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38 papers in the last four weeks, up 111% on the four weeks before. 0.5% of all new papers.

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Latest papers 279

Aug 12, 2026cs.AI

Making Your LLMs More Objective: Stabilizing LLM Safety Behavior Across Traits with Trait-Invariant Safety Tuning

Aligned large language models (LLMs) are expected to exhibit safety behavior based on the content of the user request: they should refuse unsafe requests and comply with safe ones. However, we show that the same request can elicit substantially different safety decisions under different traits assigned in the system prompt, a failure mode we call trait-induced safety variation. To measure this failure, we introduce refusal-based metrics: Trait-Induced Deviation measures dataset-level deviation from the no-trait baseline, while Trait-Induced Flip Rate measures whether the same request receives different safety decisions across traits. We then provide a representation-level analysis of the mechanism behind trait-induced safety shifts and find that traits perturb the model's safety representations within a low-dimensional subspace. To achieve trait-invariant safety, where safety behavior remains stable across traits, we introduce Trait-Invariant Safety Tuning (TIST), a simple yet effective self-distillation framework that aligns an LLM's trait-conditioned behavior with its no-trait behavior. Guided by our analysis, we further propose Trait-Subspace Neutralization (TraSN), an instantiation of TIST, which enforces invariance only within the identified trait subspace. Experiments show that TraSN improves trait-invariant safety and strengthens harmful-request safety while preserving general capability. Our results highlight traits as an important factor in LLM safety and robust model behavior.

Lang Cao

University of Illinois Urbana-Champaign

Large Language Model Safety Refusals Subspace Objectives

Aug 12, 2026cs.LG

GCPO: Diagnosing and Constraining Subspace Geometry in Rollout RL for LLMs

On-policy rollout methods such as GRPO are central to post-training of large language models, yet they frequently suffer from training instabilities, cross-task capability degradation, and response-length inflation. Although prior work has characterized the subspace geometry of aggregate updates, the stepwise variation of this geometry and its relationship to model performance remain unclear. We introduce Principal-Subspace Overlap, a dimension-corrected measure of individual rollout updates relative to the dominant singular subspaces of pretrained weights. Despite low average overlap, transient spikes often precede performance degradation. To address this, we propose GCPO (Geometrically Constrained Policy Optimization), which applies hard bilateral orthogonal projections to constrain updates to the complementary subspaces, preventing such excursions by construction. Across mathematical reasoning, code generation, and tool-use tasks on Qwen3-8B and GLM4-9B, GCPO consistently outperforms GRPO and recent variants, including DAPO and GSPO, improving over the base models and the strongest baseline by up to 27.69 and 2.37 points, respectively. Furthermore, GCPO preserves general capabilities, eliminates response-length inflation, and stabilizes policy entropy. Our findings provide a new diagnostic lens and a principled design perspective for stable reinforcement learning post-training.

Kai Yang, Jingwei Xu, Wanyu Wang +4

School of Computer Science, Shanghai Jiao Tong University · Shanghai Artificial Intelligence Laboratory · NovaCore +3

Autoregressive Rollout Rollout Subspace

Aug 11, 2026cs.LG

HyperFix: Combinatorial Nonlinear Correction for Task Vector Merging

Task vectors enable model merging without joint retraining. In practice, the subset of task vectors to be merged may vary, but many existing methods use scalar tuning for a particular subset, requiring repeated tuning across subsets and restricting task vector merging to linear rescaling. We therefore formulate merging across varying task subsets as a combinatorial correction problem and introduce HyperFix, a lightweight hypernetwork that predicts subset-conditioned nonlinear corrections in weight space. Trained once on singleton, pair, and triple subsets from a task bank, HyperFix generalizes to larger subsets without per-subset optimization. Our local perturbation analysis bounds the residual correction beyond linear merging and motivates learning it from small task updates. Experiments across diverse benchmarks show that HyperFix outperforms existing task vector merging methods while reducing tuning cost.

Hyo Seo Kim, Ren Wang

Illinois Institute of Technology

Continual Model Merging Multi--Task Learning Hypernetwork Efficient Task Adaptation Subspace

Aug 11, 2026cs.CV

When Vision Becomes Text: Visual Token Pruning via Cross-Modal Residual Guidance in VLMs

Abundant visual information strengthens vision-language model (VLM) perception, yet massive visual tokens raise inference costs. Existing visual token pruning methods rely on similarity-based guidance, which exploits pairwise text-vision and vision-vision token correlations for compression. However, such methods only capture local layer-level signals and overlook the whole inference process in VLM. In this paper, we revisit VLM inference and present a new efficient guidance scheme that complements similarity-based guidance. In particular, we identify a key observation: as LLM layers deepen, text tokens continuously aggregate visual information via self-attention and progressively absorb partial visual content into textual representations. To quantify this phenomenon, we propose Cross Modal Absorption (CMA) from a geometric representation perspective to measure how much visual information is absorbed by text, revealing that more visual tokens in deeper layers can be approximately explained by the text subspace. We accordingly propose Cross Modal Residual (CMR). It projects visual tokens onto the text subspace via Tikhonov regularized least squares and exploits reconstruction residuals to quantify visual information that cannot be explained by text. Finally, based on CMR, we present SIEVE, a training-free visual token compression method that combines CMR, text-attention relevance, and residual-space diversity to retain task-relevant and complementary tokens. Experiments on diverse VLM architectures verify the effectiveness of SIEVE. For instance, on LLaVA-NeXT-7B, SIEVE keeps only

11.1\%

of visual tokens while preserving

97.5\%

of the original average performance, achieving

3.62\times

prefill speedup,

2.49\times

end-to-end speedup, and a

6.02\times

KV-cache reduction.

Congyang Ou, Ruike Song, Yang Zhou +3

Northwestern Polytechnical University · Chongqing University · MiLM Plus, Xiaomi Inc.

Visual Token Pruning Cross-Modal Text Analysis and Detection Subspace Guidance

Aug 10, 2026cs.LG

Rethinking Factor Sharing in Federated LoRA: A Rank-Aware Adaptive Approach

Low-rank adaptation (LoRA) represents large language model (LLM) updates with two compact matrix factors, i.e.,

A

and

B

, providing an efficient way to fine-tune large models in federated learning paradigm. Inspired by the asymmetric roles of the LoRA factors, we study whether

A

should be shared across clients while

B

remains client-specific (Share-A/Local-B), or whether

B

should instead be shared while

A

remains client-specific (Share-B/Local-A). With a least-squares surrogate, we reveal that Share-A/Local-B requires the client-specific LoRA update matrices to use a common rank-

r

input-side space, whereas Share-B/Local-A requires a common rank-

r

output-side space. The two strategies therefore incur different projection residuals, indicating that the preferred strategy is the one with the smaller aggregate residual across clients. With this insight, we propose Federated Adaptive Factor Sharing Low-Rank Adaptation (FedAS-LoRA), which selects the sharing side before training to enhance fine-tuning performance. To enable adaptive factor selection before training, we design a Rank-Aware Shared-Subspace Sufficiency (RSS) metric, which effectively assesses whether a shared rank-

r

input subspace is sufficient for the local data distributions using representations extracted from a frozen LLM backbone. Experiments across different tasks, data distributions, LoRA ranks, and participation settings confirm the effectiveness of RSS and the superior performance of FedAS-LoRA.

Xinyi Xu, Bingnan Xiao, Shuang Qin +2

University of Electronic Science and Technology of China · Fudan University · Singapore University of Technology and Design

Federated Learning Subspace Exploratory Factor Analysis

Aug 10, 2026cs.CV

Beyond Global Editing: Per-Instance Disentangled Subspaces for Training-Free Hallucination Mitigation in LVLMs

Recent advances in large vision-language models (LVLMs) have enabled powerful multimodal reasoning by integrating visual encoders with large language models (LLMs). However, their reliability is frequently undermined by hallucinations, where generated text inaccurately describes the visual input. Although fine-tuning can mitigate this problem, it is computationally expensive and requires large, curated datasets, making training-free alternatives attractive. Among these, model editing is more promising than decoding-based approaches: decoding methods adapt outputs per input but introduce computational overhead and instability, whereas model editing modifies internal representations offline, providing a more efficient and stable solution. However, existing model-editing techniques typically rely on a single global subspace to correct hallucinations, treating all test samples identically and failing to capture diverse hallucination modes across inputs. To address this limitation, we propose a training-free hallucination mitigation framework for dynamic, per-instance suppression at test time. Our method first constructs a set of Disentangled Hallucination Subspaces, each isolating a distinct hallucination mode. During inference, the model adaptively calculates weights reflecting each input's relationship to these subspaces, guiding a dynamically combined projection that selectively suppresses the most probable hallucination directions while preserving image-grounded semantics. Extensive experiments across multiple vision-language benchmarks and LVLM families demonstrate consistent improvements, highlighting the robustness, generalizability, and efficiency of our approach.

Ali Cheraghian, Hamidreza Dastmalchi, Hamed Barzamini +4

Macquarie University, Australia · Australian National University, Australia · York University, Canada +4

Aug 9, 2026cs.CV

Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information

Leveraging textual information for image clustering has emerged as a promising direction, largely owing to the powerful representations learned by Vision-Language Models (VLMs). Existing approaches typically retrieve a textual counterpart for each image and then refine multimodal representations by directly enforcing cross-modal agreement, e.g., maximizing image-text similarity inherited from pretrained VLMs. However, such a strategy aligns heterogeneous representations across modalities without explicitly modeling the intrinsic structure within each modality and thus might yield unreliable alignment or distort modality-specific structures that are crucial for clustering. In this paper, we propose a simple but principled approach, termed deep modality-shared self-expressive model (DeepMORSE), which discovers cross-modal structures via a modality-shared self-expressive model and simultaneously learns structured representations that conform to a union of modality-specific subspaces. Moreover, we theoretically justify that the modality-shared self-expressive coefficients suppress inter-class noise towards a subspace-preserving solution, and show that mini-batch optimization procedure introduces an implicit regularization onto the self-expressive model. We evaluate our DeepMORSE on six widely used image clustering benchmarks and observe performance improvements exceeding 3% on the UCF-101, DTD-47, and ImageNet-Dogs datasets. In addition, we demonstrate the strong transferability of the learned representations by achieving state-of-the-art performance on downstream tasks such as image retrieval and zero-shot classification---without requiring any task-specific losses or post-processing. The code is available at: https://github.com/mengxianghan123/DeepMORSE.

Xianghan Meng, Wei He, Zhiyuan Huang +1

School of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China

Multimodal Representations Modalities Clustering Text Analysis and Detection Subspace

Aug 7, 2026cs.AI

Who Built This Model? Tracing LLM Lineage via Spectral Fingerprints in Weight Space

Open-weight large language models (LLMs) are increasingly developed through complex, multi-stage pipelines, leading to intricate lineage relationships that reflect model origin, ownership, and evolution. Understanding these relationships is important for model provenance, governance, and supply-chain integrity. In this work, we investigate the notion of LLM "biometrics" (analogous to human biometrics) to ask whether LLMs exhibit intrinsic fingerprints in weight space alone, without access to input data, that reveal their origin and lineage. We formulate this as a lineage discrimination problem, distinguishing among independent-origin, same-series, and shared-base models. To characterize these relationships, we propose a unified geometric fingerprinting framework that analyzes weight matrices from two complementary perspectives: (i) spectral energy, captured by singular value distributions to encode global magnitude patterns, and (ii) subspace alignment, quantified via subspace deviations to capture directional geometry. Our analysis uncovers a clear hierarchy of structural similarity in weight space: spectral energy reliably distinguishes independently trained models and different model families, while subspace alignment enables fine-grained discrimination among closely related models, including variations in dataset scale and post-training procedures. Extensive experiments on over 110 diverse open-weight LLM pairs demonstrate that weight-space geometry provides a robust and interpretable signal for model lineage, enabling coarse-grained regime separation and fine-grained discrimination within shared-base models.

Yiwei Chen, Bingqi Shang, Sijia Liu

Michigan State University

Model Weights Lineages Weight-Space Fingerprint Subspace Spectral Features

Aug 5, 2026stat.ML

Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift

The Subspace Constrained Mean Shift (SCMS) algorithm is a popular nonparametric method for extracting density ridges, which serve as a low-dimensional representation of high-dimensional data. It is a widely held belief in the literature that SCMS trajectories converge to the classical density ridge, which we call the "static ridge", defined via the density gradient and the eigenvalues and eigenvectors of the density's Hessian. In this paper, we demonstrate that this assumption does not hold in general, as the static definition fails to account for the rotation of the trailing eigenspace along the continuous flow of the algorithm's underlying vector field. To resolve this, we propose a paradigm shift by introducing the "stable ridge", a novel geometric structure defined through the lens of dynamical systems and the Jacobian of the projected density gradient. We prove that this stable ridge is the true theoretical target of the SCMS algorithm. Building upon this foundation, we develop a generalized SCMS framework utilizing a constant step size, establishing its uniform R-linear convergence and topological surjectivity onto the stable ridge. We further derive the rates of convergence for estimating the stable ridge in terms of the Hausdorff distance. Finally, we expose that the original SCMS algorithm suffers from polynomial-time computational complexity, which is caused by implicitly coupling the step size to the smoothing bandwidth via the Mean Shift operator, and demonstrate how our generalized framework provides a statistically consistent and more efficient solution.

Wanli Qiao

Convergence Subspace Spectral Decomposition

Aug 5, 2026cs.LG

Efficient Online Lexicographic Generalized Low-Rank Matrix Bandits

This paper studies generalized low-rank matrix bandits with multiple prioritized objectives. At each round, the learner selects a matrix-valued arm and observes a vector-valued reward, whose components correspond to multiple objectives with different priority levels. Each objective is governed by an objective-specific generalized low-rank matrix model, and the learner evaluates arms according to a lexicographic preference order, prioritizing higher-level objectives before lower-level ones. We propose \textsc{Lexi-LowGLM}, an efficient online algorithm that first estimates objective-specific low-rank subspaces and then performs lexicographic learning in the reduced feature spaces. Unlike existing single-objective algorithms that repeatedly solve a batch generalized linear estimator using all historical observations, \textsc{Lexi-LowGLM} updates each objective-specific estimator via an online Newton step, reducing the estimator-update complexity over

T

rounds from

O(T^2)

to

O(T)

. We establish a regret bound of

\widetilde O\left(W_i^{\rm lex}\sqrt{m}\,(d_1+d_2)r\sqrt{T}\right)

for each objective

i\in[m]

, where

r

is an upper bound on the ranks of the objective-specific parameter matrices and

W_i^{\rm lex}

characterizes the lexicographic trade-off effect. This bound depends on the effective low-rank dimension

(d_1+d_2)r

rather than the ambient dimension

d_1d_2

. Numerical experiments further validate the effectiveness and computational efficiency of the proposed method.

Bo Xue, Ji Cheng, Haodong Jing +2

City University of Hong Kong. · Xi’an Jiaotong University. · Northwestern Polytechnical University.

Bandits Subspace Preference Alignment Learning

Aug 4, 2026cs.LG

Random features for Grassmannian kernel approximation with bounded rank-one projections

We propose a family of random feature maps for scalable kernel machines on low-dimensional subspaces, ie on the Grassmannian manifold. Such representations are useful when data classes or clusters are well described by the span of a few samples. Classical Grassmannian kernels, including the projection and Binet-Cauchy kernels, require full Gram matrices, which leads to prohibitive computational and memory costs for large high-dimensional subspace datasets. We address this limitation using random features based on rank-one projections of subspace projection matrices followed by bounded non-linear transforms, either periodic or binary, to control the resulting distributions. We show that inner products in the random feature space approximate well-defined rotation-invariant Grassmannian kernels that depend only on the principal angles between subspaces. When the number of features is sufficiently large relative to the intrinsic subspace dimension, the approximation holds uniformly over all fixed-dimensional subspaces with high probability. For periodic transforms, the approximated kernel has a closed-form expression with tunable behaviour between inverse Binet-Cauchy and Gaussian-type regimes. Binary transforms yield compact one-bit subspace features, although no closed-form kernel is known. Structured rank-one projections based on randomised fast Fourier transforms further reduce computation without sacrificing practical accuracy. Experiments on synthetic data and ETH-80 classification tasks show that these features accurately preserve Grassmannian geometry while reducing computation, memory, and storage. Rank-one embeddings therefore provide a practical and scalable alternative to classical Grassmannian kernels.

Rémi Delogne, Laurent Jacques

INMA/ICTEAM, UCLouvain, Belgium

Atom-Averaged Features Kernel Method Subspace Approximation Random

Aug 4, 2026cs.CV

Low-Dimensional High-Leverage Subspace Optimization: Beyond Full-Parameter Coupled Training for Neural Network Quantization

Low-bit quantization suffers severe accuracy degradation on compact networks, rooted in the dominant full-parameter coupled training paradigm that ignores parameter subspace heterogeneity. Their limited feature redundancy leaves little room to absorb quantization errors. Conventional pipelines adopt monolithic optimization: PTQ reconstructs fixed pretrained models without improving inherent quantization friendliness; QAT updates all parameters jointly, suffering from gradient coupling between backbone weights and calibration parameters. In this paper, we identify normalization affine parameters as a low-dimensional high-leverage subspace dominating quantization robustness, and propose Normalization Affine Preconditioning (NAP) for targeted subspace optimization. For PTQ, NAP freezes backbone weights and fine-tunes only affine parameters under the target fake-quantization graph on full-precision models, proactively boosting quantization friendliness before downstream reconstruction. For QAT, we introduce an alternating QAT-NAP schema that decouples feature learning and numerical calibration, breaking the performance ceiling of saturated joint training. Theoretical analysis confirms BN affine parameters fully cancel the channel-wise affine component of quantization distortion, while nonlinear rounding and clipping residuals form the irreducible error boundary; distillation-guided NAP acts as directional flatness optimization, projecting teacher-student logit mismatch onto the restricted subspace. Experiments on ImageNet and CIFAR-100 show NAP recovers severely collapsed low-bit quantization, consistently boosts reconstruction-based PTQ, and outperforms saturated full-parameter QAT with negligible tuning cost. This work reveals the principle of targeted low-dimensional subspace optimization, offering a new perspective beyond full-parameter coupled training for efficient deep learning.

Peng Xia, Junbiao Pang, Zheng Huang

School of Information Science and Technology, Beijing University of Technology, Beijing, China

Post-Training Quantization Subspace Spectral Preconditioning

Aug 4, 2026math.OC

Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework

Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. This condition gives a direct way to rule out convergence to strict saddles, but it also oversimplifies the actual noise structure, and does not match many stochastic optimization regimes. In overparameterized or interpolation models, the noise may vanish near stationarity. In finite-sum problems, the stochastic gradient noise may lie in a low-dimensional, data-dependent subspace. In these (common) scenarios, UE is naturally not satisfied. In this paper, we prove an abstract almost sure avoidance theorem for stochastic recursions without UE. The theorem replaces UE-type requirements by verifiable pathwise conditions. In applications, these conditions follow, e.g., from local smoothness and finite-moment assumptions under standard i.i.d. sampling, or from the finite-sum structure under without-replacement sampling. Since the stochastically sampled maps generally do not share a fixed point, the celebrated center-stable manifold argument used in deterministic analyses is not directly applicable. Instead, we use a path-dependent change of variables together with a pathwise Lyapunov--Perron-based proof strategy. As applications, we obtain strict saddle avoidance for stochastic mirror descent (including SGD) and for random reshuffling. For nonsmooth composite objectives, we prove avoidance results for a proximal-type stochastic gradient method. Combining these insights with suitable iterate convergence guarantees, this allows establishing convergence to local minimizers of the original objective function.

Junwen Qiu, Bohao Ma, Andre Milzarek +1

Industrial Systems Engineering and Management, National University of Singapore, Singapore. · School of Data Science, The Chinese University of Hong Kong, Shenzhen, China.

Lyapunov Function Pathways Subspace

Aug 3, 2026cs.LG

RamanPFN: learning from Raman spectral structure with a tabular foundation model

Raman spectroscopy enables label-free molecular characterization across materials science, analytical chemistry, biomedicine, and industrial process monitoring. However, machine learning for high-dimensional spectroscopy remains constrained by limited labelled data and a mismatch between the physical organization of spectra and feature-agnostic models. Channel coverage alone does not ensure that related bands share a common inference context. Here we present RamanPFN, a general-purpose spectral foundation framework that enables unified in-context inference through physics-guided spectral learning. It captures full-spectrum compositional covariation via Global Compositional Unmixing (GCU), which decomposes distributed, multi-band mixture signatures into shared non-negative latent bases. Simultaneously, it resolves local vibrational structure through Local Vibrational Subspace Encoding (LVSE), which preserves fine-grained peak morphology, intensity fluctuations, and peak shifts within contiguous spectral neighborhoods. Extensive evaluation across 74 diverse public Raman datasets covered 129 regression targets and was further extended to 21 classification tasks. RamanPFN achieved state-of-the-art performance across all reported aggregate metrics against 28 independently reproduced methods spanning chemometrics, spectral neural networks, deep tabular learners and tabular foundation models. RamanPFN establishes a physics-guided paradigm for scientific spectroscopy, enabling data-efficient predictive learning across diverse chemical systems.

Xingyu Pan, Huan Wang, Jinjia Guo +3

Beihang University · Cleer Science

Raman Spectral Label-Free Subspace

Aug 2, 2026cs.CL

QR-Erase: Efficient Subspace-Based Machine Unlearning with Layer Localization

Machine unlearning seeks to remove targeted information from trained models without requiring costly retraining. Existing optimization-based methods often degrade unrelated capabilities, while subspace-based approaches rely on computationally expensive singular value decompositions (SVD). We introduce QR-Erase, a subspace-based framework that uses Pivoted QR decomposition to identify and remove task-specific representations directly from model parameters. We further propose Layer-Localized QR-Erase, which restricts updates to layers containing the highest concentration of task-specific information. We show that Pivoted QR provides accurate subspace recovery with bounded error, and that under a mild spectral gap condition, the recovered subspace approaches the optimal SVD solution. Across task-level, cross-lingual, and speech unlearning, QR-Erase achieves a stronger forgetting-retention tradeoff than optimization-based methods while remaining within 5% of SVD across all metrics. Exploiting low-rank and layer-localized structure further improves forgetting (for example, reducing speech forget-set accuracy from 53.1% to 15.7%). These results demonstrate that accurate subspace recovery, rather than optimal reconstruction, is sufficient for effective unlearning and provides an efficient and general alternative to SVD-based methods for modern foundation models.

Tyler Lizzo, Larry Heck

Georgia Institute of Technology

Machine Unlearning Subspace Singular Value Decomposition Concept Erasure Object Localization

Aug 1, 2026cs.AI

Through the LENS: Local Geometric Decomposition of Vision-Language Model Representations

Vision-language models (VLMs) process image patches and text tokens in a shared residual stream, but the local geometry through which the two modalities interact remains poorly understood. Most interpretability methods identify global linear directions, which may miss representations that are globally high-dimensional but locally low-dimensional. We introduce LENS (Local Explanation of Neighborhood Subspaces), a method that decomposes VLM activations into local low-rank Gaussian neighborhoods using a Mixture of Factor Analyzers. Applied to LLaVA-1.5-7B and Qwen3-VL-8B, LENS reveals distinct depth-dependent fusion trajectories consistent with each model's fusion mechanism: LLaVA progressively mixes modalities at later layers, whereas Qwen3-VL mixes them early, partially re-segregates them, and recombines them near the output. An automated multimodal labeling pipeline assigns concise semantic descriptions to these neighborhoods. Interpolating activations toward neighborhood centroids causally redirects generation within and across modalities and outperforms difference-in-means and VL-SAE in most evaluated conditions; in one LLaVA vision-to-vision setting, MFA achieves 5.7 times the VL-SAE score. Human evaluation finds MFA steering competitive with prompting and substantially stronger than the other intervention baselines. Finally, the MFA coefficient space improves Qwen3-VL image-to-rendered-text retrieval at the deepest evaluated layer from 14.9% to 48.6% R@1. Ablations show that the reported fusion trajectories are stable across component counts, local ranks, and modality-purity thresholds. These results support local geometric neighborhoods as useful interpretable and causal units for analyzing cross-modal representations in the evaluated VLMs.

Shalom Kachko, Raz Lapid, Margarita Vald +2

1Ben-Gurion University of the Negev · 2Intuit Inc. · 3Deepkeep

Cross-Modal Modalities Explainable AI Methods Subspace

Aug 1, 2026cs.CL

S $^4$ R: Selective Sampling, Subspaces, and Sparse Reconstruction for Compressed Long-Context KV Caching

The growth of context window lengths in Large Language Models (LLMs) significantly enhances their long-context capabilities but incurs prohibitive memory costs due to the Key-Value (KV) cache. Although low-rank compression of KV cache is a promising remedy, existing methods face a dilemma: offline approaches depend on external calibration data, whereas online approaches incur substantial compute for full-prompt decomposition and reconstruction. In this paper, we propose S

^4

R, which builds low-rank subspaces from selectively sampled tokens and computes attention over a sparsely reconstructed KV representation. S

^4

R uses prompt-aware initialization to build initial key/value bases from a representative prompt subset, trading off calibration-data dependence against prefilling cost. Because fully reconstructing the cache at every decoding step is prohibitively expensive and hurts throughput, we further adopt sparse reconstruction to retain only informative positions during decoding. Extensive experiments on LongBench and RULER with Llama and Qwen model families show that S

^4

R achieves up to 5

\times

KV compression with near full-cache accuracy, combining the efficiency of fixed compression with the adaptability of prompt-dependent methods.

Jialong Han, You Wu, Kewei Tu

School of Information Science and Technology, ShanghaiTech University · Shanghai Engineering Research Center of Intelligent Vision and Imaging

Key-Value Cache Compression Key-Value Cache Large Language Model Compression Low-Rank Structure Subspace

Jul 30, 2026cs.LG

Beyond Geometric Complementarity: Coherent Overlap in Sparse Mixture-of-Experts Routing

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled

2\times2

factorial; frozen-route interventions and a controlled Top-

k

study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.

Huiyuan Tian, Bonan Xu, Shijian Li

College of Computer Science and Technology, Zhejiang University, Hangzhou, China · Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University

Mixture-Of-Experts Complementarity Subspace

Jul 30, 2026stat.ML

On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems

We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems. It is shown that the proposed extension - that we coin as Entropy-Optimal Manifold Regression (EOMR) - allows a robust learning with linearly-scaling iteration and memory complexities. EOMR is compared to the most complete set of state-of-the-art tools from the Artificial Intelligence (AI) and Machine Learning (ML) that is available to the author, on the very challenging problems from chaotic and fluid dynamics: (i) on predicting the Lorenz-96 systems dynamics in strongly- and very-strongly chaotic regimes (with forcing parameter being

F=8

and

F=12

, respectively); and, (ii) on a data from the Hasegawa-Wakatani model on the edge of the tokamak plasma. It is demonstrated that the proposed benchmarks (i) and (ii), indeed, are the very challenging problems for the state of the art ML and AI tools - since both the general-purpose gradient boosted random forests and deep neuronal networks, as well as transformer-based AI tools like TabPFN v.03 (more spezialised for large-dimensional small data learning problems) - result in orders of magnitude inferior root mean squared prediction errors, and orders of magnitude larger model complexities, when compared to the EOMR. For a Hasegawa-Wakatani example, EOMR distills a very simple entropy-optimal and skilful description of the leading Essential Orthogonal Function (EOF) dynamics, given by linear, causal and weakly-stationary autoregressive process described by just 8 parameters.

Illia Horenko

Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.

Chaos Subspace Model Size

Jul 28, 2026math.NA

A Riemannian View on Active Subspaces

Active subspaces provide an explainable, eigenvalue-ordered principle for studying how scalar-valued quantities of interest change the most, on average, over a reduced basis of Euclidean domains. Composition with parallel transport generalizes this principle from Euclidean space to quantities of interest defined over Riemannian manifolds, and the resulting intrinsic formulation is contrasted with the extrinsic, embedding-based gradient average of manifold learning. Either strategy is studied in an intrinsically local sense, restricted to mean-centered geodesic-balls, and within that scope the two are not identical: on the central tangent space, eigenvalues agree to second order in the geodesic radius of the sampled domain, while dominant eigenspaces agree at the same order relative to the spectral gap. Extending activity beyond that central space then calls for either recomputed decompositions over changing tangent spaces or, intrinsically, parallel transport of a single central frame. Hyperspheres are emphasized throughout as a particular manifold of interest, motivated by applications over preshape spaces for statistical shape analysis. Numerical examples over the 2-sphere illustrate the formalism, including the derived ridge recovery at a curvature-limited quadratic rate.

Zachary Grey

Riemannian Manifolds Geodesic Subspace Spectral Decomposition

Jul 26, 2026cs.CV

Contrastive Parameter Disentanglement for Multi-modal Remote Sensing Image Generation

Existing remote sensing image generation methods are largely confined to single-modality synthesis and therefore fail to exploit the complementary information inherent in multimodal imagery. To address this limitation, we propose a contrastive parameter disentanglement framework for multimodal remote sensing image generation, which generates semantically consistent and structurally aligned images across multiple modalities, including optical, infrared, and synthetic aperture radar (SAR), from a single text prompt. Specifically, we introduce a contrastive parameter disentanglement module that disentangles shared semantics from modality-specific attributes at the parameter level within an orthogonal core subspace. Based on this module, we develop a disentangled optimization strategy that first constrains the parameter matrix A of the LoRA adapter to capture modality-invariant semantics through a multimodal contrastive objective and then guides multiple parameter matrices B to learn modality-specific attributes under text conditioning. This strategy enables the simultaneous generation of multimodal images with consistent semantic content and distinct modality characteristics. Furthermore, to ensure structural alignment across the generated images, we devise a query-key structure transfer mechanism that jointly models multimodal sampling trajectories during inference by transferring structural correlation priors from an anchor modality to the remaining modalities. Extensive experiments demonstrate that our method outperforms state-of-the-art remote sensing image generation approaches in terms of generation quality, semantic consistency, and structural alignment, while also achieving superior performance in the downstream object classification task.

Yu Zhang, Wenda Zhao, Haojun Tang +1

Multimodal Contrastive Learning Remote Sensing Modalities Image Generation Subspace

Jul 24, 2026cs.CL

Enough is as good as a feast: A Comprehensive Analysis of How Reinforcement Learning Mitigates Task Conflicts in LLMs

Model merging plays a crucial role in consolidating multiple specialized models into a single, unified model, especially in the era of large language models (LLMs). Recent research has primarily focused on developing strategies to enhance merging performance with the trained models, while the impact of training paradigms, such as supervised fine-tuning (SFT) and reinforcement learning (RL), on the effectiveness of model merging remains underexplored. In this study, we systematically explore the merging behavior of RL-trained LLMs compared to those trained with traditional SFT. Through comprehensive evaluations across five representative tasks, we find that RL significantly reduces task conflicts and results in less performance degradation after merging, making RL-trained models particularly well-suited for this process. To unearth the reasons behind the superior suitability of RL for model merging, we conduct extensive empirical experiments and theoretical analyses. Our findings highlight three key factors: (1) On-policy training data in RL control the gradient updates in a smaller magnitude, reducing the risk of overwriting existing knowledge for other tasks in the model. (2) The RL optimization objective, which favors ``\textit{enough is as good as a feast}", progressively reduces the magnitude and the number of conflict parameter updates as the model converges. (3) Joint optimization of positive and negative examples in RL steers the model towards an unbiased task-specific parameter subspace, ensuring robust performance while further preventing parameter conflicts.

Zixuan Ren, Jinliang Lu, Junhong Wu +5

State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, CAS, Beijing, China · School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China · Baidu Inc., Beijing, China

Large Language Model Reinforcement Learning Subspace Systematic Study

Jul 24, 2026cs.CV

Gradient-Based Latent Decomposition Reveals Mechanisms of Feature Degradation in Weakly Supervised Mammography

Weakly supervised hierarchical models exhibit a persistent asymmetry: coarse lesion-type features are preserved under reconstruction while fine-grained malignancy cues degrade---a pattern with direct consequences for the clinical reliability of breast cancer screening pipelines. We introduce gradient-based orthogonal latent decomposition for hierarchical Variational Autoencoders~(H-VAEs) to mechanistically explain this asymmetry. The latent space is partitioned into a task-aligned component~(

z_1

), shaped by coarse supervisory gradients, and an orthogonal residual~(

z_{\text{res}}

) capturing remaining representational capacity. On~~3,550 mammographic Regions of Interest~~(ROIs) from CBIS-DDSM, only~

\sim

4.4% of latent magnitude aligns with supervisory gradients, leaving~

\sim

95.6% in the orthogonal residual upon which fine-grained pathology prediction primarily depends. The model achieves Stage-1~~AUC~~0.866 and Stage 2~~AUC~~0.552, with a reconstruction stability gap of

Δ_{\text{diag}}=5\%

(

p=0.005

) and a classification gap of

Δ_{\text{AUC}}=0.314

(

p{<}0.001

). Latent ablation confirms that features for both tasks reside heavily in~

z_{\text{res}}

, structurally explaining why reconstruction degrades pathology stability disproportionately. Comparisons with Multi-Instance Learning~(MIL) and Multi-Task Learning~(MTL) confirm generalization across architectures and modalities. These findings reveal that in high-dimensional spaces, a single coarse supervisory signal isolates only a sparse 1D latent direction, forcing critical fine-grained features into the vulnerable residual subspace.

Vinceline Bertrand, Ionut Cardei

Florida Atlantic University, Boca Raton, FL, USA

3D Masked Autoencoders Gradient-Weighted Class Activation Mapping Degradation Subspace Representational Capacity Asymmetry

Jul 23, 2026cs.LG

Emergent Misalignment Recruits a Pre-existing Persona Subspace

Fine-tuning an aligned language model on a narrow stream of bad advice can make it broadly misaligned on questions unrelated to the training data, a phenomenon called emergent misalignment. We ask why the narrow lesson generalizes at all, and we find that narrow fine-tuning recruits a persona structure that is present in the model before the fine-tune exists. From a frozen instruction-tuned model (Qwen2.5-14B-Instruct) we extract per-domain persona subspaces by contrastive teacher forcing and find that 4 unrelated domains share one low-rank core at 657x a random-subspace null, with 82% of that core lying outside a style core built at matched diversity. The literal first optimizer step of fine-tuning on insecure code climbs a broad-misalignment margin harder than the same code framed as educational, and forecasts realized margin movement out to 375 steps. Projecting the subspace out of the residual stream throughout fine-tuning prevents broad misalignment (27.7% to 0.0% of judged generations) while a matched-rank random subspace changes nothing; injecting it into the never-fine-tuned model induces misalignment that grows with dose to 45.4%, past the fine-tuned model it is measured against. The same projection applied to the weight gradient is inert, and three post-hoc weight edits leave the disposition in place: the sharpest edit suppresses the behavior rather than removing it, and the ablated structure re-forms inside the subspace the edit cleared. Spreading a fixed budget of bad data across 4 domains produces more broad misalignment than mechanical weight superposition and matched diversity jointly account for. All measurements come from one model at 14B; the extraction is from an aligned instruction-tuned checkpoint, which leaves the structure's provenance open; and the intervention that prevents misalignment also abolishes the narrow trained behavior.

Mohammed Suhail B Nadaf

Independent

Emergent Misalignment Continual Fine-Tuning Language Modeling Subspace

Jul 23, 2026cs.LG

CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data

Deep subspace clustering plays a critical role in applications involving multivariate spatiotemporal data, such as sea ice monitoring, disease spread analysis, and tracking neuro-degeneration over time. Despite recent advances, existing methods primarily rely on geometric self-expressiveness, assume static subspace structures, and often fail to capture causal dependencies, local spatial interactions, and long-range temporal dynamics inherent in complex spatiotemporal systems. To address these limitations, we propose a novel Causal Adversarial Subspace Clustering (CASC) framework for discovering evolving latent regimes in high-dimensional spatiotemporal data. CASC integrates a U-Net-inspired deep adversarial clustering architecture with stacked FAConvLSTM layers to preserve spatial and temporal structure while learning robust latent representations. A graph attention transformer-based self-expressive network is introduced to jointly model local spatial relationships, global dependencies, and long-range temporal interactions. Furthermore, we propose two new learning objectives: (1) a Causal Subspace Preservation Loss that aligns self-expression coefficients with latent causal relationships, encouraging clusters to reflect underlying causal processes rather than simple feature similarity, and (2) a Dynamic Temporal Subspace Evolution Loss that captures evolving subspace structures and temporal regime transitions in nonstationary environments. Together, these components transform deep subspace clustering from a correlation-driven paradigm into a causal-temporal regime discovery framework.

Francis Ndikum Nji, Vandana Janeja, Jianwu Wang

Dept. of Information Systems University of Maryland, Baltimore County Baltimore, MD, U.S.A

Spatiotemporal Causal Discovery Methods Subspace Expressivity

Jul 22, 2026quant-ph

Machine-Learned Compact Subspace Generation for Quantum Selected Configuration Interaction within Density Matrix Embedding Framework

Sample-based Quantum Diagonalization (SQD), an extension of Quantum Selected Configuration Interaction (QSCI), has emerged as a promising hybrid quantum-classical paradigm for computing molecular ground state energies. By leveraging quantum sampling instead of variational optimization, QSCI avoids barren plateaus and enables direct reconstruction of correlated electronic wavefunctions. However, existing configuration recovery techniques primarily enforce symmetry constraints without guaranteeing optimal selection of the most physically relevant configurations, often leading to unnecessarily large subspaces and increased classical diagonalization costs. In this work, we introduce a machine-learned compact subspace generation protocol based on Restricted Boltzmann Machines (RBMs), termed QSCI-RBM, and integrate it within the Density Matrix Embedding Theory (DMET) framework. The RBM is trained on quantum-sampled configurations to learn the underlying probability distribution of dominant determinants, enabling the targeted generation of high-probability configurations. We apply this framework to the simulation of a protein-ligand complex involving the inhibitor Carmofur bound to the SARS-CoV-2 main protease (

M^{\text{pro}}

). Our results demonstrate that DMET-QSCI-RBM achieves energies within the chemical accuracy threshold by accessing only approximately 4% of the configuration subspace. In contrast, standard DMET-SQD simulations failed to reach chemical accuracy while accessing up to 20% of the subspace, even as the chemical potential itself nearly converged. These findings highlight that RBM-assisted configuration generation produces significantly more compact subspaces while preserving physical accuracy, thereby reducing classical computational overhead and enabling the scalable quantum embedding simulation of complex biological systems.

Ashish Kumar Patra, Anurag K. S. V., Ruchika Bhat +3

1Qclairvoyance Quantum Labs, Secunderabad, TG 500094, India. · 2The University of Arizona, Tucson, AZ 85721, USA. · 3Indian Institute of Technology Bombay, Mumbai, MH 400076, India.

Quantum Chemistry Density Functional Theory Subspace Gibbs

Jul 21, 2026quant-ph

Enhanced Neural Quantum State via Annealed Gradient Descent

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional

J_1

-

J_2

models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.

Shiwei Zhou, Yiming Huang, Xiao Yuan +1

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China · China Center of Advanced Science and Technology, Beijing 100190, China · Center on Frontiers of Computing Studies, School of Computer Science, Peking University, Beijing 100871, China

Annealing Post-Quantum Cryptography Metastable Samples Gradient Descent Gradient Subspace

Jul 20, 2026cs.CV

Miles: Metric Learning with Expandable Subspace for Pre-Trained Model-Based Class-Incremental Learning

Class Incremental Learning (CIL) aims to learn new concepts consistently from a data stream without forgetting. Unlike typical CIL methods which need to learn a model from scratch, pre-trained model (PTM) can easily adapt to a new task with fine-tuning. However, existing PTM-based CIL methods fail to achieve a trade-off between performance and computational expenditure, i.e., they either adopt the same parameter space so that leading catastrophic forgetting, or expand a new branch for each task but adding more computational cost. To this end, we propose MetrIc Learning with Expandable Subspace (Miles) to harness the prior information within pre-trained knowledge, thereby orchestrating an efficient expansion of the parameter space through guided optimization. Specifically, it decouples the learnable modules with the pre-trained model, exploiting prior information from intermediate features of the backbone network to enable more flexible parameter expansion. Then, a central loss is adopted to guide the new category to cluster towards the corresponding prototype in the new task subspace while incorporating an auxiliary distance regularization term to maintain metric equilibrium across tasks. Extensive experiments on six benchmark datasets demonstrate that Miles achieves state-of-the-art performance in various CIL settings.

Kai Jiang, Zisong Lin, Hongyuan Zhang +2

National Key Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China · The University of Hong Kong, Hong Kong SAR, China · Institute of Artificial Intelligence (TeleAI) of China Telecom, China

Class-Incremental Learning Meta-Learning Pretraining Subspace Regularization

Jul 19, 2026cs.CV

Orthogonal Knowledge Refreshing for Domain-Incremental Object Detection

Domain-incremental object detection (DIOD) requires models to continually adapt to new domains while preserving prior knowledge. Recently, parameter-efficient fine-tuning offers a promising avenue, wherein a pre-trained model is frozen and a small number of learnable parameters are injected for downstream tasks. However, these methods risk overwriting critical past knowledge, triggering inter-domain interference and performance degradation. To address this challenge, we propose Orthogonal Knowledge Refreshing (OKR), a simple yet effective framework for DIOD. OKR incrementally constructs independent domain-specific subspaces via dedicated low-rank branches for each domain, which are seamlessly fused for a holistic decision, enabling conflict-free capacity expansion without domain selection during inference. To minimize knowledge interference during fusion, we present a gradient-based orthogonal refreshing strategy that projects gradient updates of new domains onto the orthogonal complement of the fused historical subspace, supporting continual adaptation without forgetting. Moreover, to mitigate semantic fragmentation across domains, we enforce topology-aware consistency, aligning the semantic structures of old and new domains. Extensive experiments validate the superiority of OKR, outperforming the best exemplar-free method by significant margins of +5.6% and +6.5% mAP on the Pascal VOC and BDD100K series, respectively.

Aoting Zhang, Dongbao Yang, Chang Liu +3

Institute of Information Engineering, Chinese Academy of Sciences · School of Cyber Security, University of Chinese Academy of Sciences · Nankai University +2

Out-Of-Distribution Detection Objects Subspace

Jul 18, 2026cs.LG

MultiLoReFT: Decoupling Shared and Modality-Specific Subspaces in Multimodal Learning via Low-Rank Representation Fine-Tuning

Real-world perception and decision making are inherently multimodal, integrating complementary signals across modalities. However, training multimodal models faces two main obstacles. First, collecting large-scale, well-aligned paired multimodal datasets is often impractical, making end-to-end multimodal training difficult. Second, existing multimodal representations frequently entangle information shared across modalities with modality-specific information, hindering interpretability and control. We introduce MultiLoReFT, an efficient and scalable low-rank representation fine-tuning framework for multimodal learning with pretrained unimodal models. MultiLoReFT extends low-rank adaptation to the multimodal setting and learns interpretable projection subspaces that decouple shared and modality-specific information. Across simulated and real-world benchmarks, it produces representations that support multimodal prediction while explicitly revealing how shared and modality-specific information is distributed across modalities.

Sana Tonekaboni, Viktoria Schuster, Caroline Uhler

Massachusetts Institute of Technology, Cambridge, MA, USA · Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard, Cambridge, MA, USA · Vector Institute, Toronto, Canada +1

Multimodal Learning Modalities Subspace

Jul 18, 2026cs.LG

CT-Merging: Consensus Directions and Task-Level Scaling for LoRA Adapter Merging

LoRA adapters provide an efficient way to specialize a pretrained model for many downstream tasks, but deploying one adapter per task requires adapter storage and task selection at inference time. Model merging addresses this issue by combining independently trained adapters into one multi-task adapter. Recent SVD-based LoRA merging methods mainly focus on constructing shared or task specific directions, while the coefficients assigned to the final directions are often directly from the original task SVD. On a fixed merged basis, inherited coefficients preserve component order with high rank correlation, yet their magnitudes differ substantially from the coefficients induced by the task updates. To address this mismatch, we propose CT-Merging, a LoRA-aware merging algorithm that estimates consensus directions from average task subspace projectors and assigns task-level RMS coefficient scales in the final update. CT-Merging uses repeated support across task SVD subspaces to construct the common basis, while reducing reliance on rank wise SVD magnitudes after direction construction. On the DC-Merge CLIP adapter benchmark, CT-Merging achieves superior average normalized accuracy compared to state-of-the-art merging methods and further improves over DC-Merge by 2.56 points on ViT-B/32 and 1.51 points on ViT-L/14 KnoTS-trained checkpoints.

Keumseo Ryum, Joonhyuk Kang

KAIST

Continual Model Merging Low-Rank Adaptation Adapters Merge Subspace Task-Level Scaling

Jul 15, 2026cs.LG

Dysco: Dynamic Subspace Boosting to Mitigate LoRA Interference in Federated Learning

Federated fine-tuning of large pre-trained models increasingly relies on Low-Rank Adaptation (LoRA) to reduce communication and computation, but heterogeneous clients can make adapter aggregation unstable. We identify the data-parameter interference as a geometric source of this instability. This interference is controlled by the alignment between LoRA update subspaces and client activations, suggesting that federated LoRA aggregation should be viewed not only as parameter averaging but also as subspace allocation. We propose Dynamic Subspace Boosting (Dysco), a plug-in method that allocates client-specific LoRA subspaces in a federated and dynamic manner. In each round, clients compute activation-insensitive subspaces from local representations and transmit only the resulting bases; the server then constructs client-specific merged subspaces through a closed-form solution that maximizes compatibility with other clients' insensitive directions. To handle representation drift, Dysco performs multi-round subspace boosting to preserve past update directions while adapting to future representations. We provide a convergence analysis that embeds the data-parameter interference as an aggregation-error term in a standard federated optimization bound, and prove that Dysco's server-fixed merged subspaces yield a tighter upper bound on this error. Experiments on controlled synthetic federated tasks and on MIMIC-IV clinical-note classification with Llama-3.2-1B show that Dysco substantially reduces interference, reduces the final-round synthetic training loss by up to 9 times relative to baselines under the orthogonal-subspace partition the theory identifies, improves all five tested FL algorithms by up to 4.3% on MIMIC, outperforms recent federated LoRA methods, and adds only 0.9% wall-clock overhead. Our code is available at https://github.com/illidanlab/Dysco.

Haobo Zhang, Jiankun Wang, Suraj Rajendran +5

University of Michigan · Cornell University · University of Pennsylvania

Federated Learning Subspace Synthetic Training Data Duet

Jul 15, 2026cs.CR

Traffic-Aware Randomized Smoothing for LLM-Based Network Intrusion Detection

Large language model (LLM)-based intrusion detection systems (IDS) are increasingly studied for security monitoring, yet their robustness against feasible traffic manipulation remains largely empirical. We present Traffic-Aware Randomized Smoothing (TA-RS), a classifier-agnostic certified defense that injects Gaussian noise exclusively into the directly controllable (DC) subspace -- features a remote attacker can modify -- during both fine-tuning and certification, aligning the smoothing distribution with the attacker-controllable subspace. We identify a critical prerequisite: applying standard randomized smoothing to clean-trained LLM-IDS yields weak certified accuracy in three of four (model, dataset) pairs tested (14-33%, at or below random) and only 57% in the fourth (43 pp below the noise-augmented result); noise-augmented fine-tuning recovers to 68-100% on two of three benchmark datasets (at sigma=0.25). At the L_inf-equivalent threshold R_inf = epsilon*sqrt(|DC|) (epsilon=0.05), TA-RS achieves 55-100% certified accuracy on CIC-IDS-2018 and HIKARI-2021, with median certified radii (R approx 0.45-0.96) exceeding R_inf by 1.8-5x (across sigma=0.25-1.00). Against a fairly trained iso-trained RS baseline the residual advantage is dataset-dependent (4-19 pp on CIC-IDS-2018). The larger gap -- up to 72 pp against an isotropic RS baseline that shares the DC-noise-augmented training recipe -- primarily reflects the training-certification mismatch rather than DC alignment alone: isotropic test-time noise perturbs uncontrollable features the attacker cannot exploit, triggering abstention rates up to 68%. RT-IoT2022 probes the limits of the method: it fails under the default fine-tuning recipe but recovers to 76%/69% certified accuracy (LLaMA3-8B/Qwen3-8B) when noise augmentation is increased.

Zhenpeng Li

Intrusion Detection Smoothing Subspace

Jul 13, 2026cs.SD

Evidence Subspace Projection: Measuring How Much Evidence Explains Deepfake Detection in Self-Supervised Speech Models

Self-supervised learning (SSL) models are widely used as feature extractors for state-of-the-art audio deepfake detection, but it remains unclear how to directly and quantitatively connect what SSL models capture to detection decisions. To address this gap, we propose Evidence Subspace Projection, a method that represents both evidence factors (e.g., attack category, codec, gender, transmission) and authenticity labels in a shared space constructed from SSL models' neuron activation patterns. By projecting the decision vector onto each evidence subspace, we obtain a scalar ratio that quantifies the explanatory power of each evidence type. We evaluate SSL models in raw, fine-tuned, and post-trained settings on multiple datasets. The results confirm findings from established studies, validating the proposed method, and reveal new insights into model behavior.

Yixuan Xiao, Cheng-Wei Lin, Xin Wang +5

University of Stuttgart, Germany · National Institute of Informatics, Japan · German Research Center for Artificial Intelligence (DFKI), Germany +1

Audio Deepfake Detection Self-Supervised Speech Models Deepfake Detection Authenticity Subspace Incomplete Evidence+1

Jul 12, 2026cs.LG

Bandit PCA with Minimax Optimal Regret

We study the bandit-feedback version of online principal component analysis (Bandit PCA): in each round

t = 1,\dots,T

, the adversary selects a

d \times d

symmetric gain matrix

G_t

with spectrum in

[0,1]

and rank at most

r

; the learner simultaneously selects a unit vector

w_t \in S^{d-1}

and receives the reward

w_t^\top G_t w_t

. The learner receives no other feedback, and aims to minimize the regret against the best unit vector in hindsight. This problem was introduced by Kotlowski and Neu (2019), who gave an algorithm with regret

O(d\sqrt{rT \log T})

and showed the lower bound of

Ω(r\sqrt{T/\log T})

. We improve upon both of these bounds and essentially bridge the gap between them, establishing the minimax regret of order

r\sqrt{dT}

up to polylogarithmic factors in

d

and

T

. The upper bound is attained by a novel algorithm, which combines online mirror descent on the spectrahedron of (real) density matrices with a multiscale exploration scheme in which the eigenspaces with different spectral magnitudes are updated at different rates. For the lower bound, we construct an adaptive adversary that refines a hidden large-reward subspace based on the learner's actions, in such a way that low regret is impossible without estimating the subspace; as a result, lower-bounding the regret reduces to studying the arising subspace estimation problem. Finally, we discuss connections of Bandit PCA with adaptive-measurement quantum tomography.

Moïse Blanchard, Dmitrii Ostrovskii, Aadirupa Saha

Georgia Tech · University of Illinois, Chicago

Principal Component Analysis \Widetilde{\Mathcal{O}}(\Sqrt{T})$ Regret Regret Subspace

Jul 12, 2026cs.LG

The Spectral Structure of Latent Treatment Effects

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Hamza Virk, Bijan Mazaheri, Yihren Wu

1Dartmouth College · 2Broad Institute of MIT and Harvard · 3Hofstra University

Heterogeneous Treatment Effects Latent Confounders Causal Inferences Spectral Latent Variable Subspace

Jul 11, 2026cs.RO

Source-Lifted Flow Matching for Intervenable Multimodal Imitation

Flow-matching policies are promising for imitation learning because they model complex multimodal action distributions. However, their stochasticity is largely passive: repeated sampling may yield diverse behaviors, but users cannot directly choose among valid continuations from the same state. We propose Source-Lifted Flow Matching (SL-FM), a source-intervenable flow-matching policy that exposes such a handle while keeping the velocity field shared and latent-free (without a separate discrete-handle input). The handle selects only the source endpoint of the conditional flow, not a mode-specific field, preserving the standard formulation while avoiding decomposition into separate mode-conditioned dynamics. The core mechanism is Orthogonal Source Lifting, designed to prevent path-crossing ambiguity. Instead of partitioning target actions by mode, SL-FM lifts handle-specific sources into auxiliary orthogonal coordinates and keeps targets in the original action subspace. This preserves the demonstrated action distribution while allowing one shared field to carry different branches without merging at crossings. To keep handles usable across states, we learn a state-dependent source mixture end to end and use a responsibility floor, giving each handle weak supervision and mitigating dead modes. Experiments on crossing-flow diagnostics and robot-control benchmarks show that SL-FM converts passive source randomness into an actionable intervention variable. It removes crossing-induced composite trajectories, changes future routes in 91.1% of matched-prefix interventions, and achieves strong free-deployment performance, with improvements in several benchmark settings. Overall, source geometry provides actionable multimodal control without conditioning the velocity field on the selected mode.

He Zhang, Ying Sun, Ziyang Chen +6

The Hong Kong University of Science and Technology (Guangzhou) · AI2 Robotics

Multimodal Action Distributions Conditional Flow Matching Temporally Coherent Imitation Learning Imitation Learning Subspace

Jul 10, 2026cs.CV

REBASE: Reference-Background Subspace Elimination for Training-Free In-Context Segmentation

Training-free in-context segmentation enables new object categories to be introduced at inference time from a single annotated reference image, eliminating the retraining and memory overhead of class-incremental learning. Recent approaches achieve this by combining vision foundation models for semantic correspondence with promptable segmentation networks like SAM. However, their performance is fundamentally limited by the quality of the cross-image similarity map; shared contextual backgrounds between the reference and query systematically elevate similarity in non-target regions, degrading prompt localization. We present REBASE, a training-free framework that explicitly suppresses these spurious contextual correspondences. Our method identifies the low-rank background feature subspace from the reference image and project the reference and query features onto its orthogonal complement in closed form, yielding cleaner semantic matching. We then generate positive point prompts using similarity-weighted farthest-point sampling, paired with a refined dense similarity prior. Without any training or parameter updates, our approach establishes a new state of the art among training-free methods on PACO-Part, FSS-1000, and cross-domain datasets such as ISIC2018, demonstrating that explicit background subspace removal is a highly effective principle for one-shot localization.

Mantha Sai Gopal, Jaison Saji Chacko, Harsh Nandwana +3

CamCom Technologies Private Limited*

Few-Shot Segmentation Semantic Segmentation In-Context Learning Subspace

Jul 9, 2026cs.LG

Stochastic Linear Bandits with Partially Observed Actions

The stochastic linear bandit, where actions are represented as vectors and rewards are linear, is a central paradigm for sequential decision making. We study a partially observed variant of this problem in which the learning agent only sees a random subset of coordinates for each action. Such partial observability arises naturally in settings like recommendation and healthcare, where full action descriptions can be expensive or even impossible to obtain. In general, this makes sublinear regret information-theoretically impossible. However, we show that this barrier can be overcome when the action vectors have low intrinsic dimension. We propose an algorithm, TOFU-POV, that estimates the latent action subspace using the masked actions, imputes current actions using an epoch-wise frozen representation, and runs OFUL in the resulting low-dimensional coordinates. Our theory shows that TOFU-POV enjoys a

\sqrt{T}

regret that scales with the intrinsic action subspace dimension as opposed to the ambient dimension and quantifies the interaction between these quantities and the missingness, decision set size, and subspace conditioning. We also devise a rank-adaptive algorithm that does not require the knowledge of the intrinsic dimension. We complement these guarantees with a lower bound based on a novel product construction that separates usual reward-learning uncertainty from a missingness-dependent cost intrinsic to partial observation. Synthetic and real data experiments support our theory and show that TOFU-POV can substantially improve upon natural baselines in this challenging problem.

Gautam Dasarathy, Vineet Gattani, Lalit Jain

Arizona State University · GE Vernova · Google

Jul 8, 2026cs.NE

Sampling on Random Subspaces under Limited Data in the Context of Exploratory Landscape Analysis

Classical space-filling designs often fail to provide reliable statistical results for Exploratory Landscape Analysis (ELA) when only limited evaluation budgets are available, as commonly occurs in high-dimensional problems or other resource-constrained settings, resulting in noisy and unstable landscape descriptors. To address this challenge, we propose an alternative sampling strategy for ELA based on random linear embeddings. Rather than sampling uniformly in the full decision space, we allocate the budget to randomly oriented low-dimensional subspaces and investigate whether this improves the robustness of the resulting landscape descriptors. We compare full-space and embedding-based sampling strategies across several classical ELA feature sets on the noiseless Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) environment, in a 20-dimensional setting. Our results suggest that random linear embeddings constitute a promising alternative for budget-constrained ELA, although their effectiveness remains dependent on the feature class and the underlying problem.

Iván Olarte Rodríguez, Anja Jankovic, Thomas Bäck +1

Leiden Institute of Advanced Computer Science (LIACS), Leiden University, The Netherlands · RWTH Aachen University, Germany

Optimization Landscape Optimal Design Subspace Limited Data Optimizer Design

Jul 8, 2026cs.LG

On Adversarial Vulnerability of Vision-Language Models through the Lens of Intermediate Spectral Subspaces

Adversarial vulnerability in deep neural networks (DNNs) has been studied from the perspectives of decision-boundary geometry, feature robustness, input-output Jacobians, and the instability of inverse problems. Here, we focus on the spectral structure of intermediate linear transformations that propagate information through modern DNNs, an unexplored mechanism of adversarial vulnerability. Specifically, we investigate transformer-based vision-language models, whose linear layers admit interpretable spectral decompositions and whose widespread adoption makes understanding their robustness increasingly important. We propose a white-box spectral-subspace-guided attack (SSGRA) that aligns intermediate representations with the subspace spanned by the bottom right singular vectors. Our experiments show improved attack effectiveness over existing baselines. In addition, SSGRA offers a spectral interpretation of adversarial vulnerability in VLMs, providing insights for improving their robustness.

Chethan Krishnamurthy Ramanaik, Tobias Callies, Michael Hecht +1

University of the Bundeswehr Munich, Germany · University of Wrocław, Poland

White-Box Spectral-Subspace-Guided Attack Subspace Lens

Jul 7, 2026cs.CR

ORAN-DEFEND: Subspace Detection and Sanitization of Backdoor DRL xApps in Open RAN

Open Radio Access Networks (O-RAN) increasingly delegate near-real-time control to deep reinforcement learning (DRL) xApps obtained from third-party vendors, creating a new supply-chain attack surface. A backdoor policy behaves optimally until an adversary injects a covert trigger into the observed key performance indicator (KPI) telemetry, at which point it issues harmful control actions that degrade quality of service (QoS). We present ORAN-DEFEND, a retraining-free wrapper that sanitizes a frozen, potentially compromised xApp by projecting each KPI window onto a safe subspace estimated from a small number of trusted clean rollouts via singular value decomposition (SVD). We establish, both analytically and empirically, a precise recovery condition: the defense succeeds if the trigger energy concentrates in the orthogonal complement of the safe subspace, and we quantify this boundary through the trigger's

\Eperp

energy fraction. On the Colosseum COLORAN dataset, we evaluate four structurally distinct DRL backdoor attacks, like TrojDRL, SleeperNets, BadRL, and Q-Incept, spanning inner-loop and outer-loop poisoning regimes and demonstrate

100\%

return recovery and

\geq99.5\%

defense success rate across all four when the subspace assumption holds. A geometry ablation reveals an intrinsic and previously uncharacterized limit of any linear projection defense: when the trigger collocates with the legitimate signal, the

\Eperp

energy fraction governs recovery monotonically, and the linear residual detector collapses to chance even while a nonlinear classifier retains perfect separability.

Md Raihan Uddin, Fatemeh Lotfi, Tolunay Seyfi +1

Department of Electrical and Computer Engineering, Clemson University, Clemson, SC, USA

Clean Label Backdoor Attack Model-Agnostic Defense Open Radio Access Networks LLM Defense Mechanisms Subspace Poisoning

Jul 7, 2026cs.LG

No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training

Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked. We show that beyond a small reproducible core, there is no such object. Two estimates of the top-r subspace computed at the same step from disjoint minibatches disagree as much as estimates computed T steps apart (0.73 vs 0.74 of the maximal chordal distance sqrt(2r), at Pythia-160M with r=128): the apparent rotation at each refresh is dominated by estimator noise. This holds across four model families in three architecture classes from 70M to 6.9B parameters, strengthening with scale, and more weakly in a vision transformer. Only ~39 of 128 directions are reproducible across minibatches, and averaging cannot recover the rest: under N-fold averaging the gradient's spectral tail shrinks as N^(-1/4) rather than the N^(-1/2) of pure noise, so no averaging budget makes the subspace well defined. What helps instead follows from treating each refresh as a change of coordinates for Adam's state. Carrying the second moment blindly is provably about (r-k*)/2 worse than the best rotation-blind estimator, while the first moment transports exactly through the rotation, the optimal linear map under isotropic gradients and the rule LDAdam uses. At 1B over 40k steps (3 seeds), full LDAdam reaches 18.7 perplexity at beta2=0.999, beating untransported GaLore after its best beta2 fix (19.3); shortening the second-moment memory to beta2=0.99 helps the refreshing optimizers, though for canonical GaLore the effect is small and a full-rank control reverses it. One measurable fact, subspace non-identifiability, clarifies why GaLore works, which patches work, and what to check before trusting a low-rank assumption: the reproducible rank k*.

Noel Thomas

Mohamed bin Zayed University of Artificial Intelligence

Low-Rank Structure Adaptive Optimizers Subspace Identifiability Vision Transformer

Jul 6, 2026cs.LG

Learning Only What Valid Adapters Can Express: Subspace-Constrained Adaptation Against Fine-Tuning Poisoning

Parameter-efficient fine-tuning still leaves a broad space of behavior-changing updates reachable, so a poisoned objective can be represented and optimized. We study an alternative: adaptation constrained to the subspace estimated from a trusted pool of existing task adapters. On flan-t5-large with 196 public LoRA adapters, we show that (1) the functionally relevant content of an adapter lies in a low-dimensional shared subspace, 30 to 38 percent of its weight norm being redundant under the evaluated task distributions; (2) gradient adaptation restricted to 128 coordinates on this subspace matches full LoRA fine-tuning on clean classification data, while under targeted label inversion LoRA collapses to 3-26 percent exact match and the constrained learner keeps 62-96 percent on the tasks the pool covers; (3) the constrained learner cannot fit corrupted data, its adaptation loss separating clean from garbage by two orders of magnitude (120x), an out-of-distribution signal without an extra detector; and (4) against an adaptive backdoor attacker who optimizes within the subspace, the attack is blocked (8 percent success versus 100 for LoRA) on the task where its target behavior is unlike anything in the pool, and only partially blocked (85 percent) when the target coincides with a common pool behavior. On these two tasks the outcome is consistent with how close the target is to the pool's directions, which suggests but does not establish a pool-relative boundary. The mechanism trades peak plasticity for these properties: on tasks the pool covers poorly, unconstrained fine-tuning wins, and the protection assumes the pool itself is trusted. Code and data are public.

Fabien Polly

Independent researcher

Low-Rank Adaptation Adapters Model Fine-Tuning Subspace Validation Collective Behaviors

Jul 6, 2026cs.CV

Erasing Without Collateral Damage: Precise Concept Removal in Diffusion Models

Training-free concept erasure is an attractive mechanism for controlling text-to-image diffusion models, but precise erasure often comes at the cost of damaging semantically related non-target concepts. Existing value-space methods remove the component of each cross-attention value along the target concept direction, implicitly treating target identity and shared visual structure as the same signal. We argue that this is the source of much of the collateral damage in prior preservation. We introduce CARE, a closed-form concept erasure operator that replaces the raw target direction with a kept-subspace-aware direction computed from a small bank of retained concept anchors. The resulting edit is applied directly in cross-attention value space, requires no model fine-tuning, and adds only a negligible offline computation. A single shrinkage parameter controls the erase-preserve trade-off. We further show that the operator admits a minimum-disturbance interpretation and, in its projection form, leaves the kept subspace invariant. Experiments under the standard concept-erasure protocol show that our method preserves non-target concepts more faithfully while maintaining competitive erasure across instance, style, and celebrity concepts. Code: https://github.com/parthupman/care

Parth Upman, Nishita Jain, Shreyank N Gowda

School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK · Department of Computing, Imperial College London, London, SW7 2AZ, UK

Concept Erasure Text-To-Image Diffusion Models Diffusion Models Cross-Attention Semantic Anchor Structural Damage+1

Jul 5, 2026cs.LG

SAD-LoRA: Spectral Alignment for Low-Rank Knowledge Distillation

Distilling a fine-tuned teacher into a LoRA-adapted student is a standard recipe for parameter-efficient compression, but output-level KD does not explicitly control which rank-

r

weight subspace the adapter occupies. We propose \textbf{SAD-LoRA} (\textbf{S}pectral \textbf{A}lignment \textbf{D}istillation), which selects this subspace from the data-weighted student-space reference update

\DWT\Sigx^{1/2}

and maintains it during training via a differentiable principal-angle loss on

\colspan(B)

. We show that the data-weighted distillation error decomposes exactly into subspace misalignment, within-subspace coefficient mismatch, and irreducible rank residual; standard KD can affect the first term only indirectly through output gradients. On controlled synthetic problems with a flat teacher spectrum, SAD-LoRA reduces the subspace-misalignment term from

51\%

to nearly zero and lifts final subspace alignment from

0.49

to

1.00

. On RoBERTa-large to RoBERTa-base distillation across six GLUE tasks, SAD-LoRA improves rank efficiency: at

r{=}4

, it matches or beats the strongest included spectral baseline on five of six tasks, and at

r{=}8

it gives the best result on SST-2 and CoLA. Ablations identify subspace alignment as the load-bearing component, while coefficient matching is auxiliary.

Omer Tariq, Syed Muhammad Raza, Jeongbae Son

Neubility Inc, Seoul, South Korea

Knowledge Distillation Subspace

Jul 3, 2026eess.AS

Open-Set Source Tracing as Compositional Factors via Structured Prototypes

Recent research expands beyond binary anti-spoofing with the emergence of Source Tracing, the task of identifying the specific generative origins of synthetic speech. However, current research often equates a "source" with its generative architecture. We propose redefining a source as a compositional tuple of Architecture, Training Data, and other training factors affecting the generated speech. We propose a framework using Structured Orthonormal Prototypes to minimize class overlap and intra-class variance. Our Subspace Partitioning strategy splits the embedding into architecture and data subspaces, while a residual subspace captures stochastic variability, enabling "compositional generalization" for novel factor combinations. This approach improves performance for partially seen sources and maintains robustness in fully open-set scenarios. MLAAD evaluations for Few-Shot open-set Identification show our approach significantly outperforms angular-margin baselines.

Santiago Rubio, Antonio Almudévar, Antonio Miguel +2

ViVoLab, I3A University of Zaragoza Zaragoza, Spain

Speech Separation Open-Set Recognition Subspace Compositional Generalization Structured Context Traces

Jul 2, 2026cs.AI

Fast Multi-dimensional Refusal Subspaces via RFM-AGOP

Steering and monitoring activations in Large Language Models (LLMs) are increasingly used for both safety and interpretability. Early work assumed behaviours are encoded along single linear directions, but recent findings suggest complex behaviours, such as the refusal to answer harmful queries, live in multi-dimensional subspaces. However, existing methods for extracting these subspaces are computationally expensive, which becomes prohibitive on reasoning models who produce long reasoning traces. By adapting the Recursive Feature Machine (RFM) algorithm -- which can be computed efficiently -- with a probe-informed initialization, we are able to identify the multi-dimensional refusal subspace in seconds, on reasoning (Qwen 3) and non-reasoning (Qwen 2.5) models. While RFM allows for faster subspace identification, it also showed better performances on the ablation task than its alternatives. More work is planned to better understand the relations between subspaces found by different methods. If confirmed, RFM could be a cheap and scalable complement to existing subspace-extraction methods in LLMs.

Thomas Winninger

Télécom SudParis, Évry-Courcouronnes, France · ENS Paris-Saclay, Gif-sur-Yvette, France

LLM Reasoning Strategies Subspace Refusals Reasoning Traces Ablation Interpretability

Jul 2, 2026cs.CV

QWERTY: Training-Free Motion Control via Query-Warped Video Diffusion Transformers

Video diffusion transformers (DiTs) generate high-fidelity and temporally coherent videos, yet motion control remains implicit, primarily relying on text prompts. As a result, achieving desired motion often requires extensive prompt engineering and repeated resampling. While fine-tuning models with additional spatial prompts (e.g., bounding boxes or point trajectories) enables explicit control, it demands substantial data curation and computation, and may compromise the generative capabilities of pretrained models. Consequently, training-free motion control using such spatial prompts has been explored in U-Net-based video diffusion models, but remains largely unexplored for DiTs. We introduce QWERTY, a training-free framework that enables flexible motion control in pretrained image-to-video DiTs via user-defined object warping and optical flow. We carefully manipulate the 3D full attention of DiTs by warping the frame-invariant semantic subspace of queries. We find that the noise predicted by the query-warped DiT naturally guides the diffusion trajectory toward the desired motion, and further show that leveraging this noise as self-guidance for latent optimization improves control stability and visual quality. Experiments show that QWERTY achieves the most effective motion control among existing training-free approaches on a recent image-to-video DiT, with performance comparable to fine-tuning-based methods.

Kyobin Choo, Youngmin Kim, Hyunkyung Han +4

Department of Computer Science, Yonsei University, Seoul, Republic of Korea · Department of Artificial Intelligence, Yonsei University, Seoul, Republic of Korea

Video Diffusion Models Motion Control Motion Optical Flow Keystroke Dynamics Subspace

Jul 1, 2026cs.LG

ZO-Act: Efficient Zeroth-Order Fine-Tuning via One-Shot Activation-Informed Low-Rank Subspaces

Zeroth-order (ZO) optimization enables fine-tuning large language models when backpropagation is unavailable or memory-prohibitive, but existing methods often perturb full model weights or randomly constructed low-dimensional subspaces, yielding high-variance estimates and limited performance. We propose ZO-Act, an activation-informed ZO fine-tuning method that restricts perturbations to a fixed low-rank subspace derived from input activations. For each linear layer, ZO-Act computes a small activation basis once at initialization and optimizes only lightweight coefficient matrices using forward-only loss evaluations. This reduces the effective perturbation dimension, exposes explicit trainable variables compatible with momentum-based optimizers such as Adam, and naturally supports quantized LLM fine-tuning by keeping low-bit weights frozen. We analyze ZO-Act as zeroth-order optimization over a restricted coefficient space and show that perturbing the low-dimensional coefficients reduces both the variance-dependent convergence term and the finite-difference error of the ZO estimator, at the cost of a controlled subspace approximation bias that is mitigated by the low-rank structure of LLM activations and gradients. Experiments on Llama-3-8B, OPT-13B, and INT4 Llama-3-8B show consistent gains over strong ZO fine-tuning baselines across language understanding, question answering, and commonsense reasoning.

Xun Dong, Yibo Xu, Naigang Wang +3

University at Albany, SUNY · IBM T. J. Watson Research Center

Zeroth-Order Optimization Zeroth-Order Continual Fine-Tuning Large Language Model Fine-Tuning Large Language Model Quantization Subspace+1

Jul 1, 2026cs.SD

A Geometric Perspective on Composable Emotion Steering in Text-to-Speech Models

While prior work has explored emotion control in hybrid text-to-speech systems, the geometric properties of these modules, and their implications for steerability, remain poorly understood. We present the first comparative study of speech language model (SLM) and conditional flow-matching (CFM) modules as activation steering sites for mixed emotion speech synthesis. We first characterize emotion representations using linear probing and local intrinsic dimensionality (LID), and then evaluate single-site and joint steering for mixed-emotion synthesis. Our results show that SLM offers a clean, low-dimensional emotion-specific subspace with strong speaker--emotion disentanglement, while CFM exhibitspoor cross-speaker generalization due to speaker--emotion entanglement. Joint steering increases emotion intensity but degrades proportional control and speech quality on in-distribution data. These findings provide practical guidance for multi-site activation steering in hybrid TTS systems and highlight the importance of representation geometry in controllable speech generation.

Siyi Wang, James Bailey, Ting Dang

The University of Melbourne, Australia · Monash University, Australia

Speech Language Models Emotion Recognition Linear Activation Steering Steering Subspace

Jul 1, 2026cs.CV

MoVA: Learning Asymmetric Dual Projections for Modular Long Video-Text Alignment

Contrastive pre-training has propelled video-text alignment, yet models often inherit the critical limitations of their image-text predecessors like CLIP, resulting in entangled representations. These challenges are severely exacerbated by two fundamental properties in the video domain: Temporal Misalignment, where textual descriptions often correlate only to specific, constrained temporal windows, leaving other frames text-irrelevant; and Semantic Asymmetry, which dictates a sparse, bidirectional, and non-equivalent relevance between frame-level visual details and caption-level concepts. This failure persists whether captions are short and temporally disjoint, creating ambiguity, or long and detailed, fostering entanglement between static objects and their temporal evolution. In this paper, we establish theoretical conditions that enable flexible alignment between video and text representations across the temporal dimension and at varying levels of granularity. Building on these theoretical insights, we introduce MoVA, Modular Long Video-Text Alignment, which learns dual asymmetric projections: a text-side projection that adaptively selects frame-aware subspaces of the caption, and a video-side projection that disentangles text-relevant visual concepts. Our framework ensures that the model can preserve global cross-modal semantics while disentangling evolving, frame-specific concepts and scale naturally to long captions and videos. Empirical evaluations show that MoVA outperforms existing methods in multiple video-text alignment tasks, demonstrating the effectiveness of our method.

Peiyuan Zhu, Shaoan Xie, Zijian Li +5

Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · Carnegie Mellon University, Pittsburgh, PA, USA

Image-Text Alignment Entanglement Subspace

Jun 30, 2026cs.LG

Fora: From Weight-Space to Function-Space Protection in Capability-Preserving Fine-Tuning

Full fine-tuning adapts large language models to new tasks but can erode capabilities they already possess. Existing remedies protect through proxies such as parameter distances, importance penalties, output matching, or dominant singular directions of the weights, but none directly asks which activation directions the preserved capability relies on. We argue that a capability is characterized more faithfully by the activation subspace it induces than by the singular geometry of the weight matrix, and develop function-space protection, instantiated as FORA (Function-space Orthogonal Residual Adaptation). From label-free calibration inputs, FORA estimates, per layer, the principal directions

Q

of the input-activation covariance and forms a right projector

P_Q = I - QQ^T

. Paired with a left projector

P_U

from the weight SVD, the update is

ΔW = P_U M P_Q + U_2 D_δ V_2^T

: a high-capacity branch structurally barred from reading capability-relevant function directions, plus a narrow spectral channel for controlled plasticity. The construction extends to parameter-efficient adaptation via

M \to (α/r) BA

. Across three settings on Qwen3-1.7B, including COGS and GSM8K learned while preserving translation and translation learned while preserving math, FORA consistently improves preservation over weight-space projection and standard regularization, with only a small new-task trade-off in the math-preservation setting. A controlled ablation isolating the projection source shows that the advantage comes not from projection itself, but from projecting onto capability-derived rather than weight-derived directions. Code is available at https://github.com/zrui239/FORA.

Rui Zhou, Tianci Xie

Dalian University of Technology · Zhejiang University

Model Fine-Tuning Parameter-Efficient Adaptation Weight-Space Subspace Covariance

Jun 29, 2026cs.LG

Neural Subspace Reallocation: Continual Learning as Retrieval-Based Subspace Memory Management

We introduce Neural Subspace Reallocation (NSR), which reframes continual learning as memory management over parameter subspaces. Instead of treating Low-Rank Adaptation (LoRA) modules as disposable per-task adapters, NSR manages them as compressible, retrievable memory units on a frozen backbone through a recurring cycle: (1) compress learned LoRAs via SVD, (2) reserve them in a TaskKnowledgeBank, (3) recall related past LoRAs by embedding similarity to warm-start new or returning tasks, and (4) reallocate the active subspace accordingly, with distillation protecting prior tasks. We prove that in cyclic environments any memoryless allocation policy incurs cumulative regret Omega(T(M-1)Delta_switch) relative to a history-aware policy backed by the Bank (Theorem 1). Empirically, on Split-CIFAR-100 the Bank reduces cyclic recovery time by 10x, exactly as predicted, and on the heterogeneous 5-Datasets benchmark NSR achieves the highest accuracy and the least forgetting, about 9x closer to zero backward transfer than the memoryless heuristics. Crucially, we run a controlled study that isolates which component matters: holding the Bank fixed and varying only the allocation rule, we find that a simple similarity-based retrieval rule matches or beats a learned reinforcement-learning controller (recovering recurring tasks in 0 vs 1.8 steps and reaching equal accuracy). Our central, honest finding is therefore that the memory mechanism -- compression and similarity retrieval -- rather than a learned allocation policy, drives continual-learning performance under fixed capacity. A memory-budget analysis confirms the compressed Bank stays small -- 0.29 MB of parameter memory per task -- so a top-K retention cap bounds the total footprint while preserving fast recovery for retained tasks.

Byeong Hoon Yoon

Independent Researcher

Replay-Based Continual Learning Continual Learning Subspace Peak Memory Forgetting

Jun 28, 2026cs.LG

Nonlinear mixture model motivated subspace clustering

We derive the linear union-of-subspaces (UoS) model for subspace clustering (SC) from the nonlinear mixture model (NMM) used in blind source separation (BSS) to represent a D-dimensional observation vector as an unknown multivariate nonlinear mapping of C latent variables. Assuming the mapping is differentiable up to an unknown order K, we approximate NMM by a K-th order Taylor expansion, yielding a model equivalent to the linear UoS framework underlying SC. This establishes that: (i) the smoothness order K corresponds to the unknown subspace dimension d; (ii) KC equals the number of anchors; and (iii) the sparsity of the representation vector equals K (i.e., d). These relationships enable estimation of bounds on subspace dimension, and that is validated on six benchmark datasets using five established SC algorithms. Established theoretical results are important for post-processing of self-representation matrices estimated by SC algorithms.

Ivica Kopriva

Division of Computing and Data Science, Ruđer Bošković Instute, Zagreb, Croatia

Subspace Mixture Models Nonnegative Matrix Factorization Speech Separation

Jun 27, 2026cs.LG

A Novel Latent-Class Attack and its Detection by Class Subspace Orthogonalization

Deep learning, which in general relies on voluminous amounts of training data, is vulnerable to data poisoning attacks, including error-generic attacks and backdoors (Trojans). In this work, we propose a new data poisoning attack we dub a latent class attack. Here, all poisoned examples are from a class that is novel (unknown) for the given classification domain and are mislabeled to one of the known classes (the target class) of the domain, so that the model learns to recognize the novel class as a sub-class of the target class. Such attacks could be used e.g. to defeat AI-based access control systems, or could cause a "foe" to be classified as a "friend". We also propose a post-training defense to detect this attack, without any access to the training set. This detection approach builds on "class subspace orthogonalization" (CSO), a plug-and-play paradigm demonstrated to improve existing backdoor detectors. Here, CSO is used to seek an input (a putative unknown class instance) whose internal representation is not aligned with any of the known classes, and yet which is classified with confidence to one of these classes. Finally, specific to image classification domains, we propose a method for visualizing the estimated unknown class instance, providing explainability to our latent class detections.

Guangmingmei Yang, David J. Miller, George Kesidis

CSE & EE Depts, Penn State, University Park, PA, 16802 · Anomalee Inc., State College, PA, 16803

White-Box Spectral-Subspace-Guided Attack Poisoning Deep Learning Subspace Post-Training Orthogonality

Jun 27, 2026cs.CV

FreqOrtho-SR: Frequency-Guided Orthogonal Expert Learning for Real-World Image Super-Resolution

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises:

\textbf{Freq}

uency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and

\textbf{Ortho}

gonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at

\href{https://github.com/sonhm3029/FreqOrtho-SR}{\texttt{sonhm3029/FreqOrtho-SR}}

.

Minh Son Hoang, Dinh Phu Tran, Quyen Nguyen Duc +2

School of Computing, KAIST, Republic of Korea

Real-World Image Super-Resolution Frequency Domain Subspace Real-World Experts

Jun 26, 2026cs.CV

TextDS: Parameter-Efficient Representation Alignment for Scene Text Detection under Distribution Shifts

In real-world deployments, scene text detectors inevitably face distribution shifts beyond the training distribution. Prior work often depends on large-scale scene-text pretraining, yet evaluation under cross-domain changes and real-world imaging degradations remains limited. We propose TextDS, an efficient framework for scene text detection under distribution shifts. First, we propose a data-efficient dual-encoder design with visual foundation models, eliminating the reliance on large-scale scene-text pretraining. Second, we introduce Step-wise LoRA adaptation (SWLoRA), which performs progressive low-rank refinement with a dynamic early-exit mechanism for effective feature adaptation. Third, we propose Common Subspace Fusion (CSF) to align and fuse the two branches in a shared subspace while retaining complementary, shift-robust information. Finally, we construct adverse-condition scene text detection datasets to address the gap in evaluating under imaging degradation. Experiments show that TextDS achieves competitive performance in scene text detection, demonstrating robustness across domains and adverse imaging conditions with only 4.9M trainable parameters.

Boyuan Chen, Zichen Dang, Chuang Yang +2

School of Electrical Engineering, Xi’an Jiaotong University · Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University

Scene Text Recognition Image-Text Alignment Training-Side Stage-Aware Low-Rank Adaptation Visual Degradation Distribution Shifts Subspace

Jun 26, 2026cs.CR

SHARD: cell-keyed residual splitting for alignment-resistant private dense retrieval

Dense retrieval systems expose document geometry when vector stores are compromised, and a global protective transform can often be aligned from known pairs. We study SHARD, which splits PCA coordinates into a short routing prefix and a residual protected by independent cell-local orthogonal keys. It supports CKKS ciphertext--plaintext reranking but is evaluated as a leakage trade-off, not a cryptographic document-privacy guarantee. Corrected scoring uses centered document coordinates and an uncentered scoring query, preserving raw ranking up to a query-dependent constant. Across ten BEIR/MIRACL configurations it reproduces raw nDCG@10 and recall, whereas centering both sides loses up to 0.080 nDCG. Cell keys spread diffuse known-pair evidence across compartments, but minimum-norm alignment recovers useful signal far below full key rank, so there is no hard de-anonymization threshold. Real CKKS has maximum score error 2.29e-6 and no top-1 flips; block packing cuts query upload by 74--87% but raises in-process p50 latency by 14--26%. In a strengthened GTR case, an unknown key lowers token-F1 from 0.665 to 0.242; a wide prefix and eight pairs restore much. Under 25--90% release overlap, the unchanged prefix and clean residual norm link persistent rows with R@1 at least 0.9996, although cell-Gram linkage degrades under churn. A formally calibrated Gaussian release gives nDCG@10 at most 0.011 at epsilon=1; its only three strict utility matches occur at epsilon=32768 with linkage R@1 at least 0.995. SHARD preserves retrieval and compartmentalizes alignment evidence, but does not provide DP, unlinkability, or cancellable templates.

Sergey Kurilenko

Moscow Institute of Physics and Technology

Locality-Sensitive Hashing Shard Anonymization Subspace

Jun 26, 2026eess.IV

Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction

Diffusion posterior samplers for accelerated MRI can reconstruct accurately yet still disagree on the acquired k-space across samples, placing posterior variability on coefficients the scanner has already measured. We identify this measured-subspace leakage as a physical-admissibility failure. Under a hard-constraint model it violates the measurement constraint and inflates the reported uncertainty with disagreement about coefficients the scanner has already determined. To quantify this leakage, we introduce complementary measured- and unmeasured-subspace k-space dispersion metrics (MSD/USD). We then present Measured-Subspace Consistency (MSC), a training-free terminal correction that wraps any compatible image-space posterior sampler with a standard multi-coil consistency lock. The ideal lock follows classical range/null-space data consistency. Our contribution is to repurpose it as a black-box posterior audit and correction rather than a new reconstructor or learned sampler. Theoretically, we prove that the ideal transform confines pairwise sample differences to the MRI null space and bound the residual cross-subspace coupling left by practical sensitivity-weighted implementations. Across six base samplers and two MRI anatomies, including out-of-distribution transfer where a knee prior reconstructs brain, MSC substantially reduces measured-subspace dispersion for Soft samplers (a median 16.5x reduction for DPS across five brain contrasts, up to ~29x), while preserving unmeasured-subspace diversity and acting as a near-identity map for Consistent ones. Furthermore, MSC maintains or modestly improves PSNR/SSIM, with no retraining, retuning, or significant computational overhead.

Junhyeok Lee, Kyu Sung Choi

Interdisciplinary Program in Cancer Biology, Seoul National University College of Medicine · Department of Radiology, Seoul National University College of Medicine, Seoul National University Hospital · Healthcare AI Research Institute, Seoul National University Hospital

Magnetic Resonance Imaging Reconstruction Posterior Sampling Magnetic Resonance Imaging Diffusion Sampling Subspace Posterior+2