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15 papers in the last four weeks, up 67% on the four weeks before. 0.2% of all new papers.

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Latest papers 156

May 13, 2026cs.LG

Spectral Gradient Surgery for Domain-Generalizable Dataset Distillation

Dataset Distillation (DD) synthesizes a compact synthetic dataset that preserves the training utility of a full dataset. However, its standard formulation assumes that test data follow the same distribution as training data, an assumption that rarely holds in practice. A straightforward extension-applying post-hoc Domain Generalization (DG) techniques to distilled data-is ill-suited because existing DG methods rely on the natural diversity of real datasets, which compact synthetic sets inherently lack, while also incurring substantial augmentation overhead that conflicts with the efficiency objective of dataset distillation. To address this limitation, we introduce Domain Generalizable Dataset Distillation (DGDD), a new problem setting that explicitly targets out-of-distribution (OOD) generalization of distilled datasets. We study this problem through a widely adopted DD baseline of Distribution Matching (DM). We attribute the OOD vulnerability of DM to the entanglement of class-discriminative and domain-specific information within the compressed synthetic set, and propose Spectral Gradient Surgery (SGS) to disentangle the two. The key insight of SGS is that cross-domain agreement among domain-wise gradients in the spectral domain reveals which gradient components are shared across source domains-and are therefore class-discriminative-and which are domain-specific. Based on this observation, SGS augments the standard DM update with two complementary gradients: one that reinforces cross-domain shared components and another that explicitly promotes diversity within the distilled dataset. Extensive experiments on diverse-scale benchmarks demonstrate that SGS substantially improves OOD generalization while remaining plug-and-play compatible with existing DM methods.

Minyoung Oh, Najeong Chae, Jae-Young Sim

Graduate School of Artificial Intelligence Ulsan National Institute of Science and Technology (UNIST) Ulsan, Republic of Korea

Diffusion-Based Dataset Distillation Multimodal Domain Generalization Dataset Distillation Spectral

May 12, 2026cs.LG

Spectral Energy Centroid: a Metric for Improving Performance and Analyzing Spectral Bias in Implicit Neural Representations

Implicit Neural Representations (INRs) model continuous signals using multilayer perceptrons (MLPs), enabling compact, differentiable, and high-fidelity representations of data across diverse domains. However, due to the low-frequency bias of MLPs that prevents effective learning of small details, the model's frequency must be carefully tuned through the embedding layer. Prior work established that this tuning can be performed before training based on the target signal, but it did not account for the significant effect of model depth, indicating that our understanding of the relationship between frequency and INR performance remains limited. To gain insights into this relationship, we utilize the Spectral Energy Centroid (SEC) metric that quantifies the frequency of target images and the spectral bias of INR models. We show that SEC is a versatile tool for INR analysis, demonstrating its utility across three tasks: (1) a data-driven strategy (SEC-Conf) for hyperparameter selection that outperforms existing heuristics and is robust to model depth, (2) a reliable proxy for signal complexity, and (3) effective alignment of spectral biases across diverse INR architectures.

Tomasz Dądela, Adam Kania, Maciej Rut +1

Jagiellonian University IDEAS Kraków, Poland

Neural Representations Spectral High-Fidelity

May 12, 2026cs.LG

The Routing and Filtering Structure of Attention

The attention interaction matrix

QK^{\top}

contains two entangled computations: a skew-symmetric component that redistributes information between positions (routing) and a symmetric component that scales mutual relevance (filtering). We decompose 1776 heads across five pretrained transformers and find routing operating at low rank, well below the routing capacity allocated by the weight kernel. We introduce

S

-

D

attention as a diagnostic parameterization that disentangles routing from filtering by construction with guaranteed stability (

\mathrm{Re}(λ) \le 0

) and trains stably without layer normalization. When disentangled and unnormalized, routing self-organizes into a spectral cascade, effective rank

2

at the first layer, expanding with depth across six scales from 7M to 355M parameters. The cascade predicts where attention can be simplified: linearizing the first seven layers of 125M

S

-

D

attention costs

{<}5\%

perplexity, whereas standard attention collapses under the same intervention. The linearizable region widens with depth. Replacing the first four layers with ELU+1 linear attention reaches within

1.4\%

of baseline at full head dimension. Cascade-allocated architectures trade attention parameters for perplexity (

47\%-65\%

fewer attention parameters at

+3.9\%

to

+8.4\%

PPL). The routing-filtering decomposition makes the spectral budget legible; the cascade makes it actionable.

Shafayeth Jamil, Rehan Kapadia

Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles, CA 90089

Kimi Delta Attention Decomposition Spectral

May 12, 2026cs.SD

STRUM: A Spectral Transcription and Rhythm Understanding Model for End-to-End Generation of Playable Rhythm-Game Charts

We present STRUM (Spectral Transcription and Rhythm Understanding Model), an audio-to-chart pipeline that converts raw recordings into playable Clone Hero / YARG charts for drums, guitar, bass, vocals, and keys without any oracle metadata. STRUM is a multi-stage hybrid: a two-stage CRNN onset detector and a six-model ensemble classifier for drums; neural onset detectors with monophonic pitch tracking for guitar and bass; word-aligned ASR for vocals; and spectral keyboard detection for keys. We evaluate on a 30-song in-envelope benchmark constructed by screening candidate songs on a single audio-quality criterion -- the median 1-second drum-stem RMS after htdemucs_6s source separation. On this benchmark STRUM achieves drums onset F1 = 0.838, bass F1 = 0.694, guitar F1 = 0.651, and vocals F1 = 0.539 at a +/- 100 ms tolerance with per-song global offset search. We report a complete ablation of seven drum-pipeline components with paired per-song Wilcoxon tests, an analysis of ground-truth-to-audio timing distributions in community Clone Hero charts, and a per-class confusion matrix for the drum classifier. Code, model weights, and the full benchmark manifest are released.

Joshua Opria

Independent Researcher

Melody Keystroke Dynamics Spectral

May 12, 2026cs.LG

Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters

Gradient clipping is a standard safeguard for training neural networks under noisy, heavy-tailed stochastic gradients; yet, most clipping rules treat all parameters as vectors and ignore the matrix structure of modern architectures. We show empirically that data outliers often amplify only a small number of leading singular values in layer-wise gradient matrices, while the rest of the spectrum remains largely unchanged. Motivated by this phenomenon, we propose spectral clipping, which stabilizes training by clamping singular values that exceed a threshold while preserving the singular directions. This framework generalizes classical gradient norm clipping and can be easily integrated into existing optimizers. We provide a convergence analysis for non-convex optimization with spectrally clipped SGD, yielding the optimal

\mathcal{O}\left(K^{\frac{2 - 2α}{3α- 2}}\right)

rate for heavy-tailed noise. To minimize hyperparameter tuning, we introduce layer-wise adaptive thresholds based on moving averages or sliding-window quantiles of the top singular values. Finally, we develop efficient implementations that clip only the top

r

singular values via randomized truncated SVD, avoiding full decompositions for large layers. We demonstrate competitive performance across synthetic heavy-tailed settings and neural network training tasks.

Alexander Yukhimchuk, Mladen Kolar, Martin Takáč +1

MBZUAI · University of Southern California

Gradient Clipping Stochastic Gradient Descent Spectral Norm Singular Value Decomposition Spectral

May 11, 2026cs.LG

Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models

Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is still treated as a brittle hyperparameter, fixed before training and tuned by held-out performance. Learned factors are also identifiable only up to rotation and rescaling, so the nominal rank rarely coincides with the quantity that governs model behavior. We propose Spectral Prefix Extraction and Capacity-Targeted Representation Analysis (Spectra), which replaces rank as the unit of analysis with the spectrum of a learned positive semidefinite kernel, trace-normalized so that spectra are comparable across fits. The normalized eigenvalues form a distribution on the simplex, and their Shannon effective rank acts both as a summary of learned capacity and as a controllable training-time coordinate: a single scalar shapes this realized dimension during training, and bisection targets any desired value within the rank cap. To theoretically support that, we show local regularity and monotonicity of the realized-dimension profile. Across collaboration, social, biological, and infrastructure networks, Spectra traces performance--capacity frontiers that make the trade-off between predictive accuracy and realized dimension visible. It performs competitively with strong link-prediction baselines, yields aligned lower-capacity views of the same fitted model through spectral prefixes, and provides a principled handle on capacity in the overparameterized regime. Capacity thus becomes a property of the fitted model rather than a hyperparameter of the training.

Nikolaos Nakis, Panagiotis Promponas, Konstantinos Tsirkas +4

Human Nature Lab, Yale University · Department of Electrical and Computer Engineering, Yale University · Department of Statistics and Data Science, Yale University +1

Graph Edge Sparsification Graph Representation Learning Spectral Low-Rank Structure Capacity

May 10, 2026cs.CV

SSDA: Bridging Spectral and Structural Gaps via Dual Adaptation for Vision-Based Time Series Forecasting

Large vision models (LVMs) have recently proven to be surprisingly effective time series forecasters, simply by rendering temporal data as images. This success, how ever, rests on a largely unexamined premise: the rendered time series images are sufficiently close to natural images for knowledge in pre-trained models to transfer effectively. We argue that two gaps still remain, i.e., spectral and structural gaps, fundamentally limiting the potential of LVMs for time series forecasting. Spectrally, we systematically reveal that rendered time series images exhibit a markedly shallower power spectrum than the natural images LVMs are pre-trained to recognize. Structurally, reshaping 1D temporal sequences into 2D grids fabricates spurious spatial adjacencies while severing genuine temporal continuities, misleading the spatial inductive biases of pre-trained LVMs. To bridge these gaps, we propose SSDA, a dual-branch network that spectrally and structurally adapts to unlock the full potential of LVMs for time series forecasting. At the data level, a Spectral Magnitude Aligner (SMA) applies 2D FFT to selectively enhance the magnitude spectrum toward natural-image statistics while preserving phase. At the model level, a Structural-Guided Low-Rank Adaptation (SG-LoRA) injects position-aware temporal encodings into patch embeddings and adapts at tention via low-rank updates. The two branches are further adaptively fused to produce the final forecast. Extensive experiments on seven real-world benchmarks demonstrate that SSDA consistently outperforms strong LVM- and LLM-based baselines under both full-shot and few-shot settings. Code is publicly available at https://anonymous.4open.science/r/SSDA-8C5B.

Mingrui Zhang, Hanchen Yang, Wengen Li +4

Time Series Forecasting Spatial Encoding Spectral Inductive Bias Reasoning Gaps

May 8, 2026cond-mat.dis-nn

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer

We study the evolution of hidden-weight spectra in wide neural networks trained by (stochastic) gradient descent. We develop a two-level dynamical mean-field theory (DMFT) that jointly tracks bulk and outlier spectral dynamics for spiked ensembles whose spike directions remain statistically dependent on the random bulk. We apply this framework to two settings: (1) infinite-width nonlinear networks in mean-field/

μ

P scaling and (2) deep linear networks in the proportional high-dimensional limit, where width, input dimension, and sample size diverge with fixed ratios. Our theory predicts how outliers evolve with training time, width, output scale, and initialization variance. In deep linear networks,

μ

P yields width-consistent outlier dynamics and hyperparameter transfer, including width-stable growth of the leading NTK mode toward the edge of stability (EoS). In contrast, NTK parameterization exhibits strongly width-dependent outlier dynamics, despite converging to a stable large-width limit. We show that this bulk+outlier picture is descriptive of simple tasks with small output channels, but that tasks involving large numbers of outputs (ImageNet classification or GPT language modeling) are better described by a restructuring of the spectral bulk. We develop a toy model with extensive output channels that recapitulates this phenomenon and show that edge of the spectrum still converges for sufficiently wide networks.

Clarissa Lauditi, Cengiz Pehlevan, Blake Bordelon

John A. Paulson School of Engineering and Applied Sciences, Harvard University · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University · Center for Mathematical Sciences and Applications, Harvard University +1

Deep Network Neural Network Feature Learning Spectral Mean-Field Limit Transfer Learning+2

May 8, 2026cs.LG

Diagnosing Spectral Ceilings in Equivariant Neural Force Fields

We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone preserves: inject a controlled angular-frequency perturbation into a molecular force field, attach a lightweight Spectral Prediction Network (SPN) to the frozen backbone, and read off which frequencies are recoverable. On aspirin, a quadratic SPN attached to an L = 2 NequIP backbone recovers the boundary signal at l = 4 but collapses at l = 5: a 11.7x cliff at the predicted drL boundary, with p dropping from 0.913 to 0.078. The same boundary-vs-above contrast persists across n = 4 independently trained backbones (raw-gain delta contrast, hierarchical cluster bootstrap) and is corroborated by a denominator-free injected-residual metric (R2_inj(4) = 0.374 versus R2_inj(5) = 0.006). A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-d polynomials of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary (scoped to single-direction degree-bounded probes, not a function-class upper bound on multi-atom MPNNs). A synthetic C5 calibration plus capacity, activation, and cross-architecture controls rule out parameter count alone as the explanation.

Hyunmog Kim

Independent Researcher.

Spectral Neural Fields Frequency Diagnosis

May 8, 2026cs.LG

bispectrum: Selective $G$ -Bispectra Made Practical

Many machine learning tasks are invariant under the action of a group

G

of transformations: signal classification can be invariant under translations, image classification under 2D rotations, and spherical-image classification under 3D rotations. The

G

-bispectrum is a principled complete invariant of a signal (retaining all all signal's information up to the group action) with proven benefits in machine learning and as a pooling layer in deep networks. However, its deployment has been hampered by high computational cost and a patchwork of group-specific implementations. We present bispectrum, an open-source, fully unit-tested PyTorch library that implements selective

G

-bispectra for seven different group actions, as differentiable modules that can be directly incorporated into machine learning pipelines and deep learning architectures. For finite groups

G

, selectivity reduces the computational cost from

O(|G|^2)

to

O(|G|)

. For planar rotations, we leverage the disk bispectrum. For spherical 3D rotations, we introduce an augmented selective bispectrum at band-limit

L

which reduces the cost from

O(L^3)

to

Θ(L^2)

coefficients. We profile the entire library (for which we implemented various compute optimizations), showing that it delivers near-exact

G

-invariance with its selective

G

-bispectra computed in sub-millisecond time on GPU (up to commonly used bandlimits). We evaluate the benefits of incorporating

G

-bispectra as pooling layers into deep learning architectures on three classical benchmark datasets --comparing against norm pooling, gated pooling, Fourier-ELU pooling, max pooling, and (non-equivariant) data-augmented convolutional baselines. Results show that

G

-bispectra consistently outperform alternatives in the low-data, moderate-capacity regime.

Johan Mathe, Adele Myers, Simon Mataigne +1

Atmo, Inc. San Francisco, CA · UC Santa Barbara Santa Barbara, CA · UCLouvain Louvain-la-Neuve, Belgium

Global Average Pooling Spherical Latent Space Spectral Deep Learning Selectivity Selective

May 7, 2026cs.LG

Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning -- most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization -- and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a \emph{spike-and-flat} shape -- a few dominant eigenvalues followed by an approximately uniform tail -- across layers and training stages, holding exactly under a rank-

ρ

signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked

r

-dimensional subspace, single shared eigenvalue across the remaining

n-r

directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

Ruotong Sun, Ermin Wei

†Department of Industrial Engineering & Management Sciences, Northwestern University · ∗Department of Electrical & Computer Engineering, Northwestern University

Spectral Preconditioning Orthogonality Kullback-Leibler Divergence Whitening Spectral

May 7, 2026stat.ML

Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

Andy Zeyi Liu, Elliot Paquette, John Sous

Department of Applied Physics, Yale University, New Haven, CT 06511, United States · Department of Mathematics and Statistics, McGill University · Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA +1

Model Activations Large Language Model Training Anisotropic Loss Landscapes Spectral Covariance Lens+1

May 7, 2026cs.LG

Distributional Spectral Diagnostics for Localizing Grokking Transitions

In grokking, a model first fits the training data while test accuracy remains low, and only later begins to generalize. We ask whether this transition can be localized from observed training trajectories before the test accuracy rises, and formulate grokking transition localization as a diagnostic problem with an explicit threshold/FPR/lead-time trade-off. Task-dependent observables are summarized as empirical distributions, mapped to Wasserstein/quantile coordinates, and analyzed by Hankel dynamic mode decomposition (DMD); the resulting reconstruction residual, together with spectrum and effective rank, forms the diagnostic output. On held-out modular-addition Transformer runs, the residual achieves AUROC

\approx

0.93 for grokking-vs-non-grokking discrimination at the run level; under a fixed sustained-threshold operating rule, true-positive alarms can precede onset, with lead time reported jointly with false-alarm rate and uncertainty intervals. Perturbation experiments show that, in the tested

wd=1

pool, high-residual windows exhibit about

3\times

larger short-horizon perturbation deviation than low-residual windows. In a same-data norm-window control, perturbation sensitivity aligns with the residual ordering rather than total-parameter-norm ordering, suggesting that the residual is not merely a total-norm proxy at the window level in the studied

wd=1

dynamics. Norm signals remain strong run-level regime indicators, and log-probability performs best among the observables tested under the current protocol. We position the residual as a window-level monitoring and localization signal in the studied modular-arithmetic Transformer settings, not a universal early-warning predictor or an intervention rule.

Ziyue Wang, Yufeng Ying, Takafumi Kanamori

Institute of Science Tokyo · University of Science and Technology of China

Grokking Transformer Residual Streams Dynamic Mode Decomposition Spectral Transformer Architectures Diagnosis+1

May 6, 2026cs.LG

Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics

When a language model processes a hallucinated response, its attention routing tends to fail in one of two shapes: over-concentrating on a narrow set of positions, or spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. We study these shapes as a diagnostic characterization, computed from attention matrices under \emph{forced scoring} of benchmark-labeled responses rather than during live generation. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport \emph{capacity}; we prove that every transpose-invariant spectral diagnostic of this operator is structurally \emph{orientation-blind} (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a converse to the blindness theorem bounding any Lipschitz diagnostic's transpose sensitivity by the asymmetry coefficient

G

. Pairing this with a closed-form bipartite-Cheeger landscape for canonical causal architectures, we show that uniform causal attention satisfies an

n

-independent floor

φ\ge 1/5

, while window attention pierces the floor as

O(w/n)

; failure modes are shape-different, not just value-different. This floor is an idealized-architecture benchmark, not an empirical attractor: the fraction of real attention heads that pierce it is itself an architectural signature. The resulting two-axis diagnostic (

φ

for capacity,

G

for direction) yields a falsifiable polarity prediction: bottleneck- and diffuse-dominated benchmarks should exhibit opposite polarity. Under length-controlled evaluation, transport features retain interpretable signal (0.62-0.84 LC-AUROC) across the tested decoder-only, encoder-only, and encoder-decoder models, with polarity reversing as predicted between HaluEval and MedHallu.

Dominik Dahlem, Diego Maniloff, Mac Misiura

Red Hat AI

Linear Attention Spectral Transport Object Hallucination

May 5, 2026stat.ML

On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants

We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints. Our contributions span both algebraic structure and statistical guarantees. On the algebraic side, we characterize the rank of the multilabel between-class scatter matrix, showing that the effective discriminant dimensionality can strictly exceed the classical single-label bound of

C-1

; we establish a multilabel partition of variance and prove that all four Fisher objectives are equivalent under the

W^\top S_t^{ML} W = I_r

constraint while characterizing their divergence under the Stiefel constraint; and we prove a two-sided label-distance preservation bound relating projected distances to Hamming distances in label space. On the statistical side, we establish a finite-sample

O(k_{\max}\sqrt{d\log d/n}/gap_r)

bound on the subspace estimation error under sub-Gaussian noise with a matching

Ω(σ^2 d/(n\,gap_r))

minimax lower bound, establishing a near-minimax-optimal rate (matching up to logarithmic and

k_{\max}

factors) for multilabel discriminant subspace estimation. We further provide high-probability distance concentration, robustness guarantees under label interactions, and a regularization analysis preserving the spectral structure when

d \gg n

. All results are verified numerically on synthetic data generated from the linear label-effect model, covering both the algebraic identities and the multilabel-specific quantities (

k_{\max}

,

κ(S_t^{ML})

,

\|Γ/n\|_2

,

Δ_r

) that govern the statistical bounds. The numerical experiments are designed as a sanity check for the theorems rather than as an empirical benchmark; evaluation on real multilabel datasets is left to future work targeting application-oriented venues.

Brian Keith-Norambuena, Juan Bekios-Calfa

Department of Computing & Systems Engineering, Universidad Cat´olica del Norte, Antofagasta, Chile.

Multi-Label Classification Discriminative Models Optimal Sample Complexity Subspace Orthogonality Spectral+2

May 4, 2026cs.AI

Hidden Coalitions in Multi-Agent AI: A Spectral Diagnostic from Internal Representations

Collections of interacting AI agents can form coalitions, creating emergent group-level organization that is critical for AI safety and alignment. However, observing agent behavior alone is often insufficient to distinguish genuine informational coupling from spurious similarity, as consequential coalitions may form at the level of internal representations before any overt behavioral change is apparent. Here, we introduce a practical method for detecting coalition structure from the internal neural representations of multi-agent systems. The approach constructs a pairwise mutual-information graph from the hidden states of agents and applies spectral partitioning to identify the most salient coalition boundary. We validate this method in two domains. First, in multi-agent reinforcement learning environments, the method successfully recovers programmed hierarchical and dynamic coalition structures and correctly rejects false positives arising from behavioral coordination without informational coupling. Second, using a large language model, the method identifies coalition structures implied by descriptive prompts, tracks dynamic team reassignments, and reveals a representational hierarchy where explicit labels dominate over conflicting interaction patterns. Across both settings, the recovered partition reveals subgroup organization that a scalar cross-agent mutual-information measure cannot distinguish. The results demonstrate that analyzing hidden-state mutual information through spectral partitioning provides a scalable diagnostic for identifying representational coalitions, offering a valuable tool for monitoring emergent structure in distributed AI systems.

Cameron Berg, Susan L. Schneider, Mark M. Bailey

Reciprocal Research · New York, NY, USA · Center for the Future of AI, Mind, and Society +5

Coalition Formation Artificial Intelligence Agents Emergence Mutual Information Neural Representations Spectral

May 4, 2026cs.LG

Spectral Model eXplainer: a chemically-grounded explainability framework for spectral-based machine learning models

Spectral-based machine learning models have been increasingly deployed in chemometrics and spectroscopy, where predictive accuracy is as important as explainability. Current employed eXplainable Artificial Intelligence (XAI) methods are largely adapted from tabular or generic multivariate domains, assigning relevance to isolated spectral variables rather than to the chemically meaningful spectral zones. Widely adopted tools such as SHapley Additive exPlanations (SHAP), Permutation Feature Importance (PFI), and Variable Importance in Projection scores (VIP) were not designed for the physical continuity and high collinearity of spectral data, and their variable-level outputs require post-hoc aggregation to recover zone-level information. This study introduces the Spectral Model eXplainer (SMX), a post-hoc, global, model-agnostic XAI framework that explains spectral classifiers through expert-informed spectral zones. SMX summarizes each zone via PCA, defines quantile-based logical predicates, estimates predicate relevance with perturbation in stochastic subsamples, and aggregates bag-wise rankings in a directed weighted graph summarized by Local Reaching Centrality. A key component is threshold spectrum reconstruction, which back-projects predicate boundaries to the original spectral domain in natural measurement units, enabling direct visual comparison with measured spectra. The method was evaluated on eight real spectral datasets (six based on X-ray Fluorescence--XRF and two based on Gamma-ray Spectrometry) and one synthetic benchmark with known gr

Jose Vinicius Ribeiro, Rafael Figueira Goncalves, Fabio Luiz Melquiades +1

Applied Nuclear Physics Laboratory · State University of Londrina · Dept. of Engineering and Architecture +2

Xai Explainability Spectral Cosmic-Ray Syntactic Pool

May 3, 2026cs.LG

How Label Imbalance Shapes Geometry: A General Spectral Analysis of Multi-Label Neural Collapse

This work investigates the phenomenon of Neural Collapse (NC) in multi-label classification, extending its conceptual framework from multi-class learning to general correlated and imbalanced multi-label settings. Although recent studies have identified a ''tag-wise averaging'' structure for multi-label features, this view relies on implicit assumptions of label balance and combinatorial symmetry. Consequently, it fails to account for the geometrical distortions caused by intrinsic label correlations and data imbalance, which are common in practice. We resolve the multiplicity-one imbalance conjecture raised by Li et al. (2024), showing that higher-multiplicity prototypes obey a class-frequency-weighted synthesis rule rather than uniform averaging. To address this, we propose a rigorous spectral-control framework to analyze the terminal phase of multi-label learning under general imbalanced conditions. We introduce the label covariance spectrum

κ_m

, a scalar controlling the distribution-dependent lower-bound geometry, derived from the second-order moment matrix of the label distribution. Contrary to the averaging perspective, our analysis reveals that the centered label covariance spectrum controls the stability of terminal geometry by quantifying the weakest centered inter-class contrast directions. We prove that the classical Tag-wise Averaging emerges only as a special case under perfect orthogonality. Numerical experiments on synthetic distributions validate our theoretical bounds. This work resolves the scaled-average aspect of the imbalance conjecture and establishes a unifying theoretical framework that extends Neural Collapse to complex, imbalanced multi-label settings.

Xiaoxuan Ma, Yixuan Yang, Song Li +1

Department of Mathematics, Zhejiang University, Hangzhou, China.

Multi-Label Classification Neural Collapse Multiclass Classification Collapse Spectral Covariance+2

May 2, 2026cs.LG

Concepts Whisper While Syntax Shouts: Spectral Anti-Concentration and the Dual Geometry of Transformer Representations

We test whether the causal inner product of \citet{park2024linear} -- defined by the unembedding covariance

Σ

-- enables cross-lingual concept transport. Across 17 models and 4 language pairs, a matched-spectrum randomization test finds that Whitened Causal Alignment is indistinguishable from spectral regularization alone (

p = 0.95

). However, this failure reveals a broader phenomenon: anti-concentration is observed in residual-stream difference-of-means vectors across five architecture families (

p < 10^{-33}

) and supported by SAE features (e.g.,

p = 4.5 \times 10^{-19}

) and linear probes on Gemma and Llama. We discover a \emph{dual geometry}: activation-space concept directions anti-concentrate in the spectral tail, while static unembedding-row contrasts \emph{concentrate} in high-variance directions (

p < 10^{-4}

). Split-injection causal interventions support the functional basis on Gemma and Llama (Cohen's

d

up to

1.80

), and POS-tag probing across 8 models shows syntax preferentially encodes in the high-variance subspace in 6 of 8 architectures (

p < 0.013

), with the Qwen~2.5 family showing a significant reversal consistent with architecture-specific spectral structure. These results suggest transformers may rotate semantic content into spectrally quiet regions during contextualized processing, encoding concepts where they can be manipulated with reduced grammatical disruption.

Pratyush Acharya, Nuraj Rimal, Habish Dhakal

Token Embeddings Spectral Syntax Cross-Lingual Transfer Concentration Bounds

May 2, 2026cs.RO

An Efficient Metric for Data Quality Measurement in Imitation Learning

Imitation learning (IL) has seen remarkable progress, yet field deployment of IL-powered robots remains hindered by the challenge of out-of-distribution (OOD) scenarios. Fine-tuning pre-trained policies with end-user demonstrations collected in deployment environments is a promising strategy to address this challenge. However, end-user demonstrations are frequently of poor quality, characterized by excessive corrective motions, oscillations, and abrupt adjustments that degrade both learned and fine-tuned policy performance. Existing automated approaches for curating demonstration data require policy rollouts in the environment, making them computationally expensive and impractical for real-world deployment. In this paper, we propose a fast, efficient, and fully automated demonstration ranking metric based on the power spectral density (PSD) of demonstration trajectories. The PSD metric requires no policy learning, environment interaction, or expert labeling, making it well-suited for scalable, in-the-field data curation. Lower PSD values correspond to smoother, higher-quality demonstrations, while higher PSD values indicate erratic, artifact-laden trajectories. We evaluate the proposed metric on two benchmark imitation learning datasets comprising expert and lay-user demonstrations, and through a user study with older adults at a retirement facility, where collected demonstrations are used to fine-tune

\pi0.5

\cite{intelligence2025pi_} for a daily living task. Results demonstrate that PSD-curated data yields policies with higher task success rates and smoother execution trajectories compared to uncurated baselines and two competitive data-ranking methods.

Noushad Sojib, Momotaz Begum

Authors are with the Department of Computer Science, University of New Hampshire, USA

Imitation Learning Imitation Data Quality Spectral

May 2, 2026eess.SP

Spectral- and Energy-efficient Multi-BS Multi-RIS Pinching-antenna Systems: A GNN-based Approach

This paper investigates coordinated downlink transmission in a multi-base station (multi-BS) multi-reconfigurable intelligent surface (multi-RIS)-assisted pinching-antenna (PA) system, where each user equipment (UE) is associated with a single BS and each BS is equipped with movable PAs deployed on parallel waveguides. We formulate sum rate (SR) and energy efficiency (EE) maximization problems by jointly optimizing PA placement, RIS phase shifts, transmit beamforming, and BS-UE association under constraints of inter-PA spacing, power budget, and unit-modulus phase shift. To address the resulting highly coupled mixed-variable problem, we propose a three-stage graph neural network (GNN) that integrates heterogeneous and homogeneous graph representations and is trained end-to-end in an unsupervised manner. Extensive numerical results demonstrate that the proposed three-stage GNN consistently outperforms representative system and learning baselines, generalizes well to unseen numbers of UEs, RISs, and BSs, and maintains millisecond-level inference time. Besides, the results validate the effectiveness of the proposed design from both system and architectural perspectives. Moreover, PAs are shown to enhance SR and EE, and the performance gain is enlarged with increasing number of PAs.

Changpeng He, Yang Lu, Wei Chen +3

State Key Laboratory of Advanced Rail Autonomous Operation, and also with the School of Computer Science and Technology, Beijing Jiaotong University, Beijing 100044, China · School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China · School of Electronic Engineering and Computer Science, Queen Mary University of London, London +2

Reconfigurable Intelligent Surfaces Beamforming Gnn-Based Detectors Graph Neural Networks Spectral

Apr 30, 2026cs.AI

SpecVQA: A Benchmark for Spectral Understanding and Visual Question Answering in Scientific Images

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.

Jialu Shen, Han Lyu, Suyang Zhong +5

DP Technology

Textvqa Multimodal Large Language Models Spectral

Apr 27, 2026cs.LG

Nautile-370M: Spectral Memory Meets Attention in a Small Reasoning Model

We present Nautile-370M, a 371-million-parameter small language model designed for efficient reasoning under strict parameter and inference budgets. Nautile-370M uses a hybrid backbone in which two SeqCond Attention (SCA) layers, a linear-time spectral sequence operator inspired by SeqCondenser, alternate with one transformer layer. This design aims to retain the long-context efficiency and state-tracking benefits of structured sequential models while preserving the expressive token-to-token routing of attention. The model was trained on a single Cloud TPU v4-64 pod slice provided through the Google TPU Research Cloud (TRC) program; the subsequent reinforcement learning stage was carried out on a single NVIDIA DGX Spark. We prove that the SCA readout mechanism can exactly retrieve any individual token from the prefix summary and can reproduce any output of softmax attention as a special case, establishing that SCA is at least as expressive as full self-attention in the continuous limit. We also describe the training data pipeline and outline a reinforcement learning stage specialized for reasoning, verification, and response quality.

Maixent Chenebaux

Trickstr

Small Large Language Models Small Reasoning Model Spectral

Apr 18, 2026cs.SI

Spectral Analysis of Fake News Propagation

The propagation structure of fake news has been shown to be an important cue for detecting it; yet, existing propagation-based fake news detection methods have mainly relied on ad hoc topological features, and a unified view of cascade patterns is still lacking. To address this, we study news propagation from a spectral view by connecting graph spectra to propagation-related structural properties through rigorous spectral bounds. In particular, we introduce several new bounds and integrate them with existing ones into a unified spectral representation of information propagation. We then use these spectral bounds for downstream classification and design a discrete structural optimization framework to interpret learned propagation patterns. For efficient optimization, we rely on a first-order perturbation approximation and consider both score-guided and bound-guided objectives. Experiments on real-world data reveal meaningful spectral differences between fake and real news, competitive classification performance from spectral bounds, and interpretable evolution trajectories from structural optimization. The findings demonstrate the value of spectral analysis for understanding and modeling news propagation.

Weibin Cai, Reza Zafarani

Data Lab, Department of EECS, Syracuse University, New York, USA.

Fake News Detection Spectral Graph Edge Sparsification Fake News Propagation Headlines

Apr 18, 2026cs.CV

Hyperspectral Unmixing Hierarchies

Unmixing reveals the spatial distribution and spectral details of different constituents, called endmembers, in a hyperspectral image. Because unmixing has limited ground truth requirements, can accommodate mixed pixels, and is closely tied to light propagation, it is a uniquely powerful tool for analyzing hyperspectral images. However, spectral variability inhibits unmixing performance, the proper way to determine the number of endmembers is ambiguous, and the clarity of the endmembers degrades as more are included. Hierarchical structure is a possible solution to all three problems. Here, hierarchical unmixing is defined by imposing a hierarchical abundance sum constraint on Deep Nonnegative Matrix Factorization. Binary Linear Unmixing Tactile Hierarchies (BLUTHs) solve the hierarchical unmixing problem with a simple network architecture. Sparsity modulation unmixing growth tailors the topology of a BLUTH to each scene. The structure imposed by BLUTHs allows endmembers with varying levels of spectral contrast to be revealed, mitigating the challenge of spectral variability. The performance of BLUTHs exceeds state-of-the-art unmixing algorithms on laboratory scenes, particularly with regard to abundance estimation, while their performance remains competitive on remote sensing scenes. In addition, ocean color unmixing by BLUTHs is demonstrated on hyperspectral scenes from the HYPSO and PACE satellites.

Joseph L. Garrett, P. S. Vishnu, Pauliina Salmi +4

Department of Engineering Cybernetics, Norwegian University of Science and Technology · Department of Biology, Norwegian University of Science and Technology · Department of Automatic Control and Systems Engineering, University Politehnica Bucharest +1

Hyperspectral Image Two-Level Spatial-Frequency Fusion Strategy Spectral Tactile

Mar 31, 2026cs.LG

From Dispersion to Attraction: Spectral Dynamics of Hallucination Across Whisper Model Scales

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the \textit{Spectral Sensitivity Theorem}, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment. We validate this theory by analyzing the eigenspectra of activation graphs in Whisper models (Tiny to Large-v3-Turbo) under adversarial stress. Our results confirm the theoretical prediction: intermediate models exhibit \textit{Structural Disintegration} (Regime I), characterized by a

13.4\%

collapse in Cross-Attention rank. Conversely, large models enter a \textit{Compression-Seeking Attractor} state (Regime II), where Self-Attention actively compresses rank (

-2.34\%

) and hardens the spectral slope, decoupling the model from acoustic evidence.

Ivan Viakhirev, Kirill Borodin, Grach Mkrtchian

Information Technologies, Mechanics and Optics University, Russia · lab260, Moscow Technical University of Communications and Informatics, Russia · BitmanagerAI, UAE

Spectral Attractors End-To-End Automatic Speech Recognition Models Dispersion

Mar 16, 2026astro-ph.CO

Spectral Hierarchy of the Cosmic Web

We introduce a spectral hierarchy of cosmic-web classifications obtained by applying simple scale-weighting kernels to the density field before performing a standard eigenvalue-based web classification. This unifies and extends several widely used web definitions within a single framework: the familiar potential/tidal web (large-scale, nonlocal), a curvature-based web (more local, peak- and ridge-sensitive), and additional higher-derivative levels that progressively emphasize smaller-scale structure. Because the classification is built from second derivatives of the filtered field, successive hierarchy levels align naturally with operator families that appear in renormalised bias and effective descriptions of large-scale structure, providing an explicit bridge between cosmic-web environments and long- and short-range nonlocal bias ingredients. We quantify the information content of the hierarchy with a compact statistic: we map each cell to one of four ordered web types (void, sheet, filament, knot), construct a corresponding ``web contrast'' field, and measure its cross-correlation with halos from the AbacusSummit simulation suite on a coarse mesh with

ΔL\simeq 5.5\,h^{-1}\mathrm{Mpc}

. We find that the hierarchy retains significant tracer-relevant information from very large scales down to the mesh Nyquist limit, with the more local (curvature/higher-derivative) levels dominating toward nonlinear scales. This makes the spectral hierarchy a practical, interpretable conditioning basis for fast mock-galaxy production and field-level modelling, and a flexible tool for studying environment-dependent clustering and assembly bias.

Francisco-Shu Kitaura, Francesco Sinigaglia

Instituto de Astrofísica de Canarias, s/n, E-38205, La Laguna, Tenerife, Spain · Departamento de Astrofísica, Universidad de La Laguna, E-38206, La Laguna, Tenerife, Spain · Institute for Fundamental Physics of the Universe, Via Beirut 2, I-34151 Trieste, Italy +3

Hierarchical Spectral Kernel Method

Mar 6, 2026cs.CV

Spectral and Trajectory Regularization for Diffusion Transformer Super-Resolution

Diffusion transformer (DiT) architectures show great potential for real-world image super-resolution (Real-ISR). However, their computationally expensive iterative sampling necessitates one-step distillation. Existing one-step distillation methods struggle with Real-ISR on DiT. They suffer from fundamental trajectory mismatch and generate severe grid-like periodic artifacts. To tackle these challenges, we propose StrSR, a novel one-step adversarial distillation framework featuring spectral and trajectory regularization. Specifically, we propose an asymmetric discriminative distillation architecture to bridge the trajectory gap. Additionally, we design a frequency distribution matching strategy to effectively suppress DiT-specific periodic artifacts caused by high-frequency spectral leakage. Extensive experiments demonstrate that StrSR achieves state-of-the-art performance in Real-ISR, across both quantitative metrics and visual perception. The code and models will be released at https://github.com/jkwang28/StrSR .

Jingkai Wang, Yixin Tang, Jue Gong +6

Shanghai Jiao Tong University, China · Shenzhen Transsion Holdings Co., Ltd., China

Real-World Image Super-Resolution Diffusion Transformers Dataset Distillation Spectral

Feb 26, 2026stat.ML

Regular Fourier Features for Nonstationary Gaussian Processes

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation and treating the spectral density as a probability distribution suitable for Monte Carlo approximation. Although this probabilistic interpretation is valid for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. To avoid this limitation, we propose regular Fourier features for harmonizable processes with one-dimensional inputs. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Assuming finite spectral support, this yields an efficient low-rank approximation that is positive semi-definite by construction and consistent under mild regularity conditions. When the spectral density is unknown, the framework also extends to kernel learning from data, which we explore as a proof of concept. We demonstrate the approximation on locally stationary and harmonizable mixture kernels, the latter with a complex-valued spectral density. As a feasibility study, we then apply the kernel-learning extension to real and synthetic data, where it matches competitive baselines.

Arsalan Jawaid, Abdullah Karatas, Jörg Seewig

Institute of Measurement and Sensor Technology, University of Kaiserslautern-Landau, Kaiserslautern, Germany · Independent Researcher, Mannheim, Germany

Gaussian Process Kernel Method Fourier Spectral

Feb 12, 2026eess.SY

Grounded Laplacians of Directed Signed Matrix-Weighted Networks: Spectral Properties and Applications to Non-Trivial Consensus

Grounded Laplacians provide the spectral link between external information and network convergence. This paper establishes positive-stability results for grounded Laplacians in directed signed matrix-weighted networks, where directionality, antagonism, and singular edge weight matrices coexist. First, under in-degree dominance and positive-negative reachability, we derive explicit local thresholds for the grounding gains. Second, a scaled, kernel-based certificate replaces the unscaled degree condition with a signed matrix-weighted Dirichlet decomposition and a joint-kernel test for the scaled symmetric part. The computable margin

γ_p

lower-bounds the minimum real part of the spectrum and certifies exponential contraction in the

P

-norm. Under absolute generalized balance, the kernel-intersection test is given; the balanced and definite-edge unbalanced undirected cases follow. As an application, non-trivial consensus (NTC) on signed matrix-weighted networks is studied. Informed agents, external signals and coupling terms are designed to steer all agents to any prescribed nonzero state without requiring structural balance. Switching topology case retains non-trivial consensus result under certain conditions. Realizing NTC on signed matrix-weighted networks demonstrates that groups with both cooperative and antagonistic multi-dimensional interactions can achieve consensus, which was previously deemed exclusive to fully cooperative groups.

Tianmu Niu, Bing Mao, Hao Liao +2

Graph Laplacians Lyapunov Function Spectral

Dec 9, 2025cs.LG

Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk network, which operates directly on raw spatial or spatiotemporal coordinates through fully connected layers, often struggles to represent sharp gradients, boundary layers, and other non-periodic solution structures on bounded domains. To address these limitations, we introduce the Spectral-Embedded Deep Operator Network (SEDONet), a novel DeepONet architecture in which the trunk is driven by a fixed Chebyshev spectral dictionary instead of coordinate inputs. This non-periodic spectral embedding provides a principled inductive bias for bounded domains, enabling the learned operator to capture fine-scale features that are difficult for Fourier-based or MLP-only trunks to represent. SEDONet is evaluated on the 2-D Poisson equation, 1-D Burgers' equation, 1-D advection-diffusion equation, Allen-Cahn equation, Lorenz-96 chaotic system, and Darcy flow, covering elliptic, hyperbolic, parabolic, chaotic, and multiscale problems. Across all benchmarks, SEDONet consistently achieves the lowest or statistically comparable relative

L^2

errors among DeepONet, FEDONet, and SEDONet, with improvements of up to 54% over the baseline DeepONet and consistent gains over Fourier-embedded variants on bounded, non-periodic problems. Energy spectrum analyses further demonstrate that SEDONet more accurately preserves intermediate- and high-frequency solution structures. The proposed framework provides a simple, parameter-neutral modification to DeepONets, offering a robust and computationally efficient spectral approach for surrogate modeling of nonlinear operators in scientific computing.

Muhammad Abid, Omer San

Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville, TN 37996, USA.

Fourier Neural Operators Spectral Representation Method Fourier Spectral Approximation

Oct 12, 2025cs.CV

Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scans

With the growing volume of CT examinations, there is an increasing demand for automated tools such as organ segmentation, abnormality detection, and report generation to support radiologists in managing their clinical workload. Multi-label classification of 3D Chest CT scans remains a critical yet challenging problem due to the complex spatial relationships inherent in volumetric data and the wide variability of abnormalities. Existing methods based on 3D convolutional neural networks struggle to capture long-range dependencies, while Vision Transformers often require extensive pre-training on large-scale, domain-specific datasets to perform competitively. In this work, we propose a 2.5D alternative by introducing a new graph-based framework that represents 3D CT volumes as structured graphs, where axial slice triplets serve as nodes processed through spectral graph convolution, enabling the model to reason over inter-slice dependencies while maintaining complexity compatible with clinical deployment. Our method, trained and evaluated on 3 datasets from independent institutions, achieves strong cross-dataset generalization, and shows competitive performance compared to state-of-the-art visual encoders. We further conduct comprehensive ablation studies to evaluate the impact of various aggregation strategies, edge-weighting schemes, and graph connectivity patterns. Additionally, we demonstrate the broader applicability of our approach through transfer experiments on automated radiology report generation and abdominal CT data.

Theo Di Piazza, Carole Lazarus, Olivier Nempont +1

INSA Lyon, University of Lyon, CNRS, INSERM, CREATIS UMR 5220, U1294, Villeurbanne, France · Hospices Civil de Lyon, Lyon, France · Philips Clinical Informatics, Innovation Paris, France

Cone-Beam Computed Tomography Cnn-Transformer Tradeoff Radiology Report Generation Spectral

Oct 1, 2025cs.LG

Panorama: Fast-Track Nearest Neighbors

Approximate Nearest-Neighbor Search (ANNS) pipelines for high-dimensional neural embeddings spend the bulk of their query time in candidate verification, making it the primary bottleneck in the search process. In this paper, we present PANORAMA, a state-of-the-art refinement technique that accelerates verification by exploiting the inherent spectral decay of these embeddings. Using PCA to compact signal energy, PANORAMA evaluates candidate distances incrementally, computing at each step a strict lower bound on the full-vector distance and dynamically pruning candidates the moment this bound exceeds the running k-th nearest neighbor distance. While PCA's concentration of variance facilitates pruning, it breaks the uniform-variance assumption required by Product Quantization (PQ); we resolve this with a variance-shaping step that redistributes energy across subvectors, rendering accretive refinement compatible with quantized indexes. Optimized for modern memory hierarchies via vectorized bulk-pruning and cache-conscious data layouts, PANORAMA has been upstreamed into the FAISS library across major index families (IVFPQ/Flat, HNSW, and Refine). PANORAMA achieves higher QPS at any target recall with a cost that provably scales inversely with dataset spectral decay, delivering end-to-end speedups of up to 28.9x and outperforming probabilistic methods across all recall bands.

Vansh Ramani, Alexis Schlomer, Akash Nayar +3

IIT Delhi & CMU & UCPH · Carnegie Mellon University · Indian Institute of Technology Delhi +1

Approximate Nearest-Neighbor Search Behavioral Embeddings Neural Architecture Search Search Algorithms Principal Component Analysis Spectral+1

Sep 25, 2025cs.LG

Aligning Inductive Bias for Data-Efficient Generalization in State Space Models

The remarkable success of modern AI has been closely tied to scaling laws, yet the finite supply of high-quality data makes data efficiency--learning more from less--an increasingly important frontier. A model's inductive bias is a critical lever for data efficiency, but foundational sequence models such as State Space Models (SSMs) often rely on fixed, task-agnostic biases. When this fixed prior is misaligned with the underlying structure of a task, the model may require additional samples to overcome its own bias before learning the relevant signal. In this work, we introduce a principled framework for understanding and aligning the inductive bias of linear time-invariant SSMs. We first formalize this bias through an SSM-induced kernel and show theoretically and empirically that its spectrum is governed by the model's frequency response. This characterization motivates Task-Dependent Initialization (TDI), a fast power-spectrum matching method that aligns the initial SSM bias with the task's spectral characteristics before downstream training. Across controlled synthetic experiments, trainable one-layer SSMs, and deep SSMs on diverse real-world benchmarks, TDI can improve data-efficient generalization primarily when task-relevant spectral structure is present and the default SSM bias is spectrally mismatched. Our results provide both a theoretical lens and a practical tool for task-adaptive inductive bias, suggesting a path toward more data-efficient sequence modeling.

Qiyu Chen, Guozhang Chen

School of Computer Science, National Key Laboratory for Multimedia Information Processing, Peking University, China · School of Physics, Peking University, China

State Space Models Inductive Bias Sequence Modeling Spectral

Date pendingcs.LG

Diffract: Spectral View of LLM Domain Adaptation

We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text. Using singular value decomposition of weight matrices, we find that CPT leaves singular value spectra largely invariant, with adaptation driven mainly by changes in singular vectors. An analysis of attention-head projection matrices reveals strong, domain-dependent head heterogeneity, which we exploit to define a head importance criterion: up to 60% of head updates can be removed without measurable quality loss. Selectively rewinding low-importance heads to their pre-trained state improves benchmark accuracy by up to 4% versus the fully trained baseline. Finally, we identify domain connectivity - linear interpolation between CPT checkpoints yields smooth domain-quality interpolation without notable degradation on either domain - and release Diffract, an open-source toolkit for scalable spectral analysis of billion-parameter models.

Nikita Borodin, Maria Krylova, Artem Zabolotnyi +6

Risk AI Research Lab · Applied AI Institute

Large Language Model Adaptation Pretraining Spectral Heterogeneity Interpolation

Date pendingcs.CV

SPECTRA: Band-Routed Embedding and Stage-Wise LoRA for Cross-Sensor Fine-Tuning of Geospatial Foundation Models

Geospatial foundation models (GeoFMs), pretrained on large-scale geospatial data such as Earth observation (EO), climate, and weather data, have shown promising performance when fine-tuned on diverse downstream tasks. However, there are two challenges of adapting EO-pretrained GeoFMs to practical downstream datasets. The first challenge is how to handle spectral mismatch: pretrained patch embeddings expect a fixed set of input bands, whereas downstream sensors may provide different channels. The second challenge is how to reduce fine-tuning cost and make it efficient. While existing work has made efforts on these challenges individually, jointly improving fine-tuning performance under spectral mismatch while reducing adaptation cost remains underexplored. We propose SPECTRA, a parameter-efficient fine-tuning framework that addresses both spectral mismatch and adaptation cost. To handle spectral mismatch, SPECTRA introduces Band-Routed Embedding (BRE), which maps all available downstream bands into the band space expected by the pretrained GeoFM. By using BRE, all available bands in the downstream dataset are utilized to improve the selected-band input without changing the pretrained patch embedding interface. To reduce adaptation cost, SPECTRA further introduces a Stage-wise Transferability-aware LoRA (ST-LoRA) fine-tuning. ST-LoRA estimates stage-wise transferability before fine-tuning and assigns stage-specific LoRA ranks, concentrating trainable parameters on the stages with high transferability for the target task. Across three EO-pretrained GeoFMs and four downstream segmentation datasets, experiments show that BRE improves performance by utilizing all spectral bands, while ST-LoRA reduces trainable parameters compared with full fine-tuning and standard LoRA. Code is available at https://github.com/big-data-lab-umbc/SPECTRA.

Xingyan Li, Jordan A. Caraballo-Vega, Jie Gong +2

University of Maryland, Baltimore County Baltimore, Maryland, USA · NASA Goddard Space Flight Center Greenbelt, Maryland, USA

Geospatial Foundation Models Parameter-Efficient Fine-Tuning Methods Training-Side Stage-Aware Low-Rank Adaptation Spectral Rapid Adaptation