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01.
arXiv (CS.CL) 2026-06-17

Conformal Path Reasoning: Trustworthy Knowledge Graph Question Answering via Path-Level Calibration

Knowledge Graph Question Answering (KGQA) offers grounded, interpretable reasoning, but existing methods often fail to provide reliable coverage guarantees over retrieved answers. While Conformal Prediction (CP) offers a principled framework for producing prediction sets with statistical guarantees, prior conformal KGQA methods suffer from two critical pitfalls: violated coverage guarantees due to invalid calibration, and weak score discriminability that yields excessively large prediction sets. We propose Conformal Path Reasoning (CPR), a novel trustworthy KGQA framework built on two key innovations. First, query-level conformal calibration over path-level scores preserves exchangeability to ensure valid coverage guarantees. Second, we introduce the Residual Conformal Value Network (RCVNet), a lightweight module trained via PUCT-guided exploration to learn discriminative path-level nonconformity scores. Extensive experiments show that CPR significantly improves the Empirical Coverage Rate by 45% while reducing prediction set size by 52% on average over conformal baselines across benchmark datasets, highlighting its effectiveness for reliable conformal reasoning over knowledge graphs.

02.
arXiv (CS.CV) 2026-06-16

Double-Helix Vision (DH-V2): A Geometry-Based Visual Sampler for Bandwidth-Constrained Perception

作者:

We present Double-Helix Vision (DH), a geometry-based visual sampler that compresses 2D images into compact 1D signals using paired golden-ratio-inspired spiral trajectories. Rather than processing every pixel uniformly, DH employs two phase-shifted helices (Alpha and Beta, offset by 180 degrees) to sample the image with biologically-inspired foveation: high density at the center, sparse coverage at the periphery. At 4K resolution, DH achieves a 1,433x compression ratio (99.93% reduction) while preserving the geometric structure of the scene. The full perception pipeline – including spatial mapping, temporal collision detection, and intra-frame structural disparity estimation – runs in 0.52 ms at 1080p on CPU-only hardware, with no neural network dependencies. On CIFAR-10 at extreme sampling budgets (K=128 points per helix), DH achieves a +6.03% accuracy gain over uniform random sampling. A JSON-serializable Robotics API is provided, delivering sub-millisecond spatial perception reports in 2.7 KB packets. Code and benchmarks are available under the MIT License.

03.
arXiv (math.PR) 2026-06-15

Stationary measures for higher spin vertex models on a strip

作者:

arXiv:2309.04897v2 Announce Type: replace-cross Abstract: We introduce a higher spin vertex model on a strip with fused vertex weights. This model can be regarded as a generalization of both the unfused six-vertex model on a strip arXiv:2212.09111 and an 'integrable two-step Floquet dynamics' model introduced in arXiv:1711.08884. We solve for the stationary measure using a fused version of the matrix product ansatz and then characterize it in terms of the Askey-Wilson process. Using this characterization, we obtain the limits of the mean density along an arbitrary down-right path. It turns out that all these models share a common phase diagram, which, after an appropriate mapping, matches the phase diagram of open ASEP. This provides evidence for the universality of this phase diagram.

04.
arXiv (CS.LG) 2026-06-11

GLACIER: A Multimodal Student-Teacher Foundation Model for Molecular Property Prediction

arXiv:2606.11382v1 Announce Type: new Abstract: Deep learning models facilitate the discovery of molecules with tailored properties among billions of candidate compounds. However, the computational burden to develop and deploy state-of-the-art models continuously increases, limiting their scalability. Most large-scale models are unimodal in nature and overlook the potential to leverage complementary molecular data modalities. To address these shortcomings, this paper introduces the Graph-Language Alignment for Chemical Inference and Exploration using Representations (GLACIER) model, a student-teacher framework that integrates molecular graphs, SMILES strings, and physicochemical descriptors to learn rich molecular embeddings. Our framework consists of three stages: (1) we pretrain three student encoders on 100,000 drug-like molecules: a message-passing neural network for molecular graphs, a transformer-based encoder for SMILES strings, and a multilayer perceptron for physicochemical descriptors, (2) we fuse these student modalities using a novel Finsler geometry-aware module, and (3) distill complementary knowledge from large teacher models, including MiniMol and MolFormer, into a single lightweight model via contrastive learning. We demonstrate that GLACIER is a robust framework that delivers high predictive performance and computational efficiency in complex molecular property prediction tasks. Our code is publicly available at https://github.com/eemokey/glacier.

05.
arXiv (quant-ph) 2026-06-24

A no-go theorem for privacy in distributed sensing using Gaussian states

arXiv:2606.23796v1 Announce Type: new Abstract: In the discrete variable setting, entangled resource states allow a set of parties to learn a global function of a set of spatially separated systems, whilst keeping the local parameters of those systems completely private. In the continuous variable setting, distributed sensing has been carried out using Gaussian resource states, but without the same guarantees about privacy. Here, we show that perfect privacy is impossible to achieve for any distributed sensing protocol that uses Gaussian states as a resource. We also introduce a measure of relative privacy, bounding the degree to which any Gaussian distributed sensing protocol can keep local parameters hidden.

06.
arXiv (CS.CL) 2026-06-19

ShoppingBench: A Real-World Intent-Grounded Shopping Benchmark for LLM-based Agents

Existing benchmarks in e-commerce primarily focus on basic user intents, such as finding or purchasing products. However, real-world users often pursue more complex goals, such as applying vouchers, managing budgets, and finding multi-products seller. To bridge this gap, we propose ShoppingBench, a novel end-to-end shopping benchmark designed to encompass increasingly challenging levels of grounded intent. Specifically, we propose a scalable framework to simulate user instructions based on various intents derived from sampled real-world products. To facilitate consistent and reliable evaluations, we provide a large-scale shopping sandbox that serves as an interactive simulated environment, incorporating over 2.5 million real-world products. Experimental results demonstrate that even state-of-the-art language agents (such as GPT-4.1) achieve absolute success rates under 50% on our benchmark tasks, highlighting the significant challenges posed by our ShoppingBench. In addition, we propose a trajectory distillation strategy and leverage supervised fine-tuning, along with reinforcement learning on synthetic trajectories, to distill the capabilities of a large language agent into a smaller one. As a result, our trained agent achieves competitive performance compared to GPT-4.1.

07.
arXiv (CS.LG) 2026-06-12

Adjusted Cup-Product Neural Layer

arXiv:2606.13568v1 Announce Type: new Abstract: Many important observables in physics and geometry are cup products of cochains. The adjusted cup product neural layer has been introduced in this paper. It is a neural primitive that hard wires the cup product with an adjustment term from higher gauge theory. This creates a readout that is gauge invariant by design. Their main theoretical result shows that on a closed cycle the output relies entirely on the adjustment coefficient. Setting this coefficient to zero removes the output completely regardless of other parameters. Thus the adjustment is the only source of gauge invariant signal. They prove this observable is a nonzero quadratic form and is exactly invariant under one and two gauge transformations.

08.
arXiv (quant-ph) 2026-06-16

Towards Quantum Limited Spatial Resolution of NV-Diamond Magnetometry

arXiv:2508.13438v2 Announce Type: replace Abstract: Optically addressable ensembles of solid-state defects, such as nitrogen vacancy (NV) centers, are a leading modality for imaging-based magnetometry, thermometry and strain sensing. However, monitoring the fluorescence of individual defects within a sub-diffraction ensemble remains an outstanding challenge that currently limits access to atomic-scale features and dynamics. For compact clusters of NVs, we formulate imaging-based atomic sensing as a low-dimensional multiparameter estimation task in which one seeks to localize each defect and quantify the field strength in its immediate vicinity. In this work, we employ optical spatial mode demultiplexing (SPADE) to enhance localization and brightness estimation accuracy at sub-diffraction scales. Specifically, we develop a two-stage sensing protocol that augments direct imaging by projecting the incoming optical field onto point spread function (PSF)-adapted, i.e., PAD spatial modes and Yuen-Kennedy-Lax (YKL) spatial modes enabling efficient extraction of emitter positions and brightnesses. The YKL-SPADE measurement employed for brightness estimation is shown to be quantum-optimal in the case of two emitters and establishes a new connection between quantum detection and estimation theories. We numerically evaluate the statistical performance of our protocol for sub-diffraction optically detected magnetic resonance (ODMR) and Rabi sensing experiments. Compared to conventional focal plane intensity measurements, our protocol improves emitter localization accuracy by 6$\times$ and brightness estimation accuracy by 2$\times$ for tightly confined ensembles, residing well below the diffraction limit.

09.
arXiv (CS.AI) 2026-06-17

A T-API-Compliant ReAct Agentic Loop for Optical Networks: Generic vs. Domain-Specific Tool Abstractions

arXiv:2606.18000v1 Announce Type: cross Abstract: Optical networks need intent-driven, closed-loop agentic management, a key enabler for higher autonomy levels. We present the first T-API-compliant reasoning and act (ReAct) loop. We show that domain-specific composite tools achieve 90% oracle-validated correctness with threefold token savings compared to generic tools.

10.
arXiv (CS.CV) 2026-06-12

InterleaveThinker: Reinforcing Agentic Interleaved Generation

Recent image generators have demonstrated impressive photorealism and instruction-following capabilities in single-image generation and editing. However, constrained by their architectures, they cannot achieve interleaved generation (text-image sequence), which has crucial applications in visual narratives, guidance, and embodied manipulation. Even the latest open-source Unified Multimodal Models (UMMs) exhibit limited performance in this regard. In this paper, we introduce InterleaveThinker, the first multi-agent pipeline designed to endow any existing image generator with interleaved generation capabilities. Specifically, we employ a planner agent to organize the image-text input sequence, instructing the image generator on the required execution at each step. Subsequently, we introduce a critic agent to evaluate the generator's outputs, identify samples that deviate from the planned instructions, and refine the instructions for regeneration. To implement this pipeline, we construct the Interleave-Planner-SFT-80k and Interleave-Critic-SFT-112k to perform a format cold-start. Then we develop Interleave-Critic-RL-13k to reinforce the step-wise instruction correction capability within a generation trajectory using GRPO. Since a single interleaved generation trajectory may involve over 25 generator calls, optimizing the entire trajectory is computationally impractical. Therefore, we propose accuracy reward and step-wise reward, allowing single-step RL to effectively guide the entire generation trajectory. The results show that InterleaveThinker improves performance across various image generators. On interleaved generation benchmarks, it achieves performance comparable to Nano Banana and GPT-5. Surprisingly, it also significantly enhances the base model on reasoning-based benchmarks; for example, on 4-step FLUX.2-klein, we observe substantial gains on WISE and RISE.

11.
arXiv (CS.LG) 2026-06-25

DFMU: Data-Frugal Machine Unlearning

arXiv:2606.25410v1 Announce Type: new Abstract: Machine unlearning is an emerging domain that ensures the safe removal of elements (includes concepts, attributes, entity and class) from the trained model along with least drop in model performance. The domain of machine unlearning brings its own indigenous challenges since the removal of pre-trained elements from model will always degrade the model performance on remaining elements. The existing methods basically rely on retraining for removal of elements from the pre-trained model, which is compute extensive. In this work, we propose a machine unlearning method which helps to reduce the computational requirement for faster retain-dataset accuracy convergence which also does not require extensive retraining of the pre-trained model. The proposed method, Data-Frugal Machine Unlearning (DFMU) requires only a single forward and backward pass for computing the importance score of various computational blocks of a model. The importance score computation is based on knowledge preserving pruning which helps to converge faster and requires far less data as compared to the existing methods. Experimentally, it achieves 40% more retain-accuracy with just 13% of data samples in comparison with SOTA method on various public datasets and also averages 88% faster processing time for forgetting a given class.

12.
arXiv (CS.AI) 2026-06-25

Taxonomy of Risks on Automated Fact-Checking Systems Considering its Propagation

arXiv:2606.25645v1 Announce Type: cross Abstract: In recent years, the posting of fake news including disinformation and misinformation on social networking services (SNS) has become a social problem. To combat this fake news, fact-checking that is the process of assessing the veracity of posts on SNS has become increasingly important. While fact-checking is currently performed by fact-checking organizations, it is difficult to fact-check all posts on SNS. Therefore, the use of automated fact-checking systems is effective. Recent automated fact-checking systems utilize artificial intelligence and large language models, so there are risks of incorrect judgments and posting incorrect results on social media which can lead to the spread of misinformation or to engage in defamation. In this paper, as a first step toward enabling the safe use of automated fact-checking systems, we categorize the specific risks on automated fact-checking systems. In this categorizing, we consider a three-stage risk propagation: risk factors, hazardous situations, and harm. Our analysis revealed that 32 specific risks exist in automated fact-checking systems. In this paper, we utilize the categorized risks as analytical cues (guide words) to present the risk assessment of the automated fact-checking system DEFAME. This assessment result indicates that risks that cannot be derived using STRIDE, a conventional IT security risk assessment method can be derived using our guide words.

13.
arXiv (quant-ph) 2026-06-19

Attosecond Path Qubits in High-Harmonic Generation: Classical Dephasing and Trace-Out Decoherence

arXiv:2606.20372v1 Announce Type: cross Abstract: High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.

14.
arXiv (CS.AI) 2026-06-15

Universal Manipulation Exoskeleton: Learning Compliant Whole-body Policies with Real-time Torque Feedback

arXiv:2606.14218v1 Announce Type: cross Abstract: For robots to work safely in household environments, they need to be compliant and react to torque and force feedback during contact. However, the majority of existing data collection pipelines still lack the ability to capture force and torque data for learning active compliant policies. In this paper, we present Universal Manipulation Exoskeleton (UME), an upper-limb exoskeleton that provides real-time haptic torque feedback while recording whole-arm configurations and joint torque signals for teleoperation. With transparent torque feedback, human operators can even unsheathe kinematically constrained objects while blindfolded. UME is low-cost, lightweight, and portable. Equipped with an embedded IMU, it enables teleoperation for mobile manipulation. With our proposed universal retargeting algorithm, UME can teleoperate a range of robots, including the 7DoF OpenArm, 7DoF Franka, and 6DoF X-ARM. We demonstrate that this combination of capabilities enables learning bimanual, whole-body, and active compliant policies that operate effectively in highly constrained spaces. The learned robust autonomous policies achieve high success rates across a variety of tasks, including long-horizon mobile manipulation, force-mediated box flipping, visually occluded box pushing, and space-constrained tabletop manipulation. Videos, code, and additional information can be found at https://ume-exo.github.io.

15.
arXiv (math.PR) 2026-06-11

An Information-Theoretic Analysis of Threshold Group Testing

arXiv:2606.11353v1 Announce Type: cross Abstract: We study the Threshold Group Testing (TGT) problem in the noiseless and non-adaptive setting, where the objective is to exactly recover a sparse binary vector from pooled tests, using as few tests as possible. In TGT, each test applied to a subset of items returns a positive outcome if the number of 1's (defective items) in that subset meets or exceeds a specified threshold, and has a negative outcome otherwise. We investigate how the complexity of TGT compares to that of Classical Group Testing (CGT), corresponding to the special case of the threshold equal to one, and analyse the impact of increasing the threshold on the required number of tests. Our main contribution is the derivation of a sharp information-theoretic phase transition at $c_{\mathrm{inf}}^{\mathrm{TGT}}k\log(n/k)$ (non-adaptive) tests for TGT within the constant-column test design. The threshold constant $c_{\mathrm{inf}}^{\mathrm{TGT}}$ is expressed as a function of the prevalence of defectives and the threshold value. Our upper bound is derived under an analytic assumption, and we verify that this assumption is satisfied for a threshold value of 2. The value of $c_{\mathrm{inf}}^{\mathrm{TGT}}$ reveals that TGT on the constant-column design has the same information-theoretic behaviour as CGT in the low-prevalence regime. Yet, strikingly, at higher prevalences, the threshold leads to a significant reduction in the number of tests. On the other hand, we provide evidence that when the asymptotic proportion of defective items is positive, TGT actually becomes strictly harder than CGT (excluding trivial reductions).

16.
arXiv (quant-ph) 2026-06-15

Trap-Quenched Matter-Wave Optics for Dual Species Lensing

arXiv:2606.14577v1 Announce Type: cross Abstract: Dual-species atom interferometry in space promises precise tests of the Universality of Free Fall (UFF), with a sensitivity that grows quadratically with the extended interrogation time accessible in weightlessness. These tests demand exquisite control over the expansion energies of both condensed sources as well as over their differential center-of-mass dynamics. We propose a trap-quenched collimation technique featuring in-trap excitations of collective modes compatible with state-of-the-art atom-chip setups. Using NASA's Cold Atom Laboratory aboard the International Space Station, we demonstrate it on a single-species $^{87}$Rb condensate. By controlling the center-of-mass release dynamics we observe free expansion times up to 700 ms and measure a two-dimensional expansion energy of $k_B \cdot 78\pm 9 \;\mathrm{pK}$ in the imaging plane. A detailed model of the magnetically-induced dynamics indicates that this corresponds to a two-dimensional expansion energy of about $k_B \cdot 15^{+12}_{-5}\; \mathrm{pK}$ along two of the condensate's eigenaxes. Finally, we theoretically study this trap-quenched collimation scheme for a $^{41}$K-$^{87}$Rb mixture, predicting a simultaneous collimation that meets the expansion energy requirements for a state-of-the-art UFF test at the $10^{-15}$ accuracy level.

17.
medRxiv (Medicine) 2026-06-12

Home-based binocular serious games in virtual reality to treat visual acuity and stereovision in residual amblyopia: AMBER study

Objectives: Amblyopia is a pediatric visual disorder traditionally treated by patching the fellow eye, though many patients retain residual amblyopia post-treatment. Increasing evidence suggests that visual plasticity allows treat-ment beyond the classical therapeutic window. AMBER evaluated the efficacy of binocular serious games in virtual reality (VR) in residual amblyopia. Methods and Analysis: The monocentric, prospective, randomized, crossover trial (reported as case series) includ-ed 14 anisometropic, strabismic, or mixed residual amblyopia patients (6-35 years; 5 children, 9 adults). Participants underwent two 2-month intervention phases: optical correction (standard care) and standard care plus VR games (2.5 h/week), each with a 2-month follow-up. Best-corrected visual acuity (BCVA), stereoacuity, and reading speed were assessed (5 timepoints) using the Sloan and Landolt charts, the Titmus, TNO, Lang II, Asteroid, and Mnread tests. Compliance and adverse events (AE) were recorded. Results: VR training improved BCVA in 10 amblyopic eyes (Landolt and Sloan), with more pronounced effects in anisometropic patients. Six patients showed improved stereoacuity (Titmus; 4x mixed, 1x anisometropic, 1x stra-bismic amblyopia), persistent only in children (1x strabismic, 1x mixed amblyopia). Four improvements were ob-served with TNO (1x), Lang II (1x), Asteroid (0x), and MNread (1x). Despite positive trends, when comparing re-sults of individual patients, between both eyes, and with standard treatment, consistency of improvements cannot be conclusively demonstrated. One non-severe AE (dizziness) was reported. Conclusions: Following individual cases, VR training improved BCVA and stereoacuity, particularly in children and patients with high compliance. However, considering the cohort as a whole, consistency of effects has to be confirmed in larger groups. Thus, the methodologically sophisticated AMBER study revealed differences in VR treatment efficacy between amblyopia types, children/adults, endpoints and tests, offering precious data for the design of meaningful future studies. It shows that neurovisual plasticity gauged by VR-games offers safe, engaging treatment options for residual amblyopia.

18.
arXiv (CS.LG) 2026-06-24

Stochastic Expectation Maximization for Robust State-Space Radio Interferometric Imaging

arXiv:2606.23944v1 Announce Type: cross Abstract: State–space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state–space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation–Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state–space modeling and SAEM-based inference in interference-dominated imaging scenarios.

20.
arXiv (CS.CL) 2026-06-17

EComAgentBench: Benchmarking Shopping Agents on Long-Horizon Tasks with Distributed Hidden Intent

As LLM-based shopping agents enter production, existing benchmarks fail to capture how a shopper's requirements arrive: stated implicitly in the query, recorded in a profile, or revealed only when the right question is asked. Benchmarks that expose full intent upfront and grade only the final choice can neither pose this long-horizon challenge nor explain which requirement an agent missed. To address this gap, we introduce EComAgentBench, a benchmark of 662 tasks grounded in real Amazon products and reviews. Each task scatters these requirements across a visible query, a tool-gated profile, and scripted clarification; an agent must uncover hidden intent, verify candidates against attributes and review evidence, and commit to a single product within 100 tool calls. Moreover, typed, source-tagged rubrics grade every task, attributing each failure to a requirement and its source. Construction is automated yet reliable, with every answer fixed in code before any text is generated and every sample validated. Our evaluation of seven models reveals that even the strongest attains only 57.1% overall accuracy, and rubric satisfaction degrades from visible to hidden sources. Overall, we believe EComAgentBench will serve as a reproducible foundation for moving shopping agents from single-query search toward dependable assistance over long horizons.

21.
arXiv (CS.LG) 2026-06-12

Contrastive Geometric Learning Unlocks Unified Structure- and Ligand-Based Drug Design

arXiv:2601.09693v3 Announce Type: replace Abstract: Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce Contrastive Geometric Learning for Unified Computational Drug Design (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for predefined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

22.
arXiv (CS.CL) 2026-06-19

Creating Multilingual Mental Health Dialogue Datasets: Limits of Persona-Based Localization via Nationality and Language

AI and large language models (LLMs) have emerged as promising tools to address global mental health challenges. Despite the global nature of these challenges, there remains a critical shortage of high-quality datasets for training and evaluating such systems. To mitigate this gap, researchers increasingly generate synthetic clinical personas to simulate user data and test digital mental health support systems. However, most validated personas rely on English-centric contexts. This paper investigates whether similar persona-based methods can be used to generate multilingual mental health datasets. We modified nationality and language parameters in personas to generate clinical dialogues in Mandarin, Bengali, and Hindi. We then examined how different LLMs perform when evaluating the depression severity of these generated multilingual datasets against the baseline in English. Our findings indicate that just adding nationality and language parameters in personas might not be adequate, as it can introduce clinical inconsistency across languages. LLM judge models often exhibit inaccuracies in assessing depression severity in non-English texts, with performance varying across different models. This exposes the systemic limitations of applying English-centric personas to multilingual contexts. Ultimately, our work highlights the urgent need for culturally responsive data generation to ensure equitable mental health systems globally.

23.
arXiv (CS.CV) 2026-06-18

Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm

This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

24.
arXiv (CS.CV) 2026-06-11

VLGA: Vision-Language-Geometry-Action Models for Autonomous Driving

Vision-language-action (VLA) models can describe scenes and reason about them in language, yet still struggle to ground their actions in the dense 3D world around them. Existing approaches either inject features from a frozen 3D foundation model without an objective that ensures the policy uses them, or constrain geometry with sparse box and map losses that provide no dense spatial signal. We introduce VLGA, the first vision-language-action model supervised to reconstruct the dense 3D world it drives through. VLGA introduces geometry as a fourth modality alongside vision, language, and action through a dedicated expert supervised by a per-pixel pointmap regression loss against LiDAR. Extensive experiments conducted on challenging nuScenes and Bench2Drive datasets for open-loop and closed-loop evaluations, respectively, show the superiority of VLGA over counterpart VLA methods. In particular, on open-loop nuScenes, VLGA sets a new state of the art among VLA methods without ego status, with the lowest L2 (0.50\,m average) and 3-second collision rate (0.18\%). On closed-loop Bench2Drive, VLGA attains the state-of-the-art driving score of 79.08, +0.71 over the strongest prior VLA, at comparable efficiency and comfort.