Spectral Filtering

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1 paper in the last four weeks, down 67% on the four weeks before. 0.0% of all new papers.

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Latest papers 20

Sep 30, 2026stat.ML

Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression

We compare the instance-wise, finite-sample risks of monotone spectral filters for linear regression, a broad class of estimators including principal component regression (PCR), gradient descent (GD), and ridge regression. We show that PCR dominates all monotone spectral filters: compared to any such filter, the risk of optimally tuned PCR is no bigger by a constant factor for all problems. Furthermore, the dominance is strong if the filter is separated from step functions (e.g., GD and ridge): there exist problem instances for which the risk of PCR is smaller by a polynomial factor in sample size dependence. Our comparison results show that PCR is optimal and thus admissible among monotone filters, significantly extending Wu et al. (2026)'s result that GD strongly dominates ridge. From a technical perspective, we establish new upper and lower bounds for general spectral filters, which are instance-wise sharp when specialized to ridge or GD, recovering or improving the best-known bounds.

Juno Kim, Hengyu Fu, Peter Bartlett +2

University of California, Berkeley · Google DeepMind

Kernel Ridge Regression Spectral Filtering Principal Component Analysis Finite-Sample Gradient Descent

Sep 29, 2026cs.AI

Flattening the Connectome Spectrum: A Spectral Filter for FC Induces a Pretraining Target for fMRI Encoders

Self-supervised pretraining reshaped prediction in language and vision, and brain foundation models (BFMs) inherited its promise. Representations learned from large unlabelled corpora should capture individual functional dynamics and generalise across cohorts. However, kernel ridge regression (KRR) fitted on functional connectivity (FC) matrices still predicts individual phenotypes more accurately than any BFM we tested. In this paper, we show that KRR is weighted by the eigenvalues of the FC which are miscalibrated for phenotype prediction. We apply an efficient spectral filter to recalibrate the eigenvalues of each subject's FC matrix, enabling the model to exploit more inter-individual variance. Across the 5 datasets, 11 parcellations and 6 prediction targets we tested, we match or exceed the KRR baseline. Based on this finding, we then pretrain a small encoder model on about 4,000 hours of fMRI from 162 open datasets, whereby we align the pairwise similarities between the embeddings of recording snippets with those between the recalibrated connectomes. Our model performs on par with the best of the 6 published BFMs we tested while having an order of magnitude fewer parameters. Our encoder performs better than FC on short scans and in smaller cohorts, especially in fingerprinting. We release the pretrained model weights, the code and the pretraining data, preprocessed and parcellated.

Giovanni Marraffini, Victoria Shevchenko, Carlo Alberto Barbano +1

UNITO · MIND

Functional Connectivity Human Connectome Project Functional Magnetic Resonance Imaging Connectome Pretraining Kernel Ridge Regression+2

Sep 8, 2026math.ST

MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra

Minimum-norm confidence envelope strategies offer a nonparametric approach to constructing nonasymptotic, simultaneous confidence regions for band-limited functions, exploiting the theory of Reproducing Kernel Hilbert Spaces (RKHS). While the finite-sample coverage guarantees of these envelopes have been established, their consistency has not been analyzed so far. In this paper, we study this construction, here termed the Minimum-Norm Confidence Envelope (MiNCE) framework, and establish the strong uniform consistency of the resulting bands, both for noise-free and noisy observation models, under mild assumptions on the measurement noises. We further extend this formulation to the frequency domain, deriving nonasymptotic, simultaneous, strongly uniformly consistent confidence bands for the smoothed spectra. Numerical experiments in nonparametric regression and spectral estimation empirically confirm our theoretical results, illustrating the contraction of the confidence envelopes toward the target function as the sample size increases.

Balázs Csanád Csáji, Bálint Horváth

HUN-REN SZTAKI: Institute for Computer Science and Control, Budapest, Hungary · Institute of Mathematics, Eötvös Loránd University (ELTE), Budapest, Hungary

Confidence Intervals Exponential Family Reproducing Kernel Hilbert Spaces Spectral Filtering

Aug 30, 2026physics.soc-ph

ButterMamba: Butterworth-Enhanced Spatial-Temporal Mamba for Efficient Traffic Flow Prediction

Accurate traffic flow prediction is fundamental to intelligent transportation systems, playing a pivotal role in urban mobility optimization and smart city development. While Graph Neural Networks (GNNs) integrated with time series forecasting have emerged as promising solutions, two critical limitations persist: (1) the quadratic complexity of attention-based architectures hinders real-time deployment in large-scale networks, and (2) high-frequency noise in sensor data significantly degrades prediction reliability. These challenges are particularly acute in metropolitan scenarios where both computational efficiency and noise robustness are paramount. To address these limitations, we introduce \textbf{ButterMamba}, a novel and efficient framework based on State Space Models (SSMs). ButterMamba consists of two key components: (1) a Butterworth Spectral Filtering module that preprocesses the data by removing high-frequency noise, allowing the model to focus on significant underlying trends, and (2) a Spatial-Temporal State Mixer that uses a parallel Mamba architecture to efficiently capture both long-range temporal dependencies and complex spatial correlations across the road network. By decoupling noise filtering from spatial-temporal modeling, ButterMamba achieves superior predictive accuracy with linear computational complexity. Extensive experiments on three public datasets demonstrate that ButterMamba not only outperforms existing state-of-the-art models in terms of prediction accuracy but also considerably reduces training time and memory usage.

Limiao Zhang, Yuhui Lu, Jie Gao +3

State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, Anhui University · Institute of Physical Science and Information Technology, Anhui University · School of Innovation and Entrepreneurship, Shandong University +1

Accurate Traffic Forecasting Graph Neural Networks Spectral Filtering

Aug 12, 2026cs.CV

New Orthogonal Multiwavelet Filters Derived by Matrix Spectral Factorization

The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets. The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.

Vasil Kolev, Todor Cooklev, Fritz Keinert

Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Bl. 2, Acad. G. Bonchev St., 1113 Sofia, Bulgaria · Wireless Technology Center, Purdue University, Fort Wayne, IN 46805, USA · Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Wavelets Spectral Filtering Matrix

Aug 3, 2026math.OC

A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems

This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs. The network cost is characterized by the summation of local cost functions, where each local function is sequentially revealed only to the corresponding agent. The goal of each agent is to generate a control sequence, using only local observations and neighbor communication, that competes with the best {\it centralized} linear policy in hindsight. We extend the recently proposed Online Spectral Control framework from the centralized setting to the distributed setting. In particular, each agent applies a spectral controller obtained by convolving past disturbances with the leading eigenvectors of a Hankel matrix, while the controller parameters are updated through a distributed online gradient descent step over the local surrogate costs. We formulate this problem this problem as a {\it regret} minimization problem based on the spectral parameterization, and under standard assumptions, we establish a sublinear regret bound of

O(\frac{\sqrt{T}\text{poly}(\log T)}{γ^3})

, where

T

is the time horizon and

γ

denotes the stability margin. The resulting bound also captures the dependence on the network size and connectivity.

Ting-Jui Chang

T.J. Chang is with the Department of Aeronautics and Astronautics, National Cheng Kung University, Taiwan.

Linear Quadratic Regulator \Widetilde{\Mathcal{O}}(\Sqrt{T})$ Regret Spectral Filtering Dynamical Systems

Jul 30, 2026cs.AI

Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators

Temporal graph learning is commonly organized around the evolution of node states or the encoding of interaction histories. We study an underexplored, operator-centric question: should the graph propagation mechanism itself evolve over time? We introduce Dynamic Spectral Filtering (DSF), which represents propagation at snapshot t by a Chebyshev polynomial filter with vector-valued, time-dependent coefficients. DSF explicitly treats these compact multi-order coefficients as recurrent temporal states. A recurrent branch proposes updates, while multiplicative global and order-specific gates regulate their magnitude. The temporal state is independent of the number of nodes. On MOOC, Wikipedia, and Reddit temporal link-prediction benchmarks, converged DSF runs attain AP scores of 0.7851, 0.9088, and 0.9860, respectively, with 93K to 133K trainable parameters, 68 to 182 MB peak GPU memory, and 1.6 to 2.1 seconds of training per epoch. Against the closely related DEFT baseline, DSF is better on MOOC, within 0.001 AP on Reddit, and modestly lower on Wikipedia, while using 8.3 to 8.6 times fewer parameters, 25 to 33 times less GPU memory, and 5 to 19 times less time per epoch. Relative to all measured alternatives, it uses 3.3 to 38.6 times less GPU memory. These results support direct spectral-response evolution as a useful temporal inductive bias when computational efficiency is a first-class requirement.

Yan Kong

Nanjing University of Information Science and Technology, China

Temporal Graph Neural Networks Spectral Filtering Temporal Dynamics Zero-Shot Link Prediction Spectral Propagation+1

Jul 28, 2026cs.LG

CondPSE: A Polynomial-Filtered Structural Encoder with Conditional Modulation for Graphs

Message-passing graph neural networks are bounded by the 1-WL test and can miss topological structure that distinguishes non-isomorphic graphs. Positional and structural encodings (PSE) inject such topology-derived signals, and learned PSE encoders such as GPSE pretrain a single encoder to produce these signals from random node probes, which can then be frozen and reused as inputs across downstream graph models. We present CondPSE, a learned PSE encoder that applies a learnable polynomial graph filter bank to standard Gaussian node probes and refines the resulting structural-response branches through FiLM-style modulation conditioned on cross-filter, local message-passing, and graph-level signals. CondPSE is pretrained to reconstruct node-level positional/structural targets and graph-level invariants, and is then frozen for use as a downstream input encoding. On synthetic structural-discrimination benchmarks, CondPSE separates graph structures that 1-WL-bounded message passing cannot: it raises CSL accuracy from 42.9% to 97.3% and EXP accuracy from 68.3% to 99.9% relative to GPSE, and ablations show that the polynomial filter bank accounts for most of this gain. On real molecular property prediction, the picture is more limited. With a hybrid local-message-passing/global-attention backbone, CondPSE performs comparably to GPSE without surpassing it, and a ZINC backbone sweep shows no consistent ordering between the two encoders. We report these results and discuss why strong synthetic structural discrimination does not, on its own, yield a downstream advantage for frozen learned PSE encoders, including the role of downstream integration and possible mismatch between structural pretraining targets and molecular property labels.

Woohyun Lee, Hogun Park

Sungkyunkwan University Suwon, Republic of Korea

Spectral Filtering Encoders

Jul 23, 2026cs.LG

Filter Learning for Subgraphs: Algebras and Performance Risk Bounds

Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations. We formulate SFL as a statistical learning problem in which optimal subgraph operators are inherently data-dependent. To address the difficulty of directly estimating such operators, we develop a subgraph filter algebra based on distance-aware Laplacian constructions, defining a structured and controllable class of filters for effective approximation. We further establish performance risk bounds under the least squares loss, quantifying how well the learned operator approximates the restricted ambient mapping. Experiments real-world datasets show that, for SFL tasks, the proposed algebraic models consistently outperform polynomial filters, distribution-agnostic operators, and direct numerical filter learning baselines that attempt to recover the underlying structure from data.

Purui Zhang, Feng Ji, Yanan Zhao +2

Spectral Filtering Subgraphs Graph Laplacians Graph Signal Processing Probabilistic Operator Learning Community Detection+1

Jul 5, 2026cs.LG

FedFFT: Taming Client Drift in Federated SAM via Spectral Perturbation Filtering

Federated Learning (FL) enables decentralized training without data sharing, but suffers from statistical heterogeneity across clients, leading to client drift, poor generalization, and sharp minima compared to centralized training. Sharpness-Aware Minimization (SAM) has emerged as a promising approach to improve generalization, yet its application in federated learning still suffers from divergence problems, since perturbations are computed locally and reflect client-specific loss geometries. To better understand this issue, we provide experimental evidence from a new perspective, the frequency domain, for SAM perturbations in federated settings, revealing that inter-client perturbation inconsistencies are predominantly concentrated in the low-frequency spectrum. Motivated by this insight, we propose Federated learning with Frequency-domain Filtering of SAM perturbations (FedFFT). It is a lightweight and plug-and-play method that filters out low-frequency components of SAM perturbations without requiring additional communication, thereby suppressing inconsistent components in client updates while preserving consistent learning signals. Extensive experiments across multiple benchmarks and diverse backbones demonstrate that FedFFT consistently outperforms SAM-based FL methods, particularly under severe non-IID distributions. These results highlight the effectiveness, scalability, and general applicability of our frequency-domain perspective for sharpness-aware federated optimization.

Liyang Yuan, Yibo Yang, Dandan Guo

School of Artificial Intelligence, Jilin University, Changchun, China · King Abdullah University of Science and Technology, Saudi Arabia

Federated Learning Frequency Domain Sharpness-Aware Minimization Spectral Filtering

Jun 23, 2026cs.LG

Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks

Spectral graph neural networks (GNNs) interpret message passing as frequency-selective filtering. While low-order spectral filters are efficient, their limited selectivity often leads to weak attenuation outside the passband, whereas high-order alternatives introduce optimization challenges. We propose DCQ-GNN, a spectral GNN based on a compact bank of adaptive convex--concave quadratic filters. By restricting the filter order to two while explicitly exploiting complementary curvature, DCQ-GNN improves spectral selectivity as quantified by Dirichlet energy and entropy measures without resorting to high-order polynomial expansions. The model fuses filter outputs through a node-adaptive gating mechanism to enable node-wise structure-aware spectral selection. We provide a formal spectral analysis grounded in Dirichlet energy attenuation, von Neumann entropy, and curvature polarity, and derive explicit characterizations of filter behavior across varying levels of homophily and structural perturbations. Extensive benchmarks on 10 datasets show that DCQ-GNN ties for the top average rank (3.0) on heterophilic graphs and obtains the second-best rank (4.2) on homophilic graphs, remaining competitive with representative high-order polynomial spectral filters. Furthermore, under strong structural perturbations, DCQ-GNN exhibits substantially smaller performance degradation compared to both first-order and high-order baselines. These results demonstrate that curvature-aware quadratic banks provide a robust and efficient alternative to high-order spectral models while preserving optimization stability and computational efficiency.

Ranhui Yan, Jia Cai, Mengzhu Chen +1

School of Computing and Artificial Intelligence, Guangzhou Xinhua University, Guangzhou, Guangdong, China · School of Statistics and Data Science, Guangdong University of Finance and Economics,2026 Guangzhou, Guangdong, China

Spectral Filtering Graph Neural Networks Gnn-Based Detectors Curvature-Aware Spectral Framework

Jun 2, 2026cs.LG

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

Xianliang Li, Zihan Zhang, Weiyang Liu +1

1The Institute of Statistical Mathematics · 2The Graduate Institute for Advanced Studies, SOKENDAI · 3National Institute of Informatics +3

Muon Momentum Orthogonality Spectral Filtering Large Language Model Training Iterative Denoising Methods

May 22, 2026cs.LG

Contrast to Detect: Dynamic Graph Contrastive Regularization for Unsupervised Anomaly Detection in Multivariate Time Series

Anomaly detection in multivariate time series (MTS) is hindered by dynamic inter-variable dependencies and feature entanglement under spectral noise, and in practice, is further complicated by the absence of anomaly labels. Existing reconstruction-based detectors tend to recover anomalies as faithfully as normal patterns, while prevailing graph contrastive methods enforce invariance across views and thus assume a stationary relational structure, an assumption that breaks under structural drift in real systems. We propose ContrastAD, an unsupervised framework that turns structural evolution itself into a learning signal rather than suppressing it. A Multi-Perspective Embedder encodes inputs from temporal, attribute, and structural perspectives. A Frequency-Aware Attention Mixer then performs spectral top-K filtering before attention, preventing noise from leaking into query-key similarities. The core component, a Dynamic Graph Contrastive Learner, builds power-law-inspired sparse graph snapshots from batch-level DTW distances and contrasts the most divergent pair against a stable anchor, regularizing the latent space without imposing rigid invariance. Across five real-world benchmarks, ContrastAD attains the highest mean F1 on all five datasets and the highest AUC on three (SWaT 93.60, SMD 98.66, PSM 97.79), with statistically significant F1 and AUC margins over the strongest baseline on SWaT and PSM. On MSL and SMAP, it trails the AUC leader by under 0.7 points while still leading on F1. Ablation and sensitivity studies further confirm that the contrastive objective works best as a soft regularizer, supporting our claim that strict invariance is suboptimal under non-stationary dynamics.

Yunhua Pei, Zixing Song, Jin Zheng +1

School of Computer Science, University of Bristol, Bristol, UK · School of Engineering Mathematics, University of Bristol, Bristol, UK

Time-Series Anomaly Detection Graph Anomaly Detection Multivariate Time-Series Contrastive Learning Spectral Filtering Multimodal Embeddings+1

May 22, 2026cs.LG

S $^3$ GNN: Efficient Global Mixing and Local Message Passing for Long-Range Graph Learning

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S

^3

GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S

^3

GNN achieves up to an order-of-magnitude error reduction with up to 50% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Dai Shi, Luke Thompson, Linhan Luo +4

Department of Engineering, University of Cambridge, Cambridge, UK · University of Sydney, Australia

Message Passing Neural Networks Gnn-Based Detectors Long-Range Coherence Spectral Filtering Neural Network Jacobian

May 9, 2026cs.LG

Anchoring the Eigengap: Cross-Modal Spectral Stabilization for Sample-Efficient Representation Learning

Deep vision models degrade sharply in low-data regimes, particularly in medical imaging where labeled samples are scarce. We show this arises not merely from overfitting but from a geometric failure: finite-sample noise corrupts the embedding covariance, collapsing the eigengap and limiting the number of recoverable signal-bearing modes. We develop a spectral theory of finite-sample representation learning that quantifies the recoverable dimension K(N), the number of eigenmodes that can be stably estimated from N samples. Using perturbation theory and concentration bounds, we show that only modes with eigenvalues above the noise floor

\|\hatΣ - Σ\|_{\mathrm{op}} \sim \sqrt{D/N}

are reliable, yielding a truncated Mahalanobis energy that governs classification performance. Under a power-law spectral model, this energy can be approximated by a truncated Riemann zeta function, linking eigenvalue decay to data efficiency and AUC. Within this framework, multimodal learning acts as spectral stabilization: vision-language models impose low-rank constraints that suppress noise-dominated directions and preserve the eigengap, increasing K(N) under data scarcity. Across MNIST and multi-disease neuroimaging, we show that multimodal training maintains more stable modes and improves class separation, even when unimodal models achieve comparable few-shot accuracy. These results identify spectral collapse as a fundamental bottleneck in low-data learning. We use truncated Mahalanobis energy and K(N) to diagnose encoder quality, and introduce zeta-based spectral filtering as a principled approach to improve data efficiency.

Nikhil J. Dhinagar, Vidhi Chhatbar, Chirag Jagad +6

Imaging Genetics Center, Mark & Mary Stevens Neuroimaging & Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA · Neuroscience Graduate Program, Mark & Mary Stevens Neuroimaging & Informatics Institute, Chan Division of Occupational Science & Occupational Therapy, Biomedical Engineering, University of Southern California, Los Angeles, CA, USA

Representation Learning Spectral Filtering Finite-Sample Multimodal Neuroimaging

May 7, 2026cs.LG

Full-Spectrum Graph Neural Networks: Expressive and Scalable

It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNNs (FSpecGNNs), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering from two perspectives: (1) it lifts signals from the node domain to the node-pair domain; and (2) it extends the univariate spectral filter over eigenvalues to a bivariate filter over eigenvalue pairs. We show that classical spectral GNNs arise as a diagonal special case of FSpecGNNs, and prove that FSpecGNNs can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning. Moreover, FSpecGNN admits scalable implementations that avoid explicit node-pair-level computations; combined with a low-rank approximation that reduces full-spectrum convolution to a combination of polynomial spectral filters, it enables learning on large graphs. Empirically, FSpecGNN validates the predicted expressivity and delivers strong performance on heterophilic benchmarks.

Xiaohan Wang, Deyu Bo, Longlong Li +1

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.

Graph Neural Networks Spectral Filtering Convolutional Private Signals

May 2, 2026cs.LG

Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation

While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension

D

. Experiments on synthetic and real data confirm LHSD's superior robustness and its utility in detecting memorization in large-scale diffusion models. The code is available at github.com/geosada/LHSD

Genki Osada

LY Corporation.

Intrinsic Dimensionality Hessian Spectral Filtering

Apr 29, 2026cs.IR

TimeMM: Time-as-Operator Spectral Filtering for Dynamic Multimodal Recommendation

Multimodal recommendation improves user modeling by integrating collaborative signals with heterogeneous item content. In real applications, user interests evolve over time and exhibit nonstationary dynamics, where different preference factors change at different rates. This challenge is amplified in multimodal settings because visual and textual cues can dominate decisions under different temporal regimes. Despite strong progress, most multimodal recommenders still rely on static interaction graphs or coarse temporal heuristics, which limits their ability to model continuous preference evolution with fine-grained temporal adaptation. To address these limitations, we propose TimeMM, a time-conditioned spectral filtering framework for dynamic multimodal recommendation. TimeMM instantiates Time-as-Operator by mapping interaction recency to a family of parametric temporal kernels that reweight edges on the user--item graph, producing component-specific representations without explicit eigendecomposition. To capture non-stationary interests, we introduce Adaptive Spectral Filtering that mixes the operator bank according to temporal context, yielding prediction-specific effective spectral responses. To account for modality-specific temporal sensitivity, we further propose Spectral-Aware Modality Routing that calibrates visual and textual contributions conditioned on the same temporal context. Finally, a ranking-space Spectral Diversity Regularization encourages complementary expert behaviors and prevents filter-bank collapse. Extensive experiments on real-world benchmarks demonstrate that TimeMM consistently outperforms state-of-the-art multimodal recommenders while maintaining linear-time scalability.

Wei Yang, Rui Zhong, Zihan Lin +4

Xiaohongshu Inc. · Beijing, China

Multimodal Recommendation Model Spectral Filtering

Jan 23, 2026cs.LG

SFO: Learning PDE Operators via Spectral Filtering

Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO), a neural operator that parameterizes integral kernels using the Universal Spectral Basis (USB), a fixed, global orthonormal basis derived from the eigenmodes of the Hilbert matrix in spectral filtering theory. Motivated by our theoretical finding that the discrete Green's functions of shift-invariant PDE discretizations exhibit spatial Linear Dynamical System (LDS) structure, we prove that these kernels admit compact approximations in the USB. By learning only the spectral coefficients of rapidly decaying eigenvalues, SFO achieves a highly efficient representation. Across six benchmarks, including reaction-diffusion, fluid dynamics, and 3D electromagnetics, SFO achieves state-of-the-art accuracy, reducing error by up to 40% relative to strong baselines while using substantially fewer parameters.

Noam Koren, Rafael Moschopoulos, Kira Radinsky +1

Department of Computer Science Technion - Israel Institute of Technology · Department of Computer Science Princeton University

Neural Operators Partial Differential Equations Spectral Filtering

Jun 2, 2025cs.LG

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient computation method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column

i

, where the linear constraints restrict weight signs of edges stemming from node

i

, so that nodes of same / different polarities are connected by positive / negative edges. We derive a feasible CLIME parameter

ρ_i

for each sign-constrained column problem. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove that the row / column updates produce a non-increasing objective sequence, and show that the iterations are terminated in a finite number of steps. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph neural nets (GNN) constructed for positive graphs.

Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka +1

Graph Laplacians Spectral Filtering Balanced Learning Linear Programming Covariance