Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks involving both homophilous and heterophilous graph structures. However, The scalability of spectral GNNs on large graphs is limited because they learn the polynomial coefficients through multiple forward propagation executions during forward propagation. Existing works have attempted to scale up spectral GNNs by eliminating the linear layers on the input node features, a change that can disrupt end-to-end training, potentially impact performance, and become impractical with high-dimensional input features. To address the above challenges, we propose ''Spectral Graph Neural Networks with Laplacian Sparsification (SGNN-LS)'', a novel graph spectral sparsification method to approximate the propagation patterns of spectral GNNs. We prove that our proposed method generates Laplacian sparsifiers that can approximate both fixed and learnable polynomial filters with theoretical guarantees. Our method allows the application of linear layers on the input node features, enabling end-to-end training as well as the handling of raw text features. We conduct an extensive experimental analysis on datasets spanning various graph scales and properties to demonstrate the superior efficiency and effectiveness of our method. The results show that our method yields superior results in comparison with the corresponding approximated base models, especially on dataset Ogbn-papers100M(111M nodes, 1.6B edges) and MAG-scholar-C (2.8M features).
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We study the problem of efficiently approximating the effective resistance (ER) on undirected graphs, where ER is a widely used node proximity measure with applications in graph spectral sparsification, multi-class graph clustering, network robustness analysis, graph machine learning, and more. Specifically, given any nodes s and t in an undirected graph G, we aim to efficiently estimate the ER value R(s,t) between nodes s and t, ensuring a small absolute error ε. The previous best algorithm for this problem has a worst-case computational complexity of Õ(Lmax3/ε2d2), where the value of Lmax depends on the mixing time of random walks on G, d = mind(s), d(t), and d(s), d(t) denote the degrees of nodes s and t, respectively. We improve this complexity to Õ ( min Lmax7/3/ε2/3, Lmax3/ε2d2,mLmax ), achieving a theoretical improvement of Õ (maxLmax2/3/ε4/3d2,1, Lmax2/ε2d2m2) over previous results. Here, m denotes the number of edges. Given that Lmax is often very large in real-world networks (e.g., Lmax > 104), our improvement on Lmax is significant, especially for real-world networks. We also conduct extensive experiments on real-world and synthetic graph datasets to empirically demonstrate the superiority of our method. The experimental results show that our method achieves a 10× to 1000× speedup in running time while maintaining the same absolute error compared to baseline methods.
We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random spanning trees suitably transformed into path graphs which, despite their simplicity, are shown to retain essential topological and node information of the original input graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also improves accuracy in subsequent test phases, especially under small training set regimes, which are of great practical importance, as in many real-world scenarios labels may be hard to obtain. In these settings, our framework yields very good results as it effectively counters the training deterioration caused by overfitting when the training set is small. Our method also addresses common issues like over-squashing and over-smoothing while avoiding under-reaching phenomena. Although our framework is flexible and can be deployed in several types of GNNs, in this paper we focus on graph convolutional networks and carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we achieve simultaneous improvement of training speed and test accuracy over a wide pool of representative baselines.
Accurate mapping of irrigation methods is crucial for sustainable agricultural practices and food systems. However, existing models that rely solely on spectral features from satellite imagery are ineffective due to the complexity of agricultural landscapes and limited training data, making this a challenging problem. We present Knowledge-Informed Irrigation Mapping (KIIM), a novel Swin-Transformer based approach that uses (i) a specialized projection matrix to encode crop to irrigation probability, (ii) a spatial attention map to identify agricultural lands from non-agricultural lands, (iii) bi-directional cross-attention to focus complementary information from different modalities, and (iv) a weighted ensemble for combining predictions from images and crop information. Our experimentation on five states in the US shows up to 22.9% (IoU) improvement over baseline with a 71.4% (IoU) improvement for hard-to-classify drip irrigation. In addition, we propose a two-phase transfer learning approach to enhance cross-state irrigation mapping, achieving a 51% IoU boost in a state with limited labeled data. The ability to achieve baseline performance with only 40% of the training data highlights its efficiency, reducing the dependency on extensive manual labeling efforts and making large-scale, automated irrigation mapping more feasible and cost-effective. Code: https://github.com/Nibir088/KIIM
Despite the rapid development of neural vocoders in recent years, they usually suffer from some intrinsic challenges like opaque modeling, and parameter-performance trade-off. In this study, we propose an innovative time-frequency (T-F) domain-based neural vocoder to resolve the above-mentioned challenges. To be specific, we bridge the connection between the classical signal range-null decomposition (RND) theory and vocoder task, and the reconstruction of target spectrogram can be decomposed into the superimposition between the range-space and null-space, where the former is enabled by a linear domain shift from the original mel-scale domain to the target linear-scale domain, and the latter is instantiated via a learnable network for further spectral detail generation. Accordingly, we propose a novel dual-path framework, where the spectrum is hierarchically encoded/decoded, and the cross- and narrow-band modules are elaborately devised for efficient sub-band and sequential modeling. Comprehensive experiments are conducted on the LJSpeech and LibriTTS benchmarks. Quantitative and qualitative results show that while enjoying lightweight network parameters, the proposed approach yields state-of-the-art performance among existing advanced methods. Our code and the pretrained model weights are available at https://github.com/Andong-Li-speech/RNDVoC.
While previous diffusion-based neural vocoders typically follow a noise-to-data generation pipe-line, the linear-degradation prior of the mel-spectrogram is often neglected, resulting in limited generation quality. By revisiting the vocoding task and excavating its connection with the signal restoration task, this paper proposes a time-frequency (T-F) domain-based neural vocoder with the Schrödinger Bridge, called BridgeVoC, which is the first to follow the data-to-data generation paradigm. Specifically, the mel-spectrogram can be projected into the target linear-scale domain and regarded as a degraded spectral representation with a deficient rank distribution. Based on this, the Schrödinger Bridge is leveraged to establish a connection between the degraded and target data distributions. During the inference stage, starting from the degraded representation, the target spectrum can be gradually restored rather than generated from a Gaussian noise process. Quantitative experiments on LJSpeech and LibriTTS show that BridgeVoC achieves faster inference and surpasses existing diffusion-based vocoder baselines, while also matching or exceeding non-diffusion state-of-the-art methods across evaluation metrics.
PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems
PDF ↗Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to incomplete or unknown physical laws. Meanwhile, machine learning approaches often fail to generalize effectively when faced with scarce observational data and the challenge of capturing local and global features. To this end, we propose the Physics-encoded Spectral Attention Network (PeSANet), which integrates local and global information to forecast complex systems with limited data and incomplete physical priors. The model consists of two key components: a physics-encoded block that uses hard constraints to approximate local differential operators from limited data, and a spectral-enhanced block that captures long-range global dependencies in the frequency domain. Specifically, we introduce a novel spectral attention mechanism to model inter-spectrum relationships and learn long-range spatial features. Experimental results demonstrate that PeSANet outperforms existing methods across all metrics, particularly in long-term forecasting accuracy, providing a promising solution for simulating complex systems with limited data and incomplete physics.
Spatio-temporal time series (STTS) have been widely used in many applications. However, accurately forecasting STTS is challenging due to complex dynamic correlations in both time and space dimensions. Existing graph neural networks struggle to balance effectiveness and efficiency in modeling dynamic spatio-temporal relations. To address this problem, we propose the Dynamic Spatio-Temporal Stiefel Graph Neural Network (DST-SGNN) to efficiently process STTS. For DST-SGNN, we first introduce the novel Stiefel Graph Spectral Convolution (SGSC) and Stiefel Graph Fourier Transform (SGFT). The SGFT matrix in SGSC is constrained to lie on the Stiefel manifold, and SGSC can be regarded as a filtered graph spectral convolution. We also propose the Linear Dynamic Graph Optimization on Stiefel Manifold (LDGOSM), which can efficiently learn the SGFT matrix from the dynamic graph and significantly reduce the computational complexity. Finally, we propose a multi-layer SGSC (MSGSC) that efficiently captures complex spatio-temporal correlations. Extensive experiments on seven spatio-temporal datasets show that DST-SGNN outperforms state-of-the-art methods while maintaining relatively low computational costs.
Deep learning methods have demonstrated remarkable performance across various communication signal processing tasks. However, most signal classification methods require a substantial amount of labeled samples for training, posing significant challenges in the field of communication signals, as labeling necessitates expert knowledge. This paper proposes a novel self-supervised signal classification method called Spectral-Guided Self-Supervised Signal Classification (SGSSC). Specifically, to leverage frequency-domain information with modulation semantics as prior knowledge for the model, we design a previously unexplored pretext task tailored to the format of signal data. This task involves predicting spectral information from masked time-domain signals, enabling the model to learn implicit signal features through cross-domain pattern transformation. Furthermore, the pretext task in the SGSSC method is relevant to the downstream classification task, and using traditional fine-tuning strategies on the downstream task may lead to the loss of certain features associated with the pretext task. Therefore, we propose an attention mechanism-based fine-tuning strategy that adaptively integrates pre-trained features from different levels. Extensive experimental results validate the superiority of the SGSSC method. For instance, when the proportion of labeled samples is only 0.5%, our method achieves an average improvement of 2.3% in downstream classification tasks compared to the best-performing self-supervised training strategies.
Real-world datasets like multi-spectral images and videos are naturally represented as tensors. However, limitations in data acquisition often lead to corrupted or incomplete tensor data, making tensor recovery a critical challenge. Solving this problem requires exploiting inherent structural patterns, with the low-rank property being particularly vital. An important category of existing low-rank tensor recovery methods relies on the tensor nuclear norms. However, these methods struggle with either computational inefficiency or weak theoretical guarantees for large-scale data. To address these issues, we propose a fast guaranteed tensor recovery framework based on a new tensor nuclear norm. Our approach adaptively extracts a column-orthogonal matrix from the data, reducing a large-scale tensor into a smaller subspace for efficient processing. This dimensionality reduction enhances speed without compromising accuracy. The recovery theories of two typical models are established by introducing an adjusted incoherence condition. Extensive experiments demonstrate the effectiveness of the proposed method, showing improved accuracy and speed over existing approaches. Our code and supplementary material are available at https://github.com/andrew-pengjj/adaptive_tensor_nuclear_norm.
The principal portfolio approach is an emerging method in signal-based trading. However, these principal portfolios may not be diversified to explore the key features of the prediction matrix or robust to different situations. To address this problem, we propose a novel linear trading position with sparse spectrum that can explore a larger spectral region of the prediction matrix. We also develop a Krasnosel'skii-Mann fixed-point algorithm to optimize this trading position, which possesses the descent property and achieves a linear convergence rate in the objective value. This is a new theoretical result for this type of algorithms. Extensive experiments show that the proposed method achieves good and robust performance in various situations.
A Multi-view Fusion Approach for Enhancing Speech Signals via Short-time Fractional Fourier Transform
PDF ↗Deep learning-based speech enhancement (SE) methods focus on reconstructing speech from the time or frequency domain. However, these domains cannot provide enough information to capture the dynamics of non-stationary signals accurately. To enrich information, this work proposes a multi-view fusion SE method (MFSE). Specifically, MFSE extends the representation space of speech to the dynamic domain (also called fractional domain) between the time and frequency domains by using the short-time fractional Fourier transform (STFrFT). Subsequently, we construct inputs as modes of the primary short-time Fourier transform (STFT) spectrum and the auxiliary STFrFT spectrum views and adaptively identify the optimal fractional STFrFT spectrum from the infinitely continuous fractional domain by leveraging the average spectral centroids. The framework extracts potential features through multiple designed convolutional modules and captures the correlation between different speech frequencies through multi-granularity attention. Experimental results show that the proposed method significantly improves performance in several metrics compared to existing single-channel SE methods based on time and frequency domains. Furthermore, the results of its generalizability evaluation show that the multi-view method outperforms the single-view method under a wide range of SNR conditions.
The task of graph-level out-of-distribution (OOD) detection is crucial for deploying graph neural networks in real-world settings. In this paper, we observe a significant difference in the relationship between the largest and second-largest eigenvalues of the Laplacian matrix for in-distribution (ID) and OOD graph samples: OOD samples often exhibit anomalous spectral gaps (the difference between the largest and second-largest eigenvalues). This observation motivates us to propose SpecGap, an effective post-hoc approach for OOD detection on graphs. SpecGap adjusts features by subtracting the component associated with the second-largest eigenvalue, scaled by the spectral gap, from the high-level features (i.e., X - (λn - λn-1) u_n-1 v_n-1^T). SpecGap achieves state-of-the-art performance across multiple benchmark datasets. We present extensive ablation studies and comprehensive theoretical analyses to support our empirical results. As a parameter-free post-hoc method, SpecGap can be easily integrated into existing graph neural network models without requiring any additional training or model modification.
Towards Recognizing Spatial-temporal Collaboration of EEG Phase Brain Networks for Emotion Understanding
PDF ↗Emotion recognition from EEG signals is crucial for understanding complex brain dynamics. Existing methods typically rely on static frequency bands and graph convolutional networks (GCNs) to model brain connectivity. However, EEG signals are inherently non-stationary and exhibit substantial individual variability, making static-band approaches inadequate for capturing their dynamic properties. Moreover, spatial-temporal dependencies in EEG often lead to feature degradation during node aggregation, ultimately limiting recognition performance. To address these challenges, we propose the Spatial-Temporal Electroencephalograph Collaboration framework (Stella). Our approach introduces an Adaptive Bands Selection module (ABS) that dynamically extracts low- and high-frequency components, generating dual-path features comprising phase brain networks for connectivity modeling and time-series representations for local dynamics. To further mitigate feature degradation, the Fourier Graph Operator (FGO) operates in the spectral domain, while the Spatial-Temporal Encoder (STE) enhances representation stability and density. Extensive experiments on benchmark EEG datasets demonstrate that Stella achieves state-of-the-art performance in emotion recognition, offering valuable insights for graph-based modeling of non-stationary neural signals. The code is available at https://github.com/sun2017bupt/EEGBrainNetwork.
Heterophily emerges as a critical challenge in Graph Anomaly Detection (GAD). Recent studies reveal that neighborhood distributions, rather than heterophily itself, are the fundamental factor for the expressive power of Graph Neural Networks (GNNs). However, two key challenges remain unresolved. First, the overlap in neighborhood distributions between anomalous and normal nodes poses significant difficulties in distinguishing them effectively. Second, the dispersion in neighborhood distributions within the same class prevents the application of a fixed aggregation strategy to accommodate the diverse patterns within the class. To tackle the aforementioned challenges, we propose a novel Graph Neural Network model called Neighborhood Adaptive Aggregation and Spectral Tuning (NAAST-GNN). Specifically, we first design a neighborhood adaptive aggregation module that adjusts the message passing mechanism based on the predicted probabilities for different node classes, ensuring that nodes from distinct classes but with similar neighborhood distributions derive unique aggregated neighborhood information. We then present a spectral tuning module that dynamically selects and combines spectral filters based on the predicted neighborhood distribution, ensuring adaptability to the diverse neighborhood distributions of nodes within the same class. Comprehensive experimental results demonstrate that our method outperforms state-of-the-art baselines.
Multimodal Prior Learning with Double Constraint Alignment for Snapshot Spectral Compressive Imaging
PDF ↗The objective of snapshot spectral compressive imaging reconstruction is to recover the 3D hyperspectral image (HSI) from a 2D measurement. Existing methods either focus on network architecture design or simply introduce image-level prior to the model. However, these methods lack guiding information for accurate reconstruction. Recognizing that textual description contain rich semantic information that can significantly enhance details, this paper introduces a novel framework, CAMM, which integrates text information into the model to improve the performance. The framework comprises two key components: Fine-grained Alignment Module (FAM) and Multimodal Fusion Mamba (MFM). Specifically, FAM is used to reduce the knowledge gap between the RGB domain obtained by the pre-trained vision-language model and the HSI domain. Through the double constraints of distribution similarity and entropy, the adaptive alignment of different complexity features is realized, which makes the encoded features more accurate. MFM aims to identify the guiding effect of RGB features and text features on HSI in space and channel dimensions. Instead of fusing features directly, it integrates prior at image-level and text-level prior into Mamba's state-space equation, so that each scanning step can be accurately guided. This kind of positive feedback adjustment ensures the authenticity of the guiding information. To our knowledge, this is the first text-guided model for compressive spectral imaging. Extensive experimental results the public datasets demonstrate the superior performance of CAMM, validating the effectiveness of our proposed method.
Pansharpening fuses lower-resolution multispectral (LRMS) images with high-resolution panchromatic (PAN) images to generate high-resolution multispectral (HRMS) images that preserves both spatial and spectral information. Most deep pansharpening methods face challenges in cross-modal feature extraction and fusion, as well as in exploring the similarities between the fused image and both PAN and LRMS images. In this paper, we propose a spatial-spectral similarity-guided fusion network (S3FNet) for pansharpening. This architecture is composed of three parts. Specifically, a shallow feature extraction layer learns initial spatial, spectral and fused features from PAN and LRMS images. Then, a multi-branch asymmetric encoder, consisting of spatial, spectral and fusion branches, generates corresponding high-level features at different scales. A multi-scale reconstruction decoder, equipped with a well-designed cross-feature multi-head attention fusion block, processes the intermediate feature maps to generate HRMS images. To ensure HRMS images retain maximum spatial and spectral information, a similarity-constrained loss is defined for network training. Extensive experiments demonstrate the effectiveness of our S3FNet over state-of-the-art methods. The code is released at https://github.com/ZhangYongshan/S3FNet.
Concern for image authenticity spurs research in image forgery detection and localization (IFDL). Most deep learning-based methods focus primarily on spatial domain modeling and have not fully explored frequency domain strategies. In this paper, we observe and analyze the frequency characteristic changes caused by image tampering. Observations indicate that manipulation traces are especially prominent in phase components and span both low and high-frequency bands. Based on these findings, we propose a forensic frequency decomposition network (F2D-Net), which incorporates deep Fourier transforms and leverages both phase information and high and low-frequency components to enhance IFDL. Specifically, F2D-Net consists of the Spectral Decomposition Subnetwork (SDSN) and the Frequency Separation Subnetwork (FSSN). The former decomposes the image into amplitude and phase, focusing on learning the semantic content in the phase spectrum to identify forged objects, thus improving forgery detection accuracy. The latter further adaptively decomposes the output of the SDSN to obtain corresponding high and low frequencies, and applies a divide-and-conquer strategy to refine each frequency band, mitigating the optimization difficulties caused by coupled forgery traces across different frequencies, thereby better capturing the pixels belonging to the forged object to improve localization accuracy. Experiments on multiple datasets demonstrate that our method outperforms state-of-the-art image forgery detection and localization techniques both qualitatively and quantitatively.
HSRMamba: Contextual Spatial-Spectral State Space Model for Single Hyperspectral Image Super-Resolution
PDF ↗Mamba has demonstrated exceptional performance in visual tasks due to its powerful global modeling capabilities and linear computational complexity, offering considerable potential in hyperspectral image super-resolution (HSISR). However, in HSISR, Mamba faces challenges as transforming images into 1D sequences neglects the spatial-spectral structural relationships between locally adjacent pixels, and its performance is highly sensitive to input order, which affects the restoration of both spatial and spectral details. In this paper, we propose HSRMamba, a contextual spatial-spectral modeling state space model for HSISR, to address these issues both locally and globally. Specifically, a local spatial-spectral partitioning mechanism is designed to establish patch-wise causal relationships among adjacent pixels in 3D features, mitigating the local forgetting issue. Furthermore, a global spectral reordering strategy based on spectral similarity is employed to enhance the causal representation of similar pixels across both spatial and spectral dimensions. Finally, experimental results demonstrate our HSRMamba outperforms the state-of-the-art methods in quantitative quality and visual results. Code is available at: https://github.com/Tomchenshi/HSRMamba.
Acoustic-to-Hyper-Spectral: Hyper-Spectral Image Construction from Frequency Spectrums Through Simulated Annealing (Student Abstract)
PDF ↗This abstract presents a simulated annealing based approach that constructs hyper-spectral images from the frequency spectrums of a distributed acoustic sensing system and iteratively improves them through the training of learnable filters. The aim is to construct an image that represents features of signals from events while repressing noise. Hyper-spectral images are specifically created for downstream computer vision tasks such as object detection. Hyper-spectral images are images with more than three channels that are derived from a frequency spectrum to obtain the spectrum for each image pixel. Simulated annealing is used to train the filters to automatically select frequencies and bin them into frequency bands. Each frequency band is mapped into an image channel. We fully integrate our filtering method with an object detection network so that filters are trained in conjunction with the neural network. The detection model serves as both the measure and the selector. Our simulated annealing approach significantly outperforms current state-of-the-art methods by a margin of 22%. Limitations include a dependency on randomness and excluding parts of the search space prematuraly due to the design of the local moves.