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Jianan Fan, Dongnan Liu, Hang Chang, Heng Huang, Mei Chen, Weidong Cai

Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection it would be appealing to autonomously explore patterns and insights from observational data for discovering novel classes of phenotypes and concepts. However in the biomedical domain there are several challenges inherently presented in the cumulated data which hamper the progress of novel class discovery. The non-i.i.d. data distribution accompanied by the severe imbalance among different groups of classes essentially leads to ambiguous and biased semantic representations. In this work we present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. First we propose to parameterize the approximated posterior of instance embedding as a marginal von Mises-Fisher distribution to account for the interference of distributional latent bias. Then we incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space which in turn minimizes the uncontrollable risk for unknown class learning and structuring. Furthermore a spectral graph-theoretic method is devised to estimate the number of potential novel classes. It inherits two intriguing merits compared to existent approaches namely high computational efficiency and flexibility for taxonomy-adaptive estimation. Extensive experiments across various biomedical scenarios substantiate the effectiveness and general applicability of our method.

Mubashir Noman, Muzammal Naseer, Hisham Cholakkal, Rao Muhammad Anwer, Salman Khan, Fahad Shahbaz Khan

Recent advances in unsupervised learning have demonstrated the ability of large vision models to achieve promising results on downstream tasks by pre-training on large amount of unlabelled data. Such pre-training techniques have also been explored recently in the remote sensing domain due to the availability of large amount of unlabelled data. Different from standard natural image datasets remote sensing data is acquired from various sensor technologies and exhibit diverse range of scale variations as well as modalities. Existing satellite image pre-training methods either ignore the scale information present in the remote sensing imagery or restrict themselves to use only a single type of data modality. In this paper we re-visit transformers pre-training and leverage multi-scale information that is effectively utilized with multiple modalities. Our proposed approach named SatMAE++ performs multi-scale pre-training and utilizes convolution based upsampling blocks to reconstruct the image at higher scales making it extensible to include more scales. Compared to existing works the proposed SatMAE++ with multi-scale pre-training is equally effective for both optical as well as multi-spectral imagery. Extensive experiments on six datasets reveal the merits of proposed contributions leading to state-of-the-art performance on all datasets. SatMAE++ achieves mean average precision (mAP) gain of 2.5% for multi-label classification task on BigEarthNet dataset.

Jiangtong Tan, Jie Huang, Naishan Zheng, Man Zhou, Keyu Yan, Danfeng Hong, Feng Zhao

Pan-sharpening is a super-resolution problem that essentially relies on spectra fusion of panchromatic (PAN) images and low-resolution multi-spectral (LRMS) images. The previous methods have validated the effectiveness of information fusion in the Fourier space of the whole image. However they haven't fully explored the Fourier relationships at different hierarchies between PAN and LRMS images. To this end we propose a Hierarchical Frequency Integration Network (HFIN) to facilitate hierarchical Fourier information integration for pan-sharpening. Specifically our network consists of two designs: information stratification and information integration. For information stratification we hierarchically decompose PAN and LRMS information into spatial global Fourier and local Fourier information and fuse them independently. For information integration the above hierarchical fused information is processed to further enhance their relationships and undergo comprehensive integration. Our method extend a new space for exploring the relationships of PAN and LRMS images enhancing the integration of spatial-frequency information. Extensive experiments robustly validate the effectiveness of the proposed network showcasing its superior performance compared to other state-of-the-art methods and generalization in real-world scenes and other fusion tasks as a general image fusion framework. Code is available at https://github.com/JosephTiTan/HFIN.

Linus Scheibenreif, Michael Mommert, Damian Borth

As large-scale foundation models become publicly available for different domains efficiently adapting them to individual downstream applications and additional data modalities has turned into a central challenge. For example foundation models for geospatial and satellite remote sensing applications are commonly trained on large optical RGB or multi-spectral datasets although data from a wide variety of heterogeneous sensors are available in the remote sensing domain. This leads to significant discrepancies between pre-training and downstream target data distributions for many important applications. Fine-tuning large foundation models to bridge that gap incurs high computational cost and can be infeasible when target datasets are small. In this paper we address the question of how large pre-trained foundational transformer models can be efficiently adapted to downstream remote sensing tasks involving different data modalities or limited dataset size. We present a self-supervised adaptation method that boosts downstream linear evaluation accuracy of different foundation models by 4-6% (absolute) across 8 remote sensing datasets while outperforming full fine-tuning when training only 1-2% of the model parameters. Our method significantly improves label efficiency and increases few-shot accuracy by 6-10% on different datasets.

Haijin Zeng, Jiezhang Cao, Kai Zhang, Yongyong Chen, Hiep Luong, Wilfried Philips

Hyperspectral images (HSIs) have extensive applications in various fields such as medicine agriculture and industry. Nevertheless acquiring high signal-to-noise ratio HSI poses a challenge due to narrow-band spectral filtering. Consequently the importance of HSI denoising is substantial especially for snapshot hyperspectral imaging technology. While most previous HSI denoising methods are supervised creating supervised training datasets for the diverse scenes hyperspectral cameras and scan parameters is impractical. In this work we present Diff-Unmix a self-supervised denoising method for HSI using diffusion denoising generative models. Specifically Diff-Unmix addresses the challenge of recovering noise-degraded HSI through a fusion of Spectral Unmixing and conditional abundance generation. Firstly it employs a learnable block-based spectral unmixing strategy complemented by a pure transformer-based backbone. Then we introduce a self-supervised generative diffusion network to enhance abundance maps from the spectral unmixing block. This network reconstructs noise-free Unmixing probability distributions effectively mitigating noise-induced degradations within these components. Finally the reconstructed HSI is reconstructed through unmixing reconstruction by blending the diffusion-adjusted abundance map with the spectral endmembers. Experimental results on both simulated and real-world noisy datasets show that Diff-Unmix achieves state-of-the-art performance.

Zihang Liu, Yuanzhe Hu, Tianyu Pang, Yefan Zhou, Pu Ren, Yaoqing Yang

Recent advances in foundation models have emphasized the need to align pre-trained models with specialized domains using small, curated datasets. Studies on these foundation models underscore the importance of low-data training and fine-tuning. This topic, well-known in natural language processing (NLP), has also gained increasing attention in the emerging field of scientific machine learning (SciML). To address the limitations of low-data training and fine-tuning, we draw inspiration from Heavy-Tailed Self-Regularization (HT-SR) theory, analyzing the shape of empirical spectral densities (ESDs) and revealing an imbalance in training quality across different model layers. To mitigate this issue, we adapt a recently proposed layer-wise learning rate scheduler, TempBalance, which effectively balances training quality across layers and enhances low-data training and fine-tuning for both NLP and SciML tasks. Notably, TempBalance demonstrates increasing performance gains as the amount of available tuning data decreases. Comparative analyses further highlight the effectiveness of TempBalance and its adaptability as an “add-on” method for improving model performance.

Reinforcement Learning · Deep RL

Dohyeong Kim, Taehyun Cho, Seungyub Han, Hojun Chung, Kyungjae Lee, Songhwai Oh

The field of risk-constrained reinforcement learning (RCRL) has been developed to effectively reduce the likelihood of worst-case scenarios by explicitly handling risk-measure-based constraints.However, the nonlinearity of risk measures makes it challenging to achieve convergence and optimality.To overcome the difficulties posed by the nonlinearity, we propose a spectral risk measure-constrained RL algorithm, spectral-risk-constrained policy optimization (SRCPO), a bilevel optimization approach that utilizes the duality of spectral risk measures.In the bilevel optimization structure, the outer problem involves optimizing dual variables derived from the risk measures, while the inner problem involves finding an optimal policy given these dual variables.The proposed method, to the best of our knowledge, is the first to guarantee convergence to an optimum in the tabular setting.Furthermore, the proposed method has been evaluated on continuous control tasks and showed the best performance among other RCRL algorithms satisfying the constraints.Our code is available at https://github.com/rllab-snu/Spectral-Risk-Constrained-RL.

Reinforcement Learning · Multi-agent

Chenhao Zhou, Zebang Shen, zhang chao, Hanbin Zhao, Hui Qian

In this paper, we propose a provably efficient natural policy gradient algorithm called Spectral Dynamic Embedding Policy Optimization (\SDEPO) for two-player zero-sum stochastic Markov games with continuous state space and finite action space. In the policy evaluation procedure of our algorithm, a novel kernel embedding method is employed to construct a finite-dimensional linear approximations to the state-action value function. We explicitly analyze the approximation error in policy evaluation, and show that \SDEPO\ achieves an $\tilde{O}(\frac{1}{(1-\gamma)^3\epsilon})$ last-iterate convergence to the $\epsilon-$optimal Nash equilibrium, which is independent of the cardinality of the state space. The complexity result matches the best-known results for global convergence of policy gradient algorithms for single agent setting. Moreover, we also propose a practical variant of \SDEPO\ to deal with continuous action space and empirical results demonstrate the practical superiority of the proposed method.

Deep Learning · Robustness

Ruiming Guo, Mouxing Yang, Yijie Lin, Xi Peng, Peng Hu

Recently, contrastive multi-view clustering (MvC) has emerged as a promising avenue for analyzing data from heterogeneous sources, typically leveraging the off-the-shelf instances as positives and randomly sampled ones as negatives. In practice, however, this paradigm would unavoidably suffer from the Dual Noisy Correspondence (DNC) problem, where noise compromises the constructions of both positive and negative pairs.Specifically, the complexity of data collection and transmission might mistake some unassociated pairs as positive (namely, false positive correspondence), while the intrinsic one-to-many contrast nature of contrastive MvC would sample some intra-cluster samples as negative (namely, false negative correspondence).To handle this daunting problem, we propose a novel method, dubbed Contextually-spectral based correspondence refinery (CANDY). CANDY dexterously exploits inter-view similarities as \textit{context} to uncover false negatives. Furthermore, it employs a spectral-based module to denoise correspondence, alleviating the negative influence of false positives. Extensive experiments on five widely-used multi-view benchmarks, in comparison with eight competitive multi-view clustering methods, verify the effectiveness of our method in addressing the DNC problem.The code is available at https://github.com/XLearning-SCU/2024-NeurIPS-CANDY.

Theory · Everything Else

Noah Amsel, Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco

Approximating the action of a matrix function $f(\vec{A})$ on a vector $\vec{b}$ is an increasingly important primitive in machine learning, data science, and statistics, with applications such as sampling high dimensional Gaussians, Gaussian process regression and Bayesian inference, principle component analysis, and approximating Hessian spectral densities.Over the past decade, a number of algorithms enjoying strong theoretical guarantees have been proposed for this task.Many of the most successful belong to a family of algorithms called Krylov subspace methods.Remarkably, a classic Krylov subspace method, called the Lanczos method for matrix functions (Lanczos-FA), frequently outperforms newer methods in practice. Our main result is a theoretical justification for this finding: we show that, for a natural class of rational functions, Lanczos-FA matches the error of the best possible Krylov subspace method up to a multiplicative approximation factor. The approximation factor depends on the degree of $f(x)$'s denominator and the condition number of $\vec{A}$, but not on the number of iterations $k$. Our result provides a strong justification for the excellent performance of Lanczos-FA, especially on functions that are well approximated by rationals, such as the matrix square root.

Graph Neural Networks

YUJIE MO, Zhihe Lu, Runpeng Yu, Xiaofeng Zhu, Xinchao Wang

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations: (i) noise in graph structures is often introduced during the message-passing process to weaken node representations, and (ii) cluster-level information may be inadequately captured and leveraged, diminishing the performance in downstream tasks. In this paper, we address these limitations by theoretically revisiting SHGL from the spectral clustering perspective and introducing a novel framework enhanced by rank and dual consistency constraints. Specifically, our framework incorporates a rank-constrained spectral clustering method that refines the affinity matrix to exclude noise effectively. Additionally, we integrate node-level and cluster-level consistency constraints that concurrently capture invariant and clustering information to facilitate learning in downstream tasks. We theoretically demonstrate that the learned representations are divided into distinct partitions based on the number of classes and exhibit enhanced generalization ability across tasks. Experimental results affirm the superiority of our method, showcasing remarkable improvements in several downstream tasks compared to existing methods.

Chao Wang, Xin HE, Yuwen Wang, Junhui Wang

This paper investigates the impact of alignment between the target function of interest and the kernel matrix on a variety of kernel-based methods based on a general loss belonging to a rich loss function family, which covers many commonly used methods in regression and classification problems. We consider the truncated kernel-based method (TKM) which is estimated within a reduced function space constructed by using the spectral truncation of the kernel matrix and compare its theoretical behavior to that of the standard kernel-based method (KM) under various settings. By using the kernel complexity function that quantifies the complexity of the induced function space, we derive the upper bounds for both TKM and KM, and further reveal their dependencies on the degree of target-kernel alignment. Specifically, for the alignment with polynomial decay, the established results indicate that under the just-aligned and weakly-aligned regimes, TKM and KM share the same learning rate. Yet, under the strongly-aligned regime, KM suffers the saturation effect, while TKM can be continuously improved as the alignment becomes stronger. This further implies that TKM has a strong ability to capture the strong alignment and provide a theoretically guaranteed solution to eliminate the phenomena of saturation effect. The minimax lower bound is also established for the squared loss to confirm the optimality of TKM. Extensive numerical experiments further support our theoretical findings. The Python code for reproducing the numerical experiments is available at https://github.com/wywangen.

Miscellaneous Aspects of Machine Learning · Kernel methods

Alexander Modell

In this paper, we derive *entrywise* error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition (or singular value decomposition). While this approximation is well-known to be optimal with respect to the spectral and Frobenius norm error, little is known about the statistical behaviour of individual entries. Our error bounds fill this gap. A key technical innovation is a delocalisation result for the eigenvectors of the kernel matrix corresponding to small eigenvalues, which takes inspiration from the field of Random Matrix Theory. Finally, we validate our theory with an empirical study of a collection of synthetic and real-world datasets.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Sebastian Damrich, Philipp Berens, Dmitry Kobak

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case traditional persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for existing refinements of persistent homology. As a remedy, we find that spectral distances on the k-nearest-neighbor graph of the data, such as diffusion distance and effective resistance, allow to detect the correct topology even in the presence of high-dimensional noise. Moreover, we derive a novel closed-form formula for effective resistance, and describe its relation to diffusion distances. Finally, we apply these methods to high-dimensional single-cell RNA-sequencing data and show that spectral distances allow robust detection of cell cycle loops.

Graph Neural Networks

Aref Einizade, Fragkiskos Malliaros, Jhony H. Giraldo

Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial differential equations on graphs (TPDEGs) provide a principled framework for modeling structured data across multiple interacting graphs, addressing the limitations of the existing discrete methodologies. In this paper, we introduce Continuous Product Graph Neural Networks (CITRUS) that emerge as a natural solution to the TPDEG. CITRUS leverages the separability of continuous heat kernels from Cartesian graph products to efficiently implement graph spectral decomposition. We conduct thorough theoretical analyses of the stability and over-smoothing properties of CITRUS in response to domain-specific graph perturbations and graph spectra effects on the performance. We evaluate CITRUS on well-known traffic and weather spatiotemporal forecasting datasets, demonstrating superior performance over existing approaches. The implementation codes are available at https://github.com/ArefEinizade2/CITRUS.

Optimization

Aleksandros Sobczyk, Marko Mladenovic, Mathieu Luisier

Approximating invariant subspaces of generalized eigenvalue problems (GEPs) is a fundamental computational problem at the core of machine learning and scientific computing. It is, for example, the root of Principal Component Analysis (PCA) for dimensionality reduction, data visualization, and noise filtering, and of Density Functional Theory (DFT), arguably the most popular method to calculate the electronic structure of materials. Given Hermitian $H,S\in\mathbb{C}^{n\times n}$, where $S$ is positive-definite, let $\Pi_k$ be the true spectral projector on the invariant subspace that is associated with the $k$ smallest (or largest) eigenvalues of the GEP $HC=SC\Lambda$, for some $k\in[n]$. We show that we can compute a matrix $\widetilde\Pi_k$ such that $\lVert\Pi_k-\widetilde\Pi_k\rVert_2\leq \epsilon$, in $O\left( n^{\omega+\eta}\mathrm{polylog}(n,\epsilon^{-1},\kappa(S),\mathrm{gap}_k^{-1}) \right)$ bit operations in the floating point model, for some $\epsilon\in(0,1)$, with probability $1-1/n$. Here, $\eta>0$ is arbitrarily small, $\omega\lesssim 2.372$ is the matrix multiplication exponent, $\kappa(S)=\lVert S\rVert_2\lVert S^{-1}\rVert_2$, and $\mathrm{gap}_k$ is the gap between eigenvalues $k$ and $k+1$. To achieve such provable "forward-error" guarantees, our methods rely on a new $O(n^{\omega+\eta})$ stability analysis for the Cholesky factorization, and a smoothed analysis for computing spectral gaps, which can be of independent interest.Ultimately, we obtain new matrix multiplication-type bit complexity upper bounds for PCA problems, including classical PCA and (randomized) low-rank approximation.

Physical Models · Physics

Timothée Devergne, Vladimir Kostic, Michele Parrinello, Massimiliano Pontil

We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by this equation involve transitions between metastable states separated by high potential barriers that can hardly be crossed during a simulation. To overcome this bottleneck, data are collected via biased simulations that explore the state space more rapidly. We propose a framework for learning from biased simulations rooted in the infinitesimal generator of the process {and the associated resolvent operator}. We contrast our approach to more common ones based on the transfer operator, showing that it can provably learn the spectral properties of the unbiased system from biased data. In experiments, we highlight the advantages of our method over transfer operator approaches and recent developments based on generator learning, demonstrating its effectiveness in estimating eigenfunctions and eigenvalues. Importantly, we show that even with datasets containing only a few relevant transitions due to sub-optimal biasing, our approachrecovers relevant information about the transition mechanism.

Computer Vision

Yu Zhong, Xiao Wu, Liang-Jian Deng, ZiHan Cao, Hong-Xia Dou

Pansharpening is a significant image fusion technique that merges the spatial content and spectral characteristics of remote sensing images to generate high-resolution multispectral images. Recently, denoising diffusion probabilistic models have been gradually applied to visual tasks, enhancing controllable image generation through low-rank adaptation (LoRA). In this paper, we introduce a spatial-spectral integrated diffusion model for the remote sensing pansharpening task, called SSDiff, which considers the pansharpening process as the fusion process of spatial and spectral components from the perspective of subspace decomposition. Specifically, SSDiff utilizes spatial and spectral branches to learn spatial details and spectral features separately, then employs a designed alternating projection fusion module (APFM) to accomplish the fusion. Furthermore, we propose a frequency modulation inter-branch module (FMIM) to modulate the frequency distribution between branches. The two components of SSDiff can perform favorably against the APFM when utilizing a LoRA-like branch-wise alternative fine-tuning method. It refines SSDiff to capture component-discriminating features more sufficiently. Finally, extensive experiments on four commonly used datasets, i.e., WorldView-3, WorldView-2, GaoFen-2, and QuickBird, demonstrate the superiority of SSDiff both visually and quantitatively. The code is available at https://github.com/Z-ypnos/SSdiff_main.

Computer Vision

Chau Tran, Duy M. H. Nguyen, Manh-Duy Nguyen, TrungTin Nguyen, Ngan Le, Pengtao Xie, Daniel Sonntag, James Zou, Binh Nguyen, Mathias Niepert

Increasing the throughput of the Transformer architecture, a foundational component used in numerous state-of-the-art models for vision and language tasks (e.g., GPT, LLaVa), is an important problem in machine learning. One recent and effective strategy is to merge token representations within Transformer models, aiming to reduce computational and memory requirements while maintaining accuracy. Prior work has proposed algorithms based on Bipartite Soft Matching (BSM), which divides tokens into distinct sets and merges the top $k$ similar tokens. However, these methods have significant drawbacks, such as sensitivity to token-splitting strategies and damage to informative tokens in later layers. This paper presents a novel paradigm called PiToMe, which prioritizes the preservation of informative tokens using an additional metric termed the \textit{energy score}. This score identifies large clusters of similar tokens as high-energy, indicating potential candidates for merging, while smaller (unique and isolated) clusters are considered as low-energy and preserved. Experimental findings demonstrate that PiToMe saved from 40-60\% FLOPs of the base models while exhibiting superior off-the-shelf performance on image classification (0.5\% average performance drop of ViT-MAEH compared to 2.6\% as baselines), image-text retrieval (0.3\% average performance drop of Clip on Flick30k compared to 4.5\% as others), and analogously in visual questions answering with LLaVa-7B. Furthermore, PiToMe is theoretically shown to preserve intrinsic spectral properties to the original token space under mild conditions.

Theory · Statistics

Yihan Zhang, Marco Mondelli

We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or, when they do so, the resulting approaches (e.g., based on whitening or singular value shrinkage) remain vastly suboptimal. On top of this, most of the literature has focused on the special case of estimating the left singular vector of the signal when the noise only possesses row correlation (one-sided heteroscedasticity). In contrast, our work establishes the information-theoretic and algorithmic limits of matrix denoising with doubly heteroscedastic noise. We characterize the exact asymptotic minimum mean square error, and design a novel spectral estimator with rigorous optimality guarantees: under a technical condition, it attains positive correlation with the signals whenever information-theoretically possible and, for one-sided heteroscedasticity, it also achieves the Bayes-optimal error. Numerical experiments demonstrate the significant advantage of our theoretically principled method with the state of the art. The proofs draw connections with statistical physics and approximate message passing, departing drastically from standard random matrix theory techniques.