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At least 811 records · Page 45Linked to original sources
arXiv2026

Trace ideals of exterior powers of the module of differentials

For each $i \geq 0$, we study the trace ideal of the $i$-th exterior power of the module of differentials. In characteristic zero, we show that these ideals characterize the polynomial rank of graded rings and the formal power series rank of complete local rings with finite residue-field extension, namely the maximal number of variables for a polynomial or formal power series extension over a subring. Moreover, we introduce the top differential trace and prove that it precisely defines the singular locus of reduced equidimensional local or graded rings. Motivated by this, we introduce and investigate nearly regular rings, which are rings whose top differential trace contains the maximal ideal.

math.AC↗
arXiv2026

Universality of Quantum Gates in Particle and Symmetry Constrained Subspaces

Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates are universal for state preparation in these subspaces. The key mechanism is Pauli $Z$ dressing: commutators of overlapping gates produce Pauli $Z$ operators on shared qubits, acting as spectator projectors that decompose multi-plane rotations into single-plane generators spanning the full $\mathfrak{so}(w)$ algebra, where $w$ is the dimension of the constrained subspace, thereby guaranteeing universality for real state preparation. Adding independent complex phases extends this to $\mathfrak{su}(w)$, enabling arbitrary complex state preparation. We provide a computationally efficient Jacobian criterion for verifying that a circuit can explore any direction on the target manifold from almost any parameter configuration. Our findings are applicable to many problem areas, including Fermi-Hubbard models, Bose-Hubbard models, and molecular electronic structure. We apply our framework to two physical settings: we prove the completeness of the binary encoded multi-level particles ansatz on the conserved-particle-number subspace, and we construct symmetry-preserving circuits for the fuzzy sphere regularisation of the 3D Ising conformal field theory (CFT). For the latter, we variationally prepare the ground and excited states and extract some CFT data.

quant-ph↗
arXiv2026

Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis

We develop a coarse-to-fine generalized linear mixed model (CF-GLMM) for scalable spatial prediction of exponential-family responses. CF-GLMM extends coarse-to-fine spatial modeling (CFSM) beyond Gaussian data by sequentially increasing spatial resolution while validation deviance improves, so the terminal resolution need not be specified in advance. The latent spatial process is constructed by aggregating local models, avoiding costly operations on large spatial covariance matrices. An idealized convolution representation links the covariance of our assumed spatial process to a sum of Matern covariances with different ranges. Monte Carlo experiments show that CF-GLMM achieves predictive accuracy comparable to widely used scalable spatial GLMMs while requiring less computation and memory. Its scale-specific components also support exploratory multiscale analysis. An application to COVID-19 infection data in Tokyo illustrates fine-resolution spatial prediction and multiscale characterization of geographical variation. The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).

stat.ME↗
arXiv2026

Change-Robust Online Topological Memory for Long-Term Relocalization and Semantic Navigation

Long-term semantic navigation requires a robot to reuse past observations after appearance and scene change, but semantic memories are only useful if the robot can relocalize into the memory without corrupting it with false visual matches. We propose CROSS, a change-robust topological memory that introduces a pre-commitment localization layer between visual place recognition and map update. Instead of treating a retrieved keyframe as an immediate place association or loop-closure factor, CROSS lifts each RGB-D retrieval into a candidate global SE(3) pose mode using relative pose estimation. A bounded Gaussian-mixture filter then propagates competing continuous trajectory branches with odometry, rejects branches that are physically inconsistent, and promotes only persistent branches to loop closures. This moves ambiguity handling from discrete place IDs or post-hoc graph-factor rejection to continuous pose-space validation before map commitment. Across public long-term relocalization benchmarks and real quadruped object-navigation experiments, CROSS improves reuse of a single sparse RGB-D memory under illumination, seasonal, dynamic-scene, and object-level change. Project page: https://jiaming.im/CROSS/

cs.RO↗
arXiv2026

Detectability of Magnetar-Induced Vacuum Birefringence with IXPE and eXTP

We analyze the prospects of quantitatively detecting vacuum birefringence from magnetars using the IXPE and eXTP experiments. We adopt a realistic spatially-varying magnetic field profile for magnetars and use the one-loop refractive indices, without expanding in $B/B_{\rm c}$, to calculate the differential time delay and accumulated phase between the two photon polarization eigenmodes. Including the extended magnetosphere enhances the time delay by a factor of 1.2--1.7 relative to a constant-field estimate and can yield delays approaching the microsecond scale for the strongest catalogued magnetar fields. We also study the evolution of the polarization state in a varying projected magnetic field using the Stokes-vector precession equation, derive the corresponding adiabaticity condition and polarization-limiting radius, and recover the fixed-eigenaxis expressions used in our catalog analysis as a controlled limit. We calculate the Stokes parameters for all known magnetars and investigate their observability with IXPE and eXTP, including the effects of instrumental response and energy averaging. We find that both experiments can be sensitive to magnetar vacuum birefringence under favorable conditions, with 1RXS J170849.0$-$400910 being the most promising candidates. A quantitative prediction for an individual magnetar, however, additionally requires a source-specific treatment of the emission mechanism, viewing geometry, plasma environment, and magnetospheric scattering, which we do not tackle in this study.

hep-ph↗
arXiv2026

Dual Certified White-Box Inference for Input Convex Neural Networks

Input convex neural networks (ICNNs) are used to learn convex objectives whose minimizers define decisions, making efficient and reliable optimization central to inference. At nonsmooth inputs, automatic differentiation returns a single derivative rather than the full subdifferential governing optimality and descent. Second-order cone ICNNs (SOC-ICNNs) admit an exact representation as value functions of parametric second-order cone programs, providing a white-box approach to recovering their full subdifferentials from optimal dual multipliers and deriving explicit Hessians on smooth regions. Building on this representation, we develop dual-certified inference (DCI), which combines the network and feasible set geometries to obtain exact stationarity certificates and tangent common descent directions. DCI uses local curvature for Newton acceleration and an exact proximal safeguard. We establish global convergence and, under standard regularity conditions, local quadratic convergence near structurally nondegenerate interior minimizers. Numerical experiments validate the recovered geometry and demonstrate the reliability and efficiency of DCI. Code is avaliable at https://anonymous.4open.science/r/DCI-ICNN-507D/

cs.LG↗
arXiv2026

On Generalized Quasi-Einstein Manifolds

In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,λ)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier results of Sharma to the generalized setting. Moreover, we show that divergence-free vector fields are Killing in this context, and we derive consequences under sign conditions on $m$ and $λ$, including triviality results. We also revisit a recent theorem of Ghosh \cite{ghosh}, discuss a subtle issue in the argument, and provide a new formulation and proof. Finally, we establish rigidity results for manifolds with geodesic potential vector fields.

math.DG↗
arXiv2026

Ropelength-Filtered Swept-Area Geometry

This paper studies the swept-area cost of isotopies between thick knot representatives when the isotopy is required to stay inside a ropelength window: every intermediate curve has thickness at least one and length at most $Λ$. Without these constraints the swept area is the classical homotopy-area length on spaces of curves, and the induced distance on unparametrized curves is bounded below by the flat norm; see Yezzi--Mennucci and Michor--Mumford. We record the corresponding non-degeneracy on the ropelength-filtered moduli space, taken modulo orientation-preserving reparametrizations and Euclidean isometries, as a consequence of this classical lower bound. The ropelength window changes the theory in two ways. Distances are infinite between classes that are not yet connected at the level $Λ$, and all costs depend monotonically on the budget. We organize this dependence through budget--cost profiles and swept-area merge costs of admissible components. We prove their monotonicity and a transport estimate under whole-path simulations, and relate them to the merge scales of ropelength-filtered knot spaces. On the diagrammatic side, we construct a network with exact spatial endpoints whose path cost equals the infimal cost over diagrammatically generic isotopies, and show that the graph obtained by collapsing projection fibres gives only a lower bound, which can lose positive cost inside a fibre. We also give projected-area calibrations, exact formulas for concentric round and homothetic elliptical unknots, in which the window is not active, a labelled polygonal estimate, and a based loop-length structure on admissible fundamental groups. Existence of minimizing isotopies under the thickness and length constraints is left open.

math.GT↗
arXiv2026

Active Learning for Communication Structure Optimization in LLM-Based Multi-Agent Systems

Optimizing the communication structure of large language model based multi-agent systems (LLM-MAS) has been shown to improve downstream performance and reduce token usage. Existing methods typically rely on randomly sampled training tasks. However, tasks may differ substantially in difficulty and domain, and thus they are not equally informative for updating communication structure, making optimization often unstable and highly sensitive to the particular training set. To actively identify the most valuable tasks for communication-structure optimization, we propose an ensemble-based information-theoretic task selection framework. The proposed method estimates task informativeness by how much a candidate task changes the distribution over graph parameters, using ensemble Kalman inversion as an efficient and derivative-free approximation of the corresponding Bayesian update. The resulting estimator is especially suitable for black-box and noisy multi-agent systems. To enhance scalability, we construct a compact candidate pool through embedding-based representative selection and combine the informative selection with surrogate modeling and batch Thompson sampling. We validate the proposed framework across both benign and adversarial settings and multiple task formats. It consistently outperforms random training, demonstrating more effective task selection and greater overall cost efficiency.

cs.MA↗
arXiv2026

CoMemNet: A Continual Memory Network with Drift-Aware Sampling for Traffic Prediction

Traffic sensor networks evolve as sensors are added and traffic distributions change, whereas most forecasting models assume a fixed node set and repeatedly retrain on all available data. We propose CoMemNet, a Continual Memory Network for efficient prediction over evolving traffic sensor networks. CoMemNet uses an Online branch to adapt to the current period and an exponential-moving-average Target branch as a stable feature reference. A Wasserstein-based Drift Sampler compares node-wise Online-Target feature distributions and selects a limited set of drift-sensitive nodes for updating. A lightweight Node-Adaptive Temporal Memory Replay Buffer (TMRB-N) retains compact temporal states without repeatedly traversing all historical training data. The prediction backbone does not consume an adjacency matrix; sensor adjacency is used only to construct data and optionally expand the selected update set to a limited neighborhood. Experiments on three multi-period PeMS datasets include three-seed evaluation, strong static retraining and continual baselines, controlled sampling strategies, continual-learning metrics, robustness tests, and resource accounting. The results show that CoMemNet maintains stable prediction accuracy and efficient adaptation under bounded shared-node selection, achieving a better balance between historical knowledge preservation and current-period prediction performance. Meanwhile, as the evolving network expands, CoMemNet shows clearer accuracy and cumulative training-time advantages over current-period retraining baselines. The code is available at:https://meiwu5.github.io/CoMemNet.

cs.LG↗
arXiv2026

Trade-off Functions for DP-SGD with Subsampling based on Random Allocation: Tight Upper and Lower Bounds

Within the $f$-DP framework, we derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random allocation in which each sample is independently assigned to exactly one of $M$ minibatches per epoch, each minibatch corresponding to one of the $M$ SGD rounds within a single epoch. Our analysis holds under an explicit validity condition, whose hypotheses together force $σ\geq \sqrt{3/\ln M}$, where $σ$ is the DP noise multiplier. Unlike $f$-DP analyses for Poisson subsampling, which yield non-closed implicit formulas that can be machine computed but are non-transparent, random allocation admits a tight analysis yielding transparent and interpretable closed-form bounds. For a single epoch, our concrete bounds, derived via the Berry-Esseen theorem, are tight up to constant factors. We demonstrate worked parameter settings for a single epoch ($E=1$) with a corresponding trade-off function $\geq 1-a-δ$, that is, only $δ$ below the ideal random guessing diagonal $1-a$. For $δ= 1/100$ and $σ= 1$, roughly $M \approx 1.14\times 10^6$ rounds and $N \approx 1.14\times 10^7$ training samples suffice to achieve meaningful differential privacy. This is in contrast to recent negative results for the regime $σ\leq 1/\sqrt{2 \ln M}$ for which no significant DP guarantee can exist.

cs.LG↗
arXiv2026

AGT-CV: An Aerial-Ground Team Cross-View Dataset for Heterogeneous Robot Teams in Unstructured Environments

Heterogeneous air-ground robot teams combine complementary sensing modalities, mobility characteristics, and spatial viewpoints that can significantly enhance perception in complex outdoor environments. However, progress in multi-robot collaborative perception has been constrained by the lack of real-world datasets featuring overlapping multi-modal observations from platforms operating in unstructured terrain. We present the \textbf{AGT-CV} (\textbf{A}erial-\textbf{G}round \textbf{T}eam \textbf{C}ross-\textbf{V}iew) dataset, a real-world multi-robot collaborative perception dataset collected using a Clearpath Husky UGV and an Autel EVO~II UAV across diverse unstructured environments, including forest trails, rocky paths, muddy terrain, snow piles, and grass-covered fields. The ground platform provides 3D LiDAR, stereo camera, IMU, and GPS data, while the aerial platform contributes RGB imagery, thermal/infrared observations, and GPS from a complementary overhead viewpoint, allowing for rich cross-modal and cross-view perception. The dataset is collected in 4 unique environments, with over 13,000 synchronized frames across approximately 29 minutes of operation, and includes both SAM~3-based zero-shot segmentation and almost 8,000 manually labeled images. A unique aspect of the dataset is its early-spring collection period, during which sparse tree canopies allow the aerial robot to partially observe the ground robot and terrain through the trees, allowing for occlusion-aware collaborative perception. Unlike prior multi-robot datasets that primarily focus on SLAM or simulated cooperative driving, AGT-CV is specifically designed to support research on cross-view perception, air-ground viewpoint fusion, terrain-aware perception, and collaborative scene understanding in real off-road environments.

cs.RO↗
arXiv2026

Recursive Agent Optimization

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

cs.LG↗
arXiv2026

Improving Reasoning Ability via Asynchronous On-Policy Self-Distillation under Positive Rollouts

Distillation and reinforcement learning through verifiable rewards (RLVR) have achieved progress in enhancing the reasoning ability of large language models (LLMs). However, we note that negative rollouts may admit no gradation of failure severity, and the combinatorial vastness makes penalizing a few sampled negatives unlikely to cover a meaningful reward signal under sparse binary rewards. In this work, we propose Positive-Only Policy Optimization (POPO), an on-policy self-distillation integrated RLVR framework in which learning occurs exclusively on online positive rollouts. Specifically, POPO utilizes bounded importance sampling over the positive rollout set. Thus, no disjoint negative rollouts are used for gradient guidance during post-training. We show that implicit negative gradients can emerge naturally through reinforcing the positive probability via rollout redistribution. Next, POPO stabilizes the policy optimization through self-distillation. First, it applies a Siamese policy network with a momentum-based adaptation law for asynchronous policy evolution. Second, we replace the KL-divergence with a bounded similarity penalty term in the Siamese representation space. We conduct extensive experiments using publicly available, well-established text-LLM models across all-level mathematical benchmarks (MATH-500, AMC23, AIME 2024/2025, and Olympiad). Our experiment demonstrates that POPO achieves superior performance compared to GRPO. Notably, we show that POPO can achieve 36.67% in AIME 2025 with Qwen-Math-7B, outperforming GRPO 30.00%. Our ablation and sweep studies further illustrate the necessity and robustness.

cs.CL↗
arXiv2026

LensVLM: Selective Context Expansion for Compressed Visual Representation of Text

Vision Language Models (VLMs) offer the exciting possibility of processing text as rendered images, bypassing the need for tokenizing the text into long token sequences. Since VLM image encoders map fixed-size images to a fixed number of visual tokens, varying rendering resolution provides a fine-grained compression knob. However, accuracy deteriorates quickly as compression increases: characters shrink below the vision encoder's effective resolution, making them indistinguishable. To address this, we propose LensVLM, an inference framework and post-training recipe that enables VLMs to scan compressed images, then selectively expand only the relevant images to their uncompressed form via learned tools. Building on Qwen3.5-9B-Base, LensVLM maintains accuracy comparable to the full-text upper bound at 4.3$\times$ effective compression and outperforms retrieval-based, text- and visual-compression baselines up to 10.1$\times$ effective compression across seven text QA benchmarks. LensVLM also generalizes to multimodal document and code understanding tasks, with the accuracy gain over baselines growing as compression increases. Our analysis validates this approach: training makes visual compression robust to rendering choices, and as compression grows the model increasingly relies on expanded content rather than unreliable visual reading. The analysis also yields practical tool-choice guidance: text expansion is preferable for rendered text, while high-resolution image expansion suits native documents whose layout cues carry task-relevant information.

cs.CV↗
arXiv2026

The sigma meson ($f_0$) at finite temperature with truncated overlap fermions

We study the temperature dependence of meson screening masses in two-flavour lattice QCD using dynamical truncated overlap fermions, a type of lattice chiral fermions. The screening masses for the $π$, $ρ$, $a_1$, $a_0$, and the sigma $(f_0)$ mesons are extracted by computing spatial correlation functions. This exploratory study uses meson screening masses and the connected/disconnected decomposition of the scalar correlator as diagnostic observables to examine how the disconnected contribution changes across the pseudocritical region. Above the pseudocritical temperature $T_{\rm pc}$, the $π$ and $f_0$ screening masses become degenerate, consistent with chiral restoration. The $(ρ,a_1)$ pair also shows the expected degeneracy. Decomposition of the $f_0$ propagator reveals that the connected contribution dominates above $T_{\rm pc}$, while the disconnected part becomes significant below $T_{\rm pc}$, explaining the reduced statistical clarity observed at low $T$. These results demonstrate that dynamical truncated overlap fermion simulations can capture the qualitative thermal behaviour of the scalar sector.

hep-lat↗
arXiv2026

Dynamical Systems in Elliptical Pursuit and Evasion

This paper investigates the elliptical case of one-on-one pursuit and evasion problems. Using the simultaneous differential equations derived by Barton and Eliezer, we derive a dynamical system based on the assumption that the shape of the pursuer's trajectory is unaffected by the evader's speed. The dynamical system involves the angular difference between the velocity vectors of the players and their separation distance. We examine whether the pursuer lies inside or outside the evader's elliptical path, and how the angle between the directions of motion of the two players evolves. Moreover, using a complex variable that includes information about the logarithmic distance and the angular difference, we transform the system into a single ordinary differential equation along which the distance between any two solutions never increases. We obtain four main results. First, when the evader is slower than the pursuer, the pursuer captures the evader in finite time, and we derive an explicit upper bound for the capture time. Second, when the evader is faster than the pursuer, a pursuer starting inside the evader's elliptical path is never captured, whereas capture does occur from just outside it on a nearly head-on course. Third, in the same case, the system has a unique periodic solution, to which every solution that avoids capture converges. Fourth, this periodic solution is hyperbolic and exponentially stable, and the product of its Floquet multipliers is given explicitly.

math.OC↗
arXiv2026

Offline Policy Optimization with Posterior Sampling

A fundamental challenge in model-based offline reinforcement learning (RL) lies in the trade-off between generalization and robustness against exploitation errors in out-of-distribution (OOD) regions. The key to resolving this trade-off lies in enabling the model to explore OOD regions that remain consistent with underlying physical dynamics. However, achieving this is challenging because limited data cannot uniquely identify the dynamics model, and unconstrained exploration is risky. Existing methods often overlook this nuance, addressing the risk through excessive pessimistic regularization, which ensures robustness but sacrifices generalization. To address this, we propose PSPO, which treats the dynamics model as a random variable rather than a point estimate. This formulation inherently allows for controlled exploration of OOD regions. By alternately updating the posterior distribution and the policy, we design a regularized optimization algorithm with convergence guarantees. Experiments on standard benchmarks demonstrate that PSPO achieves superior performance compared to state-of-the-art baselines. Further analysis confirms that our method attains the desired pessimism-free property while maintaining robustness, and ablation studies verify the effectiveness of each proposed module.

cs.AI↗