approach surpasses conventional shallow PINN methods and alternative deep PINN designs across a range of challenging problems, particularly in cases featuring high-frequency solution components.

Applications · Chemistry, Physics, and Earth Sciences

Yongqi Jin, Yecheng Wang, Jun-jie Wang, Rong Zhu, Guolin Ke, Weinan E

Accurate prediction of nuclear magnetic resonance (NMR) chemical shifts is fundamental to spectral analysis and molecular structure elucidation, yet existing machine learning methods rely on limited, labor-intensive atom-assigned datasets. We propose a semi-supervised framework that learns NMR chemical shifts from millions of literature-extracted spectra without explicit atom-level assignments, integrating a small amount of labeled data with large-scale unassigned spectra. We formulate chemical shift prediction from literature spectra as a permutation-invariant set supervision problem, and show that under commonly satisfied conditions on the loss function, optimal bipartite matching reduces to a sorting-based loss, enabling stable large-scale semi-supervised training beyond traditional curated datasets. Our models achieve substantially improved accuracy and robustness over state-of-the-art methods and exhibit stronger generalization on significantly larger and more diverse molecular datasets. Moreover, by incorporating solvent information at scale, our approach captures systematic solvent effects across common NMR solvents for the first time. Overall, our results demonstrate that large-scale unlabeled spectra mined from the literature can serve as a practical and effective data source for training NMR shift models, suggesting a broader role of literature-derived, weakly structured data in data-centric AI for science.

Deep Learning · Large Language Models

Giang Do, Hung Le, Truyen Tran

Sparse Mixture of Experts (SMoE) architectures improve the training efficiency of Large Language Models (LLMs) by routing input tokens to a selected subset of specialized experts. Despite their remarkable success, both training and inference in SMoE models suffer from the *expert collapse* issue (Chi et al., 2022a), which degrades model performance. Prior studies primarily focus on improving the router; however, such methods rely on training from scratch or fine-tuning, which requires high computational and data-processing costs. Furthermore, we demonstrate that, despite these efforts, the issue persists when advancing well-pretrained SMoE models, as evidenced by both theoretical and empirical results. To fill that gap, we analyze the advanced SMoE models and observe that the eigenvectors of expert weight matrices encode rich semantic information, pointing to an effective alternative to conventional routing strategies. Building on this insight, we propose **Singular Value Decomposition SMoE (SSMoE)**, a novel and *training-free* framework that leverages spectral properties of the expert weights to address the collapse issue and enhance model performance. Extensive experiments across diverse language and vision tasks, under both clean and corrupt data settings, demonstrate the strong generalization and robustness of SSMoE. Our findings highlight how a deeper understanding of model internals can guide the development of more effective SMoE architectures.

Deep Learning · Everything Else

Xianbiao Qi, Marco Chen, Jiaquan Ye, Yelin He, Rong Xiao

The Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such as Adam remain insufficiently understood. In this work, we aim to address these questions through a unified spectral perspective. Specifically, we view Muon as the \( p = 0 \) endpoint of a family of spectral transformations of the form \( \boldsymbol{U} \boldsymbol{\Sigma}^{p} \boldsymbol{V}^{\top} \), and consider additional variants with \( p = \frac{1}{2} \), \( p = \frac{1}{4} \), and \( p = 1 \). These transformations are applied to both first-moment updates, as in momentum SGD, and to root-mean-square (RMS) normalized gradient updates as in Adam. To enable efficient computation, we develop a coupled Newton iteration that avoids explicit singular value decomposition. Across controlled experiments, we find that RMS-normalized updates yield more stable optimization than first-moment updates. Moreover, while spectral compression provides strong stabilization benefits under first-moment updates, the Muon update (\( p = 0 \)) does not consistently outperform Adam. These results suggest that Muon is best understood as an effective form of spectral normalization, but not a universally superior optimization method.

Deep Learning · Self-Supervised Learning

Yaoqi Liu, Jin Wang, Chunchen Wang, Hui Wang, Chuan Shi

In recent years, wireless signal recognition (WSR), which leverages artificial intelligence (AI) to identify properties of passively received radio signals, has garnered significant attention due to its broad applications, such as spectrum management. Existing WSR methods typically learn directly from received signals, which are distorted by physical wireless channel effects such as fading, and current denoising diffusion models lack de-channeling capabilities, which leads to performance degradation. Therefore, we propose PWC-Diff, a novel framework that integrates prior Physical Wireless Channels into the denoising Diffusion process. The framework employs a dedicated architecture named FusedFormer, which contains a fusion module and a self-attention module that jointly capture the temporal and spectral characteristics of the signals throughout the diffusion trajectory. By leveraging prior wireless channels, PWC-Diff learns to progressively “de-channel” the received signal and recover a representation closer to the transmitted signal. Extensive experiments on several datasets across three WSR tasks have achieved state-of-the-art (SOTA) performance, which demonstrates the rationality of our theory, and ablation experiments further illustrate the effectiveness of our proposed PWC-Diff.

Applications · Health / Medicine

Shuntian Zheng, Jiaqi Li, Xiaoman Lu, Shuai He, Yu Guan

Millimeter-wave (mmWave) enables privacy-preserving, illumination-robust human pose estimation (HPE), with each mmWave frame represented as a range--angle--Doppler tensor, providing spatial magnitude for localization and Doppler signatures for motion-related cues. However, existing mmWave-based HPE methods either underutilize or naïvely fuse Doppler signatures with spatial magnitude, disregarding their distinct physical semantics. As a result, non-human Doppler signatures can be misinterpreted as human motion cues, leading to jittery trajectories. We propose \textbf{PULSE}, which converts Doppler signatures into confidence-aware motion prompts and injects them into spatial magnitude reasoning through constrained interactions. By screening Doppler prompts before they influence prediction, PULSE first suppresses spurious spectral motion cues and then uses the screened prompts to stabilize prediction. Across three datasets spanning single- and multi-person settings, PULSE consistently improves pose accuracy and temporal stability, indicating that controlled Doppler prompting is a practical direction for stable mmWave HPE. Codes are available in supplementary materials.

Applications · Health / Medicine

Cuong Van, Trong-Thang Pham, Ngoc-Son Nguyen, Duy Nguyen, Ngan Le

Sparse-view Cone-Beam Computed Tomography reconstruction from limited X-ray projections remains a challenging problem in medical imaging due to the inherent undersampling of fine-grained anatomical details, which correspond to high-frequency components. Conventional CNN-based methods often struggle to recover these fine structures, as they are typically biased toward learning low-frequency information. To address this challenge, this paper presents DuFal (Dual-Frequency-Aware Learning), a novel framework that integrates frequency-domain and spatial-domain processing via a dual-path architecture. The core innovation lies in our High-Local Factorized Fourier Neural Operator, which comprises two complementary branches: a Global High-Frequency Enhanced Fourier Neural Operator that captures global frequency patterns and a Local High-Frequency Enhanced Fourier Neural Operator that processes spatially partitioned patches to preserve spatial locality that might be lost in global frequency analysis. To improve efficiency, we design a Spectral-Channel Factorization scheme that reduces the Fourier Neural Operator parameter count. We also design a Cross-Attention Frequency Fusion module to integrate spatial and frequency features effectively. The fused features are then decoded through a Feature Decoder to produce projection representations, which are subsequently processed through an Intensity Field Decoding pipeline to reconstruct a final Computed Tomography volume. Experimental results on the LUNA16 and ToothFairy datasets demonstrate that DuFal significantly outperforms existing state-of-the-art methods in preserving high-frequency anatomical features, particularly under extremely sparse-view settings.

Applications · Computer Vision

Woojung Han, Seil Kang, Youngjun Jun, Min-Hung Chen, Fu-En Yang, Seong Jae Hwang

Video diffusion models can generate visually stunning content, yet frequently produce motion that violates physical laws, objects accelerate implausibly or vanish mid-trajectory. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising, motion dynamics are $8.5\times$ more sensitive to phase corruption than magnitude, yet the refinement process progressively destroys this critical component. Building on this insight, we propose PhaseLock, a training-free framework that locks motion dynamics to fast inference priors. Rather than requiring 50 steps to establish physics, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. This decouples physical consistency from visual refinement, ensuring the final output remains grounded in valid trajectories. PhaseLock achieves strong physical consistency with negligible overhead ($1.06\times$ time, $1.02\times$ memory), eliminating the need for expensive external guidance methods ($\sim5\times$ time).

Social Aspects · Privacy

Zhiyu Sun, Minrui Luo, Yu Wang, Tianxing He, Zhili Chen

Large language models (LLMs) are pretrained on corpora containing trillions of tokens and, therefore, inevitably memorize sensitive information. Locate-then-edit methods, as a mainstream paradigm of model editing, offer a promising solution by modifying model parameters without retraining. However, in this work, we reveal a critical vulnerability of this paradigm: the parameter updates inadvertently serve as a side channel, enabling attackers to recover the edited data. We propose a two-stage reverse-engineering attack named KSTER (KeySpaceReconsTruction-then-EntropyReduction) that leverages the low-rank structure of these updates. First, we theoretically show that the row space of the update matrix encodes a "fingerprint" of the edited subjects, enabling accurate subject recovery via spectral analysis. Second, we introduce an entropy-based prompt recovery attack that reconstructs the semantic context of the edit. Extensive experiments on multiple LLMs demonstrate that our attacks can recover edited data with high success rates. Furthermore, we propose subspace camouflage, a defense strategy that obfuscates the update fingerprint with semantic decoys. This approach effectively mitigates reconstruction risks without compromising editing utility. Our code is available at https://anonymous.4open.science/r/EditATK-26B6.

Applications · Health / Medicine

Jingbo Yang, Yunfeng Zhao, Chao Qiu, Yulin Sun, Xiuyun Liu, Xiaofei Wang

Stereotactic electroencephalography (sEEG) provides temporally precise intracranial recordings but is inherently constrained by sparse and irregular spatial sampling due to clinical limitations on electrode implantation. Signal reconstruction under this setting aims to infer neural activity at unmonitored locations, potentially expanding the coverage of neural recordings without increasing the number of implanted electrodes. However, most existing sEEG reconstruction methods underutilize the spatial information of electrode contacts in both encoding and modeling, and rely on deterministic objectives that favor average patterns, leading to over-smoothed reconstructions. We propose EpiTwin, a conditional spatial graph transformer for sEEG signal reconstruction, comprising three key components. Hybrid Spatial Positional Encoding (HSPE) constructs explicit spatial identities from electrode coordinates, graph topology, and anatomical priors. Geometry–Functional Biased Attention (GFBA) incorporates geometric distance and data-driven functional similarity biases into attention computation. Adversarial Refinement Training employs a multi-scale discriminator to counter reconstruction over-smoothing. Experiments on real-world clinical sEEG data demonstrate that EpiTwin consistently achieves lower reconstruction error under electrode series-level masking, outperforming recent foundation models such as LaBraM with a 16.8\% relative reduction in RMSE. Furthermore, EpiTwin effectively mitigates spectral over-smoothing and improves reconstruction fidelity.

Reinforcement Learning · Deep RL

Sanghyeob Song, Donghyeok Lee, Jinsik Kim, Sungroh Yoon

For reinforcement learning in data-scarce domains like real-world robotics, intensive data reuse enhances efficiency but induces overfitting. While prior works focus on critic bias, representation-level instability in Self-Predictive Learning (SPL) under high Update-to-Data (UTD) regimes remains underexplored. To bridge this gap, we propose Robust Representation via Redundancy Reduction (R2R2), a regularization method within SPL. We theoretically identify that standard zero-centering conflicts with SPL's spectral properties and design a non-centered objective accordingly. We verify R2R2 on SPL-native algorithms like TD7. Furthermore, to demonstrate its orthogonality to prior advancements, we extend the state-of-the-art SimbaV2—which originally lacks SPL—by integrating a tailored SPL module, termed SimbaV2-SPL. Experiments across 11 continuous control tasks confirm that R2R2 effectively mitigates overfitting; specifically, at a UTD ratio of 20, it improves TD7 by $\sim$22\% and provides additional gains on top of SimbaV2-SPL, which itself establishes a new state-of-the-art.

Hugo Tabanelli, Yatin Dandi, Luca Pesce, FLORENT KRZAKALA

Why depth yields a genuine computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional Gaussian setting, focusing on compositional target functions. We analyze their learnability using an explicit three-layer fitting model trained via layer-wise spectral estimators. Although the target is globally a high-degree polynomial, its compositional structure allows learning to proceed in stages: an intermediate representation reveals structure that is inaccessible at the input level. This reduces learning to simpler spectral estimation problems, well studied in the context of multi-index models, whereas any shallow estimator must resolve all components simultaneously. Our analysis relies on Gaussian universality, leading to sharp separations in sample complexity between two and three-layer learning strategies.

Deep Learning · Sequential Models, Time series

Qilin Wang

We argue that long-term forecasting requires learning local Jacobians with explicit spectral structure, going beyond simple conditional mean matching. Our method, \textsc{Fern}, invokes Brenier's theorem to directly parameterize the Jacobian as a symmetric positive semi-definite (SPD) factorization, treating forecasting as the optimal transport of probability mass from a fixed Gaussian source to data-dependent ellipsoids. This formulation reduces the computational cost of eigen-decomposition from cubic to linear time while providing interpretable, geometry-aware projections. To rigorously evaluate robustness, we introduce a synthetic benchmark with controlled non-stationary shocks alongside new metrics like Effective Prediction Time (EPT). \textsc{Fern} demonstrates exceptional stability, outperforming baselines like DLinear and Koopa by over two orders of magnitude (up to $790\times$) on nonstationary settings where standard benchmarks fail to expose model brittleness.

Deep Learning · Large Language Models

Yuanjian Xu, Jianing Hao, Wanbo Zhang, Zhong Li, Guang Zhang

The annealing stage of Large Language Model (LLM) training is a critical phase where model loss drops sharply and downstream capabilities solidify. Despite its importance, current practices rely on empirical heuristics like quality filtering or context extension, lacking a principled understanding of the underlying optimization dynamics. We address this gap by providing a theoretical characterization of the spectral properties targeted during annealing. We demonstrate that effective annealing requires balancing global Hessian geometry with sample-wise gradient noise, navigating a landscape of highly anisotropic curvature. Based on these insights, we formulate sample selection as a constrained optimization problem to suppress noise in sharp directions while preserving descent signals in flat subspaces. Our method, solved via Successive Convex Programming (SCP), achieves state-of-the-art results across multiple model scales. Code is available at \url{https://anonymous.4open.science/r/LLM-Annealing-Phase}.

Applications · Computer Vision

Xian-Hua Han

Reconstructing hyperspectral images from compressive measurements is challenging due to a fundamental mismatch between locally reliable observations and globally entangled structures induced by spectral dispersion. This study formalizes this issue as a local–global dissonance in representation learning for CASSI systems. To resolve it, we propose a Hierarchical Scale-Reconciling Architecture (HSRA) that enforces local sufficiency and global consistency in a principled, scale-aware manner. HSRA combines multi-kernel token mixing, latent window interactions, and hierarchical multi-granularity spatially shifted attention to progressively reconcile physical constraints across scales. Embedded into a deep unfolding framework as a physically grounded learned prior, Extensive experiments on benchmarks demonstrate that HSRA achieves consistent and significant improvements over state-of-the-art methods.

Evan Dogariu, Anand Brahmbhatt, Elad Hazan

We study the fundamental problem of one-step prediction of a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.

Applications · Computer Vision

Jing He, Licheng Jiao, Lingling Li, Xiaoqiang Lu, Xu Liu, Wenping Ma, Fang Liu, Long Sun

3D visual grounding encompassing 3D referring expression comprehension (3DREC) and segmentation (3DRES) requires robust cross-modal representation to achieve fine-grained semantic alignment and precise geometric reasoning. However, most methods employ unimodal pre-trained encoders that transfer visual and linguistic knowledge independently, inducing domain shift and poor cross-modal alignment. Meanwhile, spatial modeling with handcrafted priors limits cross-modal geometric representation, struggling to capture complex object relations due to spectral bias. To address these challenges, we propose Text-aware Feature Tuning (TFT) and Decomposed Spectral Geometry (DSG) to enhance cross-modal semantic representation. Specifically, TFT injects linguistic context into the visual hierarchy to mitigate domain shift and facilitate early cross-modal alignment. DSG employs a learnable Fourier basis and explicitly decomposes pairwise relations into symmetric and antisymmetric spectral components, allowing the model to capture high-frequency geometric details and direction-aware relations for precise spatial reasoning. Extensive experiments on ScanRefer, Nr3D and Sr3D validate the effectiveness of our method, demonstrating state-of-the-art performance with improvements of 2.05\% Acc@0.25 for 3DREC and 1.09\% mIoU for 3DRES on ScanRefer.

Deep Learning · Generative Models and Autoencoders

Ziang Gan, Qi Zhu, Libao Zhang

Diffusion models serve as generative priors for dataset distillation, yet existing pipelines rely on per-sample update rules that evolve each synthetic image independently, limiting their ability to optimize collective set-level objectives. We propose Set-Coupled Guidance (SCG), a plug-and-play auxiliary controller that shifts from per-image to group (IPC-at-once) sampling by injecting set-symmetric feedback at each diffusion step. SCG combines spectral set-point regulation, which aligns set-level statistics to real data via empirical characteristic function matching, with cooperative kernel coupling that stabilizes joint trajectories under noisy feedback. All computations operate on lightweight descriptors extracted from predicted clean latents, adding low overhead to the base method. We provide theoretical analysis including Lyapunov descent and input-to-state stability for distributional tracking. Experiments on ImageNette, ImageWoof, ImageNet-100 and ImageNet-1K show consistent accuracy gains across multiple diffusion-based baselines.

Applications · Computer Vision

Wei Li, jieyuan pei, Junnan Xu, Xuanfeng Ding, Junwei Zhu, wanjun chen, Jianwei Zheng

Existing deep spatial–spectral fusion (SSF) methods typically learn the fusion mapping in the coordinate domain using convolutions and attentions, making it hard to scale across varying spatial resolutions and offering limited control over the frequency content of the reconstructions, which may further lead to severe spectral distortion. In this work, we propose Latent Spectral Operators (LSO), a SSF framework that learns fusion mappings between spectral functions through a structured operator parameterization. Specifically, LSO first applies a cross-attention projection, where learned latent tokens serve as spectral prompts, to compress high-dimensional observations into a compact latent representation, and then adopts a hierarchical, patch-based architecture to integrate rich multi-scale cues. Furthermore, to parameterize the latent fusion operator in a controllable manner, a Trigonometric Basis Solver is elaborated, which represents the mapping using a trigonometric basis expansion. This formulation naturally supports multi-frequency modeling, with a capacity–stability trade-off governed by the number of basis functions. Extensive experiments on the CAVE and Harvard benchmarks demonstrate that LSO achieves consistent state-of-the-art performance and exhibits strong transferability across different spatial scales. Codes are attached.

General Machine Learning · Everything Else

Bo Peng, Yuanwei Hu, Bo Liu, Ling Chen, Jie Lu, Zhen Fang

Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations untapped. Inspired by the recent success of vision-language pre-training, this paper enriches the landscape of spectral clustering from a single-modal to a multi-modal regime. Particularly, we propose Neural Tangent Kernel Spectral Clustering that leverages cross-modal alignment in pre-trained vision-language models. By anchoring the neural tangent kernel with positive nouns, i.e., those semantically close to the images of interest, we arrive at formulating the affinity between images as a coupling of their visual proximity and semantic overlap. We show that this formulation amplifies within-cluster connections while suppressing spurious ones across clusters, hence encouraging block-diagonal structures. In addition, we present a regularized affinity diffusion mechanism that adaptively ensembles affinity matrices induced by different prompts. Extensive experiments on \textbf{16} benchmarks---including classical, large-scale, fine-grained and domain-shifted datasets---manifest that our method consistently outperforms the state-of-the-art by a large margin.