Daily Papers

Vision-language models (VLMs) often generate fluent but visually unsupported descriptions, especially by mentioning objects absent from the image. We propose QK Product Steering, a data-free, training-free, and zero-inference-cost weight edit for reducing object hallucination. The method directly edits the per-head query-key product, the operator that produces pre-softmax attention logits, by suppressing a small number of dominant singular modes in selected middle layers. The edited product is then mapped back to the query weights through a closed-form query-only update while keeping shared key weights fixed, making the edit compatible with grouped-query attention. We further decompose the QK product into symmetric and antisymmetric components to distinguish mutual content-similarity patterns from directional attention patterns. Across three GQA-based VLMs, QK Product Steering achieves an average relative CHAIR_s reduction of 4.0%, while matched random-mode controls show negligible change. Interpretability ablations show that the hallucination signal is specific to dominant QK modes and is primarily localized to the symmetric mutual-attention channel. Overall, QK Product Steering offers a simple alternative to decoding-time mitigation, requiring no additional data, fine-tuning, or inference-time overhead while largely preserving general multimodal capability.

Parameterized quantum circuits are widely investigated in quantum machine learning, yet how their architecture can provide task-aligned inductive biases remains poorly understood. We study data reuploading quantum circuits with two distinct inputs: a signal that varies between samples and a fixed, task-defined spectral query that specifies how the signal should be probed. We show that encoding the query can change the circuit's hypothesis class over the signal by modulating how its existing signal frequencies are combined, without introducing new sample-dependent information. This mechanism matches tasks built on nonuniform Fourier transforms, whose evaluation frequencies specify the query and whose sampling positions guide its encoding. We examine this connection in a classification task inspired by synthetic aperture radar, where acquisition geometry determines a query for classifying unfocused spectral patches before image formation. Across small-scale spectral and radar-like tasks, aligned queries improve learning from limited data over parameter-matched circuits with mismatched or absent queries. These results provide a route from known spectral task structure to the design and validation of inductive biases in parameterized quantum circuits.

Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator M_h = W_K^{htop}W_Q^h and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient d_head-dimensional computation that avoids constructing the full d_modeltimes d_model matrix. We conducted extensive experiments across models demonstrating that at 50\% sparsity, AoH retains 96.5\% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4\% and 66.0\%, respectively, and KV-cache memory by 50.0\% at 256K tokens.

Spectra are a prevalent yet highly information-dense form of scientific imagery, presenting substantial challenges to multimodal large language models (MLLMs) due to their unstructured and domain-specific characteristics. Here we introduce SpecVQA, a professional scientific-image benchmark for evaluating multimodal models on scientific spectral understanding, covering 7 representative spectrum types with expert-annotated question-answer pairs. The aim comprises two aspects: spectra scientific QA evaluation and corresponding underlying task evaluation. SpecVQA contains 620 figures and 3100 QA pairs curated from peer-reviewed literature, targeting both direct information extraction and domain-specific reasoning. To effectively reduce token length while preserving essential curve characteristics, we propose a spectral data sampling and interpolation reconstruction approach. Ablation studies further confirm that the approach achieves substantial performance improvements on the proposed benchmark. We test the capability of prominent MLLMs in scientific spectral understanding on our benchmark and present a leaderboard. This work represents an essential step toward enhancing spectral understanding in multimodal large models and suggests promising directions for extending visual-language models to broader scientific research and data analysis.

High-dimensional vector spaces, particularly embedding spaces with dense semantic structure, are often interpreted primarily leveraging solely geometric relationships. In this work, we show that they can also be viewed as spectral energy networks induced by the topology of their underlying feature-space manifold with relevant improvements for downstream tasks. Building on this perspective, we introduce Graph Wiring, a general framework for exploiting feature-space spectral structure, together with Spectral Indexing, its task-specific instantiation for vector search. By coupling geometric similarity with spectral information, the proposed method improves Head-Tail coherence and semantic alignment relative to purely geometric retrieval methods. It further supports adaptive search behavior through tau-modulation, providing the flexibility increasingly required by modern Retrieval-Augmented Generation (RAG) pipelines. We present the complete algorithmic pipeline, establish its theoretical foundation through epiplexity, and evaluate the approach across benchmark and industrial settings using the open-source arrowspace library.

Identifying a small molecule from its mass spectrum is the primary open problem in computational metabolomics. This is typically cast as information retrieval: an unknown spectrum is matched against spectra predicted computationally from a large database of chemical structures. However, current approaches to spectrum prediction model the output space in ways that force a tradeoff between capturing high resolution mass information and tractable learning. We resolve this tradeoff by casting spectrum prediction as a mapping from an input molecular graph to a probability distribution over molecular formulas. We discover that a large corpus of mass spectra can be closely approximated using a fixed vocabulary constituting only 2% of all observed formulas. This enables efficient spectrum prediction using an architecture similar to graph classification - GrAFF-MS - achieving significantly lower prediction error and orders-of-magnitude faster runtime than state-of-the-art methods.

Recent advances in Remote Sensing Foundation Models (RSFMs) have led to significant breakthroughs in the field. While many RSFMs have been pretrained with massive optical imagery, more multispectral/hyperspectral data remain lack of the corresponding foundation models. To leverage the advantages of spectral imagery in earth observation, we explore whether existing RSFMs can be effectively adapted to process diverse spectral modalities without requiring extensive spectral pretraining. In response to this challenge, we proposed SpectralX, an innovative parameter-efficient fine-tuning framework that adapt existing RSFMs as backbone while introducing a two-stage training approach to handle various spectral inputs, thereby significantly improving domain generalization performance. In the first stage, we employ a masked-reconstruction task and design a specialized Hyper Tokenizer (HyperT) to extract attribute tokens from both spatial and spectral dimensions. Simultaneously, we develop an Attribute-oriented Mixture of Adapter (AoMoA) that dynamically aggregates multi-attribute expert knowledge while performing layer-wise fine-tuning. With semantic segmentation as downstream task in the second stage, we insert an Attribute-refined Adapter (Are-adapter) into the first stage framework. By iteratively querying low-level semantic features with high-level representations, the model learns to focus on task-beneficial attributes, enabling customized adjustment of RSFMs. Following this two-phase adaptation process, SpectralX is capable of interpreting spectral imagery from new regions or seasons. The codes will be available from the website: https://github.com/YuxiangZhang-BIT.

Attention steering is an important technique for controlling model focus, enabling capabilities such as prompt highlighting, where the model prioritises user-specified text. However, existing attention steering methods require explicit storage of the full attention matrix, making them incompatible with memory-efficient implementations like FlashAttention. We introduce Spectral Editing Key Amplification (SEKA), a training-free steering method that tackles this by directly editing key embeddings before attention computation. SEKA uses spectral decomposition to steer key embeddings towards latent directions that amplify attention scores for certain tokens. We extend this to Adaptive SEKA (AdaSEKA), a query-adaptive variant that uses a training-free routing mechanism to dynamically combine multiple expert subspaces based on the prompt's semantic intent. Our experiments show both methods significantly outperform strong baselines on standard steering benchmarks while adding much lower latency and memory overhead, in compatibility with optimised attention.

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes representational capacity, while whitening enforces isotropy at the cost of amplifying noise in the heavy-tailed eigenspectrum of retrieval embeddings. Intermediate spectral scaling methods unify these extremes by reweighting dimensions with a power coefficient γ, but treat γ as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength γ is not a global constant: it varies systematically with target dimensionality k and is governed by the signal-to-noise ratio (SNR) of the retained subspace. Based on this insight, we propose Spectral Tempering (SpecTemp), a learning-free method that derives an adaptive γ(k) directly from the corpus eigenspectrum using local SNR analysis and knee-point normalization, requiring no labeled data or validation-based search. Extensive experiments demonstrate that Spectral Tempering consistently achieves near-oracle performance relative to grid-searched γ^*(k) while remaining fully learning-free and model-agnostic. Our code is publicly available at https://anonymous.4open.science/r/SpecTemp-0D37.

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

In recent years, large language models (LLMs) have transformed natural language understanding through vast datasets and large-scale parameterization. Inspired by this success, we present SpecCLIP, a foundation model framework that extends LLM-inspired methodologies to stellar spectral analysis. Stellar spectra, akin to structured language, encode rich physical and chemical information about stars. By training foundation models on large-scale spectral datasets, our goal is to learn robust and informative embeddings that support diverse downstream applications. As a proof of concept, SpecCLIP involves pre-training on two spectral types--LAMOST low-resolution and Gaia XP--followed by contrastive alignment using the CLIP (Contrastive Language-Image Pre-training) framework, adapted to associate spectra from different instruments. This alignment is complemented by auxiliary decoders that preserve spectrum-specific information and enable translation (prediction) between spectral types, with the former achieved by maximizing mutual information between embeddings and input spectra. The result is a cross-spectrum framework enabling intrinsic calibration and flexible applications across instruments. We demonstrate that fine-tuning these models on moderate-sized labeled datasets improves adaptability to tasks such as stellar-parameter estimation and chemical-abundance determination. SpecCLIP also enhances the accuracy and precision of parameter estimates benchmarked against external survey data. Additionally, its similarity search and cross-spectrum prediction capabilities offer potential for anomaly detection. Our results suggest that contrastively trained foundation models enriched with spectrum-aware decoders can advance precision stellar spectroscopy.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

The paper is a continuation of the study started in Yorzh1. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of delta type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of L_1 and C^M edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

Understanding why trained Transformers generalize well is a fundamental problem in modern machine learning theory, and complexity-based generalization bounds provide a principled way to study this question. While existing norm-based bounds for Transformers remove the explicit polynomial dependence on the hidden dimension, they typically impose fixed norm constraints specified a priori and can exhibit unfavorable exponential dependence on depth. In this paper, we derive spectrum-adaptive post hoc generalization bounds for multi-layer Transformers. Under layerwise spectral norm control, the bounds are expressed in terms of layerwise Schatten quantities of the query-key, value, and feedforward weight matrices. Since the Schatten indices need not be fixed a priori and can instead be selected after training, separately for each matrix type and layer, the bounds adaptively trade off spectral complexity against the dimension- and depth-dependent factors according to the learned singular-value profiles. Empirical comparisons of BERT-adapted proxies for the leading complexity factors suggest that the proxies induced by our bounds grow more slowly with depth and hidden dimension than the corresponding norm-based proxies. Overall, our results provide a complexity-based perspective on how the spectral structure of trained Transformers is reflected in generalization analyses.

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

Compound identification and structure annotation from mass spectra is a well-established task widely applied in drug detection, criminal forensics, small molecule biomarker discovery and chemical engineering. We propose SpecTUS: Spectral Translator for Unknown Structures, a deep neural model that addresses the task of structural annotation of small molecules from low-resolution gas chromatography electron ionization mass spectra (GC-EI-MS). Our model analyzes the spectra in de novo manner -- a direct translation from the spectra into 2D-structural representation. Our approach is particularly useful for analyzing compounds unavailable in spectral libraries. In a rigorous evaluation of our model on the novel structure annotation task across different libraries, we outperformed standard database search techniques by a wide margin. On a held-out testing set, including 28267 spectra from the NIST database, we show that our model's single suggestion perfectly reconstructs 43\% of the subset's compounds. This single suggestion is strictly better than the candidate of the database hybrid search (common method among practitioners) in 76\% of cases. In a~still affordable scenario of~10 suggestions, perfect reconstruction is achieved in 65\%, and 84\% are better than the hybrid search.

The growing computational and memory demands of the Key-Value (KV) cache significantly limit the ability of Large Language Models (LLMs). While KV merging has emerged as a promising solution, existing methods that rely on empirical observations of KV asymmetry and gradient-based Hessian approximations lack a theoretical foundation and incur suboptimal compression and inference overhead. To bridge these gaps, we establish a theoretical framework that characterizes this asymmetry through the spectral energy distribution of projection weights, demonstrating that concentrated spectra in Query/Key weights induce feature homogeneity, whereas dispersed spectra in Value weights preserve heterogeneity. Then, we introduce KVSlimmer, an efficient algorithm that captures exact Hessian information through a mathematically exact formulation, and derives a closed-form solution utilizing only forward-pass variables, resulting in a gradient-free approach that is both memory- and time-efficient. Extensive experiments across various models and benchmarks demonstrate that KVSlimmer consistently outperforms SOTA methods. For instance, on Llama3.1-8B-Instruct, it improves the LongBench average score by 0.92 while reducing memory costs and latency by 29% and 28%, respectively.Code is available at https://github.com/lianjunl13-sudo/KVSlimmer.

Vision-language models (VLMs) remain unreliable when predictions require fine-grained visual evidence. We identify a previously overlooked cause: spectral response rigidity. Despite substantial frequency variation across images and tasks, pretrained vision encoders exhibit persistent, encoder-specific layerwise spectral profiles that change only marginally under downstream fine-tuning. Since pretrained vision encoders only receive images, they cannot adapt spectral extraction to the evidence required by the current query. We therefore propose HAFI-VLM, which introduces a task-conditioned frequency pathway while preserving the pretrained semantic representation. Hierarchical Adaptive Frequency Injection (HAFI) retrieves complementary low-, mid-, and high-frequency evidence at multiple encoder depths using text-modulated, spatially aligned cross-attention. A Visual Enrichment Layer Adapter further recalibrates shallow LLM attention to effectively utilize the enriched visual tokens. Experiments on LLaVA-1.5 and Qwen2.5-VL demonstrate consistent improvements in general VQA, text-rich understanding, and hallucination robustness, outperforming representation-level enhancement methods and most resolution- or cropping-based approaches without additional high-resolution encoding. Mechanistic analyses show that HAFI restores task-dependent spectral allocation while retaining semantic attention, establishing frequency enrichment as a distinct and effective route for improving VLM perception.

Thompson Sampling (TS) has attracted a lot of interest due to its good empirical performance, in particular in the computational advertising. Though successful, the tools for its performance analysis appeared only recently. In this paper, we describe and analyze SpectralTS algorithm for a bandit problem, where the payoffs of the choices are smooth given an underlying graph. In this setting, each choice is a node of a graph and the expected payoffs of the neighboring nodes are assumed to be similar. Although the setting has application both in recommender systems and advertising, the traditional algorithms would scale poorly with the number of choices. For that purpose we consider an effective dimension d, which is small in real-world graphs. We deliver the analysis showing that the regret of SpectralTS scales as d*sqrt(T ln N) with high probability, where T is the time horizon and N is the number of choices. Since a d*sqrt(T ln N) regret is comparable to the known results, SpectralTS offers a computationally more efficient alternative. We also show that our algorithm is competitive on both synthetic and real-world data.

The {K_{1,1}, K_{1,2},C_m: mgeq3}-factor of a graph is a spanning subgraph whose each component is an element of {K_{1,1}, K_{1,2},C_m: mgeq3}. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a {K_2}-factor. We get a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.

Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We identify the need for a systematic comparison of different combinations of weight matrices and component functions for attention learning in Transformer. Hence, we introduce Spectraformer, a unified framework for approximating and learning the kernel function in the attention mechanism of the Transformer. Our empirical results demonstrate, for the first time, that a random feature-based approach can achieve performance comparable to top-performing sparse and low-rank methods on the challenging Long Range Arena benchmark. Thus, we establish a new state-of-the-art for random feature-based efficient Transformers. The framework also produces many variants that offer different advantages in accuracy, training time, and memory consumption. Our code is available at: https://github.com/cruiseresearchgroup/spectraformer .

The exponential growth of wireless devices is driving unprecedented spectrum demand, pushing spectrum management toward more fine-grained decisions across space, time, and device constraints. As a result, spectrum policymakers and engineers must process large volumes of data that come from diverse sources and take many different forms, such as text and tables. These data sources are often disaggregated and require significant time and effort to integrate, search, and interpret. Furthermore, most of this information is formatted for human understanding and is not readily accessible to automated systems. To address this challenge, we propose SpecMind, a novel Multi-Agent Retrieval-Augmented Generation (RAG) system for spectrum intelligence that performs reasoning over heterogeneous data sources. This system enables autonomous agents to coordinate specialized sub-agents that retrieve and synthesize knowledge across policy proceedings, legal regulations, and license databases. We develop SpecBench, a question and answer (Q&A) dataset based on real-world license records and policy proceedings, addressing the lack of evaluation resources for RAG systems in the spectrum domain. Experimental results demonstrate that SpecMind outperforms traditional, general-purpose RAG systems across spectrum-related tasks, achieving over 80% win rate against strong baselines. The agent-based design enables more accurate retrieval, better contextual reasoning, and improved task completion across diverse query types.

We present a machine learning search for local, low-mass galaxies (z < 0.02 and 10^6 M_odot < M_* < 10^9 M_odot) using the combined photometric data from the DESI Imaging Legacy Surveys and the WISE survey. We introduce the spectrally confirmed training sample, discuss evaluation metrics, investigate the features, compare different machine learning algorithms, and find that a 7-class neural network classification model is highly effective in separating the signal (local, low-mass galaxies) from various contaminants, reaching a precision of 95% and a recall of 76%. The principal contaminants are nearby sub-L^* galaxies at 0.02 < z < 0.05 and nearby massive galaxies at 0.05 < z < 0.2. We find that the features encoding surface brightness information are essential to achieving a correct classification. Our final catalog, which we make available, consists of 112,859 local, low-mass galaxy candidates, where 36,408 have high probability (p_{rm signal} > 0.95), covering the entire Legacy Surveys DR9 footprint. Using DESI-EDR public spectra and data from the SAGA and ELVES surveys, we find that our model has a precision of sim 100%, 96%, and 97%, respectively, and a recall of sim 51%, 68% and 53%, respectively. The results of those independent spectral verification demonstrate the effectiveness and efficiency of our machine learning classification model.

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

Atmospheric retrieval determines the properties of an atmosphere based on its measured spectrum. The low signal-to-noise ratio of exoplanet observations require a Bayesian approach to determine posterior probability distributions of each model parameter, given observed spectra. This inference is computationally expensive, as it requires many executions of a costly radiative transfer (RT) simulation for each set of sampled model parameters. Machine learning (ML) has recently been shown to provide a significant reduction in runtime for retrievals, mainly by training inverse ML models that predict parameter distributions, given observed spectra, albeit with reduced posterior accuracy. Here we present a novel approach to retrieval by training a forward ML surrogate model that predicts spectra given model parameters, providing a fast approximate RT simulation that can be used in a conventional Bayesian retrieval framework without significant loss of accuracy. We demonstrate our method on the emission spectrum of HD 189733 b and find good agreement with a traditional retrieval from the Bayesian Atmospheric Radiative Transfer (BART) code (Bhattacharyya coefficients of 0.9843--0.9972, with a mean of 0.9925, between 1D marginalized posteriors). This accuracy comes while still offering significant speed enhancements over traditional RT, albeit not as much as ML methods with lower posterior accuracy. Our method is ~9x faster per parallel chain than BART when run on an AMD EPYC 7402P central processing unit (CPU). Neural-network computation using an NVIDIA Titan Xp graphics processing unit is 90--180x faster per chain than BART on that CPU.

Vision-language foundation models (VLFMs) promise zero-shot and retrieval understanding for Earth observation. While operational satellite systems often lack full multi-spectral coverage, making RGB-only inference highly desirable for scalable deployment, the adoption of VLFMs for satellite imagery remains hindered by two factors: (1) multi-spectral inputs are informative but difficult to exploit consistently due to band redundancy and misalignment; and (2) CLIP-style text encoders limit semantic expressiveness and weaken fine-grained alignment. We present SATtxt, a spectrum-aware VLFM that operates with RGB inputs only at inference while retaining spectral cues learned during training. Our framework comprises two stages. First, Spectral Representation Distillation transfers spectral priors from a frozen multi-spectral teacher to an RGB student via a lightweight projector. Second, Spectrally Grounded Alignment with Instruction-Augmented LLMs bridges the distilled visual space and an expressive LLM embedding space. Across EuroSAT, BigEarthNet, and ForestNet, SATtxt improves zero-shot classification on average by 4.2%, retrieval by 5.9%, and linear probing by 2.7% over baselines, showing an efficient path toward spectrum-aware vision-language learning for Earth observation. Project page: https://ikhado.github.io/sattxt/

While multimodal large language models (MLLMs) have made significant strides in natural image understanding, their ability to perceive and reason over hyperspectral image (HSI) remains underexplored, which is a vital modality in remote sensing. The high dimensionality and intricate spectral-spatial properties of HSI pose unique challenges for models primarily trained on RGB data.To address this gap, we introduce Hyperspectral Multimodal Benchmark (HM-Bench), the first benchmark designed specifically to evaluate MLLMs in HSI understanding. We curate a large-scale dataset of 19,337 question-answer pairs across 13 task categories, ranging from basic perception to spectral reasoning. Given that existing MLLMs are not equipped to process raw hyperspectral cubes natively, we propose a dual-modality evaluation framework that transforms HSI data into two complementary representations: PCA-based composite images and structured textual reports. This approach facilitates a systematic comparison of different representation for model performance. Extensive evaluations on 18 representative MLLMs reveal significant difficulties in handling complex spatial-spectral reasoning tasks. Furthermore, our results demonstrate that visual inputs generally outperform textual inputs, highlighting the importance of grounding in spectral-spatial evidence for effective HSI understanding. Dataset and appendix can be accessed at https://github.com/HuoRiLi-Yu/HM-Bench.

Spectral rendering reproduces the wavelength-dependent appearance that RGB rendering cannot: metamerism, colour shifts under spectrally rich illumination, coloured glass, metallic reflection and subsurface scattering. It requires a spectrally aware renderer, but the rendering ecosystem is predominantly RGB: game engines, cloud render farms, GPU rasterisers and most offline renderers consume RGB alone, with no access to the internal wavelength propagation that spectral rendering relies on. We introduce learned spectral codes, a compact linear representation that enables general spectral rendering through unmodified RGB pipelines. A trained encoder compresses any visible-range spectral quantity into a small latent vector; the codes are packed as RGB triplets and processed by an off-the-shelf RGB renderer. The codec preserves the arithmetic of light transport, exactly for scaling and addition and approximately for element-wise products, so two standard RGB passes suffice to produce results closely matching a full spectral rendering. The same codec handles reflectance, illumination, coloured glass, conductors, and participating media: one pipeline across material classes, with no per-material modification to the renderer. Where spectral asset data is unavailable, lightweight neural upsamplers bridge legacy RGB inputs to the latent space. Across diverse materials and illumination, the method yields substantial quality improvements on the cases where RGB rendering fails most visibly, at rendering cost comparable to efficient spectral-sampling techniques and with no changes to the renderer.

Many works have been done on salient object detection using supervised or unsupervised approaches on colour images. Recently, a few studies demonstrated that efficient salient object detection can also be implemented by using spectral features in visible spectrum of hyperspectral images from natural scenes. However, these models on hyperspectral salient object detection were tested with a very few number of data selected from various online public dataset, which are not specifically created for object detection purposes. Therefore, here, we aim to contribute to the field by releasing a hyperspectral salient object detection dataset with a collection of 60 hyperspectral images with their respective ground-truth binary images and representative rendered colour images (sRGB). We took several aspects in consideration during the data collection such as variation in object size, number of objects, foreground-background contrast, object position on the image, and etc. Then, we prepared ground truth binary images for each hyperspectral data, where salient objects are labelled on the images. Finally, we did performance evaluation using Area Under Curve (AUC) metric on some existing hyperspectral saliency detection models in literature.

Remote individual animal identification is important for food safety, sport, and animal conservation. Numerous existing remote individual animal identification studies have focused on RGB images. In this paper, we tackle individual penguin identification using hyperspectral (HS) images. To the best of our knowledge, it is the first work to analyze spectral differences between penguin individuals using an HS camera. We have constructed a novel penguin HS image dataset, including 990 hyperspectral images of 27 penguins. We experimentally demonstrate that the spectral information of HS image pixels can be used for individual penguin identification. The experimental results show the effectiveness of using HS images for individual penguin identification. The dataset and source code are available here: https://033labcodes.github.io/igrass24_penguin/

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

Spectral positional encodings (PEs) for directed graphs face two obstacles: magnetic Laplacians require an O(n^3) Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures. We propose learnable spectral PEs of the form h_θ(A_q),R, where A_q is a normalized magnetic operator, h_θ a learnable scalar spectral response, and R a block of random probes. Because the PE is a matrix function of the operator, it is gauge-invariant by construction. We compute it in a Hermitian block Krylov subspace from sparse matrix--vector products only, prove that k = O(log(1/varepsilon)) block steps suffice uniformly over heat--resolvent response families, and give a covering-number argument for why low-dimensional structured families generalize where free per-eigenvalue weights overfit. On a directed SBM whose symmetrization is uninformative by construction, direction-blind PEs stay at chance while magnetic Krylov PEs converge to the exact-eigendecomposition oracle as the depth grows. The same probes yield gauge-invariant pairwise features with 1/s Monte-Carlo error, and the undirected q{=}0 case improves heterophilous benchmarks over no-PE and polynomial baselines.

With the advent of new spectroscopic surveys from ground and space, observing up to hundreds of millions of galaxies, spectra classification will become overwhelming for standard analysis techniques. To prepare for this challenge, we introduce a family of deep learning tools to classify features in one-dimensional spectra. As the first application of these Galaxy Spectra neural Networks (GaSNets), we focus on tools specialized at identifying emission lines from strongly lensed star-forming galaxies in the eBOSS spectra. We first discuss the training and testing of these networks and define a threshold probability, PL, of 95% for the high quality event detection. Then, using a previous set of spectroscopically selected strong lenses from eBOSS, confirmed with HST, we estimate a completeness of ~80% as the fraction of lenses recovered above the adopted PL. We finally apply the GaSNets to ~1.3M spectra to collect a first list of ~430 new high quality candidates identified with deep learning applied to spectroscopy and visually graded as highly probable real events. A preliminary check against ground-based observations tentatively shows that this sample has a confirmation rate of 38%, in line with previous samples selected with standard (no deep learning) classification tools and follow-up by Hubble Space Telescope. This first test shows that machine learning can be efficiently extended to feature recognition in the wavelength space, which will be crucial for future surveys like 4MOST, DESI, Euclid, and the Chinese Space Station Telescope (CSST).

Hyperspectral unmixing (HU) is a very useful and increasingly popular preprocessing step for a wide range of hyperspectral applications. However, the HU research has been constrained a lot by three factors: (a) the number of hyperspectral images (especially the ones with ground truths) are very limited; (b) the ground truths of most hyperspectral images are not shared on the web, which may cause lots of unnecessary troubles for researchers to evaluate their algorithms; (c) the codes of most state-of-the-art methods are not shared, which may also delay the testing of new methods. Accordingly, this paper deals with the above issues from the following three perspectives: (1) as a profound contribution, we provide a general labeling method for the HU. With it, we labeled up to 15 hyperspectral images, providing 18 versions of ground truths. To the best of our knowledge, this is the first paper to summarize and share up to 15 hyperspectral images and their 18 versions of ground truths for the HU. Observing that the hyperspectral classification (HyC) has much more standard datasets (whose ground truths are generally publicly shared) than the HU, we propose an interesting method to transform the HyC datasets for the HU research. (2) To further facilitate the evaluation of HU methods under different conditions, we reviewed and implemented the algorithm to generate a complex synthetic hyperspectral image. By tuning the hyper-parameters in the code, we may verify the HU methods from four perspectives. The code would also be shared on the web. (3) To provide a standard comparison, we reviewed up to 10 state-of-the-art HU algorithms, then selected the 5 most benchmark HU algorithms, and compared them on the 15 real hyperspectral datasets. The experiment results are surely reproducible; the implemented codes would be shared on the web.

Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks.

Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In addition, it needs to construct the similarity graph for samples, which suffers from the curse of dimensionality when the data are high-dimensional. To address these two challenges, we introduce Deep Spectral Clustering (DSC), which consists of two main modules: the spectral embedding module and the greedy Kmeans module. The former module learns to efficiently embed raw samples into the spectral embedding space using deep neural networks and power iteration. The latter module improves the cluster structures of Kmeans on the learned spectral embeddings by a greedy optimization strategy, which iteratively reveals the direction of the worst cluster structures and optimizes embeddings in this direction. To jointly optimize spectral embeddings and clustering, we seamlessly integrate the two modules and optimize them in an end-to-end manner. Experimental results on seven real-world datasets demonstrate that DSC achieves state-of-the-art clustering performance.

Recent works have established that AI models introduce spectral artifacts into generated images and propose approaches for learning to capture them using labeled data. However, the significant differences in such artifacts among different generative models hinder these approaches from generalizing to generators not seen during training. In this work, we build upon the key idea that the spectral distribution of real images constitutes both an invariant and highly discriminative pattern for AI-generated image detection. To model this under a self-supervised setup, we employ masked spectral learning using the pretext task of frequency reconstruction. Since generated images constitute out-of-distribution samples for this model, we propose spectral reconstruction similarity to capture this divergence. Moreover, we introduce spectral context attention, which enables our approach to efficiently capture subtle spectral inconsistencies in images of any resolution. Our spectral AI-generated image detection approach (SPAI) achieves a 5.5% absolute improvement in AUC over the previous state-of-the-art across 13 recent generative approaches, while exhibiting robustness against common online perturbations. Code is available on https://mever-team.github.io/spai.

We study the problem of recovering low-dimensional latent geometry from a random geometric graph generated by noisy, high-dimensional data. Specifically, we analyze the performance of a spectral embedding algorithm on the Signal+Noise Graph Model, in which vertices are associated to points perturbed by Gaussian noise, and edges are included for pairs whose inner product exceeds a specified alignment threshold. In the high-dimensional regime where the number n of points and the ambient dimension d both tend to infinity, we show that under a spectral gap condition, the top eigenvectors and eigenvalues of the graph's adjacency matrix can be used to approximately recover the point cloud up to an orthogonal transformation. We illustrate our results on point clouds sampled from nested spheres and high-dimensional sinusoid curves.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

Molecular structure elucidation from spectra is a foundational problem in chemistry, with profound implications for compound identification, synthesis, and drug development. Traditional methods rely heavily on expert interpretation and lack scalability. Pioneering machine learning methods have introduced retrieval-based strategies, but their reliance on finite libraries limits generalization to novel molecules. Generative models offer a promising alternative, yet most adopt autoregressive SMILES-based architectures that overlook 3D geometry and struggle to integrate diverse spectral modalities. In this work, we present DiffSpectra, a generative framework that directly infers both 2D and 3D molecular structures from multi-modal spectral data using diffusion models. DiffSpectra formulates structure elucidation as a conditional generation process. Its denoising network is parameterized by Diffusion Molecule Transformer, an SE(3)-equivariant architecture that integrates topological and geometric information. Conditioning is provided by SpecFormer, a transformer-based spectral encoder that captures intra- and inter-spectral dependencies from multi-modal spectra. Extensive experiments demonstrate that DiffSpectra achieves high accuracy in structure elucidation, recovering exact structures with 16.01% top-1 accuracy and 96.86% top-20 accuracy through sampling. The model benefits significantly from 3D geometric modeling, SpecFormer pre-training, and multi-modal conditioning. These results highlight the effectiveness of spectrum-conditioned diffusion modeling in addressing the challenge of molecular structure elucidation. To our knowledge, DiffSpectra is the first framework to unify multi-modal spectral reasoning and joint 2D/3D generative modeling for de novo molecular structure elucidation.

Large Language Models (LLMs) have demonstrated remarkable performance across various tasks but remain prone to hallucinations. Detecting hallucinations is essential for safety-critical applications, and recent methods leverage attention map properties to this end, though their effectiveness remains limited. In this work, we investigate the spectral features of attention maps by interpreting them as adjacency matrices of graph structures. We propose the LapEigvals method, which utilises the top-k eigenvalues of the Laplacian matrix derived from the attention maps as an input to hallucination detection probes. Empirical evaluations demonstrate that our approach achieves state-of-the-art hallucination detection performance among attention-based methods. Extensive ablation studies further highlight the robustness and generalisation of LapEigvals, paving the way for future advancements in the hallucination detection domain.

Hyperspectral image classification remains a challenging task due to the high dimensionality of spectral data, significant inter-band redundancy, and the limited availability of annotated samples. While recent transformer-based models have improved the global modeling of spectral-spatial dependencies, their scalability and adaptability under label-scarce conditions remain limited. In this work, we propose LoLA-SpecViT(Low-rank adaptation Local Attention Spectral Vision Transformer), a lightweight spectral vision transformer that addresses these limitations through a parameter-efficient architecture tailored to the unique characteristics of hyperspectral imagery. Our model combines a 3D convolutional spectral front-end with local window-based self-attention, enhancing both spectral feature extraction and spatial consistency while reducing computational complexity. To further improve adaptability, we integrate low-rank adaptation (LoRA) into attention and projection layers, enabling fine-tuning with over 80\% fewer trainable parameters. A novel cyclical learning rate scheduler modulates LoRA adaptation strength during training, improving convergence and generalisation. Extensive experiments on three benchmark datasets WHU-Hi LongKou, WHU-Hi HongHu, and Salinas demonstrate that LoLA-SpecViT consistently outperforms state-of-the-art baselines, achieving up to 99.91\% accuracy with substantially fewer parameters and enhanced robustness under low-label regimes. The proposed framework provides a scalable and generalizable solution for real-world HSI applications in agriculture, environmental monitoring, and remote sensing analytics. Our code is available in the following https://github.com/FadiZidiDz/LoLA-SpecViT{GitHub Repository}.

Spectral imaging offers promising applications across diverse domains, including medicine and urban scene understanding, and is already established as a critical modality in remote sensing. However, variability in channel dimensionality and captured wavelengths among spectral cameras impede the development of AI-driven methodologies, leading to camera-specific models with limited generalizability and inadequate cross-camera applicability. To address this bottleneck, we introduce CARL, a model for Camera-Agnostic Representation Learning across RGB, multispectral, and hyperspectral imaging modalities. To enable the conversion of a spectral image with any channel dimensionality to a camera-agnostic representation, we introduce a novel spectral encoder, featuring a self-attention-cross-attention mechanism, to distill salient spectral information into learned spectral representations. Spatio-spectral pre-training is achieved with a novel feature-based self-supervision strategy tailored to CARL. Large-scale experiments across the domains of medical imaging, autonomous driving, and satellite imaging demonstrate our model's unique robustness to spectral heterogeneity, outperforming on datasets with simulated and real-world cross-camera spectral variations. The scalability and versatility of the proposed approach position our model as a backbone for future spectral foundation models. Code and model weights are publicly available at https://github.com/IMSY-DKFZ/CARL.

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Spatial-Spectral Mamba (SSM) improves computational efficiency and captures long-range dependencies, addressing Transformer limitations. However, traditional Mamba models overlook rich spectral information in HSIs and struggle with high dimensionality and sequential data. To address these issues, we propose the SSM with multi-head self-attention and token enhancement (MHSSMamba). This model integrates spectral and spatial information by enhancing spectral tokens and using multi-head attention to capture complex relationships between spectral bands and spatial locations. It also manages long-range dependencies and the sequential nature of HSI data, preserving contextual information across spectral bands. MHSSMamba achieved remarkable classification accuracies of 97.62\% on Pavia University, 96.92\% on the University of Houston, 96.85\% on Salinas, and 99.49\% on Wuhan-longKou datasets. The source code is available at https://github.com/MHassaanButt/MHA\_SS\_Mamba{GitHub}.

Half of the JWST high-contrast imaging objects will only have photometric data {{as of Cycle 2}}. However, to better understand their atmospheric chemistry which informs formation origin, spectroscopic data are preferred. Using HIP 65426 b, we investigate to what extent planet properties and atmospheric chemical abundance can be retrieved with only JWST photometric data points (2.5-15.5 mum) in conjunction with ground-based archival low-resolution spectral data (1.0-2.3 mum). We find that the data is consistent with an atmosphere with solar metallicity and C/O ratios at 0.40 and 0.55. We rule out 10x solar metallicity and an atmosphere with C/O = 1.0. We also find strong evidence of silicate clouds but no sign of an enshrouding featureless {{dust}} extinction. This work offers guidance and cautionary tales on analyzing data in the absence of medium-to-high resolution spectral data.

We present the discovery of 118 new ultracool dwarf candidates, discovered using a new machine learning tool, named SMDET, applied to time series images from the Wide-field Infrared Survey Explorer. We gathered photometric and astrometric data to estimate each candidate's spectral type, distance, and tangential velocity. This sample has a photometrically estimated spectral class distribution of 28 M dwarfs, 64 L dwarfs, and 18 T dwarfs. We also identify a T subdwarf candidate, two extreme T subdwarf candidates, and two candidate young ultracool dwarfs. Five objects did not have enough photometric data for any estimations to be made. To validate our estimated spectral types, spectra were collected for 2 objects, yielding confirmed spectral types of T5 (estimated T5) and T3 (estimated T4). Demonstrating the effectiveness of machine learning tools as a new large-scale discovery technique.

We study ratios of eigenvalues of the Laplacian on compact metric graphs. Our goals are threefold: First, we prove a sharp Ashbaugh--Benguria-type bound for the ratio of the first two eigenvalues on compact trees with Dirichlet conditions at all leaves, concretely showing that the ratio is maximized when the graph is an interval or an equilateral star. This improves a previous Payne--Pólya--Weinberger-type result due to Nicaise [Bull. Sci. Math., II. Sér. 111 (1987), 401--413]. Second, we extend this bound to a set of inequalities for the ratio of any pair of eigenvalues of such compact Dirichlet trees which respect the Weyl asymptotics up to an absolute constant. Third, we show that on non-trees, on which we also allow any mix of Neumann and Dirichlet conditions at the leaves, it is possible to recover bounds on the eigenvalue ratios depending only on the number of independent cycles and the number of Neumann leaves, in addition to the eigenvalue indices. This complements previously known counterexamples to analogues of the Ashbaugh--Benguria bound for general quantum graphs, by showing that the only way the bound can fail is through cycles and Neumann leaves, and by explicitly quantifying the extent to which it can fail.

While spectral-based optimizers like Muon operate directly on the spectrum of updates, standard adaptive methods such as AdamW do not account for the global spectral structure of weights and gradients, leaving them vulnerable to two empirical issues in large language model (LLM) training: (i) the optimizer updates can have large spectral norms, potentially destabilizing training and degrading generalization; (ii) stochastic gradient noise can exhibit sparse spectral spikes, with a few dominant singular values much larger than the rest. We propose SPECTRA, a general framework addressing these by (i) post-spectral clipping of updates to enforce spectral-norm constraints; (ii) optional pre-spectral clipping of gradients to suppress spectral noise spikes. We prove that post-clipping constitutes a Composite Frank-Wolfe method with spectral-norm constraints and weight regularization, recovering Frobenius and ell_{infty}-norm regularization with SGD-based and sign-based methods. We further analyze how pre-clipping mitigates sparse spectral spikes. We propose efficient soft spectral clipping via Newton-Schulz iterations, avoiding expensive SVD. Experiments on LLM pretraining show SPECTRA uniformly improves validation loss for various optimizers, including AdamW, Signum, and AdEMAMix, with the best-performing variants achieving state-of-the-art results. Models trained with SPECTRA exhibit smaller weight norms, confirming the link between spectral clipping and regularization.

Whitening loss offers a theoretical guarantee against feature collapse in self-supervised learning (SSL) with joint embedding architectures. Typically, it involves a hard whitening approach, transforming the embedding and applying loss to the whitened output. In this work, we introduce Spectral Transformation (ST), a framework to modulate the spectrum of embedding and to seek for functions beyond whitening that can avoid dimensional collapse. We show that whitening is a special instance of ST by definition, and our empirical investigations unveil other ST instances capable of preventing collapse. Additionally, we propose a novel ST instance named IterNorm with trace loss (INTL). Theoretical analysis confirms INTL's efficacy in preventing collapse and modulating the spectrum of embedding toward equal-eigenvalues during optimization. Our experiments on ImageNet classification and COCO object detection demonstrate INTL's potential in learning superior representations. The code is available at https://github.com/winci-ai/INTL.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

As machine learned models increase in complexity and expressive power, features of simpler models, such as intrinsic coefficient transparency and control over the shape of the modeled function are lost. On the one edge of the spectrum we have simple linear models that possess coefficient transparency, but have a limited expressive power. On the other edge we have neural networks, that have expressive power that improves with scaling, but are mostly opaque. In this work we develop the spectral neuron concept: a scalar model given by f(x)=λ_k (A_0 + A_1 x + ... + A_n x_n), with learned real symmetric matrices A_0, ..., A_n. The input enters the model through an affine matrix function, but the prediction is obtained by reading one of its eigenvalues. Thus, the model is nonlinear, but the source of nonlinearity is still mathematically explicit. This gives us a useful middle ground: the model can become more expressive as the matrix dimension grows, while retaining coefficient transparency through the learned matrices. For example, extremal eigenvalues yield convex or concave functions, semidefinite constraints on the coefficient matrices impose monotonicity, and the associated eigenspaces characterize local feature influence. We study coefficient transparency, feature-influence bounds, and shape-control properties of this model family, and then test whether it can be learned and scaled in practice. We develop a systematic study of this model family, bringing together spectral results from several mathematical literatures to characterize its expressivity, coefficient transparency, feature influence, and shape-control properties. Code available at https://github.com/alexshtf/spectral_neuron_paper.

This paper introduces the first two pixel retrieval benchmarks. Pixel retrieval is segmented instance retrieval. Like semantic segmentation extends classification to the pixel level, pixel retrieval is an extension of image retrieval and offers information about which pixels are related to the query object. In addition to retrieving images for the given query, it helps users quickly identify the query object in true positive images and exclude false positive images by denoting the correlated pixels. Our user study results show pixel-level annotation can significantly improve the user experience. Compared with semantic and instance segmentation, pixel retrieval requires a fine-grained recognition capability for variable-granularity targets. To this end, we propose pixel retrieval benchmarks named PROxford and PRParis, which are based on the widely used image retrieval datasets, ROxford and RParis. Three professional annotators label 5,942 images with two rounds of double-checking and refinement. Furthermore, we conduct extensive experiments and analysis on the SOTA methods in image search, image matching, detection, segmentation, and dense matching using our pixel retrieval benchmarks. Results show that the pixel retrieval task is challenging to these approaches and distinctive from existing problems, suggesting that further research can advance the content-based pixel-retrieval and thus user search experience. The datasets can be downloaded from https://github.com/anguoyuan/Pixel_retrieval-Segmented_instance_retrieval{this link}.

For a locally linear graph G, which is a graph built out of triangles, it is possible to construct another graph G^* that would consist of triangles of G as vertices, while sharing (or not sharing) a common vertex between a pair of triangles would define a binary relation for edges of G^*. In this paper we show that the spectrum of G^* is uniquely defined by G. We will also show some structural similarities of these graphs; in particular, that the number of quadrilaterals and pentagons in both graphs are the same; that G^* does not contain K_4-e and K_{1,4}; and that G can be reconstructed from G^*.

The coldest Y spectral type brown dwarfs are similar in mass and temperature to cool and warm (sim200 -- 400 K) giant exoplanets. We can therefore use their atmospheres as proxies for planetary atmospheres, testing our understanding of physics and chemistry for these complex, cool worlds. At these cold temperatures, their atmospheres are cold enough for water clouds to form, and chemical timescales increase, increasing the likelihood of disequilibrium chemistry compared to warmer classes of planets. JWST observations are revolutionizing the characterization of these worlds with high signal-to-noise, moderate resolution near- and mid-infrared spectra. The spectra have been used to measure the abundances of prominent species like water, methane, and ammonia; species that trace chemical reactions like carbon monoxide; and even isotopologues of carbon monoxide and ammonia. Here, we present atmospheric retrieval results using both published fixed-slit (GTO program 1230) and new averaged time series observations (GO program 2327) of the coldest known Y dwarf, WISE 0855-0714 (using NIRSpec G395M spectra), which has an effective temperature of sim 264 K. We present a detection of deuterium in an atmosphere outside of the solar system via a relative measurement of deuterated methane (CH_{3}D) and standard methane. From this, we infer the D/H ratio of a substellar object outside the solar system for the first time. We also present a well-constrained part-per-billion abundance of phosphine (PH_{3}). We discuss our interpretation of these results and the implications for brown dwarf and giant exoplanet formation and evolution.

Hyperspectral images (HSIs) often suffer from diverse and unknown degradations during imaging, leading to severe spectral and spatial distortions. Existing HSI restoration methods typically rely on specific degradation assumptions, limiting their effectiveness in complex scenarios. In this paper, we propose MP-HSIR, a novel multi-prompt framework that effectively integrates spectral, textual, and visual prompts to achieve universal HSI restoration across diverse degradation types and intensities. Specifically, we develop a prompt-guided spatial-spectral transformer, which incorporates spatial self-attention and a prompt-guided dual-branch spectral self-attention. Since degradations affect spectral features differently, we introduce spectral prompts in the local spectral branch to provide universal low-rank spectral patterns as prior knowledge for enhancing spectral reconstruction. Furthermore, the text-visual synergistic prompt fuses high-level semantic representations with fine-grained visual features to encode degradation information, thereby guiding the restoration process. Extensive experiments on 9 HSI restoration tasks, including all-in-one scenarios, generalization tests, and real-world cases, demonstrate that MP-HSIR not only consistently outperforms existing all-in-one methods but also surpasses state-of-the-art task-specific approaches across multiple tasks. The code and models will be released at https://github.com/ZhehuiWu/MP-HSIR.

The recent surge in contrast-based graph self-supervised learning has prominently featured an intensified exploration of spectral cues. Spectral augmentation, which involves modifying a graph's spectral properties such as eigenvalues or eigenvectors, is widely believed to enhance model performance. However, an intriguing paradox emerges, as methods grounded in seemingly conflicting assumptions regarding the spectral domain demonstrate notable enhancements in learning performance. Through extensive empirical studies, we find that simple edge perturbations - random edge dropping for node-level and random edge adding for graph-level self-supervised learning - consistently yield comparable or superior performance while being significantly more computationally efficient. This suggests that the computational overhead of sophisticated spectral augmentations may not justify their practical benefits. Our theoretical analysis of the InfoNCE loss bounds for shallow GNNs further supports this observation. The proposed insights represent a significant leap forward in the field, potentially refining the understanding and implementation of graph self-supervised learning.

Let F be a graph, and let B_r(F) be the class of r-uniform Berge-F hypergraphs. In this paper, we establish a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure through walks. Based on the relationship, we give a spectral asymptotic bound for B_{r}(C_3)-free linear r-uniform hypergraphs and upper bounds for the spectral radii of B_{r}(K_{2,t})-free or {B_{r}(K_{s,t}),B_{r}(C_{3})}-free linear r-uniform hypergraphs, where C_{3} and K_{s,t} are respectively the triangle and the complete bipartite graph with one part having s vertices and the other part having t vertices. Our work implies an upper bound for the number of edges of {B_{r}(K_{s,t}),B_{r}(C_{3})}-free linear r-uniform hypergraphs and extends some of the existing research on (spectral) extremal problems of hypergraphs.

Machine learning models in astrophysics are often limited in scope and cannot adapt to data from new instruments or tasks. We introduce SpectraFM, a Transformer-based foundation model architecture that can be pre-trained on stellar spectra from any wavelength range and instrument. SpectraFM excels in generalization by combining flexibility with knowledge transfer from pre-training, allowing it to outperform traditional machine learning methods, especially in scenarios with limited training data. Our model is pre-trained on approximately 90k examples of synthetic spectra to predict the chemical abundances (Fe, Mg, O), temperature, and specific gravity of stars. We then fine-tune the model on real spectra to adapt it to observational data before fine-tuning it further on a restricted 100-star training set in a different wavelength range to predict iron abundance. Despite a small iron-rich training set of real spectra, transfer learning from the synthetic spectra pre-training enables the model to perform well on iron-poor stars. In contrast, a neural network trained from scratch fails at this task. We investigate the Transformer attention mechanism and find that the wavelengths receiving attention carry physical information about chemical composition. By leveraging the knowledge from pre-training and its ability to handle non-spectra inputs, SpectraFM reduces the need for large training datasets and enables cross-instrument and cross-domain research. Its adaptability makes it well-suited for tackling emerging challenges in astrophysics, like extracting insights from multi-modal datasets.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Time-domain surveys such as the Zwicky Transient Facility (ZTF) have opened a new frontier in the discovery and characterization of transients. While photometric light curves provide broad temporal coverage, spectroscopic observations remain crucial for physical interpretation and source classification. However, existing spectral analysis methods -- often reliant on template fitting or parametric models -- are limited in their ability to capture the complex and evolving spectra characteristic of such sources, which are sometimes only available at low resolution. In this work, we introduce SpectraNet, a deep convolutional neural network designed to learn robust representations of optical spectra from transients. Our model combines multi-scale convolution kernels and multi-scale pooling to extract features from preprocessed spectra in a hierarchical and interpretable manner. We train and validate SpectraNet on low-resolution time-series spectra obtained from the Spectral Energy Distribution Machine (SEDM) and other instruments, demonstrating state-of-the-art performance in classification. Furthermore, in redshift prediction tasks, SpectraNet achieves a root mean squared relative redshift error of 0.02, highlighting its effectiveness in precise regression tasks as well.

The information recoverable from galaxy spectra depends fundamentally on spectral resolution, yet assembling large samples at high resolution remains observationally expensive. We present a deep-learning framework for spectral super-resolution that enhances low-resolution galaxy spectra by a factor of sim10 in resolving power (Rsim100 to Rsim1000). The model is trained on 1,187 paired JWST/NIRSpec observations from the JADES program, where low-resolution prism spectra are matched with medium-resolution grating spectra (G140M, G235M, G395M) combined into a unified reference covering 1-5 μm. Our three-stage architecture performs an initial super-resolution, infers the redshift from the coarse reconstruction, and then applies a physics-informed residual refinement that uses attention across emission-line tokens to learn inter-line relationships and predict parametric line profiles, alongside a convolutional branch for continuum corrections. Evaluated on a 20% held-out sample, the model achieves noise-limited residuals over most of the spectral range and systematically improves the signal-to-noise ratio of key diagnostic lines including [OII], Hβ, [OIII], and Hα, often by factors of several. The super-resolved spectra successfully deblend features that are entirely unresolved at prism resolution, such as the [OIII] λlambda4959,5007 doublet and Hβ. As a proof of concept using JWST data, this approach is readily extensible to the low-resolution grism spectroscopy that will be delivered by Euclid and the Roman Space Telescope, potentially enabling population-level diagnostics across millions of galaxy spectra that would otherwise be inaccessible at grism resolution.

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (HSS), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, HSS yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

Post-hoc image explanations usually show where a model looks using spatial heatmaps or indicate which channels matter using global channel scores. These separate views are limiting for multispectral data because channel relevance is often spatially localized and physically meaningful. We introduce Spectral-Spatial Interpretation (SSI), a full-grid attribution method over position-channel players (g,c). For each spatial position, SSI fixes the observed surrounding context, defines a conditional game over the channels at that position, and applies the Shapley value to this local game. The result is a full spectral-spatial attribution matrix rather than a single heatmap or a global channel ranking. SSI has a clear local interpretation. It satisfies Shapley fairness within each position, and aggregating its channel attributions exactly recovers the position-level contextual contrast obtained by replacing that position with the baseline. SSI also differs from context-averaged Owen-style hierarchical accounting, which uses the same position-channel grouping but averages over external spatial coalitions. On HLS Burn Scar, SSI outperforms an MC-Owen estimator across retained attribution metrics while using only about 6% of its evaluation budget. Across CUB-200, EuroSAT, and HLS Burn Scar under both per-channel mean and zero baselines, SSI achieves the best joint deletion and insertion AUC over dense, flat, and rank-1 baselines, yields the strongest spectral hit rates and channel deletion, and leads spatial localization on both annotated datasets. Code is available at https://github.com/AtheavenMa/Spectral-Spatial-Interpretation.

The foundation model has recently garnered significant attention due to its potential to revolutionize the field of visual representation learning in a self-supervised manner. While most foundation models are tailored to effectively process RGB images for various visual tasks, there is a noticeable gap in research focused on spectral data, which offers valuable information for scene understanding, especially in remote sensing (RS) applications. To fill this gap, we created for the first time a universal RS foundation model, named SpectralGPT, which is purpose-built to handle spectral RS images using a novel 3D generative pretrained transformer (GPT). Compared to existing foundation models, SpectralGPT 1) accommodates input images with varying sizes, resolutions, time series, and regions in a progressive training fashion, enabling full utilization of extensive RS big data; 2) leverages 3D token generation for spatial-spectral coupling; 3) captures spectrally sequential patterns via multi-target reconstruction; 4) trains on one million spectral RS images, yielding models with over 600 million parameters. Our evaluation highlights significant performance improvements with pretrained SpectralGPT models, signifying substantial potential in advancing spectral RS big data applications within the field of geoscience across four downstream tasks: single/multi-label scene classification, semantic segmentation, and change detection.

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.

Elucidating molecular structures from spectra is a foundational problem in chemical and materials characterization, yet remains challenging due to spectral ambiguity and the vast molecular space. Although recent diffusion-based generators show strong promise for spectra-conditioned elucidation, existing methods struggle to learn robust spectra-structure relationships from limited paired data when relying solely on global spectral representation. Moreover, the repeated full sampling inference strategy incurs substantial computation overhead. To address these limitations, we propose MAST, a Motif-Augmented diffusion framework with Search Tree, for joint 2D-3D spectroscopic molecular structure elucidation. MAST introduces explicit, interpretable motif priors as intermediate evidences throughout denoising, reducing conditional ambiguity and facilitating spectra-conditioned optimization. We further cast diffusion sampling as reward-guided tree search to prioritize high-reward denoising trajectories, yielding a compact set of spectra-consistent candidates under limited budgets. On the QM9S multi-spectra benchmark, MAST achieves 94.89\% exact recovery and improves 3D fidelity, while preserving high chemical validity and stability. Code is available at https://github.com/Jia040223/MAST.

Image Retrieval aims to retrieve corresponding images based on a given query. In application scenarios, users intend to express their retrieval intent through various query styles. However, current retrieval tasks predominantly focus on text-query retrieval exploration, leading to limited retrieval query options and potential ambiguity or bias in user intention. In this paper, we propose the Style-Diversified Query-Based Image Retrieval task, which enables retrieval based on various query styles. To facilitate the novel setting, we propose the first Diverse-Style Retrieval dataset, encompassing diverse query styles including text, sketch, low-resolution, and art. We also propose a light-weighted style-diversified retrieval framework. For various query style inputs, we apply the Gram Matrix to extract the query's textural features and cluster them into a style space with style-specific bases. Then we employ the style-init prompt tuning module to enable the visual encoder to comprehend the texture and style information of the query. Experiments demonstrate that our model, employing the style-init prompt tuning strategy, outperforms existing retrieval models on the style-diversified retrieval task. Moreover, style-diversified queries~(sketch+text, art+text, etc) can be simultaneously retrieved in our model. The auxiliary information from other queries enhances the retrieval performance within the respective query.

Multi-hop question answering in retrieval-augmented gener?ation (RAG) often benefits from retrieving beyond the few candidates that will finally be read: narrow retrieval can miss an indispensable hop, while expanded retrieval introduces topical distractors. This challenge is not tied to a particu?lar knowledge-base format. Candidate pools may come from standalone retrievers, standard RAG backends, or graph-based retrieval pipelines. What is needed is a query-aware selection layer that can use relational structure to filter candidates be?fore generation. PAGE-RAG addresses this setting by using a graph as a temporary selection structure, rather than assum?ing a graph-structured knowledge base. It builds a query-local graph over retrieved candidates, records why candidates are connected, and treats each connection as a support hypothe?sis rather than support itself. We identify the resulting failure mode as a connectivity-support gap: connected candidates do not necessarily support the answer. We propose PAGE-RAG, a Provenance-Aware Graph Evidence promotion method that scores candidate paths with relevance, source-tracing meta?data, specificity, hubness, noise, and coherence signals, and applies minimal sufficient selection to promote supporting facts into a compact reader context. PAGE-RAG can serve as a complete retrieval-to-reading pipeline, and the same promo?tion stage can be inserted after existing retrieval or RAG sys?tems without replacing their upstream retrieval logic. Across three multi-hop QA benchmarks under the same final bud?get, PAGE-RAG improves support F1 and answer F1 by 10.4 and 3.3 points on a weighted average over a strong retriever. As a plug-in, PAGE-RAG further improves all reported RAG backends, including reasoning-oriented, compression-based, graph-based, and document/chunk-level systems.

Query suggestion, a technique widely adopted in information retrieval, enhances system interactivity and the browsing experience of document collections. In cross-modal retrieval, many works have focused on retrieving relevant items from natural language queries, while few have explored query suggestion solutions. In this work, we address query suggestion in cross-modal retrieval, introducing a novel task that focuses on suggesting minimal textual modifications needed to explore visually consistent subsets of the collection, following the premise of ''Maybe you are looking for''. To facilitate the evaluation and development of methods, we present a tailored benchmark named CroQS. This dataset comprises initial queries, grouped result sets, and human-defined suggested queries for each group. We establish dedicated metrics to rigorously evaluate the performance of various methods on this task, measuring representativeness, cluster specificity, and similarity of the suggested queries to the original ones. Baseline methods from related fields, such as image captioning and content summarization, are adapted for this task to provide reference performance scores. Although relatively far from human performance, our experiments reveal that both LLM-based and captioning-based methods achieve competitive results on CroQS, improving the recall on cluster specificity by more than 115% and representativeness mAP by more than 52% with respect to the initial query. The dataset, the implementation of the baseline methods and the notebooks containing our experiments are available here: https://paciosoft.com/CroQS-benchmark/

Hyperspectral image (HSI) classification is widely used for the analysis of remotely sensed images. Hyperspectral imagery includes varying bands of images. Convolutional Neural Network (CNN) is one of the most frequently used deep learning based methods for visual data processing. The use of CNN for HSI classification is also visible in recent works. These approaches are mostly based on 2D CNN. Whereas, the HSI classification performance is highly dependent on both spatial and spectral information. Very few methods have utilized the 3D CNN because of increased computational complexity. This letter proposes a Hybrid Spectral Convolutional Neural Network (HybridSN) for HSI classification. Basically, the HybridSN is a spectral-spatial 3D-CNN followed by spatial 2D-CNN. The 3D-CNN facilitates the joint spatial-spectral feature representation from a stack of spectral bands. The 2D-CNN on top of the 3D-CNN further learns more abstract level spatial representation. Moreover, the use of hybrid CNNs reduces the complexity of the model compared to 3D-CNN alone. To test the performance of this hybrid approach, very rigorous HSI classification experiments are performed over Indian Pines, Pavia University and Salinas Scene remote sensing datasets. The results are compared with the state-of-the-art hand-crafted as well as end-to-end deep learning based methods. A very satisfactory performance is obtained using the proposed HybridSN for HSI classification. The source code can be found at https://github.com/gokriznastic/HybridSN.

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method from the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly.

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to address both problems by analyzing the eigenvalue structure of hidden activations. The first contribution, EigenTrack, is a real-time method for detecting hallucinations and out-of-distribution behavior in language and vision-language models using spectral features and their temporal dynamics. The second contribution, RMT-KD, is a principled compression method that identifies informative spectral components and applies iterative knowledge distillation to produce compact and efficient models while preserving accuracy. Together, these results show that spectral statistics provide interpretable and robust signals for monitoring uncertainty and guiding compression in large-scale neural networks.

We present a new method for generating emission spectra from polycyclic aromatic hydrocarbons (PAHs) in arbitrary radiation fields. We utilize the single-photon limit for PAH heating and emission to treat individual photon absorptions as independent events. This allows the construction of a set of single-photon emission "basis spectra" that can be scaled to produce an output emission spectrum given any input heating spectrum. We find that this method produces agreement with PAH emission spectra computed accounting for multi-photon effects to within simeq10% in the 3-20~{rm mu m} wavelength range for radiation fields with intensity U<100. We use this framework to explore the dependence of PAH band ratios on the radiation field spectrum across grain sizes, finding in particular a strong dependence of the 3.3 to 11.2~mum band ratio on radiation field hardness. A Python-based tool and a set of basis spectra that can be used to generate these emission spectra are made publicly available.

Over the past decade, the study of extrasolar planets has evolved rapidly from plain detection and identification to comprehensive categorization and characterization of exoplanet systems and their atmospheres. Atmospheric retrieval, the inverse modeling technique used to determine an exoplanetary atmosphere's temperature structure and composition from an observed spectrum, is both time-consuming and compute-intensive, requiring complex algorithms that compare thousands to millions of atmospheric models to the observational data to find the most probable values and associated uncertainties for each model parameter. For rocky, terrestrial planets, the retrieved atmospheric composition can give insight into the surface fluxes of gaseous species necessary to maintain the stability of that atmosphere, which may in turn provide insight into the geological and/or biological processes active on the planet. These atmospheres contain many molecules, some of them biosignatures, spectral fingerprints indicative of biological activity, which will become observable with the next generation of telescopes. Runtimes of traditional retrieval models scale with the number of model parameters, so as more molecular species are considered, runtimes can become prohibitively long. Recent advances in machine learning (ML) and computer vision offer new ways to reduce the time to perform a retrieval by orders of magnitude, given a sufficient data set to train with. Here we present an ML-based retrieval framework called Intelligent exoplaNet Atmospheric RetrievAl (INARA) that consists of a Bayesian deep learning model for retrieval and a data set of 3,000,000 synthetic rocky exoplanetary spectra generated using the NASA Planetary Spectrum Generator. Our work represents the first ML retrieval model for rocky, terrestrial exoplanets and the first synthetic data set of terrestrial spectra generated at this scale.

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Matryoshka Representation Learning (MRL) is designed to support flexible representation sizes by jointly optimizing nested prefixes. While effective, this design lacks an explicit constraint to ensure that the leading portion provides a suitable compact encoding. To address this, we propose SpecMRL, which reorganizes the feature space to enable more effective prefix readout. Specifically, we extend MRL with a parameter-derived spectral basis organized with feature importance. SpecMRL otherwise follows standard MRL, with prefix readout performed in the learned spectral space. Experiments on MTEB show that SpecMRL outperforms MRL at all evaluated reduced dimensions, with larger gains under more aggressive compression. These results suggest that the learned spectral basis better prioritizes informative directions, enabling more effective representation compression. Notably, SpecMRL extends the performance frontier of MRL, surpassing full-dimensional MRL with only half the embedding dimensions.

Fix a strip width \(ρ>0\), a Diophantine frequency \(α\), an integer \(N\ge2\), and \(λ>1\). For the family \[ V_{\varepsilon,δ}(x) =2λ\cos(2πN x)+\varepsilonδ(x), \] we prove that there is an open prevalent set \(\mathcal P_{\rm strat}\) of real-analytic strip-\(ρ\) perturbations such that every \(δ\in\mathcal P_{\rm strat}\) admits \(\varepsilon_0(δ)>0\) for which \[ gathered Leb\left\{ E\inΣ(V_{\varepsilon,δ},α): ω(α,E;V_{\varepsilon,δ})=s \right\}>0, 0<\varepsilon<\varepsilon_0(δ), \qquad s=1,\ldots,N. gathered \] The proof relates acceleration to the total multiplicity of real zeros of analytic overlap coefficients for first-return cocycles. Under quantitative control of the return products, Poisson integration and Kac normalization identify acceleration with half this multiplicity. A positive analytic dual state gives the finite-volume spectral gaps and Schur curvature needed at the upper spectral edge. Schur variations separate the perturbed maxima, and parameter exclusion preserves \(s\) pairs of simple zeros on a positive-measure spectral set.

Establishing the relationship between 3D structures and the energy states of molecular systems has proven to be a promising approach for learning 3D molecular representations. However, existing methods are limited to modeling the molecular energy states from classical mechanics. This limitation results in a significant oversight of quantum mechanical effects, such as quantized (discrete) energy level structures, which offer a more accurate estimation of molecular energy and can be experimentally measured through energy spectra. In this paper, we propose to utilize the energy spectra to enhance the pre-training of 3D molecular representations (MolSpectra), thereby infusing the knowledge of quantum mechanics into the molecular representations. Specifically, we propose SpecFormer, a multi-spectrum encoder for encoding molecular spectra via masked patch reconstruction. By further aligning outputs from the 3D encoder and spectrum encoder using a contrastive objective, we enhance the 3D encoder's understanding of molecules. Evaluations on public benchmarks reveal that our pre-trained representations surpass existing methods in predicting molecular properties and modeling dynamics.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

In the domain of semantic parsing, significant progress has been achieved in Text-to-SQL and question-answering tasks, both of which focus on extracting information from data sources in their native formats. However, the inherent constraints of their formal meaning representations, such as SQL programming language or basic logical forms, hinder their ability to analyze data from various perspectives, such as conducting statistical analyses. To address this limitation and inspire research in this field, we design SIGMA, a new dataset for Text-to-Code semantic parsing with statistical analysis. SIGMA comprises 6000 questions with corresponding Python code labels, spanning across 160 databases. Half of the questions involve query types, which return information in its original format, while the remaining 50% are statistical analysis questions, which perform statistical operations on the data. The Python code labels in our dataset cover 4 types of query types and 40 types of statistical analysis patterns. We evaluated the SIGMA dataset using three different baseline models: LGESQL, SmBoP, and SLSQL. The experimental results show that the LGESQL model with ELECTRA outperforms all other models, achieving 83.37% structure accuracy. In terms of execution accuracy, the SmBoP model, when combined with GraPPa and T5, reaches 76.38%.

We present a probabilistic data-driven weather model capable of providing an ensemble of high spatial resolution realizations of 87 variables at arbitrary forecast length and ensemble size. The model uses a stretched grid, dedicating 2.5 km resolution to a region of interest, and 31 km resolution elsewhere. Based on a stochastic encoder-decoder architecture, the model is trained using a loss function based on the Continuous Ranked Probability Score (CRPS) evaluated point-wise in real and spectral space. The spectral loss components is shown to be necessary to create fields that are spatially coherent. The model is compared to high-resolution operational numerical weather prediction forecasts from the MetCoOp Ensemble Prediction System (MEPS), showing competitive forecasts when evaluated against observations from surface weather stations. The model produced fields that are more spatially coherent than mean squared error based models and CRPS based models without the spectral component in the loss.

In this paper, we present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Challenges in adapting transformer for HSI arise from the capabilities to tackle existing limitations of CNN-based methods in capturing the global and local spatial-spectral correlations while maintaining efficiency and flexibility. To address these issues, we introduce a hybrid approach that combines the advantages of both models with a Spatial-Spectral Separable Convolution (S3Conv), Guided Spectral Self-Attention (GSSA), and Self-Modulated Feed-Forward Network (SM-FFN). Our S3Conv works as a lightweight alternative to 3D convolution, which extracts more spatial-spectral correlated features while keeping the flexibility to tackle HSIs with an arbitrary number of bands. These features are then adaptively processed by GSSA which per-forms 3D self-attention across the spectral bands, guided by a set of learnable queries that encode the spectral signatures. This not only enriches our model with powerful capabilities for identifying global spectral correlations but also maintains linear complexity. Moreover, our SM-FFN proposes the self-modulation that intensifies the activations of more informative regions, which further strengthens the aggregated features. Extensive experiments are conducted on various datasets under both simulated and real-world noise, and it shows that our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead. Code is at https: //github.com/Zeqiang-Lai/HSDT.

Vision-language models for Earth observation (EO) typically rely on the visual spectrum of data as the only model input, thus failing to leverage the rich spectral information available in the multispectral channels recorded by satellites. Therefore, in this paper, we introduce Llama3-MS-CLIP, the first vision-language model pre-trained with contrastive learning on a large-scale multispectral dataset and report on the performance gains due to the extended spectral range. Furthermore, we present the largest-to-date image-caption dataset for multispectral data, consisting of one million Sentinel-2 samples and corresponding textual descriptions generated with Llama3-LLaVA-Next and Overture Maps data. We develop a scalable captioning pipeline, which is validated by domain experts. We evaluate Llama3-MS-CLIP on multispectral zero-shot image classification and retrieval using three datasets of varying complexity. Our results demonstrate that Llama3-MS-CLIP significantly outperforms other RGB-based approaches, improving classification accuracy by 6.77% on average and retrieval performance by 4.63% mAP compared to the second-best model. Our results emphasize the relevance of multispectral vision-language learning. We release the image-caption dataset, code, and model weights under an open-source license.

Training Large Language Models (LLMs) at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data. By formalizing the connection between Zipfian statistics and random matrix theory, we prove that the power-law decay in the singular value spectra of embeddings is a fundamental requisite for semantic encoding. We derive theoretical bounds showing that uniform quantization introduces a noise floor that disproportionately truncates this spectral tail, which induces spectral flattening and a strictly provable increase in the stable rank of representations. Empirical validation across diverse architectures including GPT-2 and TinyLlama corroborates that this geometric degradation precipitates representational collapse. This work not only quantifies the spectral sensitivity of LLMs but also establishes spectral fidelity as a necessary condition for stable low-bit optimization.

Small-molecule identification from tandem mass spectrometry (MS/MS) remains a bottleneck in untargeted settings where spectral libraries are incomplete. While deep learning offers a solution, current approaches typically fall into two extremes: explicit generative models that construct molecular graphs atom-by-atom, or joint contrastive models that learn cross-modal subspaces from scratch. We introduce SpecBridge, a novel implicit alignment framework that treats structure identification as a geometric alignment problem. SpecBridge fine-tunes a self-supervised spectral encoder (DreaMS) to project directly into the latent space of a frozen molecular foundation model (ChemBERTa), and then performs retrieval by cosine similarity to a fixed bank of precomputed molecular embeddings. Across MassSpecGym, Spectraverse, and MSnLib benchmarks, SpecBridge improves top-1 retrieval accuracy by roughly 20-25% relative to strong neural baselines, while keeping the number of trainable parameters small. These results suggest that aligning to frozen foundation models is a practical, stable alternative to designing new architectures from scratch. The code for SpecBridge is released at https://github.com/HassounLab/SpecBridge.

Due to the limited generalization and interpretability of deep learning classifiers, The final vetting of rare celestial object candidates still relies on expert visual inspection--a manually intensive process. In this process, astronomers leverage specialized tools to analyze spectra and construct reliable catalogs. However, this practice has become the primary bottleneck, as it is fundamentally incapable of scaling with the data deluge from modern spectroscopic surveys. To bridge this gap, we propose Spec-o3, a tool-augmented vision-language agent that performs astronomer-aligned spectral inspection via interleaved multimodal chain-of-thought reasoning. Spec-o3 is trained with a two-stage post-training recipe: cold-start supervised fine-tuning on expert inspection trajectories followed by outcome-based reinforcement learning on rare-type verification tasks. Evaluated on five rare-object identification tasks from LAMOST, Spec-o3 establishes a new State-of-the-Art, boosting the macro-F1 score from 28.3 to 76.5 with a 7B parameter base model and outperforming both proprietary VLMs and specialized deep models. Crucially, the agent demonstrates strong generalization to unseen inspection tasks across survey shifts (from LAMOST to SDSS/DESI). Expert evaluations confirm that its reasoning traces are coherent and physically consistent, supporting transparent and trustworthy decision-making. Code, data, and models are available at https://github.com/Maxwell-Jia/spec-o3{Project HomePage}.

This paper presents the first numerical realization of Suzuki's Weil-Quadratic-Form operator, a candidate for the Hilbert--Pólya program linking spectral positivity to the Riemann Hypothesis (RH). Suzuki's 2026 construction was purely theoretical; here, the operator is instantiated via P1 finite-element discretization and Richardson extrapolation. Key results include: (R1) In the prime-free regime, the spectrum follows a closed Archimedean law A_k(a) = log(1/a) + log(k-2) + B_0 + O(a), with B_0 = log q - 2log 2, confirmed to 30-digit precision. (R2) A Mellin double-pole argument proves the head coefficient B(ν) and shows B_0 depends only on the conductor q, independent of the Archimedean parameter. (R2b) The degree d of an L-function appears directly as the logarithmic slope of the spectrum. (R3) Total spectral intensity follows the prime number theorem, S(a) sim (2a)^3/6. (R4) Nontrivial zeros are not eigenvalues but occur in the explicit-formula error term of the prime symbol. (R5) The best-match line σ^*(a) descends toward the critical line. (R6) Weil's positivity criterion is realized in operator form: bounded residual growth corresponds to all zeros on the line, while an injected off-line zero causes exponential blow-up. (R7) The lowest eigenvalue λ_1(a) is strictly positive, decays superexponentially, and passes smoothly through the first prime threshold. (R8) The characteristic function W(a,0;z) is computed for the first time, with all zeros confirmed real. (R9) Indirect traces of GUE statistics appear in the moment structure, even where direct detection is blocked. The authors emphasize that this work does not prove RH. All results are Archimedean and universal, with significance lying in the faithful numerical realization of classical identities rather than new arithmetic.

Large Language Models (LLMs) have shown improved generation performance through retrieval-augmented generation (RAG) following the retriever-reader paradigm, which supplements model inputs with externally retrieved knowledge. However, prior work often evaluates RAG holistically, assessing the retriever and reader jointly, making it difficult to isolate the true contribution of retrieval, particularly given the prompt sensitivity of LLMs used as readers. We introduce Spectrum Projection Score (SPS), a lightweight, supervision-free metric that allows the reader to gauge the semantic alignment of a retrieved summary with its hidden representation by comparing the area formed by generated tokens from the summary, and the principal directions of subspace in the reader and to measure the relevance. Building on SPS we present xCompress, an inference time controller framework that dynamically samples, ranks, and compresses retrieval summary candidates. Extensive experiments on five QA benchmarks with four open source LLMs show that SPS not only enhances performance across a range of tasks but also provides a principled perspective on the interaction between retrieval and generation.

Nuclear Magnetic Resonance (NMR) spectroscopy is fundamental for molecular structure elucidation, yet interpreting spectra at scale remains time-consuming and highly expertise-dependent. While recent spectrum-as-language modeling and retrieval-based methods have shown promise, they rely heavily on large corpora of computed spectra and exhibit notable performance drops when applied to experimental measurements. To address these issues, we build NMRSpec, a large-scale corpus of experimental ^1H and ^{13}C spectra mined from chemical literature, and propose NMRTrans, which models spectra as unordered peak sets and aligns the model's inductive bias with the physical nature of NMR. To our best knowledge, NMRTrans is the first NMR Transformer trained solely on large-scale experimental spectra and achieves state-of-the-art performance on experimental benchmarks, improving Top-10 Accuracy over the strongest baseline by +17.82 points (61.15% vs. 43.33%), and underscoring the importance of experimental data and structure-aware architectures for reliable NMR structure elucidation.

On-board processing of hyperspectral data with machine learning models would enable unprecedented amount of autonomy for a wide range of tasks, for example methane detection or mineral identification. This can enable early warning system and could allow new capabilities such as automated scheduling across constellations of satellites. Classical methods suffer from high false positive rates and previous deep learning models exhibit prohibitive computational requirements. We propose fast and accurate machine learning architectures which support end-to-end training with data of high spectral dimension without relying on hand-crafted products or spectral band compression preprocessing. We evaluate our models on two tasks related to hyperspectral data processing. With our proposed general architectures, we improve the F1 score of the previous methane detection state-of-the-art models by 27% on a newly created synthetic dataset and by 13% on the previously released large benchmark dataset. We also demonstrate that training models on the synthetic dataset improves performance of models finetuned on the dataset of real events by 6.9% in F1 score in contrast with training from scratch. On a newly created dataset for mineral identification, our models provide 3.5% improvement in the F1 score in contrast to the default versions of the models. With our proposed models we improve the inference speed by 85% in contrast to previous classical and deep learning approaches by removing the dependency on classically computed features. With our architecture, one capture from the EMIT sensor can be processed within 30 seconds on realistic proxy of the ION-SCV 004 satellite.

Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Most existing image datasets focus on trichromatic intensity images to mimic human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although spectro-polarimetric datasets exist, these datasets have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets: trichromatic Stokes images and hyperspectral Stokes images. These novel datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research. Dataset and code will be publicly available.

Attempts to probe the atmospheres of rocky planets around M dwarfs present both promise and peril. While their favorable planet-to-star radius ratios enable searches for even thin secondary atmospheres, their high activity levels and high-energy outputs threaten atmosphere survival. Here, we present the 0.6--2.85\,mum transmission spectrum of the 1.1\,rm R_oplus, sim340\,K rocky planet TRAPPIST-1\,c obtained over two JWST NIRISS/SOSS transit observations. Each of the two spectra displays 100--500\,ppm signatures of stellar contamination. Despite being separated by 367\,days, the retrieved spot and faculae properties are consistent between the two visits, resulting in nearly identical transmission spectra. Jointly retrieving for stellar contamination and a planetary atmosphere reveals that our spectrum can rule out hydrogen-dominated, lesssim300times solar metallicity atmospheres with effective surface pressures down to 10\,mbar at the 3-sigma level. For high-mean molecular weight atmospheres, where O_2 or N_2 is the background gas, our spectrum disfavors partial pressures of more than sim10\,mbar for H_2O, CO, NH_3 and CH_4 at the 2-sigma level. Similarly, under the assumption of a 100\% H_2O, NH_3, CO, or CH_4 atmosphere, our spectrum disfavors thick, >1\,bar atmospheres at the 2-sigma level. These non-detections of spectral features are in line with predictions that even heavier, CO_2-rich, atmospheres would be efficiently lost on TRAPPIST-1\,c given the cumulative high-energy irradiation experienced by the planet. Our results further stress the importance of robustly accounting for stellar contamination when analyzing JWST observations of exo-Earths around M dwarfs, as well as the need for high-fidelity stellar models to search for the potential signals of thin secondary atmospheres.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4\%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

Multi-spectral imagery plays a crucial role in diverse Remote Sensing applications including land-use classification, environmental monitoring and urban planning. These images are widely adopted because their additional spectral bands correlate strongly with physical materials on the ground, such as ice, water, and vegetation. This allows for more accurate identification, and their public availability from missions, such as Sentinel-2 and Landsat, only adds to their value. Currently, the automatic analysis of such data is predominantly managed through machine learning models specifically trained for multi-spectral input, which are costly to train and support. Furthermore, although providing a lot of utility for Remote Sensing, such additional inputs cannot be used with powerful generalist large multimodal models, which are capable of solving many visual problems, but are not able to understand specialized multi-spectral signals. To address this, we propose a training-free approach which introduces new multi-spectral data in a Zero-Shot-only mode, as inputs to generalist multimodal models, trained on RGB-only inputs. Our approach leverages the multimodal models' understanding of the visual space, and proposes to adapt to inputs to that space, and to inject domain-specific information as instructions into the model. We exemplify this idea with the Gemini2.5 model and observe strong Zero-Shot performance gains of the approach on popular Remote Sensing benchmarks for land cover and land use classification and demonstrate the easy adaptability of Gemini2.5 to new inputs. These results highlight the potential for geospatial professionals, working with non-standard specialized inputs, to easily leverage powerful multimodal models, such as Gemini2.5, to accelerate their work, benefiting from their rich reasoning and contextual capabilities, grounded in the specialized sensor data.

Hyperspectral sensors have enjoyed widespread use in the realm of remote sensing; however, they must be adapted to a format in which they can be operated onboard mobile robots. In this work, we introduce a first-of-its-kind system architecture with snapshot hyperspectral cameras and point spectrometers to efficiently generate composite datacubes from a robotic base. Our system collects and registers datacubes spanning the visible to shortwave infrared (660-1700 nm) spectrum while simultaneously capturing the ambient solar spectrum reflected off a white reference tile. We collect and disseminate a large dataset of more than 500 labeled datacubes from on-road and off-road terrain compliant with the ATLAS ontology to further the integration and demonstration of hyperspectral imaging (HSI) as beneficial in terrain class separability. Our analysis of this data demonstrates that HSI is a significant opportunity to increase understanding of scene composition from a robot-centric context. All code and data are open source online: https://river-lab.github.io/hyper_drive_data

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Deep spectrophotometry has proved to be a fundamental tool to improve our knowledge on the chemical content of planetary nebulae. With the arrival of very efficient spectrographs installed in the largest ground-based telescopes, outstanding spectra have been obtained. These data are essential to constrain state-of-the-art nucleosynthesis models in asymptotic giant branch stars and, in general, to understand the chemical evolution of our Galaxy. In this paper we review the last advances on the chemical composition of the ionized gas in planetary nebulae based on faint emission lines observed through very deep spectrophotometric data.

Hyperspectral pansharpening has received much attention in recent years due to technological and methodological advances that open the door to new application scenarios. However, research on this topic is only now gaining momentum. The most popular methods are still borrowed from the more mature field of multispectral pansharpening and often overlook the unique challenges posed by hyperspectral data fusion, such as i) the very large number of bands, ii) the overwhelming noise in selected spectral ranges, iii) the significant spectral mismatch between panchromatic and hyperspectral components, iv) a typically high resolution ratio. Imprecise data modeling especially affects spectral fidelity. Even state-of-the-art methods perform well in certain spectral ranges and much worse in others, failing to ensure consistent quality across all bands, with the risk of generating unreliable results. Here, we propose a hyperspectral pansharpening method that explicitly addresses this problem and ensures uniform spectral quality. To this end, a single lightweight neural network is used, with weights that adapt on the fly to each band. During fine-tuning, the spatial loss is turned on and off to ensure a fast convergence of the spectral loss to the desired level, according to a hysteresis-like dynamic. Furthermore, the spatial loss itself is appropriately redefined to account for nonlinear dependencies between panchromatic and spectral bands. Overall, the proposed method is fully unsupervised, with no prior training on external data, flexible, and low-complexity. Experiments on a recently published benchmarking toolbox show that it ensures excellent sharpening quality, competitive with the state-of-the-art, consistently across all bands. The software code and the full set of results are shared online on https://github.com/giu-guarino/rho-PNN.

The reciprocal distance Laplacian matrix of a connected graph G is defined as RD^L(G)=RT(G)-RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Since RD^L(G) is a real symmetric matrix, we denote its eigenvalues as λ_1(RD^L(G))geq λ_2(RD^L(G))geq dots geq λ_n(RD^L(G)). The largest eigenvalue λ_1(RD^L(G)) of RD^L(G) is called the reciprocal distance Laplacian spectral radius. In this article, we prove that the multiplicity of n as a reciprocal distance Laplacian eigenvalue of RD^L(G) is exactly one less than the number of components in the complement graph G of G. We show that the class of the complete bipartite graphs maximize the reciprocal distance Laplacian spectral radius among all the bipartite graphs with n vertices. Also, we show that the star graph S_n is the unique graph having the maximum reciprocal distance Laplacian spectral radius in the class of trees with n vertices. We determine the reciprocal distance Laplacian spectrum of several well known graphs. We prove that the complete graph K_n, K_n-e, the star S_n, the complete balanced bipartite graph K_{n{2},n{2}} and the complete split graph CS(n,α) are all determined from the RD^L-spectrum.

There will be a paradigm shift in chemical and biological research, to be enabled by autonomous, closed-loop, real-time self-directed decision-making experimentation. Spectrum-to-structure correlation, which is to elucidate molecular structures with spectral information, is the core step in understanding the experimental results and to close the loop. However, current approaches usually divide the task into either database-dependent retrieval and database-independent generation and neglect the inherent complementarity between them. In this study, we proposed Vib2Mol, a general deep learning model designed to flexibly handle diverse spectrum-to-structure tasks according to the available prior knowledge by bridging the retrieval and generation. It achieves state-of-the-art performance, even for the most demanding Raman spectra, over previous models in predicting reaction products and sequencing peptides as well as analyzing experimental spectra and integrating multi-modal spectral data. Vib2Mol enables vibrational spectroscopy a real-time guide for autonomous scientific discovery workflows.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

Molecular line lists disagree at a level that measurably shifts retrieved C/O, so retrievals conditioned on a single list omit a dominant systematic from their error bars. Classical marginalization re-runs a full retrieval under K opacity realizations per object. We move that cost into simulation: while generating the training set we randomize opacities (smooth multiplicative Fourier fields in logν plus a discrete line-list mixture, under a deliberately broad prior informed by measured inter-list differences), so a neural posterior estimator learns an already-marginalized posterior. Conceptually, this is the amortized analogue of repeating a conventional retrieval under many plausible opacity realizations and averaging the resulting posteriors. On perturbed held-out spectra (n=2048) a standard NPE covers nominal 90% C/O intervals 43.3% of the time against 82.4% for a compute-matched marginalized network; three-seed control ensembles reach 93.2% on clean data but 61.4% under perturbation, against 89.4% marginalized, isolating the deficit as opacity-induced (TARP joint expected-coverage deviation 0.005 against 0.035). An axis ablation traces the gain to the continuous field (45.4% for the discrete swaps alone, 79.3% for the field alone). Applying the 105 real bad-pixel masks with median filling then collapsed the ensemble's C/O coverage from 0.901 to 0.479; retraining on the same mask distribution and pooling three such seeds returns a nominal 0.905 C/O and 0.891 overall under the full deployment path, still in simulation (n=1024, same 105 masks), at 0.21 to 0.31 of the prior width. On 105 JWST/G395H spectral products of 13 late-T/Y dwarfs, single marginalized networks bracket the Hood et al. (2024) T8 benchmark C/O where the control excludes it, a consistency check rather than a validation, at 1.6-2.6x wider intervals.

Context: Recent research indicates that Web queries written by software developers are not very successful in retrieving relevant results, performing measurably worse compared to general purpose Web queries. Most approaches up to this point have addressed this problem with software engineering-specific automated query reformulation techniques, which work without developer involvement but are limited by the content of the original query. In other words, these techniques automatically improve the existing query but can not contribute new, previously unmentioned, concepts. Objective: In this paper, we propose a technique to guide software developers in manually improving their own Web search queries. We examine a conversational approach that follows unsuccessful queries with a clarification question aimed at eliciting additional query terms, thus providing to the developer a clear dimension along which the query could be improved. Methods: We describe a set of clarification questions derived from a corpus of software developer queries and a neural approach to recommending them for a newly issued query. Results: Our evaluation indicates that the recommendation technique is accurate, predicting a valid clarification question 80% of the time and outperforms simple baselines, as well as, state-of-the-art Learning To Rank (LTR) baselines. Conclusion: As shown in the experimental results, the described approach is capable at recommending appropriate clarification questions to software developers and considered useful by a sample of developers ranging from novices to experienced professionals.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

This work introduces composed image retrieval to remote sensing. It allows to query a large image archive by image examples alternated by a textual description, enriching the descriptive power over unimodal queries, either visual or textual. Various attributes can be modified by the textual part, such as shape, color, or context. A novel method fusing image-to-image and text-to-image similarity is introduced. We demonstrate that a vision-language model possesses sufficient descriptive power and no further learning step or training data are necessary. We present a new evaluation benchmark focused on color, context, density, existence, quantity, and shape modifications. Our work not only sets the state-of-the-art for this task, but also serves as a foundational step in addressing a gap in the field of remote sensing image retrieval. Code at: https://github.com/billpsomas/rscir

Many real-world questions over business, legal, and scientific corpora are natural-language versions of database-style queries over records latent in text. Existing retrieval-augmented generation (RAG) systems are optimized primarily for semantic relevance, but retrieving plausible passages does not guarantee correct query execution. We introduce QO-Bench, a diagnostic benchmark for query-operator question answering over typed event tuples. The benchmark covers 22,984 news articles and 614 corporate events across 18 query templates, evaluated on 785 questions. Each gold answer is deterministically computed from typed event tuples and scored by recall, with answers matched to the gold tuples by exact match rather than an LLM judge. This design enables operator-level diagnosis such as joins and intersection. We evaluate RAG, ReAct RAG, GraphRAG, and information-extraction-to-SQL under matched conditions, with a long-context oracle ceiling to isolate retrieval failure. A two-axis framework -- index-time preservation versus query-time execution -- predicts where each paradigm fails, and the results bear it out: systems retrieve relevant text but discard the typed values operators need, and the deployable paradigm ranking inverts across operators, with similarity retrieval leading on filter/project and extraction-to-SQL on intersection and counting. Even given the gold evidence, a long-context oracle stays far from saturated, so operator execution -- not retrieval alone -- is a core bottleneck that a stronger answer model does not remove. QO-Bench reframes the goal from passage relevance to query-operator-preserving retrieval.

We discover that large language models exhibit spectral phase transitions in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across 11 models spanning 5 architecture families (Qwen, Pythia, Phi, Llama, DeepSeek-R1), we identify seven core phenomena: (1)~Reasoning Spectral Compression -- 9/11 models show significantly lower α for reasoning (p < 0.05), with larger effects in stronger models; (2)~Instruction Tuning Spectral Reversal -- base models show reasoning α< factual α, while instruction-tuned models reverse this relationship; (3)~Architecture-Dependent Generation Taxonomy -- prompt-to-response shifts partition into expansion, compression, and equilibrium regimes; (4)~Spectral Scaling Law -- α_reasoning propto -0.074 ln N across 4 Qwen base models (R^2 = 0.46); (5)~Token-Level Spectral Cascade -- per-token alpha tracking reveals local synchronization that decays exponentially with layer distance, and is weaker for reasoning than factual tasks; (6)~Reasoning Step Spectral Punctuation -- phase-transition signatures align with reasoning step boundaries; and (7)~Spectral Correctness Prediction -- spectral α alone achieves AUC = 1.000 (Qwen2.5-7B, late layers) and mean AUC = 0.893 across 6 models in predicting correctness before the final answer is generated. Together, these findings establish a comprehensive spectral theory of reasoning in transformers, revealing that the geometry of thought is universal in direction, architecture-specific in dynamics, and predictive of outcome.

Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. However, the prevailing CNN-based approaches have shown limitations in building long-range dependencies and capturing interaction information between spectral features. This results in inadequate utilization of spectral information and artifacts after upsampling. To address this issue, we propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure. Specifically, we first introduce a robust and spectral-friendly similarity metric, \ie, the spectral correlation coefficient of the spectrum (SCC), to replace the original attention matrix and incorporates inductive biases into the model to facilitate training. Built upon it, we further utilize the kernelizable attention technique with theoretical support to form a novel efficient SCC-kernel-based self-attention (ESSA) and reduce attention computation to linear complexity. ESSA enlarges the receptive field for features after upsampling without bringing much computation and allows the model to effectively utilize spatial-spectral information from different scales, resulting in the generation of more natural high-resolution images. Without the need for pretraining on large-scale datasets, our experiments demonstrate ESSA's effectiveness in both visual quality and quantitative results.

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

Quantum kernels are among the most promising methods in quantum machine learning, providing a natural way to embed data into high-dimensional Hilbert spaces via quantum circuits and capturing non-linear relationships in data. Their learning behaviour is governed by the function class they represent, which is formally characterized by the structure of the associated Reproducing Kernel Hilbert Space (RKHS). However, a theoretical characterization of this function class, and of how it depends on the choice of feature map and its hyperparameters, is still lacking. In this work, we focus on the Instantaneous Quantum Polynomial (IQP) feature map and derive a Fourier representation of the associated RKHS generators as finite sums of trigonometric functions evaluated on polynomially transformed input variables, with a finite set of accessible frequencies determined by the circuit construction and scaled by the bandwidth hyperparameter. This representation identifies three bandwidth regimes with qualitatively distinct expressive properties from localised, through multimodal, to periodic. Numerical experiments on synthetic datasets with controlled periodic and multimodal structure, across data dimensions and feature-map configurations, reproduce the three regimes in both supervised classification and unsupervised anomaly detection, benchmarked against a classical Gaussian kernel. These results make the relationship between expressivity and data structure explicit for IQP kernels: expressive power translates into a practical benefit only when the accessible frequencies match with the structure of the data, which provides a criterion for selecting the bandwidth when the periodic or multimodal structure of data is known.

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, plan-net, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.

Retrieval models are often evaluated on partially-annotated datasets. Each query is mapped to a few relevant texts and the remaining corpus is assumed to be irrelevant. As a result, models that successfully retrieve false negatives are punished in evaluation. Unfortunately, completely annotating all texts for every query is not resource efficient. In this work, we show that using partially-annotated datasets in evaluation can paint a distorted picture. We curate D-MERIT, a passage retrieval evaluation set from Wikipedia, aspiring to contain all relevant passages for each query. Queries describe a group (e.g., ``journals about linguistics'') and relevant passages are evidence that entities belong to the group (e.g., a passage indicating that Language is a journal about linguistics). We show that evaluating on a dataset containing annotations for only a subset of the relevant passages might result in misleading ranking of the retrieval systems and that as more relevant texts are included in the evaluation set, the rankings converge. We propose our dataset as a resource for evaluation and our study as a recommendation for balance between resource-efficiency and reliable evaluation when annotating evaluation sets for text retrieval.

Architecture design and optimization are challenging problems in the field of artificial neural networks. Working in this context, we here present SPARCS (SPectral ARchiteCture Search), a novel architecture search protocol which exploits the spectral attributes of the inter-layer transfer matrices. SPARCS allows one to explore the space of possible architectures by spanning continuous and differentiable manifolds, thus enabling for gradient-based optimization algorithms to be eventually employed. With reference to simple benchmark models, we show that the newly proposed method yields a self-emerging architecture with a minimal degree of expressivity to handle the task under investigation and with a reduced parameter count as compared to other viable alternatives.

We propose a novel spectral generative modeling framework for natural language processing that jointly learns a global time varying Fourier dictionary and per token mixing coefficients, replacing the ubiquitous self attention mechanism in transformer architectures. By enforcing reconstruction losses in both the time domain (embedding reconstruction) and the frequency domain (via Short Time Fourier Transform magnitude matching) alongside a standard language modeling objective, and fitting a Gaussian Mixture Model (GMM) prior over the learned mixing vectors, our approach achieves competitive perplexity and generation quality on standard benchmarks such as WikiText2 and Penn Treebank. In contrast to the quadratic computation complexity of self attention, our method operates with linear complexity, delivering substantial efficiency gains. We demonstrate that spectral dictionary models can achieve competitive performance compared to transformer baselines while significantly reducing inference latency and memory footprint, offering a compelling alternative for scalable language modeling.

Hyperspectral target detection (HTD) aims to identify specific materials based on spectral information in hyperspectral imagery and can detect extremely small objects, some of which occupy a smaller than one-pixel area. However, existing HTD methods are developed based on per-pixel binary classification, which limits the feature representation capability for instance-level objects. In this paper, we rethink the hyperspectral target detection from the point object detection perspective, and propose the first specialized network for hyperspectral multi-class point object detection, SpecDETR. Without the visual foundation model of the current object detection framework, SpecDETR treats each pixel in input images as a token and uses a multi-layer Transformer encoder with self-excited subpixel-scale attention modules to directly extract joint spatial-spectral features from images. During feature extraction, we introduce a self-excited mechanism to enhance object features through self-excited amplification, thereby accelerating network convergence. Additionally, SpecDETR regards point object detection as a one-to-many set prediction problem, thereby achieving a concise and efficient DETR decoder that surpasses the state-of-the-art (SOTA) DETR decoder. We develop a simulated hyperSpectral Point Object Detection benchmark termed SPOD, and for the first time, evaluate and compare the performance of current object detection networks and HTD methods on hyperspectral point object detection. Extensive experiments demonstrate that our proposed SpecDETR outperforms SOTA object detection networks and HTD methods. Our code and dataset are available at https://github.com/ZhaoxuLi123/SpecDETR.

This work studies Hyperspectral image (HSI) super-resolution (SR). HSI SR is characterized by high-dimensional data and a limited amount of training examples. This exacerbates the undesirable behaviors of neural networks such as memorization and sensitivity to out-of-distribution samples. This work addresses these issues with three contributions. First, we observe that HSI SR and RGB image SR are correlated and develop a novel multi-tasking network to train them jointly so that the auxiliary task RGB image SR can provide additional supervision. Second, we propose a simple, yet effective data augmentation routine, termed Spectral Mixup, to construct effective virtual training samples to enlarge the training set. Finally, we extend the network to a semi-supervised setting so that it can learn from datasets containing only low-resolution HSIs. With these contributions, our method is able to learn from heterogeneous datasets and lift the requirement for having a large amount of HD HSI training samples. Extensive experiments on four standard datasets show that our method outperforms existing methods significantly and underpin the relevance of our contributions. Code has been made available at https://github.com/kli8996/HSISR.

Effectively discerning spatial-spectral dependencies in HSI denoising is crucial, but prevailing methods using convolution or transformers still face computational efficiency limitations. Recently, the emerging Selective State Space Model(Mamba) has risen with its nearly linear computational complexity in processing natural language sequences, which inspired us to explore its potential in handling long spectral sequences. In this paper, we propose HSIDMamba(HSDM), tailored to exploit the linear complexity for effectively capturing spatial-spectral dependencies in HSI denoising. In particular, HSDM comprises multiple Hyperspectral Continuous Scan Blocks, incorporating BCSM(Bidirectional Continuous Scanning Mechanism), scale residual, and spectral attention mechanisms to enhance the capture of long-range and local spatial-spectral information. BCSM strengthens spatial-spectral interactions by linking forward and backward scans and enhancing information from eight directions through SSM, significantly enhancing the perceptual capability of HSDM and improving denoising performance more effectively. Extensive evaluations against HSI denoising benchmarks validate the superior performance of HSDM, achieving state-of-the-art results in performance and surpassing the efficiency of the latest transformer architectures by 30%.

The annotation (assigning structural chemical identities) of MS/MS spectra remains a significant challenge due to the enormous molecular diversity in biological samples and the limited scope of reference databases. Currently, the vast majority of spectral measurements remain in the "dark chemical space" without structural annotations. To improve annotation, we propose MADGEN (Mass-spec Attends to De Novo Molecular GENeration), a scaffold-based method for de novo molecular structure generation guided by mass spectrometry data. MADGEN operates in two stages: scaffold retrieval and spectra-conditioned molecular generation starting with the scaffold. In the first stage, given an MS/MS spectrum, we formulate scaffold retrieval as a ranking problem and employ contrastive learning to align mass spectra with candidate molecular scaffolds. In the second stage, starting from the retrieved scaffold, we employ the MS/MS spectrum to guide an attention-based generative model to generate the final molecule. Our approach constrains the molecular generation search space, reducing its complexity and improving generation accuracy. We evaluate MADGEN on three datasets (NIST23, CANOPUS, and MassSpecGym) and evaluate MADGEN's performance with a predictive scaffold retriever and with an oracle retriever. We demonstrate the effectiveness of using attention to integrate spectral information throughout the generation process to achieve strong results with the oracle retriever.