论文检索

Applications · Neuroscience, Cognitive Science

Xiran Chen, Xiaoke Yang, Cunhang Fan, Jian Zhou, Zhao Lv

Auditory attention decoding (AAD) based on Electroencephalography (EEG) aims to identify the attended speaker in multi-speaker environments. However, existing methods typically overlook the crucial phase information of EEG signals, which limits their ability to distinguish structured neural patterns from random noise in the frequency domain and hinders robust decoding. To address these issues, this paper proposes a Phase-aware Complex Refinement Network (PCRNet) for AAD, which consists of a Temporal Context Calibration (TCC) module and a Dual-Domain Integration (DDI) module. Specifically, the TCC module captures long-range temporal dependencies through multi-scale temporal attention mechanism, while the DDI module employs a phase-guided spectral filtering strategy to dynamically suppress noise-dominated frequencies and refine the real and imaginary components separately. This design enables effective phase recalibration and enhances the discriminability of target features in the complex domain. Experimental results on three public datasets demonstrate that PCRNet outperforms state-of-the-art (SOTA) methods, particularly under challenging ultra-short 0.1-second windows.

Applications · Computer Vision

Mamoona Javaid, Mubashir Noman, Abdul Hannan, Shah Nawaz, Mustansar Fiaz, Sajid Ghuffar

Rapid expansion of urban areas and population growth is causing an immense increase in waste production, which demands the need for efficient and automated waste management. In this scenario, automated waste recycling (AWR) that utilizes deep learning methods to separate the recyclable waste objects may emerge as a savior to humanity. Recent deep learning approaches for AWR provide promising waste segmentation performance, however, these methods rely on large backbone networks that are inefficient for AWR systems and suffer from performance deterioration in cluttered scenes. To this end, an optimal waste segmentation network is introduced which effectively utilizes the spatial domain to capture localized structural dependencies and the spectral domain to efficiently extract global contextual relationships. This cascaded design allows the network to progressively leverage both local and global representations across complementary domains to highlight the semantic information necessary for effective segmentation of various waste objects. Furthermore, auxiliary feature enhancement module (AFEM) is introduced to enhance the target objects' boundaries and blob amplification for better segmentation in cluttered scenarios. Extensive experimentation on ZeroWaste-aug, ZeroWaste-f and SpectralWaste reveals the merits of the proposed method.

Applications · Computer Vision

Zhenggang Wang, Wang Wu, Lianghuazhe, Tai-Xiang Jiang

Pansharpening fuses high-resolution panchromatic (PAN) images with low-resolution multispectral (LMS) images. For spatial-spectral fusion, Fast Fourier Transform (FFT)-based methods provide a global receptive field to capture long-range dependencies and naturally separate frequency components. However, most existing approaches directly transplant spatial operators like convolution or self-attention, while disregarding the fundamental structure of the spectrum: a strict spatial correspondence where each coordinate represents a specific frequency component, and a highly non-uniform, radially decaying energy distribution. To address this, we revisit the classical Butterworth filter, a frequencydomain operator defined directly on spectral coordinates that is inherently suited for processing such structured representations. We generalize the standard isotropic Butterworth filter into an anisotropic, learnable frequency-domain gating mechanism, establishing an efficient alternative to self-attention, and propose the Anisotropic Butterworth Fusion Network (ABFNet). Its core is a novel dual-branch gating module that employs learnable anisotropic Butterworth filters to perform adaptive direction-aware feature selection, integrating global context and local details with linear complexity. Extensive experiments show that ABFNet achieves state-of-the-art (SOTA) performance on pansharpening benchmarks with low computational overhead. Furthermore, its superior accuracy on CIFAR-100 classification validates the broader applicability of this frequency-domain learning paradigm.

Applications · Time Series

YingHao Ai, Yukai Zhou, Ruoxi Jiang, Junyi An, Chao Qu, Zhijian Zhou, Shiyu Wang, Fenglei Cao, Zenglin Xu, Furao Shen 等

Spatio-temporal forecasting is critical for real-world applications like traffic management, yet capturing complex interactions under high-noise conditions remains challenging. While current methods have shown improved accuracy using spatial physical priors, they often struggle with evolving temporal correlations and systematic errors. In this work, we propose a nested forecasting framework that couples future macro-level regional trends with micro-level historical observations, enabling top-down guidance from abstract future representations for fine-grained forecasting. Specifically, we construct semantically coherent regions via spectral clustering and design a progressive coarse-to-fine predictor to inject macro-dynamics into node-level forecasting. Extensive experiments on multiple real-world datasets demonstrate that our method consistently outperforms state-of-the-art baselines, validating the effectiveness of future macro-guided nested forecasting.

Optimization · Non-Convex

Jian-Feng Cai, Xueyang Quan, Yang Wang, Jiaxi Ying

Spectrally sparse signal reconstruction arises in a wide range of applications and can be formulated as a low-rank Hankel matrix completion problem. We develop a Jacobi-preconditioned gradient descent method that preserves the low per-iteration complexity of first-order algorithms while achieving linear convergence at a rate independent of the condition number. By introducing a generator that maps factor-based iterates to matrix space, we establish equivalence with manifold-based methods, enabling direct convergence analysis while avoiding the need to define distances under complex-symmetric factorization ambiguity. Extensive experiments demonstrate that the proposed algorithm outperforms state-of-the-art methods in both iteration count and computational time across a broad range of problem settings.

Deep Learning · Large Language Models

Di He, Songjun Tu, Keyu Wang, Lu Yin, Shiwei Liu

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their effectiveness as the backbone of Large Language Models (LLMs). In this paper, we introduce \textbf{Layerwise Learning Rate (LLR)}, an adaptive scheme that assigns distinct learning rates to individual Transformer layers. Our method is grounded in Heavy-Tailed Self-Regularization (HT-SR) theory, which characterizes the empirical spectral density (ESD) of weight correlation matrices to quantify heavy-tailedness. Layers with weaker heavy-tailedness are assigned larger learning rates to accelerate their training, while layers with stronger heavy-tailedness receive smaller learning rates. By tailoring learning rates in this manner, LLR promotes balanced training across layers, leading to faster convergence and improved generalization. Extensive experiments across architectures (from LLaMA to GPT-nano), optimizers (AdamW and Muon), and parameter scales (60M–1B) demonstrate that LLR achieves up to 1.5× training speedup and outperforms baselines, notably raising average zero-shot accuracy from 47.09% to 49.02%. A key advantage of LLR is its low tuning overhead: it transfers nearly optimal LR settings directly from the uniform baseline. Our code is submitted.

Applications · Computer Vision

Binfeng Wang, Di Wang, Haonan Guo, Ying Fu, Jing Zhang

Unified hyperspectral image (HSI) restoration aims to recover diverse degradations within a single model. However, current methods often rely on impractical explicit priors or opaque black-box representations that overfit to training distributions, hampering generalization to unseen scenarios. To bridge this gap, we propose Degradation-Aware Metric Prompting (DAMP), a novel framework that characterizes multi-dimensional degradations through interpretable spatial-spectral metrics. These metrics serve as Degradation Prompts (DP), enabling the model to capture shared characteristics across tasks and adapt to unknown corruptions. Central to our framework is the Degradation-Adaptive Mixture-of-Experts (DAMoE), where Spatial-Spectral Adaptive Modules (SSAMs) serve as experts that utilize learnable fusion coefficients to specialize in distinct degradation degrees. By using DP as a gating router, DAMoE dynamically activates specialized experts tailored to the specific degradation profile. Extensive experiments on natural and remote sensing HSI datasets demonstrate that DAMP achieves state-of-the-art performance and exhibits exceptional zero-shot generalization on unseen restoration tasks. The source code will be released.

Applications · Time Series

Guikang Du, Haoran Li, Xinyu Liu, Zhibo Zhang, Xiaoli Gong, Jin Zhang

Cross-subject generalization in biomedical time-series (BTS) refers to training on data from some subjects and testing on unseen subjects. The key challenge is to suppress subject-specific variability in BTS representations. Most existing methods implicitly suppress the variability through model building or subject adversarial learning, but rarely model it explicitly. We introduce \textit{\textbf{spectral drift}} as a new perspective to characterize subject-specific variability. Specifically, BTS signals under the same label often share consistent oscillatory structure, yet exhibit subject-dependent magnitude or phase shifts in specific frequency components, which we interpret as subject-specific variability. Building on this insight, we propose \textbf{BioFormer}. At its core is a Frequency-Band Alignment Module (FBAM) that generates band-wise modulation factors from the spectral distribution and adaptively adjusts amplitude and phase to align spectral structure, thereby mitigating variability. We further pair FBAM with Sample-Conditional Layer Normalization, which infers normalization parameters from intrinsic signal statistics rather than subject identity, stabilizing cross-subject representations. Extensive experiments on six datasets demonstrate that BioFormer outperforms 12 baselines, yielding absolute F1-score improvements of 6\%.

Social Aspects · Robustness

Sen Nie, Jie Zhang, Zhuo Wang, Shiguang Shan, Xilin Chen

Vision-language models (VLMs) such as CLIP have demonstrated remarkable zero-shot generalization, yet remain highly vulnerable to adversarial examples (AEs). While test-time defenses are promising, existing methods fail to provide sufficient robustness against strong attacks and are often hampered by high inference latency and task-specific applicability. To address these limitations, we start by investigating the intrinsic properties of AEs, which reveals that AEs exhibit severe feature inconsistency under progressive frequency attenuation. We further attribute this to the model's inherent spectral bias. Leveraging this insight, we propose an efficient test-time defense named Contrastive Spectral Rectification (CSR). CSR optimizes a rectification perturbation to realign the input with the natural manifold under a spectral-guided contrastive objective, which is applied input-adaptively. Extensive experiments across 16 classification benchmarks demonstrate that CSR outperforms the SOTA by an average of 18.1% against strong AutoAttack with modest inference overhead. Furthermore, CSR exhibits broad applicability across diverse visual tasks. Code is available at https://anonymous.4open.science/r/CSR-3935.

Applications · Time Series

Ruituo Wu, Hongyu Zhang, Qiang Wang, Jiawei Du, Wei Cui, Ce Zhu, Bing Li

Learning from continuous-time trajectories requires modeling multivariate sensor measurements generated by underlying physical or dynamical processes. Under extreme data compression and heterogeneous sampling, directly optimizing synthetic signals as discrete sample values becomes fundamentally misaligned with the underlining \emph{continuous-time physical processes}, often producing high-frequency, non-physical artifacts that overfit specific models and break reuse across architectures and sampling rates. We propose CHESS, a \emph{function-first} synthesis framework shifts optimization from discrete samples to underlying continuous-time signal trajectories. CHESS injects physics-induced structure by jointly enforcing low-rank spatial coherence and piecewise Chebyshev polynomial temporal parameterization, constraining synthesis to a physically meaningful function manifold. We provide theoretical analysis establishing explicit smoothness and stability guaranties. Experiments on diverse sensor testbeds under the dataset distillation protocol demonstrate CHESS consistently outperform state-of-the-art methods with a compression ratios up to $133\times$ for each synthetic sample. Furthermore, CHESS exhibits strong cross-architecture generalization and enables zero-shot adaptation across different sampling resolutions.

General Machine Learning · Everything Else

Andong Wang, Yuning Qiu, Haonan Huang, Zhong Jin, Guoxu Zhou, Qibin Zhao

The Tensor Nuclear Norm (TNN), derived from the tensor singular value decomposition, is a widely used low-rank modeling tool that enforces element-wise sparsity on frequency-domain singular values. However, as a direct extension of the matrix nuclear norm, TNN fundamentally assumes single-level spectral sparsity, which is misaligned with the multi-level spectral structures prevalent in real-world data, where low-rankness within frequency components coexists with sparsity across them. To overcome this limitation, we propose the tensor $\ell_p$-Schatten-$q$ quasi-norm ($p,q\in(0,1]$), which enables explicit control of dual spectral sparsity by jointly regularizing inter-frequency sparsity and intra-frequency low-rankness. This formulation strictly generalizes TNN and subsumes several existing tensor regularizers by coupling global frequency sparsity with local spectral low-rankness, leading to a fundamentally different modeling principle. We establish the first minimax error bounds under this model and develop an efficient reweighted optimization algorithm for the resulting nonconvex problem. Numerical experiments on noisy and Poisson tensor completion as well as image clustering demonstrate the effectiveness and robustness of our method across reconstruction and representation learning tasks involving complex multi-way data.

Deep Learning · Theory

Mengqi Li, Wensheng Lin, Jinshuai Yang, Lixin Li

Effective sequence modeling fundamentally requires balancing the retention of unbounded history with the high-resolution detection of abrupt short-term variations common in real-world phenomena. However, existing state space models (SSMs) relying on high-order polynomial projection operators (HiPPO) face a critical trade-off where uniform measures dilute recent information to maintain timescale invariance, while exponential measures sacrifice global context to capture local dynamics. This paper proposes a Fractional Recurrent Architecture for Computational Temporal Analysis of Long sequences (FRACTAL), a novel architecture integrating fractional measure theory into recursive memory updates to address this limitation. By deriving projection operators with analytically characterized spectral properties and a tunable singularity index, the proposed method amplifies sensitivity to recent signal perturbations while preserving the spectral structure that encodes scale-invariant memory dynamics. This theoretical innovation is instantiated within a simplified diagonalized state space framework by modulating input projection initialization to enable simultaneous capture of multi-scale temporal features. FRACTAL achieves an average score of 87.11\% on the Long Range Arena benchmark, including 61.85\% on the ListOps task, outperforming the S5 model.

General Machine Learning · Kernel methods

Rikhav Shah, Sandeep Silwal, Haike Xu

This paper studies the use of *kernel density estimation* (KDE) for linear algebraic tasks involving the *kernel matrix* of a collection of $n$ data points in $\mathbb{R}^d$. In particular, we improve upon the best existing algorithms for computing the following up to $(1+\varepsilon)$ relative error for a Gaussian kernel matrix and other kernels: matrix-vector products, matrix-matrix products, the spectral norm, and sum of all entries. The runtimes of our algorithms depend linearly on the dimension $d$, sub-quadratically in the number of points $n$, and polynomially on the target error $\varepsilon$. Importantly, the dependence on $n$ in each case is far lower when accessing the kernel matrix through KDE queries as opposed to reading individual entries. Our improvements over existing best algorithms (particularly those of [Backurs et al. ICML `21]) for these tasks reduce the polynomial dependence on $\varepsilon$, and additionally decrease the dependence on $n$ in the case of computing the sum of all entries of the kernel matrix. For example, we reduce the power of $1/\epsilon$ from $\approx 7.7$ to $\approx 3.2$ for a $1-\varepsilon$ relative error estimation of the spectral norm of a Gaussian kernel matrix. We complement our upper bounds with several lower bounds for related problems, which provide (conditional) quadratic time hardness results and additionally hint at the limits of KDE based approaches for the problems we study.

General Machine Learning · Causality

Alek Fröhlich, Vladimir Kostic, Karim Lounici, Daniel Rodrigues Perazzo, Daniel Tiezzi, Massimiliano Pontil

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity, slow convergence, and poor scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

General Machine Learning · Causality

Dimitri Meunier, Jakub Wornbard, Vladimir Kostic, Antoine Moulin, Alek Fröhlich, Karim Lounici, Massimiliano Pontil, Arthur Gretton

We address the problem of causal effect estimation in the presence of hidden confounders using nonparametric instrumental variable (IV) regression. An established approach is to use estimators based on learned \emph{spectral features}, that is, features spanning the top singular subspaces of the operator linking treatments to instruments. While powerful, such features are agnostic to the outcome variable. Consequently, the method can fail when the true causal function is poorly represented by these dominant singular functions. To mitigate, we introduce Augmented Spectral Feature Learning, a framework that makes the feature learning process outcome-aware. Our method learns features by minimizing a novel contrastive loss derived from an augmented operator that incorporates information from the outcome. By learning these task-specific features, our approach remains effective even under spectral misalignment. We provide a theoretical analysis of this framework and validate our approach on challenging benchmarks.

General Machine Learning · Clustering

Yuemeng Huang, Huibing Wang, Jinjia Peng, Lu Jiang, Qian Liu, Zetian Mi, Jiqing Zhang

Anchor-based multi-view clustering has garnered wide attention for its ability to reduce the computational complexity of large-scale spectral clustering.However, existing methods mostly adopt a unidirectional optimization paradigm confined to sample-anchor bipartite graphs, treating the construction of the consensus graph and discrete clustering assignments as separate sub-problems to be solved independently. This weakens the information exchange between continuous representation and discrete structure, confining the optimization process to iterative updates within local modules.To address these limitations, we propose a Discretely-Refined Multi-view Clustering(DRMC) via Aligned Anchor Learning. Unlike approaches that directly perform fusion in the anchor space, our method starts from the anchor graph, elevates sample-anchor associations to sample-level similarity graph representations, and thereby enhances both within-cluster similarity and between-cluster separation. Furthermore, we design a discrete feedback module that jointly conducts spectral embedding learning and discrete label assignment by orthogonally aligning the continuous embedding matrix with the discrete indicator matrix. The resulting discrete partition is then fed back into the consensus graph construction, continuously refining the graph structure. Experiments on multiple benchmark datasets demonstrate that the proposed method exhibits significant advantages over existing state-of-the-art approaches.

Optimization · Stochastic

Egor Shulgin, Mohamed Awad, Peter Richtarik, Eduard Gorbunov

We study a broad family of momentum *Linear Minimization Oracle* (LMO) methods that includes normalized SGD with momentum, sign-based (Adam-like) directions, and Muon (spectral) updates. Our focus is on subsampling regimes where the classical uniformly-bounded-variance model can be fragile even for finite-sum objectives on unbounded domains. To obtain subsampling-faithful guarantees, we analyze this LMO family under *expected smoothness* (ABC condition), which captures common sampling schemes. We establish a unified nonconvex convergence theory via a new self-bounding closure that handles the history-coupling induced by momentum under ABC. Our bounds recover known bounded-variance results as a special case and simplify in strong-growth regimes. Specializing to $\tau$-nice sampling, we derive explicit batch-size scaling laws, predicting that the optimal momentum must increase with the batch size to maximize sample efficiency. We further identify a theoretical **optimal batch size** that minimizes total sample complexity. Experiments on linear and matrix regression corroborate these predictions, showing a distinct diagonal shift in the optimal momentum-batch landscape that matches our theoretical scaling.

Theory · Learning Theory

Arie Zurich, Bruno Loureiro, Federica Gerace, Yue Lu

In the era of transformer models, masked self-supervised learning (SSL) has become a foundational training paradigm. A defining feature of masked SSL is that training aggregates predictions across many masking patterns, giving rise to a joint, matrix-valued predictor rather than a single vector-valued estimator. This object encodes how coordinates condition on one another and poses new analytical challenges. We develop a precise high-dimensional analysis of masked modeling objectives in the proportional regime where the number of samples scales with the ambient dimension. Our results provide explicit expressions for the generalization error and characterize the spectral structure of the learned predictor, revealing how masked modeling extracts structure from data. For spiked covariance models, we show that the joint predictor undergoes a Baik–Ben Arous–Péché (BBP)-type phase transition, identifying when masked SSL begins to recover latent signals. Finally, we identify structured regimes in which masked self-supervised learning provably outperforms PCA, highlighting potential advantages of SSL objectives over classical unsupervised methods.

Deep Learning · Large Language Models

Siqi Lu, Wei Suo, Yongbin Zheng, Jianhang Yao, Wanying XU, Peng Wang

While Large Vision-Language Models (LVLMs) achieves remarkable success, hallucinations remain a significant barrier to their reliable deployment. Recent studies primarily attribute these defects to cross-modal attention imbalances, with most solutions focusing on re-weighting visual tokens or suppressing language priors. Such approaches often overlook the spectral characteristics of the visual information flow and frequently rely on Contrastive Decoding (CD), which doubles the inference time. Instead of following conventional approaches, we identify two distinct hallucination patterns—Perceptual-Semantic Dissociation and Localized Fixation—and accordingly develop FLASH (Frequency-Localized Attention SHaping), a training-free and CD-free framework. FLASH utilizes a Spectral Vortex Score to detect visual heads within multi-head attention layers, applying adaptive spectral modulation to rectify the visual information flow during the decoding phase. Empirical results demonstrate that FLASH offers a superior balance between performance and efficiency compared to SOTA methods.

Applications · Chemistry, Physics, and Earth Sciences

Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park

Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, making the global receptive field—essential for PDE dynamics—computationally expensive. Conversely, Fourier Neural Operators (FNOs) efficiently capture global interactions, yet establishing 3D equivariance within them remains impractical due to the prohibitive cost of spectral group convolutions. To bridge this gap, we introduce EqGINO, a geometrically robust framework that enforces isotropy in the spectral domain. By design, EqGINO guarantees exact equivariance to the discrete symmetries inherent to the discretized computational domain. Beyond this discrete guarantee, our structural prior enables effective generalization to arbitrary continuous orientations even with a limited number of SE(3)-transformed training samples. Consequently, our method robustly models coordinate-invariant physical laws on complex irregular 3D geometries. Our code is available at https://anonymous.4open.science/r/EqGINO/