Pansharpening is to fuse high-resolution panchromatic (PAN) images with low-resolution multispectral (LR-MS) images to generate high-resolution multispectral (HR-MS) images. Most of the deep learning-based pansharpening methods did not consider the inconsistency of the PAN and LR-MS images and used simple concatenation to fuse the source images, which may cause spectral and spatial distortion in the fused results. To address this problem, a multi-scale spatial-spectral attention guided fusion network for pansharpening is proposed. First, the spatial features from the PAN image and spectral features from the LR-MS image are independently extracted to obtain the shallow features. Then, a spatial-spectral attention feature fusion module (SAFFM) is constructed to guide the reconstruction of spatial-spectral features by generating a guidance map to achieve the fusion of reconstructed features at different scales. In SAFFM, the guidance map is designed to ensure the spatial-spectral consistency of the reconstructed features. Finally, considering the difference between multiply scale features, a multi-level feature integration scheme is proposed to progressively achieve fusion of multi-scale features from different SAFFMs. Extensive experiments validate the effectiveness of the proposed network against other state-of-the-art (SOTA) pansharpening methods in both quantitative and qualitative assessments. The source code will be released at https://github.com/MELiMZ/ssaff.
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Pan-sharpening aims to spatially enhance the low-resolution multispectral image (LRMS) by transferring high-frequency details from a panchromatic image (PAN) while preserving the spectral characteristics of LRMS. Previous arts mainly focus on how to learn a high-resolution multispectral image (HRMS) on the i.i.d. assumption. However, the distribution of training and testing data often encounters significant shifts in different satellites. To this end, this paper proposes a generalizable pan-sharpening network via domain-irrelevant feature learning. On the one hand, a structural preservation module (STP) is designed to fuse high-frequency information of PAN and LRMS. Our STP is performed on the gradient domain because it consists of structure and texture details that can generalize well on different satellites. On the other hand, to avoid spectral distortion while promoting the generalization ability, a spectral preservation module (SPP) is developed. The key design of SPP is to learn a phase fusion network of PAN and LRMS. The amplitude of LRMS, which contains 'satellite style' information is directly injected in different fusion stages. Extensive experiments have demonstrated the effectiveness of our method against state-of-the-art methods in both single-satellite and cross-satellite scenarios. Code is available at: https://github.com/LYL1015/DIRFL.
With the proliferation of multimedia applications, data is frequently derived from multiple sources, leading to the accelerated advancement of multi-view clustering (MVC) methods. In this paper, we propose a novel MVC method, termed GLSEF, to handle the inconsistency existing in multiple spectral embeddings. To this end, GLSEF contains a two-level learning mechanism. Specifically, on the global level, GLSEF considers the diversity of features and selectively assigns smooth weights to partial more discriminative features that are conducive to clustering. On the local level, GLSEF resorts to the Grassmann manifold to maintain spatial and topological information and local structure in each view, thereby enhancing its suitability and accuracy for clustering. Moreover, unlike most previous methods that learn a low-dimension embedding and perform the k-means algorithm to obtain the final cluster labels, GLSEF directly acquires the discrete indicator matrix to prevent potential information loss during post-processing. To address the optimization involved in GLSEF, we present an efficient alternating optimization algorithm accompanied by convergence and time complexity analyses. Extensive empirical results on nine real-world datasets demonstrate the effectiveness and efficiency of GLSEF compared to existing state-of-the-art MVC methods.
In image fusion tasks, images obtained from different sources exhibit distinct properties. Consequently, treating them uniformly with a single-branch network can lead to inadequate feature extraction. Additionally, numerous works have demonstrated that multi-scaled networks capture information more sufficiently than single-scaled models in pixel-level computer vision problems. Considering these factors, we propose U2Net, a spatial-spectral-integrated double U-shape network for image fusion. The U2Net utilizes a spatial U-Net and a spectral U-Net to extract spatial details and spectral characteristics, which allows for the discriminative and hierarchical learning of features from diverse images. In contrast to most previous works that merely employ concatenation to merge spatial and spectral information, this paper introduces a novel spatial-spectral integration structure called S2Block, which combines feature maps from different sources in a logical and effective way. We conduct a series of experiments on two image fusion tasks, including remote sensing pansharpening and hyperspectral image super-resolution (HISR). The U2Net outperforms representative state-of-the-art (SOTA) approaches in both quantitative and qualitative evaluations, demonstrating the superiority of our method. The code is available at https://github.com/PSRben/U2Net.
Pansharpening is to fuse a high-resolution panchromatic (PAN) image with a low-resolution multispectral (LRMS) image to obtain an enhanced LRMS image with high spectral and spatial resolution. The current Transformer-based pansharpening methods neglect the interaction between the extracted long- and short-range features, resulting in spectral and spatial distortion in the fusion results. To address this issue, a novel cross Transformer and convolutional neural network (CNN) for pansharpening (CTCP) is proposed to achieve better fusion results by designing a cross mechanism, which can enhance the interaction between long- and short-range features. First, a dual branch feature extraction module (DBFEM) is constructed to extract the features from the LRMS and PAN images, respectively, reducing the aliasing of the two image features. In the DBFEM, to improve the feature representation ability of the network, a cross long-short-range feature module (CLSFM) is designed by combining the feature learning capabilities of Transformer and CNN via the cross mechanism, which achieves the integration of long-short-range features. Then, to improve the ability of spectral feature representation, a spectral feature enhancement fusion module (SFEFM) based on a frequency channel attention is constructed to realize feature fusion. Finally, the shallow features from the PAN image are reused to provide detail features, which are integrated with the fused features to obtain the final pansharpened results. To the best of our knowledge, this is the first attempt to introduce the cross mechanism between Transformer and CNN in pansharpening field. Numerous experiments show that our CTCP outperforms some state-of-the-art (SOTA) approaches both subjectively and objectively. The source code will be released at https://github.com/zhsu99/CTCP.
Cross-modality images that combine visible-infrared spectra can provide complementary information for object detection. In particular, they are well-suited for autonomous vehicle applications in dark environments with limited illumination. However, it is time-consuming to acquire a large number of pixel-aligned visible-thermal image pairs, and real-time alignment is challenging in practical driving systems. Furthermore, the quality of visible-spectrum images can be adversely affected by complex environmental conditions. In this paper, we propose a novel neural network called TIRDet, which only utilizes Thermal InfraRed (TIR) images for mono-modality object detection. To compensate for the lacked visible-band information, we adopt a prior Thermal-To-Visible (T2V) translation model to obtain the translated visible images and the latent T2V codes. In addition, we introduce a novel attention-based Cross-Modality Aggregation (CMA) module, which can augment the modality-translation awareness of TIRDet by preserving the T2V semantic information. Extensive experiments on FLIR and LLVIP datasets demonstrate that our TIRDet significantly outperforms all mono-modality detection methods based on thermal images, and it even surpasses most State-Of-The-Art (SOTA) multispectral methods using visible-thermal image pairs. Code is available at https://github.com/zeyuwang-zju/TIRDet
Multimodal recommender systems utilizing multimodal features (e.g., images and textual descriptions) typically show better recommendation accuracy than general recommendation models based solely on user-item interactions. Generally, prior work fuses multimodal features into item ID embeddings to enrich item representations, thus failing to capture the latent semantic item-item structures. In this context, LATTICE proposes to learn the latent structure between items explicitly and achieves state-of-the-art performance for multimodal recommendations. However, we argue the latent graph structure learning of LATTICE is both inefficient and unnecessary. Experimentally, we demonstrate that freezing its item-item structure before training can also achieve competitive performance. Based on this finding, we propose a simple yet effective model, dubbed as FREEDOM, that FREEzes the item-item graph and DenOises the user-item interaction graph simultaneously for Multimodal recommendation. Theoretically, we examine the design of FREEDOM through a graph spectral perspective and demonstrate that it possesses a tighter upper bound on the graph spectrum. In denoising the user-item interaction graph, we devise a degree-sensitive edge pruning method, which rejects possibly noisy edges with a high probability when sampling the graph. We evaluate the proposed model on three real-world datasets and show that FREEDOM can significantly outperform the strongest baselines. Compared with LATTICE, FREEDOM achieves an average improvement of 19.07% in recommendation accuracy while reducing its memory cost up to 6x on large graphs. The source code is available at: https://github.com/enoche/FREEDOM.
Multi-spectral image stitching leverages the complementarity between infrared and visible images to generate a robust and reliable wide field-of-view~(FOV) scene. The primary challenge of this task is to explore the relations between multi-spectral images for aligning and integrating multi-view scenes. Capitalizing on the strengths of Graph Convolutional Networks (GCNs) in modeling feature relationships, we propose a spatial graph reasoning based multi-spectral image stitching method that effectively distills the deformation and integration of multi-spectral images across different viewpoints. To accomplish this, we embed multi-scale complementary features from the same view position into a set of nodes. The correspondence across different views is learned through powerful dense feature embeddings, where both inter- and intra-correlations are developed to exploit cross-view matching and enhance inner feature disparity. By introducing long-range coherence along spatial and channel dimensions, the complementarity of pixel relations and channel interdependencies aids in the reconstruction of aligned multi-view features, generating informative and reliable wide FOV scenes. Moreover, we release a challenging dataset named ChaMS, comprising both real-world and synthetic sets with significant parallax, providing a new option for comprehensive evaluation. Extensive experiments demonstrate that our method surpasses the state-of-the-arts.
Pansharpening is a challenging low-level vision task whose aim is to learn the complementary representation between spectral information and spatial detail. Despite the remarkable progress, existing deep neural network (DNN) based pansharpening algorithms are still confronted with common limitations. 1) These methods rarely consider the local specificity of different spectral bands; 2) They often extract the global detail in the spatial domain, which ignore the task-related degradation, e.g., the down-sampling process of MS image, and also suffer from limited receptive field. In this work, we propose a novel bidomain modeling paradigm for pansharpening problem (dubbed as BiMPan), which takes into both local spectral specificity and global spatial detail. More specifically, we first customize the specialized source-discriminative adaptive convolution (SDAConv) for every spectral band instead of sharing the identical kernels across all bands like prior works. Then, we devise a novel Fourier global modeling module (FGMM), which is capable of embracing global information while benefiting the disentanglement of image degradation. By integrating the band-aware local feature and Fourier global detail from these two functional designs, we can fuse a texture-rich while visually pleasing high-resolution MS image. Extensive experiments demonstrate that the proposed framework achieves favorable performance against current state-of-the-art pansharpening methods. The code is available at https://github.com/coder-qicao/BiMPan.
Graph based methods have been widely used in incomplete multi-view clustering (IMVC). Most recent methods try to fill the original missing samples or incomplete affinity matrices to obtain a complete similarity graph for the subsequent spectral clustering. However, recovering the original high-dimensional data or complete n X n similarity matrix is usually time-consuming and noise-sensitive. Besides, they generally separate the cluster indicator learning into an individual step, which may result in sub-optimal graphs or spectral embeddings for clustering. To address these problems, this paper proposes a robust Spectral Embedding Completion based IMVC (SEC-IMVC) method, which incorporates spectral embedding completion and discrete cluster indicator learning into a unified framework. SEC-IMVC performs completion on spectral embeddings, and the embedding noise is eliminated to reduce the negative influence of original data noise. The discrete cluster indicator matrix is seamlessly learned by using spectral rotation, and it can explore the first-order feature consistency among different views. To further improve the completion robustness, the second-order correlation consistency is also captured by pairwise relations alignment. We compare our method with some state-of-the-art approaches on several datasets, and the experimental results show the effectiveness and advantages of our method.
Hyperspectral images (HSIs) offer great potential for computational pathology. However, limited by the spectral redundancy and the lack of spectral prior in popular 2D networks, previous HSI based techniques do not perform well. To address these problems, we propose to segment HSIs from a deformable perspective, which processes different spectral bands independently and fuses spatiospectral features of interest via deformable attention mechanisms. In addition, we propose Deformable Self-Supervised Spectral Regression (DF-S3R), which introduces two self-supervised pre-text tasks based on the low rank prior of HSIs enabling the network learning with spectrum-related features. During pre-training, DF-S3R learns both spectral structures and spatial morphology, and the jointly pre-trained architectures help alleviate the transfer risk to downstream fine-tuning. Compared to previous works, experiments show that our deformable architecture and pre-training method perform much better than other competitive methods on pathological semantic segmentation tasks, and the visualizations indicate that our method can trace the critical spectral characteristics from subtle spectral disparities. Code will be released at https://github.com/Ayakax/DFS3R.
Continual Relation Extraction (CRE) aims to continuously train a model to learn new relations while preserving its ability on previously learned relations. Similar to other continual learning problems, in CRE, models experience representation shift, where learned deep space changes in the continual learning process, which leads to the downgrade in the performance of the old tasks. In this work, we will provide an insight into this phenomenon under the spectral viewpoint. Our key argument is that, for each class shape, if its eigenvectors (or spectral components) do not change much, the shape is well-preserved. We then conduct a spectral experiment and show that, for the shape of each class, the eigenvectors with larger eigenvalue are more preserved after learning new tasks which means these vectors are good at keeping class shapes. Based on this analysis, we propose a simple yet effective class-wise regularization that improve the eigenvalues in the representation learning. We observe that our proposed regularization leads to an increase in the eigenvalues. Extensive experiments on two benchmark datasets, FewRel and TACRED, show the effectiveness of our proposed method with significant improvement in performance compared to the state-of-the-art models. Further analyses also verify our hypothesis that larger eigenvalues lead to better performance and vice versa.
Probabilistic Methods/Gaussian Processes
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to conditioning. We explore stochastic gradient algorithms as a computationally efficient method of approximately solving these linear systems: we develop low-variance optimization objectives for sampling from the posterior and extend these to inducing points. Counterintuitively, stochastic gradient descent often produces accurate predictions, even in cases where it does not converge quickly to the optimum. We explain this through a spectral characterization of the implicit bias from non-convergence. We show that stochastic gradient descent produces predictive distributions close to the true posterior both in regions with sufficient data coverage, and in regions sufficiently far away from the data. Experimentally, stochastic gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks. Its uncertainty estimates match the performance of significantly more expensive baselines on a large-scale Bayesian~optimization~task.
Miscellaneous Aspects of Machine Learning/Kernel methods
Non-linear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled by a number of algorithms. In this work we present for the first time non-asymptotic learning bounds for the Koopman eigenvalues and eigenfunctions. We focus on time-reversal-invariant stochastic dynamical systems, including the important example of Langevin dynamics. We analyze two popular estimators: Extended Dynamic Mode Decomposition (EDMD) and Reduced Rank Regression (RRR). Our results critically hinge on novel {minimax} estimation bounds for the operator norm error, that may be of independent interest. Our spectral learning bounds are driven by the simultaneous control of the operator norm error and a novel metric distortion functional of the estimated eigenfunctions. The bounds indicates that both EDMD and RRR have similar variance, but EDMD suffers from a larger bias which might be detrimental to its learning rate. Our results shed new light on the emergence of spurious eigenvalues, an issue which is well known empirically. Numerical experiments illustrate the implications of the bounds in practice.
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to conditioning. We explore stochastic gradient algorithms as a computationally efficient method of approximately solving these linear systems: we develop low-variance optimization objectives for sampling from the posterior and extend these to inducing points. Counterintuitively, stochastic gradient descent often produces accurate predictions, even in cases where it does not converge quickly to the optimum. We explain this through a spectral characterization of the implicit bias from non-convergence. We show that stochastic gradient descent produces predictive distributions close to the true posterior both in regions with sufficient data coverage, and in regions sufficiently far away from the data. Experimentally, stochastic gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks. Its uncertainty estimates match the performance of significantly more expensive baselines on a large-scale Bayesian~optimization~task.
We study a spiked Wigner problem with an inhomogeneous noise profile. Our aim in this problem is to recover the signal passed through an inhomogeneous low-rank matrix channel. While the information-theoretic performances are well-known, we focus on the algorithmic problem. First, we derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem and show that its rigorous state evolution coincides with the information-theoretic optimal Bayes fixed-point equations. Second, we deduce a simple and efficient spectral method that outperforms PCA and is shown to match the information-theoretic transition.
Reinforcement Learning
We study matrix estimation problems arising in reinforcement learning with low-rank structure. In low-rank bandits, the matrix to be recovered specifies the expected arm rewards, and for low-rank Markov Decision Processes (MDPs), it characterizes the transition kernel of the MDP. In both cases, each entry of the matrix carries important information, and we seek estimation methods with low entry-wise prediction error. Importantly, these methods further need to accommodate for inherent correlations in the available data (e.g. for MDPs, the data consists of system trajectories). We investigate the performance of simple spectral-based matrix estimation approaches: we show that they efficiently recover the singular subspaces of the matrix and exhibit nearly-minimal entry-wise prediction error. These new results on low-rank matrix estimation make it possible to devise reinforcement learning algorithms that fully exploit the underlying low-rank structure. We provide two examples of such algorithms: a regret minimization algorithm for low-rank bandit problems, and a best policy identification algorithm for low-rank MDPs. Both algorithms yield state-of-the-art performance guarantees.
Theory/Learning Theory
We study the problem of list-decodable Gaussian covariance estimation. Given a multiset $T$ of $n$ points in $\mathbb{R}^d$ such that an unknown $\alpha<1/2$ fraction of points in $T$ are i.i.d. samples from an unknown Gaussian $\mathcal{N}(\mu, \Sigma)$, the goal is to output a list of $O(1/\alpha)$ hypotheses at least one of which is close to $\Sigma$ in relative Frobenius norm. Our main result is a $\mathrm{poly}(d,1/\alpha)$ sample and time algorithm for this task that guarantees relative Frobenius norm error of $\mathrm{poly}(1/\alpha)$. Importantly, our algorithm relies purely on spectral techniques. As a corollary, we obtain an efficient spectral algorithm for robust partial clustering of Gaussian mixture models (GMMs) --- a key ingredient in the recent work of [BakDJKKV22] on robustly learning arbitrary GMMs. Combined with the other components of [BakDJKKV22], our new method yields the first Sum-of-Squares-free algorithm for robustly learning GMMs, resolving an open problem proposed by Vempala and Kothari. At the technical level, we develop a novel multi-filtering method for list-decodable covariance estimation that may be useful in other settings.
Deep Learning/Theory
Recent years have witnessed significant progress in understanding the relationship between the connectivity of a deep network's architecture as a graph, and the network's performance. A few prior arts connected deep architectures to expander graphs or Ramanujan graphs, and particularly,[7] demonstrated the use of such graph connectivity measures with ranking and relative performance of various obtained sparse sub-networks (i.e. models with prune masks) without the need for training. However, no prior work explicitly explores the role of parameters in the graph's connectivity, making the graph-based understanding of prune masks and the magnitude/gradient-based pruning practice isolated from one another. This paper strives to fill in this gap, by analyzing the Weighted Spectral Gap of Ramanujan structures in sparse neural networks and investigates its correlation with final performance. We specifically examine the evolution of sparse structures under a popular dynamic sparse-to-sparse network training scheme, and intriguingly find that the generated random topologies inherently maximize Ramanujan graphs. We also identify a strong correlation between masks, performance, and the weighted spectral gap. Leveraging this observation, we propose to construct a new "full-spectrum coordinate'' aiming to comprehensively characterize a sparse neural network's promise. Concretely, it consists of the classical Ramanujan's gap (structure), our proposed weighted spectral gap (parameters), and the constituent nested regular graphs within. In this new coordinate system, a sparse subnetwork's L2-distance from its original initialization is found to have nearly linear correlated with its performance. Eventually, we apply this unified perspective to develop a new actionable pruning method, by sampling sparse masks to maximize the L2-coordinate distance. Our method can be augmented with the "pruning at initialization" (PaI) method, and significantly outperforms existing PaI methods. With only a few iterations of training (e.g 500 iterations), we can get LTH-comparable performance as that yielded via "pruning after training", significantly saving pre-training costs. Codes can be found at: https://github.com/VITA-Group/FullSpectrum-PAI.
ReParameterization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. However, recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes with exploding gradient variance, which leads to slow convergence. This is in contrast to the conventional belief that reparameterization methods have low gradient estimation variance in problems such as training deep generative models. To comprehend this phenomenon, we conduct a theoretical examination of model-based RP PGMs and search for solutions to the optimization difficulties. Specifically, we analyze the convergence of the model-based RP PGMs and pinpoint the smoothness of function approximators as a major factor that affects the quality of gradient estimation. Based on our analysis, we propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls. Our experimental results demonstrate that proper normalization significantly reduces the gradient variance of model-based RP PGMs. As a result, the performance of the proposed method is comparable or superior to other gradient estimators, such as the Likelihood Ratio (LR) gradient estimator. Our code is available at https://github.com/agentification/RP_PGM.