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A digraph consisting of a set of vertices $V$ and a set of arcs $E$ is called an interval digraph if there exists a family of closed intervals $\{I_u,J_u\}_{u \in V}$ such that $uv$ is an arc if and only if the intersection of $I_u$ and $J_v$ is non-empty. Interval digraphs naturally generalize interval graphs, by extending the classical interval intersection model to directed graphs. Several subclasses of interval digraphs have been studied in the literature-such as balanced, chronological and catch interval digraphs-each characterized by admitting interval representations that satisfy specific restrictions. Among these, interval nest digraphs are the ones that admit an interval representation in which $J_u$ is contained in $I_u$ for all vertices $u$ of $V$. In this work, we provide a complete characterization of interval nest digraphs in terms of vertex linear orderings with forbidden patterns, which we call nest orderings. This result completes the picture of vertex-ordering characterizations among the main subclasses of interval digraphs.

A small fine-tuned parser that emits a well-formed but wrong tree fails silently: nothing downstream can tell. We ask whether the output format, a free design choice, controls how often this happens. On the PIZZA ordering benchmark we fine-tune two sub-billion models (Qwen3.5-0.8B and LFM2.5-350M) with LoRA on six lossless encodings of the same target tree, from 44.3 down to 10.9 tokens per order, including two matched-length pairs that vary surface form at fixed length. Across 300 runs (5 training pool sizes, 5 seeds) with a hierarchical bootstrap and Holm correction fixed before the results were read, shortening alone never helps, but writing the target in ordinary words does. The word encoding is the most accurate format on both models (87.5% vs. 85.8% exact match for the native s-expression on Qwen) while emitting 4.1x fewer tokens, and it cuts the silent error rate by 2.3x on Qwen and 1.8x on LFM2, separating at every pool size. Error analysis locates much of the gain in negation. All runs also learn to refuse off-menu input (held out: 95.9-99.0% handled) and to apply in-utterance self-corrections. Strict refusal has a measured price: 2.1-10.1% of real, mostly polite, orders are refused.

Decision models answer a question with a typed output, such as a choice among options with a probability for each, so one model can choose an agent's actions, evaluate actions already taken, or score every action to teach a policy with reinforcement learning. Prior work has studied them mainly as actors, judging their usefulness by how well they act. We ask whether a decision model that acts poorly can still teach well. We compare three decision models and three general LLMs as actors and judges on ALFWorld, and use JEV as a teacher on ALFWorld and WebShop. As actors, all six models are pulled away from a subgoal that must come first by an easier one. As judges that see the whole trajectory, the same models credit the steps toward that subgoal, and asking whether each action helped, rather than whether the task will succeed, separates useful from useless actions. As a teacher, JEV raises a Qwen2.5-1.5B policy over GRPO from 72.8% to 82.9% success on ALFWorld and from 56.8% to 71.4% on WebShop. These results suggest that a poor actor can still teach well, because judging an action after the episode ends reveals the consequences that acting must anticipate. Code is available at https://github.com/ZJU-REAL/decision-agents.

This tutorial provides an accessible and implementation-oriented introduction to Gaussian process learning-based model predictive control (GP-MPC), which combines probabilistic residual modeling with receding-horizon control. Its central tutorial contribution is a detailed, step-by-step derivation of multi-step mean and covariance propagation for GP-augmented prediction models. The derivation shows how commonly used propagation formulas follow from the laws of total expectation and total covariance, and clarifies the roles of the GP posterior mean, GP posterior covariance, uncertain inputs, and query-output cross-covariances. Building on this foundation, the article distinguishes mean-only unconstrained GP predictive control from uncertainty-aware constrained GP-MPC, clarifies regulation and output-tracking formulations, and provides concise implementation and computational-complexity guidance, including practical software-tool references and discussion of the scope of closed-loop guarantees. Mobile-robot path-following examples illustrate mean-only unconstrained implementations, whereas mixed-vehicle platooning illustrates uncertainty-aware constrained GP-MPC with uncertainty-dependent safety-distance tightening. The tutorial is intended to help researchers and practitioners understand, implement, and critically evaluate GP-MPC designs for robotic and autonomous systems operating under modeling uncertainty.

Lightweight methods like QuickCheck have proven to be successful in functional languages and beyond, as they let users specify properties as Boolean functions directly in code. We can replicate some of their benefits for (bounded) proofs via symbolic execution. If we can execute arbitrary functions symbolically, we can specify properties just as easily. Unfortunately, existing symbolic execution tools for Haskell are restricted to a subset of the language that excludes many real-world applications like IO; they also have a hard time scaling to larger programs, making them a poor fit for general purpose lightweight verification. One reason behind these limitations is that existing techniques only offer fixed symbolic semantics for SMT base types. This makes it hard to cover more programming constructs and libraries; it also makes it difficult to fine-tune symbolic representations for better performance. We present SymFC, a new symbolic execution method for Haskell that offers configurable semantics via embeddings. An embedding of a function in SymFC is just another Haskell function that can use arbitrary code, as well as SMT primitives. Embeddings make it easy to support new programming constructs and fine-tune symbolic representations for speed. To integrate embeddings into Haskell's type system, we make use of Haskell's coercions, which let us transparently convert between a Haskell type and the type of its embedding. We realize embeddings in SymFC, an all-paths symbolic execution engine for Haskell, which lets us symbolically represent arbitrary types and values in GHC core. We implement SymFC as a GHC plugin, and evaluate it by checking properties of Haskell's container library, and the iproute library. We build embeddings for IORef, Haskell's Ptr/ForeignPtr interface, and the hardware library Clash, and our evaluation reports a 6.25x speedup on G2's own benchmarks.

Language-guided UAV navigation has largely focused on long-horizon route planning, leaving short-range, object-relative flight maneuvers underexplored. To address this gap, we formulate Flying-on-a-Word (Flow), a task requiring a UAV to convert concise natural-language instruction, egocentric visual observation, and current state dynamics into continuous flight actions. Flow encompasses both primitive motion commands and complex object-interactive behaviors, assessing motion intent comprehension and spatial context grounding. To enable policy learning and closed-loop evaluation, we introduce UAV-Flow, a comprehensive dataset comprising 30,692 expert-piloted real-world trajectories across eight distinct motion categories, alongside 10,109 simulation trajectories in the UAV-Flow-Sim environment equipped with task-specific completion criteria. Furthermore, we develop FlowVLA, which undergoes imitation pretraining on mixed real-sim demonstrations and online post-training via Tail-Aware GRPO (TGRPO). By leveraging group reward distributions, TGRPO effectively reinforces high-reward action sequences. Evaluated on 273 held-out UAV-Flow-Sim episodes, pretrained FlowVLA achieves a mean success rate of 75.58%, outperforming the strongest baseline by 6.72 percentage points, which TGRPO post-training further elevates to 93.16% with superior sample efficiency. Physical UAV experiments demonstrate robust execution of object-relative commands in both indoor and outdoor real-world scenes. Together, Flow establishes a novel benchmark and learning framework for language-conditioned flight maneuvers.

When an LLM agent fails, repair methods choose which action to replace and what to put in its place. They often score candidate repairs with greedy replay, a stronger model, an environment oracle, or a judge that reads the failed log. We ask whether these evaluators pick repairs that help the agent that will actually execute them. Holding failed trajectories and candidate single-step repairs fixed, we label every candidate with independent rollouts of the deployed policy and measure how much deployment value each evaluator's choice loses. On failures not screened for repair value, pre-specified tests show that greedy replay loses 0.08-0.13 in expected net success gain in ALFWorld and 0.06-0.13 in net reward in WebShop, relative to selection with the deployed agent's own rollouts. At an equal rollout budget, selecting repairs for Qwen2.5-7B with Qwen2.5-14B rollouts loses 0.25 in ALFWorld and 0.07 in WebShop, twenty 14B rollouts per candidate are worth no more than two of the 7B agent's own, and fresh rollouts confirm that the two models prefer opposite repairs on selected disagreement cases. The agent's own fine-tuned successor is a worse evaluator still: after one round of training on verified repairs, its rollouts lose 0.55-0.60 when they select repairs for the agent it was trained from, as a pre-specified test confirms. Relative to what selection is worth, substitute models forgo 11-53%; on $τ^2$-bench, where selecting is worth only 0.10, they lose 0.03. Repairs should be verified with the executor that will run them, and repair labels should name their executor, including its training version.

State space models (SSMs) are an emerging alternative to Transformers. SSMs offer linear-time inference and parallel training, but most implementations make the parallel scan efficient by making the recurrence diagonal: each channel of the hidden state is multiplied by an input-dependent real or complex number. These numbers commute, so the state records which inputs occurred but not their order. We formalize this with representation theory, which explains and fixes the state-tracking failures previously reported for SSMs. The state update defines a linear representation of the monoid of input sequences, and we show that an SSM tracks a group at every sequence length exactly when that group is a quotient of the group generated by its transition matrices. Two consequences follow. Diagonal real- and complex-valued SSMs can track only commutative groups, while the transition matrices of any SSM that can track a group must split into independent blocks over the real, complex, and quaternion numbers. We then introduce HyperSSM, which adds quaternion channels while keeping linear-time inference and parallel training. Trained only on final answers, HyperSSM solves the group tasks of recent state-tracking benchmarks exactly with at most five state numbers. This includes $S_5$ with 32 generators, where previous SSMs are at chance, and HyperSSM generalizes to sequences 25 times longer than those seen in training. Because the theory says what the transitions must encode, the learned weights of the linear recurrence can be interpreted directly. We demonstrate this by recovering the calibration of a real gyroscope, the rotations of imperfect qubit gates and the geometry of protein backbones.

Retrieval-augmented generation systems attach citations to attribute claims to their sources. These citations frequently misstate provenance, and standard verification cannot detect this. We measure provenance by counterfactual value substitution: a fact in the retrieved passages is replaced with a false variant and the model re-queried. We find that across five sizes of one model family and a second comparator family, 1.2% to 15.7% of citable claims derive from parametric memory rather than the retrieved context. At the most conservative substitution distance these figures are 4.6% and 8.5% on the two models we tested at it, with the rate rising with model size within a family. We further find that natural language inference verification, the standard approach, gives results indistinguishable from chance across models, even when restricted to the cited passage. We determine that the cause is structural: a model answering from memory selects a citation that agrees with its output. Comparing ten attribution methods on identical claims, the contrast between the model's distribution with and without context best separates provenance. Acting on that signal does not improve provenance honesty at these base rates. The resulting detector is hence still not accurate enough to act on: it measures what the model knew rather than what it used, and separating those remains the open problem.

Multi-teacher on-policy distillation can yield uneven domain capabilities. We propose Domain-Routed Delta Optimization (DRD-MOPD), composing a frozen base with expert-initialized trainable deltas. Domains update their deltas with independent optimizer states and clipping. After joint training, Post-separate exports the base plus one trained delta per domain, selected by known task domain without retraining. Using AdamW, the unweighted full student reaches 32.83% Macro across six benchmarks after 20 updates, versus 32.21% for a matched shared control. Post-separate raises Macro with Open-MOPD weighting.

Embodied interaction requires an agent to integrate multimodal perception with verbal and nonverbal behaviors to effectively communicate its intentions, including speech, body motion, and facial expressions. We present XBot-Omni, a Thinker--Talker--Actor architecture that extends the Omni paradigm to robotic modalities, including body motion and facial expressions, with ``X'' representing the extensibility to robotic-specific modalities. The Thinker processes text, images, audio, and video to formulate contextually appropriate responses, which are then realized by the Talker and Actor through speech and coordinated bodily expressions, respectively. In this report, we innovatively introduce the concept of ``Actor'' as a dedicated component for embodied agents: a coordinated, streaming module that leverages the native representations of the Thinker and Talker within an end-to-end pipeline, introducing only modest latency overhead. This unified architecture enables multimodal generation conditioned on omni-modal inputs directly to prevent information loss in staged designs. We comprehensively evaluate XBot-Omni across seven benchmarks, demonstrating strong multimodal understanding capabilities on both general-domain and robot-centric videos, as well as high-quality, natural, and well-coordinated motion generation. Furthermore, our results validate its capability to generate embodied multimodal responses directly from omni inputs, meeting the diverse requirements of embodied interaction. XBot-Omni enables robots not only to perceive the omni world but also to express themselves through speech and bodily behaviors, extending Omni models from conversational interaction to embodied communication in physical environments.

Robots that learn from demonstrations should extrapolate their policy despite state perturbations such as sensor noise, scene variation, and compounding errors. One approach to this robustness is regularization. Prior regularizers consider each state on its own and limit how sensitive the policy is to any perturbation at that state. By contrast, we explore how the policy's output shifts when given the same perturbation at different states. Our insight is that, locally, the robot should respond to state perturbations in a consistent manner: e.g., if changing an irrelevant object position does not impact the policy at one state, that same change should not shift the policy output at a nearby state. Applying this insight, we develop inner product regularization (InneR). We show that the inner product on action space induces an inner product on state space through the policy Jacobian (the Fisher information for stochastic policies), and that the null space of this inner product governs which state perturbations have a first-order effect on the policy. By clustering states whose inner products are aligned, averaging the inner products within each cluster, and minimizing the smallest eigenvalues of that average, InneR shapes the learned policy so that nearby states share a common null space. InneR enforces consistent responses to perturbations without limiting policy expressiveness, and can be appended to existing imitation learning pipelines for deterministic or stochastic policies. In simulated experiments, InneR makes learned policies more robust to irrelevant state dimensions and shifts between training and test distributions, whereas norm penalties often perform worse than behavior cloning. On a real robot arm performing three manipulation tasks, InneR raises the average success rate of a diffusion policy from 18% to 57% without additional data.

Graph neural surrogates for granular flow can resolve the motion of individual grains, but propagating information across a large amount of grains requires repeated, costly updates on the full particle graph. This study introduce a Hierarchical Coarse-Grained Graph Neural Network (HCG-GNN) that couples direct interactions between neighboring grains with information exchange on two coarser graphs of occupied spatial cells. In discrete element method (DEM) benchmarks of granular flows down incline planes, HCG-GNN captured key flow characteristics, including front propagation, lateral spreading, deposition morphology, free surface evolution, internal shear behavior, and energy conversion. Results also show that preserving grain-specific features as coarse information returned to the particle graph and integrating predicted accelerations to advance particle motion both improved multi-step accuracy. With 5 of its 7 message-passing steps performed on coarse graphs, HCG-GNN achieved accuracy comparable to a conventional particle-level GNN with a 6.47-fold training speedup and 46.2% lower GPU memory use. A model trained on up to 5000 grains predicted a 2 s release of 10000 grains in 31 s, compared with 2000 s for DEM under the benchmark conditions. This combination of speed and grain-scale resolution supports particle-resolved inverse design, with prescribed runout or discharge targets guiding the search for suitable geometries and grain dynamics revealing the basis for differences in performance.

A zero-forcing set of a graph is a set for which, after regarding each of its vertices as being blue, and applying the rule that a blue vertex with exactly one white neighbor forces said neighbor to become blue, all of the vertices in the graph are blue. Let $z(G;k)$ denote the number of zero forcing sets of size $k$. A conjecture of Boyer et al.\ asserts that the path $P_n$ maximizes these numbers coefficientwise among all $n$-vertex graphs. We prove this path-extremal conjecture for distance-hereditary graphs, which is the class of all graphs $G$ such that for each of the connected induced subgraphs of $G$, the distances between any two vertices in that subgraph are the same as they are in $G$. This extends the previously known tree case in which the path-extremal conjecture was known to be true to a much larger class that includes, in particular, all trees and all cographs. We then use canonical split decomposition to push the argument we used to show the distance-hereditary result into the more general setting of a connected graph with at most one prime bag in its canonical split decomposition. Specifically, we show that if a split-prime graph $H$ and all of its induced subgraphs are path-extremal, then every connected graph whose canonical split decomposition has a unique prime bag whose label graph is isomorphic to $H$ is also path-extremal. As a corollary of this result, for each fixed $m$, if every induced subgraph of every split-prime graph on at most $m$ vertices is path-extremal, then so is every connected graph whose canonical split decomposition has a unique prime bag of size at most $m$. Additionally, we prove that the path-extremal conjecture holds when all prime bags have order at most six, without restricting their number; under the preceding hereditary hypothesis, one additional prime bag labelled by $H$ is also allowed.

Beyond Visual Line of Sight (BVLOS) unmanned aerial vehicle (UAV) operations increasingly use 5G standalone (SA) networks for command and control (C2) between the UAV and the ground control station (GCS). The 3rd Generation Partnership Project (3GPP) has specified mechanisms for authentication and authorization of unmanned aircraft systems (UAS) in this architectural setting. As a result, operators may treat registration state, Protocol Data Unit (PDU) session status, and IP reachability as evidence that the C2 path is available. In practice, however, these connectivity indicators alone do not guarantee that closed-loop control remains operationally safe. Attacks can degrade UAS C2 when timeliness degrades under shared User Plane contention, mobility continuity fails during Control Plane instability, or command integrity is violated at a trusted next-generation Node B (gNodeB). Such failures undermine connectivity as the central security indicator for UAV operations. In this paper, we demonstrate these issues using three distinct threat models on a reproducible Open5GS and UERANSIM testbed that carries Micro Air Vehicle Link (MAVLink) over the 5G User Plane, and we use a commercial Nokia core to ground deployment assumptions. We address timeliness, availability, and integrity through experiments in which attack success is defined as forcing an unsafe closed-loop state without a clean disconnect. We observe stale telemetry and heavy-tailed delay under co-tenant User Plane contention, failsafe after handover under Control Plane instability, and navigation hijacking after command rewriting at a compromised gNodeB. We further discuss why each threat model arises and evaluate mitigations for these cross-layer failures. Across the study, we disclosed five robustness issues, all with assigned CVEs.

Neural surrogates for computational fluid dynamics (CFD) are trained and ranked on datasets that each vary one design family in one flow domain. Such datasets cannot test the least that an aerodynamic foundation model must do: predict CFD-quality incompressible flow in seconds for new shapes in new enclosures. On DrivAerML, larger models and longer training barely lower Transolver's error; doubling the training cases cuts it by about 12% up to 400 cases, exhausting the dataset. We introduce AeroZoo, a benchmark and training corpus of 3,815 time-mean solutions to the unsteady Reynolds-averaged Navier--Stokes (RANS) equations with a transition model, across seven geometry families, eight enclosure configurations and Reynolds numbers from $10^3$ to $10^8$. Each sample poses a well-posed PDE problem in the form a solver receives it: the boundary meshes grouped by condition type, the prescribed values and the fluid properties. The 2,816 samples with a stable time mean form the canonical benchmark: two tasks, engineering metrics and 22 frozen splits, disjoint in geometry, that hold out geometry families, enclosures, boundary-condition layouts and Reynolds ranges. On the random split, boundary-condition tokens cut GeoTransolver's median velocity error from 76.9% to 8.4% of the inlet speed in single-seed runs (uniform inlet flow: 11.0%). ISLA, a transformer for boundary-driven PDEs, reaches 5.3% over four seeds, about 4 times the change from a finer mesh. On the same test samples, a held-out geometry family barely changes ISLA's error relative to uniform flow, and a held-out enclosure or boundary-condition layout raises it 2.4 to 9.2 times. The data and the scoring code will be released.

Across domains as varied as ecology, economics, and online platforms, individuals are incentivized to position themselves within resource-rich strategy spaces. In this work we introduce a new spatial game framework called the influencer's game. Within this new framework players' strategies are represented as positions within a trait space. Players then receive a share of a portion of a resource based on their relative influence at that resource's points traits. For the influencer's game, we show that there is a unique symmetric Nash equilibrium that exists under strict log-concavity of the influence kernel. Using the unique equilibrium we show that the stability of the system depends on the influence kernel's parameters, number of players, and the resource distribution shape. For any dimension we demonstrate a stability threshold that depends on both the scatter and curvature of the players. When this threshold is crossed, the symmetric equilibrium destabilizes and gives way to a variety of bifurcation types; including, specialist clusters, limit cycles, and sub-games that reproduce the larger game's structure. We ground these results using real-world data for resources as a demonstration of the game's application. Finally we extend the game dynamics to use multi-agent reinforcement learning and further show that the predicted bifurcation structure persists under partial observability and discretized strategy spaces. In all, the influencer's game provides a novel framework for predicting when competitive pressure drives convergence versus fragmentation with possible applications across domains.

The proliferation of user-generated video content has made accurate and robust no-reference video quality assessment (NR-VQA) a highly important challenge. Existing research increasingly relies on architecturally complex multi-branch pipelines or computationally intensive fine-tuning of single-branch backbones. In this paper, we investigate whether a single frozen video foundation model can serve as an effective NR-VQA backbone, and propose HiVE-VQA, the first framework (to our knowledge) to apply a JEPA-based video encoder to this task. HiVE-VQA extracts token grids from multiple depths of a pre-trained V-JEPA 2.1 encoder and stacks them into a hierarchical spatio-temporal volume, which a compact 3D convolutional head fuses across its layer, spatial, and temporal axes, combining low-level distortion cues from shallow layers with the semantic and temporal context captured at greater depths. The encoder remains frozen throughout, so only the head is trained: 5.2M parameters (5.7\% of the total), with no auxiliary multi-modal models and an inference cost that is invariant to video resolution. Trained solely on LSVQ and evaluated without any fine-tuning, HiVE-VQA outperforms 17 state-of-the-art (SOTA) methods in SROCC and PLCC on both intra-dataset (LSVQ-test, LSVQ-1080p) and cross-dataset (KoNViD-1k, LIVE-VQC) benchmarks. These results indicate that hierarchical, depth-wise fusion of features from a single frozen video foundation model provides a more effective and efficient basis for NR-VQA than task-specific multi-network fusion. Code and model checkpoints are available at https://github.com/RobHam99/HiVE-VQA.

Understanding how visual attention influences human preference formation is a fundamental problem in consumer behavior and cognitive science. In this work, we investigate how eye movement patterns can be used to predict preference decisions when subjects compare two alternatives. To address this problem, we analyze an eye-tracking dataset, where subjects view pairs of face images and their gaze behavior is recorded throughout the decision process. We model this problem using multiple machine learning classifiers and apply the Multi-layer Combinatorial Fusion (MCF) framework to iteratively combine diverse models. The MCF framework expands models to a large pool of model fusions and then reduces them based on cognitive diversity, repeating this process across layers until diversity diminishes. Experimental results show that MCF significantly improves performance over individual models. The best single model achieves a Pre@k of 0.90, which is improved to 0.9143 after the first layer of MCF, and further increased to 0.9286 in the second layer. This progression demonstrates that the second layer not only surpasses the performance of the first layer but also outperforms the best individual model, highlighting the effectiveness of leveraging diversity through multi-layer fusion.

We study data poisoning attacks on logistic regression with $\ell_2$-regularization, where an attacker chooses the features of a fixed number of injected observations with prescribed labels to maximize the logistic loss on the clean training data. Strong convexity of the defender's problem yields an exact reformulation through its first-order optimality conditions. Using convex conjugacy of the softplus function, we replace the sigmoid relations by a single convex optimality-gap inequality and express the attacker's objective as a concave function. A change of variables makes the stationarity condition affine, leaving bounded bilinear equalities as the only nonconvex constraints. We derive finite bounds on all variables involved in these equalities, including a global bound on the coefficient norm and tighter bounds obtained by preprocessing based on convex optimization. Experiments on eight binary classification datasets evaluate attack effectiveness and compare the two reformulations when solved with \textsf{SCIP}. Attacks obtained by local optimization degrade predictive performance on most datasets, while the convex-analytic formulation produces substantially stronger reported dual bounds within a fixed time limit.

Humanoid loco-manipulation requires coordinated locomotion, balance regulation, and manipulation under frequent contacts, making teleoperated demonstration collection difficult: a practical controller must simultaneously provide precision, stability, and contact awareness. We propose FORGE, a force-aware multi-granularity control system with a coarse-to-fine command space spanning velocity navigation, planar foot placement, wrist-pose tracking, and optional force-conditioning inputs. Policy training requires no full-body human motion trajectories or joint-angle references; deployment consumes only sparse bilateral wrist poses relative to the pelvis, coarse motion commands, and optional desired wrist-load inputs. For sustained contact, FORGE combines a momentum observer with a learned correction trained using simulator contact-force supervision. At deployment, it estimates low-frequency, wrist-equivalent interaction forces from proprioception and reconstructed low-level arm PD torques, without wrist force/torque sensors. A quasi-static virtual-target loop uses this estimate and an optional desired applied-force input to adapt the wrist target. A frozen locomotion prior and asymmetric residual actions stabilize manipulation-induced whole-body corrections. Experiments evaluate unified-control stability, task-space tracking, quasi-static wrist-equivalent force estimation, squeezing forces during sustained contact with a rigid box, and downstream diffusion-policy execution of a squat-and-lift task across payload conditions. Website: https://bb0928.github.io/forge/.

A foundational principle of physics is that all coordinate systems are equally valid: the behavior of a PDE-governed system does not depend on the origin or orientation of the frame, nor on the units or mesh used to write it down, and neither should a surrogate model. Yet the neural surrogates with the lowest errors on today's aerodynamics benchmarks lack these invariances and fail under simple transformations of the same problem: for models trained on PDEs of cars in one pose (i.e., translation and rotation) and from one mesher, rotating the full PDE raises the surface-pressure error from 4% to more than 100%, and re-sampling its boundary raises it to about 30%. We introduce ISLA (Invariant Slice Attention), a slice-attention transformer for steady, boundary-driven PDEs in which no learned operation receives a coordinate and every sum over the boundary is a quadrature. Positions enter only as distances and relative angles to learned slice anchors, lengths are measured in a unit computed from the boundary, and interior points query the boundary through a tree-accelerated learned kernel without influencing one another. With every boundary cell a token and an exact boundary read, ISLA is equivariant to rigid motions and reflections, invariant to the units of its declared data, and consistent under mesh refinement, while at every setting each query is independent of all other queries. On AeroZoo, 2,816 flows that vary in shape, size, speed, and boundary conditions, its mean reference-scaled velocity and pressure errors are at least 3.1 and 3.3 times lower than any baseline's. On AirfRANS its errors are second only to those of a boundary-integral model (GLOBE) and at least 1.6 times lower than those of Transolver and GeoTransolver.

Large language models (LLMs) show growing promise in specialty medicine, yet existing evaluations largely focus on isolated clinical encounters rather than assessing the distinct clinical responsibilities along longitudinal care pathways. We introduce NPC-RubricBench, a phase-aware benchmark for evaluating multistage clinical reasoning across the cancer care continuum, using nasopharyngeal carcinoma as a defined disease context. Curated from real-world records of 405 patients at two cancer centers, it comprises 941 evaluation units across six sequential care stages, from work-up through follow-up, and 17,688 patient-specific criteria across five dimensions. Each assessment is restricted to clinical evidence available at the corresponding decision point. Across 30 general-purpose and medical LLMs, we find strong diagnostic scores did not ensure reliable downstream care. Decision Quality ranged from 56.8 to 94.7 in diagnosis on a 0-100 scale, but dropped to 8.9-56.0 in staging and spanned 32.4-94.2 in treatment. Crucially, failure modes differed across phases: explicit decision errors predominated in anatomical staging (48.2%), whereas decision omissions were more frequent during initial work-up (33.4%) and post-treatment follow-up (30.4%). Varying query granularity revealed a trade-off between decision quality and other clinical requirements. Broad open-ended requests reduced decision quality across all 30 models, whereas more detailed, checklist-like prompts improved decision quality but were accompanied by lower evidence faithfulness and safety adherence. These findings highlight the need to assess clinical reliability against the distinct clinical requirements of each phase along the longitudinal care pathway. Finally, NPC-RubricBench informs the design of stage-aware clinical guardrails and offers a reusable blueprint for evaluating LLMs across other cancers and chronic diseases.

Managing children on ECMO (Extracorporeal Membrane Oxygenation) requires balancing short-term physiological stability with the long-term goal of preventing neurological injury. Standard reinforcement learning can propose risky, out-of-distribution actions, while imitation learning is limited to reproducing clinician behavior. We introduce Support-Constrained Fitted Q-Iteration (FQI-SC), an offline reinforcement learning framework that cautiously improves upon expert behavior by restricting optimization to empirically supported state-action pairs and defaulting to the clinician baseline in low-data regions. On 78 pediatric trajectories totaling over 6,000 hours of clinical data, we evaluate our framework using Fitted Q-Evaluation (FQE) and a behavioral disagreement. Additionally, we formalize the performance-safety trade-off by introducing a unified Balance Score ($S(π)$). Our empirical evaluation shows that support-constrained policy improves the Balance Score by 38\% relative to FQI, improves estimated value by 1.28 FQE units over imitation learning, and reduces disagreement with clinician actions by 71\% relative to FQI.

LLM agents combine information from multiple principals while acting externally. We formalise privilege escalation (PE) as the system-level security objective: an action may proceed only if every principal that influenced it would allow it. Model-level defences remain probabilistic, so enforcement must sit outside model judgement. We present Conflux, a principal-context defence. Its kernel, ITES, derives authority from provenance and the organisation's existing access-control system and intersects the permissions of every influencing principal. We prove a conditional authority-confinement theorem: under complete mediation, no-laundering provenance, a known non-empty decision context, fresh permission checks, and action binding, the kernel admits no action that escalates privilege with respect to any recorded influencing principal. The theorem covers the represented value-influence fragment; control influence from tool, branch, recipient, or plan-step selection remains a refinement obligation. Conflux extends the kernel with independent policy ports, argument-aware authorisation, disclosure, consent, delegation, restriction, and exposure planning. We describe two system- level evaluators. SLED is a black-box evaluator: it exhaustively explores a declared finite model of a defence up to a bound. SLED-V is a white-box evaluator: it checks a serialisable intermediate representation against security and provenance properties. The evidence is bounded and partial. The appendix reports retained AgentDojo, SLED, and SLED-V results, including the limits of those runs. No result in this paper is an unbounded deployment guarantee.

Hierarchical Reinforcement Learning promises, among other benefits, to efficiently capture and utilize the temporal structure of a decision-making problem and to enhance transfer learning capabilities, but theoretical guarantees lag behind practice. In this paper, we propose a Feudal Q-learning scheme and investigate under which conditions its coupled updates converge and are stable. By leveraging the theory of Stochastic Approximation and the ODE method, we present a theorem stating the convergence and stability properties of Feudal Q-learning. This provides a principled convergence and stability analysis tailored to Feudal RL. Moreover, we show that the updates converge to a point that can be interpreted as an equilibrium of a suitably defined game, opening the door to game-theoretic approaches to Hierarchical RL. Lastly, experiments based on the Feudal Q-learning algorithm support the outcomes anticipated by theory.

Federated learning experiments can produce reasonable-looking results even when the experiment implementation differs from the intended experimental protocol. Small errors in configuration, data partitioning, aggregation, randomness, evaluation, or checkpoint recovery may therefore affect a comparison without causing the program to fail. We present FedBrew, a research codebase for controlled and reproducible federated learning experiments. Its focus is controlled simulation with checks of specified conditions of the intended experimental protocol. FedBrew uses configuration checks, identifiable client data partitions, checkpoint recovery checks, self-describing run records, and development-time checks of scientific conditions. These checks assess, for example, whether client partitions are disjoint and exhaustive and aggregation weights match the prescribed rule; numerical and recovery checks examine non-finite client model states and interrupted runs. The same structure also provides clear extension points and automated checks for new algorithms, datasets, models, and tasks, whether they are added by researchers or AI coding agents. FedBrew therefore supports reproducible and inspectable FL experiments through checks of specified software and scientific conditions and the run records associated with reported results.

Smaller language models (SLMs) make it feasible to deploy clinical natural language processing where large proprietary models are too costly, and parameter-efficient fine-tuning allows them to be specialised on commodity hardware. One obstacle persists after training: on medical tasks these models answer at far greater length than the clinical question requires. In clinical decision support and point-of-care use, where time is short, such verbosity is hard to act on even when the underlying reasoning is sound. Existing length-control methods depend on preference optimisation, reward models, or proprietary teachers that undercut the accessibility making SLMs attractive. We introduce Parameter-Efficient Conciseness Adaptation (PECA), which adds a single differentiable conciseness term to the QLoRA supervised fine-tuning objective. Because the token count is discrete and non-differentiable, PECA instead raises the end-of-sequence probability once generation exceeds a token budget, a smooth signal optimised during ordinary training, with no preference data, no auxiliary model, and a single commodity GPU. On a 1.7-billion-parameter model fine-tuned on the medical-o1-reasoning-SFT corpus, PECA reduces mean response length by 72.8% while improving multiple-choice diagnostic accuracy from 40.8% to 44.0%. A sweep over the conciseness strength traces an interpretable accuracy-to-length frontier for balancing brevity and diagnostic completeness.

Distributed fiber-optic sensing (DFOS) technologies such as Distributed Acoustic Sensing (DAS) generate continuous, high-resolution spatio-temporal data at rates exceeding hundreds of megabytes per second, creating severe challenges for real-time storage and transmission. While neural compression methods can achieve strong rate-distortion performance on sensing data, prior approaches either require per-segment retraining incompatible with streaming, or have only been validated offline. None have been demonstrated end-to-end on a continuously streaming DAS acquisition system at scale. We present STeP-C (Spatio-Temporal Predictive Compression), a neural compression framework that decouples spatial encoding, temporal prediction, and entropy-optimized residual coding, trained end-to-end with a rate-distortion objective motivated by conditional entropy reduction. Critically, we identify entropy coding as the dominant bottleneck for streaming deployment. We address it through GPU-side symbol computation, cached probability tables, and parallel GIL-free arithmetic coding, together with FP16 inference and batched entropy coding, enabling a full real-time pipeline built around a GPU ring buffer. We validate this pipeline on a live DAS testbed, achieving a 98.85% file size reduction at 31.04 dB full-band PSNR and an average throughput of 535 MB/s, exceeding the 324 MB/s requirement for 1 kHz, 81 km DAS streams. We further show that STeP-C substantially outperforms conventional codecs at practical streaming bitrates, can be applied to unseen channel ranges within the same acquisition system without retraining, and largely maintains downstream detector consistency, with 96.62% high-confidence class agreement and 100% Jaccard similarity on detected event types.

We introduce graded intersection types, in which arrow domains are multisets of types with coefficients in a semiring. Boolean and natural number grades recover idempotent and non-idempotent intersection types. We give algebraic conditions on the semiring for subject reduction and expansion in finite systems and in locally finite systems with guarded infinite types. We construct a lifting to multisets of grades corresponding, in this general setting, to lifting the idempotent system to the non-idempotent one. We recall the main existing operational characterisations from the literature, and show some general extensions.