Papers

A multi-domain eXtended Physics-Informed Neural Network (XPINN) framework is developed for nonsmooth Delay Differential Equations (DDEs). This is the first implementation to demonstrate the efficacy of partitioning the temporal domain into subdomains of integer multiples of the characteristic time delay and progressively training the associated subnetworks while freezing previously learned parameters. The efficacy of the proposed framework is demonstrated using a machining dynamics model that incorporates both regenerative and nonsmooth frictional effects. Results demonstrate that the proposed multi-domain XPINN framework leads to better solution reconstruction in DDEs and improved parameter estimation compared to a generic PINN (SPINN) formulation. The proposed method works particularly well for extended temporal domains and non-constant history functions. The robustness of inverse XPINN (I-XPINN) is also assessed using reference data contaminated with Gaussian measurement noise. Results indicate that I-XPINN remains resilient to measurement noise and the physics-informed constraints guide the network toward accurately recovering the underlying dynamics. This demonstrates, for the first time, the potential of the proposed framework for reliable parameter identification in DDEs characterised by nonsmoothness and large time delays.

Spherical data arise in many scientific applications. Often spherical transformers disregard the geometry of the underlying spherical domain, causing distortions and coordinate singularities near the poles. We introduce SO(3)-RoPE, a relative positional embedding that incorporates spherical geometry into transformer attention through unitary SO(3) representations. Our formulation is SO(3)-equivariant and compatible with FlashAttention, retaining efficiency of vanilla transformers. On shallow water dynamics prediction over a rotating sphere, our SO3ViT outperforms an S2Transformer baseline with lower errors and reduced runtime.

A temporal graph is a sequence of graphs on a common set of $n$ vertices, its snapshots, one for each time step. An agent, knowing the entire sequence in advance, may at each time step wait or move along an edge of the current snapshot, and the temporal graph is explored once the agent has visited every vertex. We consider always-connected temporal graphs, in which every snapshot is connected, and ask how long exploration can be forced to take when the underlying graph, the union of all snapshots, has maximum degree at most~$\Delta$. Two lower bounds were known in this setting, $\Omega(\Delta n)$ and $\Omega(n\log n)$, realised by different constructions. We establish a stronger lower bound, answering a question of Bastide, Groenland, Michel and Rambaud. Specifically, for every $n$ and $\Delta$ with $\Delta_0\le\Delta\le n-1$ we construct an always-connected temporal graph on $n$ vertices with underlying maximum degree at most~$\Delta$ that cannot be explored in fewer than $\gamma\,\Delta n\,(1+\log(n/\Delta))$ time steps from any start vertex, where $\gamma>0$ and $\Delta_0$ are absolute constants. The construction is deterministic, and every snapshot is a spanning tree with exactly one vertex of degree greater than three. Time is divided into phases. In each phase, a rotating-cycle gadget prevents the agent from reaching more than half of the trees attached to it. Between phases, we reassign target vertices among these trees using walks on a constant-degree expander, and a Gray code order of the targets keeps the underlying degree bounded. The reassignment guarantees that, for any walk of the agent, some target remains unvisited throughout all phases.

Establishing ordinary differential equations (ODEs) describing population data is a fundamental part of mathematical modeling in pharmacology, crucial to developing digital twins. However, doing so from sparse, noisy data is a slow, expert-driven task. Existing automated methods either search a restricted model space or ignore population inter-individual variability. Here we introduce APOD (Agentic Population ODE Discovery), a language-model agent that iteratively reasons over biological knowledge and fit diagnostics in an open-ended search space to discover a population digital twin (PDT), i.e., a shared ODE system with between-subject variability. On synthetic pharmacokinetic and tumor-dynamics benchmarks, APOD recovered ground-truth structures in 94-100% of runs, 12-fold faster in median than an established library-based search. On real cohorts it converged to valid structures, and proposed a PDT of radioligand-therapy-induced platelet dynamics that predicts thrombocytopenia from first-cycle data and simulates alternative dosing schedules that lower the predicted risk of toxicity.

Prior audio-visual self-supervised learning methods rely on mechanisms such as EMA target encoders, prediction heads, reconstruction decoders, and contrastive losses. We introduce LeAVJEPA, the first audio-visual encoder trained under LeJEPA's collapse-free objective. A single early-fusion Vision Transformer processes audio, video, and joint audio-video inputs. Modality dropout treats a missing modality as another view of the same event, making cross-modal alignment implicit in the objective. The model aligns global embeddings with modality-specific local embeddings, and SIGReg prevents representational collapse. A controlled ablation identifies modality dropout as the key mechanism for audio-visual alignment. Despite the architectural simplicity, LeAVJEPA reaches 36.0 mAP on AudioSet-20K and 91.3% accuracy on ESC-50 under frozen evaluation. After fine-tuning, it reaches 61.1% accuracy on VGGSound, and its embeddings support zero-shot audio-visual retrieval.

Pretrained diffusion models provide powerful image priors for training-free posterior sampling in image restoration. To guide this sampling process, frequency-aware methods progressively incorporate measurement information across frequency bands, facilitating coarse-to-fine reconstruction. However, existing methods typically do not explicitly separate frequency activation from degradation-induced attenuation, leaving attenuation differences among inactive frequencies insufficiently modeled. In this work, we propose frequency-decoupled posterior guidance to separate frequency activation from attenuation-aware spectral regularization. Specifically, a progressive low-to-high frequency schedule determines the active measurement band, while a kernel-derived attenuation map defines a selective spectral prior over inactive components. To stabilize the sampling process, we also introduce a local trajectory regularizer that suppresses spatially irregular state-to-clean deviations. For a fixed endpoint energy, we provide a KL-regularized path-space interpretation. In practice, we construct time-dependent guidance through local energy corrections using a Tweedie plug-in approximation. Experiments on natural-image benchmarks demonstrate strong PSNR and SSIM performance across challenging non-blind deblurring settings, even at higher measurement noise levels.

Pre-generation success probes estimate response correctness from a language model's hidden activations before decoding, enabling cost-aware routing. While prior work has demonstrated their utility primarily on English inputs, we study their reliability across languages along three dimensions: (1) whether they preserve the ranking of likely successes and failures (DISCRIMINATION); (2) whether they retain probabilities that match observed success frequencies (CALIBRATION); and (3) whether they produce scores comparable enough across candidate models for cost-aware multilingual routing (UTILITY). Using 3,000 MATH problems in 10 languages and 8 open-weight model configurations, we compare cross-lingual transfer from English-trained probes and equal-budget pooled multilingual probes. English-trained probes retain useful cross-lingual discrimination but become less well calibrated after transfer. Pooled multilingual supervision improves both properties and yields more reliable estimates of success. In routing experiments, the pooled router achieves a 0.7% higher test success rate while reducing modeled cost by 13.0% relative to always selecting the model with the highest average success. These results show that multilingual routing requires success estimates that remain well calibrated and comparable across languages and models.

Micro unmanned aerial vehicles (micro-UAVs) are small enough to reach confined spaces that larger robots cannot access, but too small to carry the sensing and computing power required for autonomous flight. We move the localization stack entirely off the aerial platform onto a quadruped robot with a 7-degree-of-freedom (DOF) arm, which supplies the micro-UAV (27 g bare, 42 g with fiducial markers) its full 6-DOF pose. A camera at the arm's end-effector detects AprilTag fiducial markers on the drone and composes that observation with the quadruped's own self-localization to place the drone in a shared map frame, so the ground robot localizes its partner, rather than only tracking it relative to the camera. The arm acts as an actively-controlled observer, repositioning to keep the drone in view as both robots move; the drone carries only an inertial measurement unit and fuses the external pose to fly commanded setpoints. In lab flights the external pose is accurate to 12-16 mm, enough to fly the drone autonomously within 2-5 cm of motion-capture-fed control. Having the quadruped actively follow the drone reduces the tracking error from 11.0 cm to 6.9 cm by holding the camera in the close range, where the markers are most accurate.

We study the sampling allocation of LinUCB in the small-gap regime, where the reward gaps are of order at most $n^{-1/2}$ over the decision horizon $n$. This scaling captures the hard instances underlying worst-case regret lower bounds, for which LinUCB is known to be near optimal up to logarithmic factors in $n$. Using a mean-field perspective, we characterize this allocation through the empirical sampling distribution, a macroscopic object that averages the effect of adaptive decisions over the horizon, and identify its limit as $n\to\infty$. We establish that in this regime, the empirical sampling distribution induced by LinUCB converges to the set of D-optimal designs. This central result reveals that, in the small-gap regime, LinUCB not only achieves near optimal minimax regret but also allocates samples in a way that is asymptotically efficient for learning the reward parameter, thereby connecting regret-driven online learning with information-efficient experimental design. Building on the optimal design limit, we obtain two useful consequences. First, we refine the asymptotic regret analysis of LinUCB in the small-gap regime by characterizing its leading-order constant in the limit. Second, we show that, despite LinUCB's adaptive sampling strategy, the regularized least-squares estimator satisfies a central-limit-type theorem in the small-gap regime, thereby enabling valid statistical inference for the reward parameter.

Online agents can improve future service by constructing reusable tools, guidance, or model states, but this work competes with current requests for the same GPUs. Exploiting idle compute for self-evolution faces a fundamental systems constraint: benefits arrive only after an artifact is published and used, while pausing evolution leaves service capacity waiting for memory release and runtime recovery. An investment worth completing may therefore be worth postponing. We present LearnSched, a state-aware scheduler that brings the reuse window of a capability and the timely return of compute into a common investment model. LearnSched incorporates candidate progress, checkpoint overhead, and the current recovery path into action values. Under the same information and capacity constraints, it uses one-step counterfactual rollout to choose progress, checkpointing, or waiting relative to a fully costed window policy. We characterize handoff costs through independent A100 component measurements and evaluate action selection in 1920 paired finite-model scenarios. When cold recovery is expensive, waiting for longer execution windows can improve net value by avoiding handoffs; in evaluated warm-recovery scenarios, the strong window policy already achieves the same value. Retaining recoverable state can shorten capacity return and reduce the need for complex evolution scheduling.

Learned models for industrial control are usually judged by aggregate accuracy, but accuracy at the component level does not guarantee safety once it is embedded in the system it is meant to serve. We study this gap on a behavior-cloning task: imitating an expert Nonlinear Model Predictive Control (NMPC) policy for load-following of a Pressurized Water Reactor (PWR), an industrial system with tight safety constraints. We propose a structured architecture encoding variables from each timescale into separate latent spaces, reflecting the physical decomposition of the system, before training a controller to imitate the expert on the product latent space. On long-horizon rollouts, separated embeddings improve both accuracy and feasibility compared with a shared-embedding baseline. Sensitivity analysis further shows that our model yields interpretable representations aligned with the system's physics. However, standalone deployment still leaves several percent of trajectories infeasible regardless of the architecture. Using our method to warmstart the NMPC optimizer rather than acting standalone, we recover full feasibility and near-optimal cost while still cutting computation time by $\sim$15% relative to the expert controller, and even more for abrupt operating changes.

Autoregressive generation is natural for language, where predicted tokens can be directly reused as the next prediction state, but trajectory forecasting lacks such a clean token: motion is continuous, multimodal, and expressed in local coordinate frames that evolve with the predicted trajectory. We present MoCAR (Motion-code Coordinate-aware AutoRegression), a decoder-only framework that casts trajectory forecasting as next-code prediction in a coordinate-aware continuous latent space. MoCAR learns a continuous motion-code space from endpoint-normalized trajectory segments, where each code jointly captures local trajectory geometry and the reference-frame transition induced by that segment. Historical motion codes are used as a teacher-forced prefix, future codes are generated autoregressively under temporal, map, agent, and mode interactions, and predicted codes persist in latent memory while decoded endpoints update the local scene context. This enables rollout without trajectory-space re-tokenization, trajectory queries, goal candidates, or proposal-and-refinement pipelines. On Argoverse (AV) benchmarks, MoCAR achieves top-tier performance with a simple single-stage architecture, transfers strongly from AV2 to AV1 in zero-shot evaluation, and improves on turn-heavy scenarios. Ablations confirm that the learned continuous motion-code space, latent alignment, weak KL regularization, and joint tokenizer-predictor optimization are essential for stable latent autoregression.

In this work, we propose and analyze low-order nonconforming face-based finite element methods for elliptic problems on complex hybrid three-dimensional meshes, composed of arbitrary polytopal cells. The focus is on scalar problems, but the approach can be extended in a tensor manner to design generalizations of the classical Crouzeix–Raviart and Rannacher–Turek methods for mixed formulations. We adopt a nonparametric construction of the local approximation spaces. We demonstrate that it avoids the degradation of approximation properties commonly induced by parametric mappings on distorted meshes. Using these approximation spaces, we define finite element schemes for very general cells. We further demonstrate that, on strongly degraded meshes, an approach inspired by discontinuous Galerkin methods enables removing consistency errors, even in the presence of potentially curved faces. Explicit examples of the construction of the polynomial space are given for prismatic (of triangular basis) and pyramidal (of quadrilateral basis) cells. The resulting schemes are shown theoretically and numerically to be stable and convergent, with an optimal convergence rate.

Large Language Models (LLMs), Retrieval-Augmented Generation (RAG), and AI agents are increasingly embedded in operational business processes. Yet Business Process Management (BPM) curricula and frameworks still largely treat artificial intelligence (AI) as an add-on technology, leaving graduates (as potential future process developers) unprepared to reason about AI as a first-class design element of end-to-end processes. This paper addresses that gap by proposing AI-decision checkpoints: explicit moments in a process development trajectory where process developers identify AI-candidate sub-processes, assess expected effects on time, cost, quality, and flexibility, consider legal and organisational constraints, and document a reasoned decision to adopt, constrain, or reject specific AI components. The checkpoints are instantiated through a fictitious customer onboarding process as a BPM Teaching Case, embedded in a lifecycle-driven framework spanning six modules that combine process modeling, simulation, workflow execution with AI agents, and process mining, with each module's output serving as the next module's input. A preliminary formative reflection draws on instructor observations, submitted artifacts, and discovered process maps from learning-management-system logs. These exploratory observations suggest that the approach supported clearer distinctions between task-level automation and process-level value.

Conversational sales agents must distinguish questions about products from purchase commitments, preserve explicit requirements, and ground the next action in current business information. We report an aggregate census of 725,219 records in an accessible conversation table provided by Aiso and develop a reference architecture for this setting. All records have distinct non-null conversation hashes. Existing metadata labels identify 41,800 commercial records (5.76%) and 2,387 transactional records (0.33%); their union contains 44,187 records (6.09%). Within the commercial category, 54.31% are labeled English, 41.59% have recorded depth of at least two, and 13.51% have depth of at least four. Commercial-label prevalence varies from 4.87% to 6.35% across three source batches. These measurements motivate explicit separation of corpus inventory, commercial relevance, training eligibility, and observed business outcomes. The proposed architecture combines business-grounded knowledge, provenance-bearing conversation state, and a constrained next-action policy. A quality specification addresses source rights, privacy, label validation, deduplication, and training-test separation. The study is a metadata audit and technical design, not a validation of label accuracy, model training volume, or sales conversion. No raw conversation text or personal identifiers are released.

LLM agents are starting to own the full customer experience. Soon, LLMs may be selling and buying on behalf of companies and customers respectively. Small models are more cost-efficient at scale, but can reinforcement learning train them into competent sellers? We train four Gemma 4 checkpoints (2.3B to 31B effective parameters) with GRPO on a programmatic utility reward for bilateral multi-issue bargaining, and evaluate every arm on the same 1,152 negotiations against two frontier buyers it never saw in training. With the same learning rate ($10^{-6}$) for every size, the gain of the RL model over its base rises from $+0.001$ at 2.3B to $+0.078$ at 31B. Each size was trained once and the two smallest checkpoints use a different architecture, so we fit no scaling law. Tripling the learning rate, with the same or fewer training steps, improves on the shared rate at every size by $+0.032$ (2.3B) to $+0.081$ (4.5B). In exploratory comparisons with two frontier models run as sellers, the 12B seller trained at the tripled rate scores above both, though its untrained base already scores as high as they do. The 4.5B seller at that rate shows no detectable difference from either and fits on one 48 GB GPU. A further 2.3B arm at ten times the shared rate raises pooled score, but its gain concentrates on the evaluation buyer that shares a model family with the training pool. These results suggest tuning the learning rate before concluding that a small model cannot learn to negotiate, and testing against buyers from more than one model family.

Cutting is a recurring operation in robotic au tomation, from food preparation to surgical tissue resection. For highly compliant targets, blade motion may deform or displace the material rather than advance the intended cut, while progressive failure changes load transfer and subsequent tool tissue interaction. A computational description must therefore connect cut formation to the evolving mechanical response, rather than specifying the incision independently of material failure. We present STC-MPM (Soft Tissue Cutting with the Material Point Method), a framework that couples finite-strain deformation, history-driven continuum damage, and configurable post-failure treatment. Damage initiates only when a tensile strain history exceeds a material threshold within the blade process zone. Progressive degradation changes stress transmission before the post-failure policy is applied, while the remaining tissue continues to deform, move, and interact with the tool. Numerical scalpel studies using delayed particle deactivation follow this response through insertion and withdrawal. Under identical blade motion, reducing the damage-rate limit leaves the first recorded damage time unchanged but delays and increases peak reaction force, delays particle deactivation, and increases the fixed-cohort displacement statistic at maximum insertion. The matched comparison illustrates how post-initiation failure evolution alters subsequent tool loading and recorded material motion. STC-MPM thus supports joint analysis of cut formation and accompanying tissue response without a pre-inserted cutting interface.

Remote sensing images often carry composite degradations, in which haze, cloud, noise, blur, low light, and low resolution coexist. Restoring them requires deciding which tool to apply, in what order, and when to stop, yet no clean reference is available at inference time to verify these decisions. All-in-one models trained on single degradations converge to a narrow PSNR band as degradations accumulate. To formulate real-world remote sensing restoration as a traceable trajectory, we present EORestore-Agent, which replaces this unmeasurable objective with reference-free, verifiable per-step decisions. A fine-tuned vision-language model reports all residual degradation types, whose tool pools are scored together, so the restoration order emerges from step-wise selection. A relative quality scorer, trained with full-reference supervision on synthetic degradation chains, predicts the changes in PSNR, SSIM, and LPIPS from the current image to each candidate. A step is accepted only when no predicted change is negative and the predicted PSNR gain is positive. Otherwise, the agent keeps the current image. On a synthetic Landsat-8 benchmark with six degradation types, EORestore-Agent improves PSNR by 2.3 to 3.2 dB over the strongest retrained all-in-one baseline on composites of two to six degradations, whereas zero-shot natural-image agents fall below the degraded input in PSNR in 17 of 18 settings. Replacing the learned scorer with no-reference quality differences costs 1.1 to 4.6 dB. The remaining harmful steps are small and cluster near the acceptance threshold. Sentinel-2 examples illustrate transfer to real atmospheric degradation without retraining.

Learned feature representations in neural networks often contain structure beyond that directly used by the final task output. We study this structure using $\textit{passive probes}$ that apply fixed, untrained, property-independent projections to representations as they evolve during training. We motivate this approach through the task of prediction on $S^2$ where equivalent vector and Hermitian parameterizations reveal an additional loss-invariant trace coordinate. This motivates a general construction in which fixed random projections serve as observers of learned features. Because the observer is loss-invariant and independent of the property being studied, changes in accessibility reflect changes in the representation relative to the fixed observer rather than adaptation of the observer itself. We show that ensembles of passive probes can directly reflect task-relevant information such as target alignment. Under our constructions, the accessibility of eventual difficulty evolves differently across tasks. It increases during training in the regression tasks of surface-normal estimation and image inpainting but remains near its initial level in image classification. Comparisons with learned linear probes further show that recoverability and passive accessibility can evolve differently during training. Together, these results show how passive probes can separately characterize changes in representation geometry and the accessibility of eventual task difficulty.

Autonomous coding agents now resolve a substantial share of real-world GitHub issues. However, passing functional tests differs fundamentally from producing a high-quality contribution acceptable for merging. Mature open-source projects publish repository-specific contribution policies, spanning style, git, testing workflows, to ensure code quality and long-term maintainability. Because existing benchmarks evaluate patches solely on unit tests, agent compliance with repository governance remains unknown. In this paper, we introduce SWE-CC, a benchmark evaluating code and process compliance in autonomous software engineering. We develop a semi-automated pipeline that converts developer documentation across 12 open-source repositories into 823 machine-checkable atomic policies. SWE-CC introduces two features: 1) lightweight, deterministic checker functions that represent each policy, 2) a comprehensive auditing mechanism that inspects both agent runtime behaviors and final deliverables. We evaluate the compliance of agent workflows in 500 end-to-end software contribution tasks extended from SWE-bench Verified. Our evaluation of four LLMs under two agent scaffolds shows that modern agents suffer from coding compliance issues: although agents produce functionally correct patches, they still violate 43.1 percent of applicable project policies, with nearly half of all violations occurring during intermediate execution steps. These results show that functional correctness does not guarantee real-world readiness, highlighting that future software engineering agents must reliably conform to repository governance to enable safe and trustworthy deployment.

Multi-agent systems built on large language models (LLMs) restate observations as a matter of course: relays forward them, shared boards repeat them and discussion rounds echo them. An aggregator that pools such messages should count sources, not statements. We convert a reported probability into units of independent readings, which assigns every restatement a copy weight, 0 for an aggregator that counts sources and 1 for one that counts every statement, and yields the implied decision under any cost structure. Three testbeds hold the evidence fixed and vary how it is restated: message logs with an exact Bayesian oracle, web documents with appended copies, and logs written by LLM agent teams under four communication protocols. Across four models from three providers, a forwarded copy counts for 0.06 to 0.42 of a new reading, mostly because some replies count every statement. On 5% to 40% of logs that state one reading three times, the reported belief implies an early commitment that the oracle never makes. The models that count copies least and most on controlled logs do so on web copies and agent-written logs as well. A one-paragraph declaration of what a copy contributes brings the copy weight on controlled logs to 0.08 or less. A rule that has agents refer to readings instead of restating them cuts belief-implied early commitment from 11.2% to 1.1% and preserves genuine corroboration.

An agent whose tool keeps returning nothing useful should stop relying on it. In a retrieval environment with controlled source failures, we separate how agents judge results from what they do. We compare stopping at the same step after longer and shorter runs of results the agent judged useless; this contrast is zero for clock- or deadline-driven stopping. Where we record their judgments, the seven agents we test call a failing source's results useless 97-100% of the time, yet most of them rarely stop on that judgment. Prompt cues change when they stop but not what they stop on. Permission to answer from memory and a reasoning mode can bring early stops regardless of evidence, a stated budget moves the 7-8B models' stops to the deadline, and a stopping rule or call cost in the prompt is followed at most partly. Stopping follows the evidence only when the harness enforces an integration step that makes the agent answer after five consecutive results it judged useless. This step raises failing-source success for every model, keeps the stopping point fixed when the budget doubles, and needs no extra judgment call when the agent states its judgments. A pre-registered replication on 300 fresh questions confirms the dissociation and the rule's effect.

Large language models (LLMs) can reason over scientific literature to devise design strategies, yet fail to reliably implement them for biological sequences. While protein generative models learn sequence patterns, they lack the capacity to incorporate literature evidence for multi-step reflective reasoning, forming an evidence-to-execution gap between scientific reasoning and sequence manipulation. We present EASER (Evidence-Aware Sequence Engineering with Reflection), a reflective agent bridging reasoning and sequence generation via a learned property interface of offline-trained, fixed low-rank matrices. The agent steers a diffusion generator by combining these matrices, proposing intervention hypotheses (anchors, editable positions, control coefficients) grounded in retrieved evidence, sequence context and past results. A Probe-and-Steer mechanism validates interventions and allocates samples according to predicted property responses, with outcome reflection informing subsequent decisions. Evaluated on multi-objective antimicrobial peptide design (optimizing activity, non-hemolysis and non-toxicity), explicit hypothesis formulation delivers better multi-objective performance than direct action generation under identical decision conditions. Ablation studies verify the importance of evidence retrieval, episodic history, reflection and Probe-and-Steer. Over six repeated trials, EASER obtains the highest mean hypervolume and lowest mean IGD+ on screened candidates compared with competing baselines. Our work demonstrates how an executable property interface and iterative feedback link scientific reasoning to targeted peptide sequence generation.

This work identifies the dominance regions for discrete, simultaneous-move pursuit-evasion games on graphs. Existing geometric approaches provide efficient characterizations of winning regions, but typically provide only sufficient conditions and rely on open-loop strategies. To address these challenges, we develop a set-based dynamic programming approach to characterize the pursuer's winning and losing regions, providing necessary and sufficient winning conditions under worst-case behavior. The reachability analysis admits a set-chasing interpretation, allowing translation of dominance sets to feedback strategies that adapt to the players' positions in real time. For states where neither player can guarantee victory, we introduce an instantaneous matrix-game formulation and establish upper and lower bounds on the pursuer's winning probability. Simulation results validate the correctness of the dominance-region characterization and the proposed bounds.

In this paper, we study CONFLICT-FREE EDGE CUT (CF-CUT), which is a recently introduced conflict-free version of the MIN-CUT problem that asks to find the minimum number of edges to disconnect a connected graph. The CF-CUT takes as input a connected undirected graph G = (V, E), a conflict graph $\widehat{G}$ such that $E(G) = V(\widehat{G})$, and the objective is to decide whether there exists $F \subseteq E(G)$ such that $G - F$ is disconnected and $F$ is an independent set in $\widehat{G}$. Rauch et. al. [IPL-2025] proved that CF-CUT is NP-Complete and also provided some results on the parameterized complexity of CF-CUT. A related variant MIN CONFLICT-FREE EDGE CUT (MIN-CF-CUT) takes a connected graph $G$, a conflict graph $\widehat{G}$ such that $V(\widehat{G}) = E(G)$, and an integer $k$ as input and asks if there is a set $F$ of at most $k$ edges such that $G - F$ is disconnected and $F$ is an independent set in $\widehat{G}$. In this paper, we extend the work of Rauch et al. [IPL-2025] and provide a systematic study on the CF-CUT and MIN-CF-CUT from the perspective of parameterized complexity and polynomial kernelization. We prove that CF-CUT is NP-hard when the dissociation number of the input graph is at most two. We also complement it by proving that CF-CUT is poly-time solvable when the dissociation number of an input graph is at most one. Additionally, for MIN-CF-CUT, we consider both solution size and various structural parameters of the input graph as parameters, and provide fixed-parameter tractability and W[1]-hardness results when the conflict graph is restricted to various graph classes. We also prove that unless NP $\subseteq$ coNP/poly, MIN-CF-CUT admits no polynomial kernel when parameterized by the vertex cover number of the input graph; and also when parameterized by the sum of the solution size and the vertex integrity of the input graph.

Generalization in multi-arm collaboration can be studied as composing familiar atomic skills in new ways across arms. However, existing evaluations offer limited insight into which training and architectural choices support this ability under different coordination requirements. We introduce ACG-Bench, a benchmark for Arm-wise Compositional Generalization that provides a common testbed for studying skill recomposition in dual-arm policies. It contains 23 task–condition pairs across 8 task families, with 6 in-domain conditions and 17 unseen compositions covering reordering, synchronization, their combination, and cross-task composition. All methods receive the same per-arm atomic prompts, and success requires achieving the task goal while satisfying physical milestones and specified order or timing constraints. Using $\pi_{0.5}$ as a common vision-language-action backbone, we compare representative data-augmentation and architectural strategies with shared source data and a common evaluation protocol. Our architectural study examines arm-token grouping, skill-specific LoRA adapters (SkillLoRA), and arm-wise attention (AWA), highlighting the complementarity of skill-conditioned parameters and attention structure. Combining these choices yields AE-VLA, which achieves 21.53% generalization success in simulation, compared with 2.94% for Single $\pi_{0.5}$, 3.06% for MA-VLA, and 5.53% for two independently controlled $\pi_{0.5}$ policies. On physical SO101 robots, AE-VLA reaches 39.00% mean success across five unseen conditions, compared with 10.00% for the strongest baseline. These findings provide empirical guidance for designing dual-arm policies that generalize beyond fixed training routines.

Lloyd's algorithm and the discrete local (D-local) optimization method (Li et al., 2025) for $k$-means provide only weak local-optimality guarantees, and their solution quality remains sensitive to initialization. In this paper, we introduce $r$-point local optimality, under which no reassignment of at most $r$ samples decreases the objective function, and focus on $r=2$. The main computational obstacle is the $\mathcal{O}(n^2(k^2+d))$ cost of exhaustive two-point certification for $n$ samples in $d$ dimensions and $k$ clusters. To address this challenge, we prove that (i) every improving two-point move of a D-local optimum must involve a cluster shared by both reassignments, and (ii) only certificate-defined boundary points can participate in an improving pair. Exploiting this structure, we propose Boundary-Point-Screened Two-Point Local Search (BPS-2PLS), which terminates at a two-point local optimum. For fixed $k,d$ and nonvanishing cluster occupancy, the number $m$ of retained candidates satisfies $m=\mathcal{O}_{\mathbb{P}}(\log n)$ under i.i.d. sampling from a bounded-support distribution with bounded density or from a Gaussian mixture. Across twelve benchmarks, BPS-2PLS attains the lowest available mean WCSS on ten. In a subsampling study, screening retains 0.10% to 2.81% of samples on average at the largest tested sizes. The code is available at https://github.com/lwl-learning/BPS-2PLS.

Whether a time-series pattern is anomalous often depends on the operating regime of the monitored process. A missing event can signal a fault in one regime and be routine in another, and the query alone may not reveal which regime applies. We study in-context learning (ICL) for time series anomaly detection (TSAD) through reference-conditioned detection, where a reference record provides evidence about expected behavior and model parameters remain fixed at inference. Supplying the reference is not enough: when training anomalies are recognizable from the query alone, the detector can fit its targets while ignoring the reference. We therefore introduce counterfactual supervision, which pairs one query with two references that support different normal rules and labels the query under each. At positions where the two labels disagree, no detector that ignores the reference can fit both targets. Anlu learns from this supervision by adding a reference memory and zero-initialized gated adapters to a frozen time-series foundation model (TSFM) pretrained for anomaly detection. On the 350 TSB-AD-U evaluation sequences, Anlu raises the mean VUS-PR of the frozen TSFM from 0.542 to 0.607. Replacing the reference with zeros lowers Anlu's score to 0.499.

Geo-restricted content is increasingly common on the Internet, forcing users to rely on circumvention techniques, such as VPNs, to access the web from a seemingly different location. However, these often come with a financial cost and can degrade performance. The rise in popularity of the QUIC protocol, which allows connections to migrate between paths, opens opportunities to circumvent such restrictions. We scan web servers and find that a large portion of geo- blocked content is enforced on the server, at the application layer, rather than on-path. This check is performed once, when the request arrives, and is not repeated as the connection continues. This allows a client to issue its request from a whitelisted IP address and, once the server has accepted it, migrate the connection to an otherwise unauthorized address for the rest of the transfer (post-header migration). It bypasses the block while maximizing direct traffic, thereby reducing eventual circumvention-related costs. Building on this insight, we introduce Stork, an HTTP/2-to-HTTP/3 web proxy that bypasses geo-blocking while introducing negligible additional latency. We demonstrate that our solution is compatible with popular clients and servers. In controlled experiments with 2 MB requests, our proxy migrates 99% of the transferred data onto the unauthorized path. Across real-world targets that support QUIC migration, it migrates at least 75% of the data for more than 52% of them. On real geo-blocked content, post-header migration bypasses the block for 90% of domains, whereas post-handshake migration, as used by prior work, succeeds for only 60%.

A patient-timeline reconstruction system is auditable only if it keeps the mentions behind each answer, records how facts were revised, and declines to answer when the evidence is not in the text. This study tests these three properties on a fully synthetic corpus (1,000 patients, 3,353 notes, 220 revision edges). Two provenance-aware Evidence Graph operators reduced the node-plus-edge count to 67% and 63% (77-78% of serialized size) while preserving every answer and mention link across 6,813 query points answerable by recency; a fixed-window baseline returned no value for 53.4% of points, unflagged. On evidence-unavailable controls that announce the omission, a BioClinicalBERT gate and a zero-shot LLM gate responded mainly to the announcement. On marker-free controls, BERT abstained on 0 of 81 notes while its accuracy fell from 93.8% to 59.3% across all three relation classes; the LLM's coverage fell from 75.6% to 27.7% on notes its own model family judged undeterminable. Against 482 regenerated gold spans, the LLM's cited evidence reached recall 0.850 and precision 0.864; BERT's span head, trained without span labels, did not localize evidence. A temporally versioned provenance graph stored abstentions as typed, queryable edges. The clean task admits a 0.651-accuracy shortcut, and results describe implementation behaviour on synthetic data, not clinical performance.