The approximation and convergence properties of implicit neural representations (INRs) are known to be highly sensitive to parameter initialization strategies. While several data-driven initialization methods demonstrate significant improvements over standard random sampling, the reasons for their success -- specifically, whether they encode classical statistical signal priors or more complex features -- remain poorly understood. In this study, we explore this phenomenon through a series of experimental analyses leveraging noise pretraining. We pretrain INRs on diverse noise classes (e.g., Gaussian, Dead Leaves, Spectral) and measure their ability to both fit unseen signals and encode priors for an inverse imaging task (denoising). Our analyses on image and video data reveal a surprising finding: simply pretraining on unstructured noise (Uniform, Gaussian) dramatically improves signal fitting capacity compared to all other baselines. However, unstructured noise also yields poor deep image priors for denoising. In contrast, we also find that noise with the classic 1/|f^\alpha| spectral structure of natural images achieves an excellent balance of signal fitting and inverse imaging capabilities, performing on par with the best data-driven initialization methods. This finding enables more efficient INR training in applications lacking sufficient prior domain-specific data.
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Recent automated transcription systems have focused on end-to-end orthographic approaches driven by deep neural networks and sequence-to-sequence transformers. Growing public interest in transcription at the phonemic or phonetic level has led to re-purposing these systems to segment and identify phones, the basic sounds which comprise human speech. However, they miss the mark on a fundamental component of time-series analysis, namely time. For linguistic applications which require high fidelity in the temporal domain, the loss of timing information is untenable. Our work proposes a deadline-bounded expectation maximization (EM) algorithm with a novel initialization method to estimate formants, i.e., salient speech frequencies, for enhanced phonetic segmentation. Based on the concept of spectral gravity, i.e., treating spectral energy as mass attenuated by the square of frequency distance across the spectrum, our technique outperforms the recent state of the art on key clustering metrics, generating reasonable alignments across multiple languages with no a priori training.
ElasticFlow: One-Step Physics-Consistent Policy with Elastic Time Horizons for Language-Guided Manipulation
PDF ↗Diffusion policies have demonstrated exceptional performance in embodied AI. However, their iterative denoising process results in high latency, and existing acceleration methods often sacrifice physical consistency. To address this, we propose ElasticFlow, a distillation-free, physics-consistent one-step policy framework. We reconstruct the Mean Field Theory by directly modeling the average velocity field, enabling a direct single-step mapping from noise to action. Addressing the Temporal Heterogeneity of robotic tasks, we introduce the Elastic Time Horizons mechanism. This mechanism effectively overcomes Spectral Bias by explicitly encoding control granularity, achieving efficient alignment between semantic instructions and physical execution horizons. Experiments on benchmarks such as LIBERO, CALVIN, and RoboTwin demonstrate that ElasticFlow achieves efficient 1-NFE inference (approximately 71Hz). Furthermore, it outperforms state-of-the-art methods, including OpenVLA and \pi_0, on long-horizon tasks, highlighting its potential for efficient, robust, and semantically aligned control.
Multi-round batch knowledge editing often suffers from performance degradation as edits accumulate. Focusing on the locate-then-edit paradigm, we analyze this phenomenon from a spectral perspective and identify a previously overlooked structural factor: the intrinsic knowledge of the model and historical edit memories exhibit markedly different spectral characteristics and information distributions, yet are naively coupled and jointly inverted during editing. Based on this insight, we propose SpecEdit to improve the model editing from a spectral perspective. SpecEdit performs spectral decoupling to isolate editing-critical directions and reduce destructive coupling, followed by spectral-structure-aware information compensation and spectral fusion to construct a refined closed-form solution. The module integrates seamlessly into existing editing methods without altering their original optimization procedures. Experiments on multiple LLMs and editing methods show that SpecEdit consistently improves performance, demonstrating that modeling spectral structure is an effective, interpretable approach and a promising direction for future research.
As Large Language Models asymptotically approach human-level fluency in natural language generation, solely relying on surface-level semantic artifacts for detecting LLM-generated texts has become increasingly precarious. Existing detectors often falter when facing three critical challenges: adversarial perturbations, cross-domain shifts, and the rapid temporal evolution of the foundation model. To address these issues, we propose , a novel framework that reformulates text detection as a signal processing task within the time-frequency domain. Unlike previous methods that analyze static token probability distributions, models the generated output as a probability signal, upon which a differentiable Continuous Wavelet Transform is applied to convert them into learnable spectral representations. This process reveals the intrinsic “spectral fingerprints” in machine-generated texts–patterns that remain invisible in time domain. Comprehensive evaluations on three well-curated datasets (RAID, EvoBench, and Domain-Shift) show that our method achieves a new state-of-the-art. It not only achieves superior accuracy but also exhibits remarkable robustness against sophisticated attacks, generalization across out-of-distribution topics and unseen evolving LLMs. Our results validate the efficacy of spectral analysis as a promising paradigm for LLM-generated texts detection.
Multi-Scale Spectral Selection and Entropy-Guided Uncertainty Fusion for Multimodal Rumor Detection
PDF ↗Multimodal content combining textual and visual information poses significant challenges for rumor detection on social media. Compared to traditional spatial domain features, frequency domain features have attracted increasing attention due to their stronger discriminative capabilities. However, existing methods still fall short in capturing cross-modal semantic inconsistencies and often overlook inherent noise in multimodal features, which limits overall detection performance. To address these issues, we propose a novel multimodal rumor detection method based on multi-scale spectral selection and entropy-guided uncertainty fusion. Specifically, we first apply the Discrete Cosine Transform (DCT) to image and text features to convert them into the frequency domain. Then, multi-scale convolutional filters are employed to extract fine-grained information across different frequency scales. Next, modality separation is performed to capture both shared and modality-specific features, enabling more effective cross-modal representation learning. Finally, entropy is used to estimate the uncertainty of each prediction branch, calculate confidence scores, and perform adaptive weighted fusion accordingly. Experimental results on multiple benchmark datasets demonstrate that our method outperforms existing state-of-the-art approaches in multimodal rumor detection, demonstrating stronger detection capability and robustness.
The Dominance of Text Space: Unveiling the Asymmetric Nature of Cross-Modal Alignment in Large Language Models
PDF ↗Recent advancements in Multimodal Large Language Models (MLLMs) have largely been driven by aligning visual encoders with pre-trained Large Language Models (LLMs). While effective, the geometric nature of this alignment remains under-explored. Existing methods often assume a symmetric interaction between visual and textual modalities, implying that both spaces adapt to each other. In this paper, we challenge this assumption and propose the "Text Space as Anchor" hypothesis. We argue that the semantic space of LLMs is rigid, anisotropic, and dominant; thus, effective cross-modal alignment may be an asymmetric projection of visual features onto this pre-existing text manifold without distorting it. We identify a potential issue in current parameter-efficient tuning paradigms where task-specific visual adjustments inadvertently disrupt the projector’s geometry, leading to "catastrophic forgetting" of the alignment mechanism itself. To address this, we introduce Anchor-Preserving Projection (APP), a novel method that regularizes the projector to maintain the geometric structure of the text embedding space via spectral filtering. Extensive experiments on 8 diverse cross-modal tasks and 3 pure language benchmarks demonstrate that APP preserves the LLM’s inherent linguistic capabilities (e.g., MMLU, GSM8K) and reduces object hallucination significantly better than standard fine-tuning methods. We release our code.
Test-time scaling evaluates reasoning LLMs by sampling multiple outputs per prompt, but ranking models in this regime remains underexplored. We formalize dense benchmark ranking under test-time scaling and introduce Scorio, a library that implements statistical ranking methods such as paired-comparison models, item response theory (IRT) models, voting rules, and graph- and spectral-based methods. Across 20 reasoning models on four Olympiad-style math benchmarks (AIME’24, AIME’25, HMMT’25, and BrUMO’25; up to N = 80 trials), most full-trial rankings agree closely with the Bayesian gold standard Bayes_𝒰@80 (mean Kendall’s τ_b = 0.93–0.95), and 19–34 methods recover exactly the same ordering. In the single-trial regime, the best methods reach τ_b ≈ 0.86.Using greedy decoding as an empirical prior (Bayes_R₀@N) reduces variance at N = 1 by 16–52%, but can bias rankings when greedy and stochastic sampling disagree. These results identify reliable ranking methods for both high- and low-budget test-time scaling. We release Scorio as an open-source library at https://github.com/mohsenhariri/scorio.
Sequential knowledge editing in large language models often causes catastrophic collapse of the model’s general abilities, especially for parameter-modifying methods. Existing approaches mitigate this issue through heuristic constraints on parameter updates, the mechanisms underlying such degradation remain insufficiently understood. In this work, we present a systematic spectral analysis of sequential knowledge editing and show that a model’s general abilities are closely associated with dominant singular directions of pretrained weight matrices. These directions are highly sensitive to perturbations and are progressively disrupted by repeated edits, closely tracking the collapse in both editing efficacy and general performance. Building on this insight, we propose REVIVE, a plug-and-play framework that prevents model collapse by explicitly preserving this dominant subspace. REVIVE analyzes parameter updates in the spectral basis of the original weights and filters out components that would interfere with the dominant subspace. Extensive experiments across multiple models and benchmarks show that REVIVE consistently improves editing efficacy while substantially preserving general abilities under long-horizon sequential editing, including extreme settings with up to 20,000 edits.
HiSVD: Principled Low-Rank Approximation of LLMs via Hierarchical Modeling of Information Capacity and Spectral Structure
PDF ↗Singular Value Decomposition (SVD) enables hardware-agnostic LLM compression via low-rank approximation, yet optimal rank allocation remains a bottleneck. Existing methods predominantly derive layer importance from performance-oriented proxies. Yet, these metrics fail to distinguish between representational importance and structural compressibility, consequently obscuring the fine-grained influence of spectral distribution shape. We demonstrate this disconnect through spectral analysis, revealing that layers with similar information capacity can exhibit markedly different singular value decay behaviors, corresponding to varying degrees of redundancy in the spectral tail. This imperfect coupling implies that allocation strategies driven solely by importance leave significant compression opportunities underexploited. To address this gap, we propose HiSVD, a hierarchical rank allocation framework with two stages: (1) Capacity-Anchored Baseline Allocation, which preserves representational stability by aligning rank budgets with information capacity; and (2) Redundancy-Aware Refinement, which modulates this baseline using tail redundancy to penalize structural excess. Experiments on LLMs demonstrate that HiSVD achieves superior compression efficiency, significantly outperforming state-of-the-art baselines by effectively exploiting this spectral heterogeneity.
Large Language Models (LLMs) often suffer from "Reasoning Collapse" on challenging mathematical reasoning tasks, where stochastic sampling produces lexical variations of the same erroneous logic rather than genuine semantic exploration. We observe that failed reasoning traces are often associated with a low-rank bias manifold in the model’s hidden-state geometry, which reduces exploration toward corrective solution directions. To address this, we propose Spectral Orthogonal Exploration (SOE), a geometric inference framework under a "Student Guides Teacher" paradigm. Instead of using a weak auxiliary agent for imitation, SOE uses it as an orthogonal probe to introduce semantically heterogeneous reasoning signals into the teacher’s orthogonal complement of its dominant subspace. This intervention steers the teacher toward more diverse reasoning trajectories and improves exploration beyond standard sampling. Experiments on mathematical benchmarks show that SOE improves average accuracy by 62.4% and average sampling efficiency by 113.7% over baseline methods, suggesting that geometric interventions can be effective for mitigating reasoning collapse in mathematical reasoning. We further provide preliminary evidence that SOE is also effective on logic and code generation benchmarks. Code is available at https://github.com/dayuwang401/spectral-orthogonal-exploration.
Selecting a single high-quality output from multiple stochastic generations remains a fundamental challenge for large language models (LLMs), particularly in open-ended tasks where no canonical answer exists. While Best-of-N and self-consistency methods show that aggregating multiple generations can improve performance, existing approaches typically rely on external evaluators, reward models, or exact string-match voting, limiting their applicability and efficiency. We propose Mode Extraction (ModeX), an evaluator-free Best-of-N selection framework that generalizes majority voting to open-ended text generation by identifying the modal output representing the dominant semantic consensus among generated texts. ModeX constructs a similarity graph over candidate generations and recursively applies spectral clustering to select a representative centroid, without requiring additional inference or auxiliary models. We further instantiate this selection principle as ModeX Decoding, a drop-in decoding scheme with early pruning for efficiency. Across open-ended tasks—including text summarization, code generation, and mathematical reasoning—our approaches consistently outperform standard single- and multi-path baselines, providing a computationally efficient, drop-in solution for robust open-ended text generation.
Spectral Disentanglement: Rank-Aware Task Adaptation for Rehearsal-free Continual Learning in LLMs
PDF ↗Continual Learning (CL) for Large Language Models (LLMs) faces a fundamental Stability-Plasticity Dilemma: balancing the plasticity to acquire new capabilities with the stability to preserve prior knowledge. While Parameter-Efficient Fine-Tuning methods, such as LoRA, enable efficient adaptation, we identify a critical flaw in current approaches termed Rank-Blindness: the enforcement of a single rank constraint across diverse tasks, which entangles task-shared and task-specific knowledge, leading to catastrophic forgetting of earlier tasks and underfitting on complex new ones. To address this, we propose SpaRTA, a novel rehearsal-free framework guided by a rank-spectrum perspective that explicitly disentangles knowledge into two orthogonal subspaces. Specifically, SpaRTA employs a low-rank branch to capture task-shared representations and a high-rank branch to model task-specific features. To integrate these complementary representations, we introduce a context-aware dynamic router that adaptively fuses the two branches based on input semantics, while an explicit orthogonality constraint minimizes interference between shared and specific parameter subspaces. This design effectively isolates task-specific updates from shared knowledge, preventing the overwriting of prior capabilities while preserving strong adaptation capacity. Extensive experiments demonstrate that SpaRTA achieves a superior stability-plasticity balance compared to single-rank baselines. Notably, the proposed spectral disentanglement strategy substantially reduces inter-task interference and yields strong zero-shot generalization on unseen tasks. Our code will be available at https://github.com/Xnhyacinth/SpaRTA.
Deep Learning · Generative Models and Autoencoders
Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by their iterative nature requiring costly sampling and lacking interpretability of the intermediate states. Recent approaches accelerate sampling by straightening trajectories or distilling endpoints, yet they treat the original generative process as a black box, discarding the teacher’s intermediate dynamics. We propose a fundamentally different perspective: globally linearizing flow dynamics via Koopman theory to achieve trajectory-preserving linearization. By lifting Conditional Flow Matching (CFM) into a higher-dimensional Koopman space, we represent its evolution with a single linear operator. Crucially, unlike boundary-only distillation, our method enforces infinitesimal consistency with the teacher's vector field along *the full generative path*. We derive a practical, simulation-free training objective that ensures this global alignment and yields two key benefits. First, sampling becomes one-step and parallelizable. Second, because the linearization is faithful to the dynamics, the Koopman operator provides unique insights on the generation. We demonstrate that this structure enables novel applications unavailable in prior approaches, including discovery of semantically coherent editing directions, inversion with a teacher-aligned linear operator and class-conditional spectral signatures. Empirically, our approach achieves competitive sample quality, while enabling spectral analysis and control of the *entire trajectories* of generative flows.
Deep Learning · Robustness
While data augmentation is essential for robust point cloud recognition, conventional spatial mixup strategies often compromise geometric integrity by generating physically unrealistic samples. To overcome this limitation, we propose PSMix, which shifts the mixing paradigm to the spectral domain via the Spherical Harmonic Transform. Instead of simple coordinate interpolation, PSMix performs a rotation-aware hierarchical mixing on spectral coefficients. This approach explicitly preserves global structural properties while diversifying local details, achieving a balance that spatial methods struggle to maintain. Complementing this, we introduce an adversarial rotation optimization strategy to enforce invariance against challenging orientations. Extensive experiments on ModelNet-C and ScanObjectNN-C demonstrate that PSMix achieves state-of-the-art robustness, while also serving as an orthogonal plug-in that further boosts the performance of existing spatial strategies.
Theory · Optimization
Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escape phase, high-variance but uninformative directions are multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this anisotropic magnification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under more general anisotropic covariances.
Applications · Computer Vision
Test-Time Adaptation (TTA) empowers pre-trained models to adapt online to distribution shifts during inference, but such online updates often become unstable in long-horizon deployments. Prevailing approaches attribute this failure to error accumulation from noisy pseudo-labels, relying on heuristics to gate which samples are used for updates. We argue that this statistical view is insufficient: the problem lies not only in the quality of samples but also in the directionality of their gradients. In this work, we identify a geometric failure mode termed manifold erosion. Through spectral analysis, we find that reliable gradients concentrate in a stable low-rank subspace, while gradients from confident mispredictions are high-rank yet exhibit a persistent directional leakage into this protected subspace. This leakage can accumulate coherently and gradually erode core representations, eventually leading to collapse. To address this, we propose Manifold-Aware Gradient Projection (MGP), a geometric intervention that tracks the dominant subspace online and projects gradients onto its orthogonal complement. By blocking the leakage path, MGP decouples stability from plasticity. Extensive experiments on diverse TTA benchmarks demonstrate the long-horizon stability of our method, whereas prior methods often fail.
Theory · Optimization
Synchronization over the special Euclidean group $\mathrm{SE}(3)$ aims to recover absolute poses from noisy pairwise relative transformations and is a core primitive in robotics and 3D vision. Standard approaches often require multi-step heuristic procedures to recover valid poses, which are difficult to analyze and typically lack theoretical guarantees. This paper adopts a dual quaternion representation and formulates $\mathrm{SE}(3)$ synchronization directly over the unit dual quaternion. A two-stage algorithm is developed: A spectral initializer computed via the power method on a Hermitian dual quaternion measurement matrix, followed by a dual quaternion generalized power method (DQGPM) that enforces feasibility through per-iteration projection. The estimation error bounds are established for spectral estimators, and DQGPM is shown to admits a finite-iteration error bound and achieves linear error contraction up to an explicit noise-dependent threshold. Experiments on synthetic benchmarks and real-world multi-scan point-set registration demonstrate that the proposed pipeline improves both accuracy and efficiency over representative matrix-based methods.
Many optimizers can be interpreted as steepest-descent methods under norm-induced geometries, and thus inherit corresponding implicit biases. We introduce Orthogonal Lion which combines spectral control from orthogonalized update directions with $\ell_\infty$-style coordinate control from sign updates. OLion forms a Lion-style momentum direction, approximately orthogonalizes it via a few Newton--Schulz iterations, and then applies an entrywise sign, providing an efficient approximation to taking a maximal step over the intersection of the spectral and $\ell_\infty$ constraint sets (a scaled Hadamard-like set for matrix parameters). Despite the strong nonlinearity of orthogonalization and sign, we prove convergence under a mild, empirically verified diagonal-isotropy assumption. Across large-scale language and vision training, including GPT-2 and Llama pretraining, SiT image pretraining, and supervised fine-tuning, OLion matches or outperforms AdamW and Muon under comparable tuning while using only momentum-level optimizer state, and it mitigates optimizer mismatch when fine-tuning AdamW-pretrained checkpoints.
Applications · Chemistry, Physics, and Earth Sciences
Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts, heterogeneous structure, and multi-scale dynamics absent from available training data. We present SENDAI, a hierarchical $\textbf{S}$parse-measurement, $\textbf{E}$fficie$\textbf{N}$t $\textbf{D}$ata $\textbf{A}$ss$\textbf{I}$milation Framework that reconstructs full spatial states from hyper sparse sensor observations by combining simulation-derived priors with learned discrepancy corrections. We demonstrate the performance on satellite remote sensing, reconstructing MODIS (Moderate Resolution Imaging Spectroradiometer) derived vegetation index fields across six globally distributed sites. Using seasonal periods as a proxy for domain shift, the framework consistently outperforms established baselines that require substantially denser observations---SENDAI achieves a maximum SSIM improvement of 185% over traditional baselines and a 36% improvement over recent high-frequency-based methods. These gains are particularly pronounced for landscapes with sharp boundaries and sub-seasonal dynamics; more importantly, the framework effectively preserves diagnostically relevant structures---such as field topologies, land cover discontinuities, and spatial gradients. By yielding corrections that are more structurally and spectrally separable, the reconstructed fields are better suited for downstream inference of indirectly observed variables. The results therefore highlight a lightweight and operationally viable framework for sparse-measurement reconstruction that is applicable to physically grounded inference, resource-limited deployment, and real-time monitor and control.