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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

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arXiv2026

Dual Representations and Proxy Characterization of $H_2$ Norm for Partial Integral Equations

Duality and dual representations are essential tools for systems theory and controller synthesis. For any finite-dimensional causal linear time-invariant (CLTI) system, there exists a dual CLTI system with identical $H_\infty$ and $H_2$ norm. These relations are found by simply taking the adjoint of the transfer function. For nonlinear, time-varying or infinite-dimensional systems, however, such a transfer function may not exist or be difficult to obtain. For duality in the $H_\infty$ norm, this obstacle is overcome by using the equivalent time-domain, induced $L_2$-norm characterization. For $H_2$ norms there is no such equivalent characterization and hence proxy norms such as induced energy to peak and impulse to energy norms are used. These proxy norms bound the $H_2$ norm in the CLTI case. However, neither of these $H_2$ proxy norms equal the same $H_2$ proxy of the canonical dual representation. In this paper, we overcome this by proposing a dual representation whose induced energy to peak proxy equals the impulse to energy proxy of the primal and vice-versa. This relation is developed in the context of Partial Integral Equation (PIE) representations. The result is then used to establish primal-dual operator inequalities for both proxy norms similar in form to the primal-dual LMIs used to characterize the $H_2$ norm.

math.OC↗

arXiv2026

L2GSSL: Label-Efficient Local-to-Global Self-Supervised Learning for Volumetric Healthcare Data

Healthcare institutions routinely accumulate high-dimensional computed tomography (CT) volumes, but only a fraction can be annotated by experts. We present L2GSSL, a local-to-global self-supervised learning framework that leverages unlabeled volumes by decomposing pretraining into intra-slice and inter-slice representation spaces. A slice encoder learns view-invariant local features, and a global encoder aggregates the resulting tokens to model volumetric context. The stop-gradient isolates the local space from the global objective, while slice-wise execution and a three-phase schedule support training under constrained GPU memory. On LIDC-IDRI lung nodule malignancy classification, L2GSSL reaches $0.9229$ AUROC with only $10\%$ of the labels and $0.9377$ with $25\%$, exceeding the volume-level VICReg by $0.0229$ and $0.0294$, respectively. With all labels, the strongest supervised baseline exceeds L2GSSL by only $0.0044$ AUROC, consistent with self-supervised pretraining providing its greatest value when annotations are limited. Without adaptation to the external LNDb cohort, a model fine-tuned on $25\%$ of LIDC-IDRI obtains $0.8138$ AUROC and $0.7589$ AUPRC, improving over the strongest evaluated self-supervised baseline by $0.1130$ and $0.0954$. Experiments across data sources, thoracic and abdominal anatomy, downstream tasks, and two backbones examine healthcare-data variety, while lesion-slice masking shows that the predictions depend on lesion-bearing content.

cs.CV↗

arXiv2026

Stitched surface codes: planar concatenation through GHZ corridors

We present a fault-tolerant quantum-memory architecture that concatenates four distance-t rotated surface-code patches with the [[4,2,2]] outer code, encoding two logical qubits at code distance d = 2t in a physical footprint of N < 2(2t+1)^2 qubits on a square lattice with nearest-neighbor connectivity. The outer-code stabilizer generators XXXX and ZZZZ, each of physical weight 4t, are measured in situ via verified Greenberger-Horne-Zeilinger (GHZ) ancillae distributed through narrow corridors between adjacent patches, without lattice surgery or long-range gates. The outer-code gadgets introduce hyperedge fault mechanisms, but by design each decomposes into graphlike components, so the complete syndrome is decoded by a single minimum-weight-perfect-matching pass. Circuit-level simulations show logical error rates that scale as p^t, consistent with distance-2t protection. Finally, we implement the construction experimentally on a 105-qubit Willow superconducting processor in both the ZZ and XX memory bases. With the correlated-matching decoder, increasing the code distance from d = 4 to d = 6 reduces the block logical error rate by a factor of 1.52. The construction thus provides a near-term testbed for concatenated architectures beyond the standard surface code.

quant-ph↗

arXiv2026

Fundamental Groups and Coregularity: Klt Pairs with Trivial and Nef Log-Anticanonical Class

In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we show that for a projective klt log pair $(X,D)$ of absolute coregularity $c$ and arbitrary dimension the fundamental group $π_1^{\rm reg}(X,D)$ admits a normal abelian subgroup of finite index and rank at most $2c$. We reduce this statement to klt Calabi-Yau pairs with standard coefficients of dimension $c$. In the cases $0\le c\le2$ and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. Combining the reduction with the recent regular-locus theorem of Fu-Guo-Song-Wang, we prove the coregularity bound in every dimension. In particular, for a projective klt pair $(X,D)$ with $-(K_X+D)$ nef, the orbifold fundamental group of the smooth locus is virtually abelian of rank at most $2\, {\rm dim}X$.

math.AG↗

arXiv2026

SWE-at-Scale: Scalable Issue Synthesis from Historical Bug Fixes

As coding agents become increasingly capable, robust evaluation requires a broader and more diverse supply of verifiable software engineering (SWE) tasks. However, real-world tasks are constrained by the natural frequency of issue reporting and the substantial cost of manual curation. Furthermore, existing synthetic approaches rely primarily on the pretrained knowledge of large models coupled with heuristic prompting, often failing to capture the authentic, complex mechanics of software failures. To exponentially scale SWE task production, we introduce SWE-at-Scale, a framework that automatically synthesizes realistic issues by reverse-engineering real-world software fixes. Our key insight is that historical fixes encapsulate deep mechanistic knowledge of bug formation: inverting a fix transforms repair supervision into bug-induction supervision grounded in actual development scenarios. SWE-at-Scale transfers these learned bug patterns to novel code contexts, repeatedly sampling diverse bug typologies to construct executable SWE tasks. Extensive experiments show that SWE-at-Scale generates more diverse and realistic SWE tasks than current synthesis baselines while posing greater challenges to state-of-the-art coding agents. Notably, SWE-at-Scale can generate distinct bug types from a single code context, with bug diversity scaling robustly even up to 200 generations per file. Overall, SWE-at-Scale turns finite real-world fixes into reusable supervision for scalable synthesis of realistic, diverse, and challenging SWE tasks.

cs.SE↗

arXiv2026

Controlling the False Discovery Rate via Model-Agnostic Importance Measures

Selecting covariates while controlling the false discovery rate (FDR) is critical for interpretable scientific discovery, especially with complex machine learning models. Traditional variable selection methods often rely on specific model assumptions, while Model-X knockoffs provide a general way that leverages knowledge of the covariate distribution to produce a variable selection algorithm. This study puts forward a complementary method to Model-X knockoffs, named Model-Agnostic Selection with agent-X importance (MAS), which utilizes the sample-splitting strategy and a novel variable importance measure to bypass distributional assumptions on covariates. The proposed model-agnostic agent-X importance is defined to evaluate the difference of oracle predictiveness on both the original distribution and the distribution with agent variable in population level, and can be efficiently estimated by constructing the agent variable as some constant and cross-fitting strategy. The MAS method integrates a resplit-per-covariate strategy to decouple estimator dependencies and a data aggregation technique to enhance power. Theoretical guarantees for asymptotic FDR control are established under mild conditions. Extensive simulations and real-data analyses demonstrate that MAS provides competitive performances with existing works in FDR control, computational efficiency and power.

stat.ME↗

arXiv2026

Hierarchical Building-Floo-Room Framework for Privacy-Preserving Autonomous Delivery in Large-Scale Buildings

Autonomous delivery in large scale buildings requires coordinated planning across multiple spatial levels, including building, floor, and room, while ensuring scheduling efficiency. Existing methods often focus solely on algorithmic development, neglecting integration with physical robotic platforms, and rarely validate performance in real world scenarios. Many approaches also overlook hierarchical building structures and room level privacy constraints, limiting practical applicability. To address these challenges, this paper presents a hierarchical delivery framework based on a Building-Floor-Room abstraction, which decomposes the problem across multiple levels to significantly reduce optimization complexity. We formulate a building aware extension of the capacitated vehicle routing problem (CVRP) that explicitly models inter building and inter floor connectivity, room level access constraints, and privacy sensitive areas, enabling globally feasible and privacy compliant task assignment and routing. Based on this hierarchical model, the framework can evaluate delivery efficiency across different building layouts and optimize depot placement for specific configurations. At the execution level, we introduce a novel hardware design for non interactive, privacy preserving delivery, supported by reachability aware distances and a closed loop mapping, localization, and navigation system, ensuring consistency between planned routes and physical navigation. The proposed framework is validated on a real multi sensor robotic platform, demonstrating reliable multi floor delivery with improved path rationality and overall efficiency.

cs.RO↗

arXiv2026

LTM: Latent Transition Based In-Context Memory for Vision-Language-Action Models

Robotic manipulation often requires remembering interactions that are no longer visible. We introduce Latent Transition Memory (LTM), which stores history as compact latent transitions between consecutive observations. Instantiated on $π_{0.5}$ as LTM-$π$, our method uses a frozen latent action encoder, a lightweight adapter, and causal KV caching for incremental inference without memory-specific semantic annotations or external reasoning-model calls. With DreamDojo transitions, LTM-$π$ achieves 58.54% success on RoboMME and 80.5% on LIBERO-Mem, performing best among baselines without external reasoning models or memory-specific annotations. Ablations support the contribution of transition content beyond temporal cues and the efficiency of delayed memory admission. Scaling RoboMME demonstrations tenfold improves success from 57.67% to 87.50%, while a Cup Swap diagnostic highlights the role of process supervision in temporal composition. Under a 200-token memory budget, success remains 84.00%, versus 87.50% without compression. Finally, real-robot counting success improves from 11.25% to 82.50%. Together, these results demonstrate the effectiveness, scalability, and efficiency of latent transition memory, highlighting its capacity for complex temporal information, bounded-context operation, and real-world robotic control.

cs.RO↗

arXiv2026

Two Sample Sizes in Test-Time LLM Ensembling: Buffered ERM and Minimax Theory

Test-time scaling can improve the performance of large language models by generating multiple answers to a question and aggregating them. Weighted ensembles extend this idea by drawing answers from several models, with the weights determining how often each model is used. Learning these weights from a training dataset involves two sample sizes: $Q$ labeled questions and $N$ generations per model and question. We study their interplay through the clean risk, the population error of the ensemble's infinite-generation voting rule. Under a margin condition with exponent $β$, we show that empirical risk minimization (ERM) with a calibrated margin buffer achieves excess risk of order $Q^{-1/2}+N^{-β/2}$, up to logarithmic factors, for fixed numbers of models and candidate answers. To investigate the optimality of this dependence on $Q$ and $N$, we analyze a simplified submodel with two models and two possible answers per question. We characterize its minimax excess risk up to constants by a Hellinger modulus for a binomial-mixture experiment. Polynomial approximation and spectral analysis reveal three regimes. When questions are relatively scarce, the $Q^{-1/2}$ term governs learning and the general buffered ERM is optimal. In an intermediate regime, pooling generation counts across questions improves upon estimating each answer distribution separately, with only logarithmic gains from additional questions. With sufficiently many questions, the minimax excess risk reaches an $N^{-β}$ identification floor that persists even with infinitely many questions. The submodel's lower bounds also apply to general ensembles, matching the buffered-ERM upper bound up to logarithmic factors when questions are scarce and in parts of the intermediate regime. Questions remain about the transitions between regimes and the construction of matching pooled estimators for general ensembles.

math.ST↗

arXiv2026

CoDeFont: One-Shot Font Generation via Multi-Scale Factor-Specific Representation Learning

One-shot Font Generation (OFG) aims to synthesize a target glyph by transferring the stylistic characteristics of a single reference glyph while preserving the structure of the target character. However, accurately capturing font style from a single reference image remains challenging due to the limited stylistic information available in a single glyph, and this challenge is further amplified for complex scripts. We propose CoDeFont, a script-agnostic OFG framework that addresses this challenge through multi-level style-content factorization and progressive style-content reconciliation. CoDeFont independently aggregates complementary style and structural information across multiple spatial levels to obtain factor-specific representations, while a contrastive objective explicitly encourages separation between style and content embeddings. During reconstruction, the disentangled representations are progressively injected through multi-level style conditioning, enabling stylistic information to be incorporated at different decoding resolutions while preserving the underlying glyph structure. We evaluate CoDeFont on structurally distinct Bengali and Latin scripts across seen and unseen font styles. Extensive quantitative and qualitative analyses demonstrate consistent improvements over existing state-of-the-art methods, highlighting the effectiveness of the proposed framework for OFG across diverse writing systems.

cs.CV↗

arXiv2026

Anti-successors and anti-replicators, Manin products and Koszul duality

We develop an operadic theory of anti-splitting and anti-replication for binary operads. For a binary operad $\opd$, we define its anti-bisuccessor $\ABSu(\opd)$ and anti-trisuccessor $\ATSu(\opd)$, with the property that an operation of $\opd$ splits into a negative sum of two or three operations, yielding canonical operad morphisms $\opd \to\ABSu(\opd)$ and $\opd\to\ATSu(\opd)$. For binary quadratic operads, the process gives Manin black products, \[ \ABSu(\opd) \cong \antiprelie \bullet \opd, \qquad \ATSu(\opd)\cong \antipostlie\bullet\opd. \] Dually, we introduce the anti-duplicator $\ADup(\mathcal P)$ and anti-triplicator $\ATrip(\mathcal P)$ and prove \[ \ADup(\opd^!)\cong \ABSu(\opd)^!, \qquad \ATrip(\opd^!)\cong \ATSu(\opd)^!. \] Consequently, the anti-duplicator gives a new way to calculate Manin white products. %, in particular, $\ADup(\opd)\cong \antiperm\circ\opd$. The framework recovers known anti-splittings, including anti-dendriform, anti-pre-Lie, and anti-pre-Poisson structures, in a uniform operadic form and produces further examples and dual pairs.

math.RA↗

arXiv2026

RenoLayout: Unified Floorplan Renovation and Furniture Layout for Constraint-Aware Residential Design

Residential design aims to transform existing homes into functional living spaces while satisfying diverse design preferences and physical constraints. However, existing floorplan generation methods typically assume empty building boundaries as input, whereas renovation requires reasoning over existing floorplans. Furthermore, floorplan renovation and furniture layout are commonly addressed as separate tasks, overlooking their inherent spatial dependency. Consequently, practical residential design must preserve immutable structural components while transforming editable spatial elements. It must also optimize furniture placement under design objectives and physical constraints. To address these challenges, we formulate residential design as a design-point-guided conditional generation task and propose RenoLayout, a framework that translates a pre-design residential state together with a design-point set into an executable Geometry-as-Code program. To enable controllable supervision, we construct a Design Map comprising 123 fine-grained design points covering structural renovation and furniture layout. We further introduce Difference-Grounded Design-Point Annotation to derive design-point sets automatically from before--after design pairs with VLM-based consistency verification. RenoLayout is trained using a three-stage CPT--SFT--RL pipeline, progressively improving spatial reasoning, instruction following, and constraint compliance. We also introduce the RenoLayout Benchmark, a set of 200 real-world before--after renovation cases with complete furniture layouts. To the best of our knowledge, it is the first benchmark for unified residential design. These cases include design-critical structural and building-service constraints.

cs.CL↗

arXiv2026

SATOR: Backpropagation-Free 3D Test-Time Adaptation via Sample-Adaptive Token Routing

Test-time adaptation (TTA) mitigates the performance degradation of source-pretrained models on unlabeled test data under distribution shifts. Recent backpropagation-free token-purging methods address 3D point cloud distribution shifts by filtering unreliable tokens. However, their reliance on predefined purge-size candidates requires multiple forward passes per sample and increases inference cost. We propose SATOR (Sample-Adaptive TOken Routing), a source-free and backpropagation-free 3D TTA framework that eliminates this search by deriving both the partitioning threshold and routing decision directly from each sample. SATOR computes token abnormality scores from complementary attention and geometric relation graphs. It then derives a sample-specific partition into retained and pruned tokens via Otsu-based separability, without evaluating candidate sizes. Keep-ratio-calibrated routing then selects the pruned prediction only when its entropy, penalized by the keep ratio, is lower than that of the original prediction. Experiments on ModelNet40-C, ScanObjectNN-C, and ShapeNet-C demonstrate that SATOR achieves state-of-the-art accuracy on three 3D corruption benchmarks.

cs.CV↗

arXiv2026

ESG-Kor: A Korean Dataset for ESG-related Information Extraction and Practical Use Cases

With the expansion of pre-trained language model usage in recent years, the importance of datasets for performing tasks in specialized domains has significantly increased. Therefore, we have built a Korean dataset called ESG-Kor to automatically extract Environmental, Social, and Governance (ESG) information, which has recently gained importance. ESG-Kor is a dataset consisting of a total of 118,946 sentences that extracted information on each ESG component from Korean companies' sustainability reports and manually labeled it according to objective rules provided by ESG evaluation agencies. To verify the effectiveness and applicability of the ESG-Kor dataset, classification performance was confirmed using several Korean pre-trained language models, and significant performance was obtained. Additionally, by extending the ESG classification model to documents of small and medium enterprises and extracting information based on ESG key issues and in-depth analysis, we demonstrated potential and practical use cases in the ESG field.

cs.CL↗

arXiv2026

Pairing-channel reconstruction by Ising spin-orbit coupling in a multiorbital triangular-lattice model

Ising spin-orbit coupling (SOC) is widely known for locking electronic spins and protecting superconductivity against in-plane paramagnetic pair breaking. Here we show that, in a correlated multiorbital system, Ising SOC can play a qualitatively different role: it reconstructs the hierarchy of spin-fluctuation-mediated pairing channels by reshaping the low-energy Fermi surfaces, orbital-spin coherence factors, and momentum-resolved scattering phase space. We study a noncentrosymmetric two-orbital triangular-lattice model with Rashba SOC, Ising SOC, and onsite SOC. We solve the pairing problem within a multiorbital random-phase-approximation framework. In the single-orbital limit, an $E$-representation state with a dominant $S_z=0$ component emerges only at relatively strong Ising SOC. Orbital degrees of freedom facilitate the stabilization of this pairing state at a smaller nominal Ising SOC strength and generate a broad competition between $E$ and $A_1$ pairing channels. The $E$ state can maintain the same $S_z=0$ triplet character, whereas the $A_1$ state becomes a fully gapped sign-changing $\splusminus$ superconductor. The latter also realizes a topologically nontrivial phase in the time-reversal-invariant weak-pairing regime, with a nonzero $\mathbb{Z}_2$ index, Wilson-loop spectral flow, and boundary modes. Its topology is not carried by a single orbital pairing component, but emerges cooperatively from the dominant intra- and inter-orbital pairing components. These results establish a microscopic route by which Ising SOC and orbital hybridization can reconstruct interaction-driven superconductivity, producing both Ising-triplet and topological singlet-dominated phases in correlated non-centrosymmetric systems.

cond-mat.supr-con↗

arXiv2026

Same Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation

Neural PDE solvers commonly generate multi-step predictions through autoregressive rollout, recursively applying a learned evolution operator and feeding each prediction back as input for the next step. Approximation errors can therefore propagate through the rollout, causing predictions at a shared target time to depend on their temporal origins and rollout depths. For a well-posed deterministic PDE flow, however, states at different times along the same physical trajectory should, under exact evolution, reach the same target state. To this end, we propose Align Latent Rollout (ALR), a regularization approach that promotes consistency across rollout origins through the neural PDE solver's internal representations. A second-order Taylor analysis of latent discrepancy propagation motivates two objectives: zeroth-order latent state consistency, which aligns representations at a shared target time, and first-order latent dynamics consistency, which aligns local evolution responses to shared perturbations. ALR can be integrated into different neural PDE solvers by regularizing suitable internal representations, without modifying their backbone architectures. Experiments across multiple PDE benchmarks and neural-operator backbones show that ALR improves prediction accuracy while reducing shared-target discrepancies across rollout origins.

cs.LG↗

arXiv2026

Geometric Hashing in MPC with Applications to Clustering and Stochastic Embeddings

In this paper we study consistent hashing (a.k.a. sparse partitions) for doubling metrics in the Massively Parallel Computation (MPC) model. A $(Γ,Λ)$-hash with diameter bound $Δ$ partitions a metric space into clusters of diameter at most $Δ$ such that every ball of radius $Δ/Γ$ intersects at most $Λ$ clusters in expectation. Consistent hashing has emerged as a central tool in geometric MPC algorithms. However, so far it has been solely used in Euclidean spaces, where it can be pre-computed. On the other hand, in cases where the metric space is received as input and unknown in advance, no previous parallel construction was known. We present the first fully scalable MPC algorithm over machines with local space $n^σ$, that given an $n$-point metric space with doubling dimension $d\leq O(σ\log n)$, samples a randomized $(Γ,2^{O(d/Γ)})$-hash in $O(d/σ^3)$ rounds. There is a dichotomy: if the doubling dimension is $d=Ω(σ\cdot\log n)$, a polynomial number of rounds is required to compute such a hash. We conclude by showing that this MPC primitive yields $O(d/σ^3)$-round fully scalable MPC algorithms for a broad class of fundamental geometric problems in doubling metrics, including stochastic tree embeddings with $O(\log n)$ expected distortion, constant factor approximation for facility location, bicriteria $(O(ε^{-2}),1+ε)$-approximation for $k$-median and $k$-means.

cs.DS↗

arXiv2026

Agentic Dependency Transformations: Lessons from an Exploratory Case Study of Flask

Modern software relies heavily on third-party libraries, requiring maintainers to balance the benefits of reuse against dependency-related maintenance and risk. We define dependency transformation as an emerging approach in which an AI coding agent alters how a repository handles external dependencies. Local reimplementation is one transformation strategy that recreates required functionality as local code; dependency transformation is broader and may include other strategies. In this emerging-results paper, we report an exploratory case study of Flask to explore dependency transformation strategies. We design experiments that show how available context shapes an agent's dependency discovery and iterative transformation of dependencies. The case yields five preliminary lessons. These lessons and the five-part research agenda position dependency transformation as an emerging research direction and motivate explicit transformation contracts, provenance constraints, preservation requirements, and independent validation criteria.

cs.SE↗