Papers

A four-stage LLM pipeline gives up as much as 40.5 accuracy points at its own interfaces (gemma-3-12B on MATH-500, Holm-corrected p = 1.66e-19; the largest tax in the primary family). We hold model, problem, stages, stage prompts and completion budget fixed, vary only whether each stage can still see the original problem, and call the accuracy difference the decomposition tax. Across 21 open-weight models from nine organisations, on GSM-Hard and MATH-500 at n = 200 paired items per cell, 70 of 118 primary-family tests survive Benjamini-Hochberg correction and 54 survive Holm. On GSM-Hard, a placebo recovers nothing: it carries at least 60% of the extra tokens and at most one word of the problem. Builders design a pipeline one stage at a time, and its bill arrives at the interfaces between stages. Rewriting one stage's instruction moves gemma-3-12B's tax from 4.5 to 36.5 points, and adding "every relationship stated between them" to a stage that lists the numerical quantities lowers the tax on 9 of 9 models on MATH-500. Re-grounding, which shows a stage the original problem again, belongs after the loss. With one lossy interface, re-grounding the stage after it beats re-grounding the stage before it on 7 of 7 models on both benchmarks; on MATH-500 the earlier repair is worse than none on 7 of 7. Newer models still pay: gemma-4-12B gives up 37.0 points, and the repair holds on all three of the newest models we test. A sealed held-out test refuted a stronger rule we registered, which predicted the paying stage from the interface and receiver types, so we locate the tax by measuring one stage at a time. The prescription has two parts: re-ground the stage after the lossy interface, and if a stage must list the quantities, tell it to keep the relationships.

Gromov-Wasserstein Distances (GWDs) provide quantitative ways of comparing probabilistic distributions defined on different metric spaces by applying techniques from the optimal transport theory. As such, GWD can be potentially useful in a large variety of applications ranging from graph matching problems to 3D object detection. However its practical use at scale is significantly limited by cubic time complexity computations involving dense intra-space distance matrices. Even though in the Euclidean metric spaces several techniques (e.g. involving scalable kernel methods) were proposed to address it, to the best of our knowledge, analogous techniques for general geodesic distances on manifolds, or shortest-path distance on graphs in their discretized variants, were not developed. In this paper, we present Efficient Geodesic Gromov-Wasserstein methods (EGGroW), a new class of efficient algorithms designed to calculate geodesic Gromov-Wasserstein distances with entropic Sinkhorn-like approaches, leveraging recently introduced GenusSink methods \citep{genussink} and the theory of random features. We provide important downstream applications, namely: 3D pose estimation and 3D template detection. In the latter setting, we formulate a partial 3D template recovery as a staged problem: capacity-constrained scene selection is followed by semi-relaxed recovery of template visibility and correspondence. Our empirical findings show that EGGroW provides accurate solutions when standard Euclidean-based techniques fail and is characterized by light computational footprint, as our theoretical analysis predicts.

The speed at which software can be created and deployed today has increased dramatically. But what is the point of all this software if it does not contribute to society? The ultimate goal of building software should be bettering human lives and society. And this goes beyond publishing the software as open source; it requires considering how it is developed, the societal qualities it embodies, and the purposes it serves. This is what I call Social3Source. This paper presents the concept, principles, and initial discussion for the implementation of Social3Source, illustrating how it integrates social considerations into open-source software development. We have never generated as much software as we do today. Let's make sure it counts.

Direction of departure estimation in Multiple-Input-Multiple-Output (MIMO) radar is based on transmitting a set of orthogonal (or at least separable) waveforms, one per transmit element. Assuming orthogonality is preserved, these waveforms can then be separated into different channels at the receiver before beamforming. In practice, however, MIMO waveforms are not perfectly orthogonal, and at different points in the processing chain, this can manifest as phase errors in the steering manifolds used in beamforming. Furthermore, due to resource constraints, either by the channel or the sensing scenario, a mixture of orthogonality techniques, mixed division strategies, are often employed, resulting in further phase errors. Naturally, such errors will interfere in the beamforming process, spoiling the beam, introducing direction finding errors, or increasing sidelobe levels, and consequently reducing SNR. In this paper, we demonstrate how mixing division strategies significantly degrades orthogonality of otherwise orthogonal waveforms resulting in degraded beamforming performance. Specifically, we show that waveforms which exhibit favourable sidelobe levels may still induce large direction of departure errors and vice versa. Additionally, through multiple exhaustive searches of potential mixed division strategies with combinations of time-, Doppler- and code-based division techniques we show that large numbers of the possible waveforms exhibit poor beamforming qualities.

Model merging efficiently combines specialized large language models (LLMs) without joint retraining, but can substantially alter expert routing in Mixture-of-Experts (MoE) models. Such routing drift is often interpreted as routing failure, raising a fundamental question that remains unclear: does routing drift after MoE merging actually indicate routing failure, and what evidence should justify repair? We investigate these questions across DeepSeekMoE, OLMoE, and Qwen3-MoE proposing a routing analysis toolkit for controlled counterfactual interventions and token-level analysis. By crossing source and merged router inputs and parameters, we attribute most expert reassignments to input shifts rather than parameter changes at the same layer. However, source-relative routing differences poorly predict next-token likelihood gains from source-route restoration, and different expert selections can produce directionally similar mixture outputs. We therefore operationalize routing failure as task loss recoverable under a specified routing intervention, with non-routing parameters fixed. These tests detect recoverable loss under deliberate router corruption, whereas source-route restoration does not establish reliable task benefits in the evaluated merged models. Motivated by these, we propose Selective Router Repair (SRR) as a case study, and find that source-specialist token-likelihood advantages do not reliably identify beneficial local corrections. Together, these findings show that routing drift alone is insufficient evidence of routing failure: source-informed corrections must be judged by their task-level intervention effects. The analysis toolkit and SRR code are released.

This paper studies learning of shuffle ideals with membership queries as well as with contrastive queries—a form of membership query that reveals not only whether a selected word $w$ is in the target language or not, but also provides a most similar word $w'$ that belongs to the target language if %and only if $w$ does not. For both settings, it is shown that even some very simple classes of shuffle ideals cannot be learned efficiently. By contrast, we obtain positive learnability results for classes of shuffle ideals that meet certain structural conditions. In the case of membership queries, these structural conditions are related to the previously studied notion of universal words, and raise new questions in word combinatorics. In the case of contrastive queries, the structural conditions relate to partitioning sets of words that are listed in shortlex order.

Raising the update-to-data (UTD) ratio breaks off-policy critics in two ways grouped as "plasticity loss": collapsing representations and growing value magnitude $|Q|$. We separate them in Soft Actor-Critic (SAC) with scaled critics (width 2048, no normalization). Collapse is survivable: at UTD ratio 16, HalfCheetah critics with most units dormant keep learning, and the training guard, which stops runs whose loss or $|Q|$ explodes, never flags them. Within one high-UTD SAC configuration, runs start close together, and how far a critic's $\log_{10}|Q|$ has climbed by step 15k, its early growth, ranks the runs by how soon the guard flags them. At 15k, a flagged run's $|Q|$ sits a median of over a hundredfold below its flag level, yet the climb's rate already orders the flags (Harrell's C and out-of-sample AUC 0.78 on Walker2d, 0.98 on Ant, at UTD ratio 4). Dormancy does not. Aborting on this rate saves about a tenth of held-out Walker2d compute and stays net-positive live. A LayerNorm critic lowers the rate, removes the flag on Walker2d at UTD ratio 4 and lowers the return.

Fine-tuning a language model on new data can make it forget facts that it should keep. We ask whether measurements taken at the start of a fine-tuning run can bound, for each protected fact, the probability that the run makes the model forget it. In LoRA fine-tuning with stochastic gradient descent on models from 0.6B to 14B parameters, a first-order response model estimated by finite-difference probes predicts changes of per-fact margins with correlation 0.974-0.998. Predictions of forgetting built on this model nevertheless failed, because forgetting requires parameter changes far outside the region in which the model was validated. The probes can, however, bound the probability that a margin first falls below a boundary near zero: we derive Freedman and Azuma first-passage bounds for a linear surrogate of the margin and test on new runs whether they hold for the model. The bounds contain a term R that measures how much the response coefficients change during the run. The simplified Freedman bound, which sets R = 0, certified most facts but was violated in 14 of 112 conditions, and every fact on which it was violated had R >= a, where a is the distance of the fact's margin to the boundary. The complete Freedman bound certifies only facts with R < a, and it held in every condition. On the violated facts, the spread of the margin across test runs was a median of 14.6 times the prediction of the response model, so the failures are breakdowns of the model, and in our data they occurred only where R >= a. We found this pattern post hoc and tested it in two preregistered confirmatory studies with 43 new conditions: the complete bound held in all of them, and the simplified bound failed there on only 3 facts, each with R >= a. First-order models of fine-tuning can thus bound forgetting on the facts whose response coefficients change by less than their distance to the boundary.

Clinical Large Language Models (LLMs) achieve strong medical-exam accuracy; however, a correct answer does not guarantee that the explanation names the concepts that actually drove the decision. We introduce three lightweight, directly interpretable metrics for this faithfulness gap: the Explanation Stability Index (ESI), which measures reasoning consistency across repeated queries; the Causal Faithfulness Score (CFS), which tests whether cited concepts drive predictions via concept ablation; and the Perturbation Stability Score (PSS), which measures robustness to semantic-preserving paraphrases. By evaluating six LLMs on 150 MedQA-USMLE questions (900 model-question observations), we found that only 23.3% of the cited clinical concepts were causally necessary. Correct answers had lower CFS than incorrect answers (0.212 vs. 0.398), answer consistency negatively predicted CFS (Spearman r = -0.466), and model pairs could agree on answers while sharing only 8.8% of cited reasoning concepts. These results show that accuracy, consistency, and consensus are incomplete safety signals for clinical decision-making support. The evidence is behavioral rather than mechanistic: concept ablation tests counterfactual sensitivity of outputs, not internal circuits.

We deformalize an LLM-generated proof within the formalism of Homotopy Type Theory that an iterated pushout construction for $\operatorname{SP}^3(X)$ is a set whenever $X$ is a set. The proof expands on a similar proof by Buchholtz for $\operatorname{SP}^2(X)$, employing a similar encode-decode strategy and the same formal machinery.

In this paper, we study the infinite reciprocal cubic sum $\sum_{k=n}^{\infty}\frac{1}{B_k^3}$ of balancing numbers. We obtain explicit bounds for this sum and use them to determine the integer part of its reciprocal.

Fast matrix multiplication algorithms keep the product fixed and search for a cheaper way to evaluate it. We instead ask whether a Transformer's learned projections can use a different, cheaper product altogether. Building on an associative-algebra construction that replaces ordinary matrix multiplication with a sparser interaction table over the same weight blocks, we construct a family with quadratic arithmetic in the matrix dimension when the physical block size remains fixed, and derive finite-shape constraints for GPU execution. The construction is provably optimal for its bilinear rank by the Alder–Strassen bound and can be realized as row-typed rectangular projections compatible with causal masking and KV-cached decoding. We provide an empirical test of this approach by training two approximately 110M-parameter decoder-only Transformer LMs from the same recipe and 12.3B-token budget, differing only in their feed-forward layer: one uses ordinary dense matrix multiplication and the other uses the associative-algebra product. Across four prompt domains, the algebraic model achieves a 6.2–7.8% increase in end-to-end generation throughput, while obtaining lower scores on all three reported downstream metrics. We treat these results as a feasibility and trainability check for the proposed approach at small scale, leaving further investigation to future work.

Large vision-language models (VLMs) have emerged as a powerful paradigm for urban and spatial AI. However, current state-of-the-art large VLMs still struggle with quantitative reasoning on remote sensing imagery. Existing benchmarks and algorithms are predominantly based on qualitative Visual Question Answering (VQA), providing limited insights into the quantitative reasoning capabilities of VLMs for built environment metrics. To address this gap, we develop Quantitative Urban and Spatial AI benchmark (USAI-Quant), the first benchmark designed to quantitatively evaluate VLM's reasoning capabilities on built environment metrics via remote sensing imagery. USAI-Quant is curated from the 335 largest U.S. cities, aligning high-resolution remote sensing images with quantitative built environment metrics. We then evaluate both general-purpose and remote sensing VLMs (RS-VLMs) by applying VQAs to tens of built environment metrics across three complexity levels. Our results reveal that current state-of-the-art models consistently fall short on numeric reasoning tasks. We further conduct in-depth analyses across models, question types, and geographic locations, uncovering insights into performance variability and task-specific challenges.

We consider singular Liouville systems on closed Riemann surfaces with a common sign-changing coefficient. Direct continuation from a positive coefficient is obstructed by the unavoidable appearance of degenerate zeroes along such a homotopy. We instead identify an intrinsic ray in the parameter space on which the system admits synchronized solutions and reduces exactly to a scalar sign-changing mean-field equation. Combining this reduction with the variational existence theory of De Marchis–López-Soriano–Ruiz and the nodal singularity compactness theorem of Wu, we obtain existence for every noncritical parameter on this ray. Positive singular sources are allowed on the nodal curve. In particular, when the surface has nonpositive Euler characteristic and every negative component of the coefficient is a disk, the topological hypothesis required by the scalar min–max construction is automatic.

Accident anticipation aims to recognize anomalous driving cues before a crash while avoiding false alarms during normal driving. Existing approaches typically formulate this task as binary classification, focusing on whether an accident will occur rather than when it will occur. We propose PRE-ACT, a framework that models accident risk as a continuously evolving signal that increases as the crash approaches. By explicitly enforcing temporal ordering and distance-to-accident awareness, our method progressively raises risk while suppressing premature alarms, leading to significant improvements on MM-AU subsets and Nexar. We further introduce a Separation Score to evaluate the global behavior of predicted risk curves beyond local temporal windows. Code and visualizations are available at https://github.com/giddyyupp/PRE-ACT.

Multidisciplinary tumor boards integrate multimodal clinical observations and longitudinal patient histories through specialist discussions, yet benchmarks rarely capture these real-world trajectories. We introduce OpenTumorBoard, a benchmark with 611 patient cases and 19,157 discussion turns across ten specialist roles, transcribed from 12,534 minutes of publicly available tumor board recordings on YouTube. The benchmark evaluates two settings: SPECIALIST TURN, in which an LLM responds to a clinically significant question posed during a real discussion, and BOARD SIMULATION, in which it generates an entire back-and-forth discussion and reaches a consensus on therapy recommendations, surgical plans, next actions and clinical trial matching. Evaluation of 14 general-purpose frontier and medical LLMs reveals substantial limitations: the best models score 3.43 out of 5 in clinical equivalence to specialist answers and 2.78 out of 5 in alignment with recorded board conclusions. Supervised finetuning and reinforcement learning improve performance on a held-out test set, suggesting that real-world discussion trajectories can support model adaptation. Three M.D. experts review a subset of the benchmark, finding high information coverage and factuality of patient cases and strong fidelity of extracted consensus conclusions. We will release OpenTumorBoard and its automated curation pipeline to support the development and evaluation of LLMs for multidisciplinary, personalized cancer decision-making.

Multiple-choice and candidate-selection evaluations are widely used to assess LLM reasoning and decision-making, yet most benchmarks contain relatively small candidate sets. It remains unclear whether conclusions drawn from these settings remain valid as the candidate space scales. We systematically evaluate LLMs as the number of competing candidates increases and find substantial accuracy degradation across tasks, prompting strategies, and model scales. Controlled analyses show that standard long-context retrieval explanations cannot fully account for this degradation. Instead, we identify two systematic failure patterns. First, gold-margin collapse: the score gap between the correct answer and the strongest distractor progressively shrinks, driven primarily by weakening confidence in the correct answer. Second, earlier candidate preferences become increasingly difficult to overturn, with later candidates exerting progressively weaker influence on the final prediction. Motivated by these findings, we evaluate hierarchical partitioning and permutation-based inference, which improve accuracy by roughly 20 percentage points at $N=160$ on both HotpotQA and MIMIC. Overall, our results identify candidate-set scale as an important evaluation-protocol variable and show that strong small-option performance does not necessarily imply robust large-scale candidate comparison.

Large vision-language models (LVLMs) inherit massive activations from their text-only bases: spikes where a few fixed hidden channels receive values thousands of times above the typical magnitude. The text spike systematically appears in early layers at a fixed initial position, independently of input content. Visual spikes vary across images, but whether their formation follows a consistent pattern across LVLMs and how they respond to image perturbations remain open questions. We find that some LVLMs do not form visual spikes, while others spike at different rates, typically in deeper layers. We identify the trigger direction from model weights and an interpretable location rule: before the language model decoder runs, eventual spike tokens are largely restricted to those sharing least with the rest of the image. Crucially, visual spikes are strikingly brittle. Common corruptions frequently create and relocate spikes, and less often remove them, raising overall incidence. Our trigger-guided spike attack deliberately creates or removes spikes under a small $\ell_\infty$ budget, with 1/255 enough in nine of the ten models that spike. Finally, our preventive intervention removes only the trigger component before spikes erupt, eliminating or substantially reducing spikes on clean and perturbed images while leaving the other image tokens nearly unchanged. Our study spans 25 adapter-based LVLMs built on 18 released text-only bases from 10 families, ranging from 2B to 72B parameters.

Clinical LLM evaluation often emphasizes answer accuracy; however, accuracy alone does not test counterfactual consistency or demographic robustness. We evaluated six LLMs on 150 MedQA USMLE questions using two automated perturbation tests to assess their performance. The counterfactual validity (CFV) test asked each model to make a minimal, plausible clinical change that would make a different answer correct. The demographic robustness test added six demographic prefixes to the same vignette and compared the answers and explanations with a no demographic baseline. Of the 900 CFV attempts, 228 (25.3 %) were valid and 672 were invalid. Across 5,400 demographic comparisons, 1,097 answers were changed (20.3%). Automated judging identified 3,128 stereotype evidence flags, including 1,932 in the broad Other category. MedGemma 27B achieved the highest accuracy (87.1%) and CFV (63.3%), lowest answer change rate (16.0%), and low mean Explanation Demographic Dissonance (EDD) score (0.169). However, its accuracy still exceeded its CFV, indicating that correct answers do not guarantee reliable performance on the counterfactual validity task. OpenBioLLM had the highest answer change rate and EDD, whereas GLM had the highest stereotype flag rate. These findings show that accuracy, CFV, answer stability, EDD, and stereotype evidence capture different evaluation aspects. Because all judgments were automated and no clinician validation was available, the results support safety screening but do not establish clinical deployability of the model.

Motion planning in robotics requires not only computing collision-free paths but also certifying infeasibility when no such path exists. Complete methods are limited to low-dimensional spaces, while sampling-based planners scale efficiently but cannot provide finite-time infeasibility certificates, leaving this problem largely unresolved in high-dimensional spaces. In this letter, we present a geometry-driven framework for certifying infeasibility through an explicit resolution-dependent analysis of configuration space topology. Leveraging signed distance field representations, the proposed method traces separating manifolds induced by obstacle boundaries directly in configuration space, enabling both detection of infeasibility and identification of the specific geometric cause. To address computational challenges, we develop a parallel frontier-expansion algorithm that exploits GPU acceleration for efficient simplicial reconstruction in high-dimensional spaces. We validate the approach on 4-DOF and 5-DOF robot scenarios, certifying infeasibility within seconds for 4-DOF cases and under four minutes for 5-DOF cases. We further discuss avenues for improving scalability to higher-dimensional spaces.

Long tasks produce more history than an LLM agent can hold in its context, and more than it uses reliably even when the history fits. A growing line of work therefore has agents carry a short written state instead: at every step a writer rewrites the state, and a reader acts from the state alone. Steps stay cheap, but anything the writer drops is lost before later decisions reveal that they need it. We quantify this loss and ask whether training can reduce it. Comparing the written state with the best state of the same size written in hindsight, we split the reader's loss into a budget loss, which any state of that size must incur, and a write-time regret, which comes from the writer's choices. In TextWorld cooking games where we control how long a fact must be carried before it is needed, a 128-token state holding the facts wins nearly every game, while prompted language-model writers win at most 17%. Almost all of the loss is write-time regret, and it grows with the delay. We then train the writer from the reader's own loss. DSSR (decision-sufficient state representations) scores candidate states by how well the reader acts after the writer carries them forward, and teaches the writer to prefer the better ones. This forward-rolled score predicts game outcomes ($\rho = 0.48$), whereas scoring a candidate as a fixed context, as hindsight methods usually do, does not ($\rho \leq 0.07$). On a pre-registered test split opened once, training adds +7.0 [+1.9, +12.2] points of success when facts are needed soon, bringing a plain summary writer to the level of belief- and slot-based memory prompts. The gain shrinks as the delay grows and is significant only at the shortest delay. We trace this limit to credit assignment: keeping a fact now pays off only if every later rewrite keeps it too, which a per-step score cannot see.

Audio emotion recognition (AER) typically assigns a single label to an entire recording, leaving the temporal scope of that label ambiguous when multiple speakers and affective events are present. We address this limitation by reformulating AER as a Temporal Affective Grounding (TAG) task that associates emotions with temporally bounded speech spans and vocal tone descriptions. To support this formulation, we curate temporally annotated versions of existing emotion recognition datasets and construct recordings containing two to four affective speech spans, including overlapping speech. Training in this longer format with a standard language-modeling objective can degrade both emotion recognition and temporal grounding performance, while tone descriptions can provide shortcuts for emotion prediction. To address these challenges, we introduce Masked Temporal Affective Grounding (M-TAG), a supervised training objective that combines full-sequence language modeling with emotion and timestamp cross-entropy losses under attention masking. The masking varies the context visible to emotion-label tokens to reduce reliance on shortcuts and improve generalization, while the timestamp loss incorporates a distance-aware weight to penalize larger temporal errors. We evaluate EMO-TAG, a model fine-tuned using our dataset and objective, on emotion recognition and affective temporal-grounding against three AER and audio-language baselines: Flamingo-Next, Audio-Reasoner, and AffectGPT. Our results show that existing models achieve limited affective temporal-grounding despite competitive emotion recognition performance.

Generative and Agentic IoT systems offer a promising foundation for digital healthcare applications that combine sensing, personalized reasoning, and autonomous interaction in real-world environments. Nutrition assistance is a natural use case, but existing Large Language Model (LLM)-based systems are often limited to passive text interaction and static context, making them unreliable when food descriptions are ambiguous or nutritional evidence is missing. We propose Nutri-ATLAS, an Embodied Agent for Tabulated Lookup and Assistance for smarter nutrition in the real world. It integrates graph-grounded nutrition reasoning, hardware-aware LLM selection, and robot-based evidence acquisition. Nutri-ATLAS builds a unified Food-Nutrient knowledge graph from USDA FoodData Central and FoodKG and learns 64-dimensional GATv2 food and recipe embeddings. A shared hybrid graph-text scoring mechanism supports food nutrition extraction, nutritional gap filling, substitute retrieval, and recipe-level meal composition, while an LLM-guided skill interface navigates landmarks, updates dietary-context and food-accessibility memory, and grounds recommendations in observed food availability. We evaluate Nutri-ATLAS across nutrient estimation, substitution retrieval, recipe recommendation, patient-profile adherence, edge deployment, and real-world embodied execution. On HealthyFoodSubs, the hybrid retriever achieves 37.9% MAP, 80.7% RR@5, and 90.1% RR@10. On NutriBench v2, Dense+GAT retrieval grounds nutrient estimation across nine quantized Qwen3.5-9B configurations. On PFoodReQ, Nutri-ATLAS reaches 78.8% MAP, 83.0% MAR, and 77.5% F1. A patient-profile study shows adherence to allergy and healthy-target constraints for all selected cases.

One variable sets what an upstream fault costs a staged pipeline of language-model agents: re-derivability, how much of what a stage needs it can rebuild from the original problem. Grounding an inspector agent in that problem is worth +0.608 [+0.517, +0.700] to +0.358 over a blind one on four open-weight backbones served with thinking disabled, and on the two Qwen backbones the blind inspector changes no item at all. That head-to-head is exploratory. One deterministic fault enters the first stage, and we re-expose the original problem to $k = 0,\dots,3$ of the downstream stages with agents, items, fault and topology held fixed, on 120 gsm_hard items per arm at temperature zero. Accuracy under fault rises on four of four backbones, from +0.233 to +0.392, the largest Holm-adjusted $p$ being $2.1\times10^{-6}$. A registered kill test rules out tokens. Blanking every word holds the word slots fixed, and retention tracks the visible fraction on four of four, climbing from 0.221 to 0.692 on the primary. Those two families are confirmatory and everything else here is exploratory. The interaction excludes zero on two of four backbones under the registered pipeline, four of four under a three-stage pipeline, and three of four under full message history, the primary at +0.317. On Llama-3.1-8B the fault carries no detectable cost at any dose, so the other three carry every claim about what a fault costs. Re-derivability also sets what the architecture costs, and no decomposition we measured reliably beats one direct call. With no fault injected the registered pipeline loses to that call by -0.267, -0.125 and -0.317, and on Phi-4 reads +0.058 at $p = 0.118$, which the test fails to separate from zero. The repair that works is cheap and front-loaded: the first re-grounded stage buys +0.394 of matched retention for +59.8 tokens per item on Qwen3-14B, and the stages after it buy nothing.

Embodied task planners may produce multi-step plans whose subtask dependencies and interactions with the environment create physical risks during execution. Yet existing safeguards overlook such compositional risks, as general-purpose guardrails focus on semantic harm and embodied safety detectors assess subtasks in isolation. To address this gap, we introduce PlanGuard, the first pre-execution detector that evaluates the physical safety of a complete multi-step plan in its current environment. For training and evaluation, we construct a Multi-Step Plan Safety (MSP-Safe) dataset through paired task construction, plan generation using diverse planners, and safety annotation by three judges. Task-oriented SFT on MSP-Safe establishes fundamental plan-safety assessment capabilities, yet a substantial gap remains between compact models suitable for real-time deployment and stronger but costlier large models. Accordingly, we propose Strong-Teacher Adaptive Compensation for On-Policy Distillation (STAC-OPD), which provides compact models with adaptive strong-teacher supervision along their on-policy trajectories. It combines token-level distribution transfer from a fine-tuned strong teacher with probability-routed sequence-level compensation, retaining student-generated targets when the student favors the reference safety decision and using teacher-reconstructed targets otherwise. Across all test subsets, PlanGuard-2B achieves average 87.15% ACC and 87.21% F1, demonstrating effective whole-plan physical-risk detection at compact model scale. Code and dataset will be publicly released.

We initiate the study of quantum state tomography—the experimental reconstruction of the complete spin density matrix—of massless and massive quark-antiquark pairs produced at the future Electron-Ion Collider (EIC). We show that all components of the spin density matrix can be accessed through azimuthal angular correlations between hadron and dihadron pairs generated by the Collins and dihadron fragmentation functions. This enables the experimental investigation of a variety of quantum information properties at the EIC, such as entanglement and Bell-nonlocality. We predict that the recently discovered maximal entanglement in the heavy-quark sector is signaled by a strong modification of the usual Collins angular dependence $\cos(\phi+\phi')$

In the unrestricted polynomial decision-tree model, only the number of polynomial sign tests is charged. A parity test asks for the sign of a product of pairwise differences. Such tests underlie low-depth randomized algorithms for maximum finding and top-$k$ selection, but their usual analysis assumes distinct inputs because a tie makes the product vanish. We give a black-box lifting theorem that removes this assumption. After $O(\log n)$ polynomial tests determine the number of nonzero pairwise differences, every subsequent parity test is simulated by one polynomial test, consistently with a fixed lexicographic tie-breaking order. The simulator is an elementary symmetric polynomial in masked first and second powers of all pairwise differences. Thus a depth-$D$ parity-test tree on distinct inputs becomes a polynomial decision tree of depth $D+O(\log n)$ on arbitrary inputs, with no increase in randomized pointwise error for order-selection problems. We obtain maximum finding in depth $O(\log n[\log n+\log(1/\delta)])$ with error $\delta$, and top-$k$ selection in depth $O(\log^2 n+k\log n)$ with inverse-polynomial error, both without any promise on ties.

This paper investigates adaptive and resilient dual-layer resource slicing in hovering aerial agent (HAA)-assisted backhaul networks for heterogeneous 5G/6G services, including enhanced mobile broadband (eMBB), ultra-reliable and low-latency communications (URLLC), and massive machine-type communications (mMTC). To address the complex coupling of this dual-layer architecture in non-stationary environments, we propose the resilient adaptive priority orchestration enhanced twin delayed deep deterministic policy gradient (RAPO-TD3) framework. We introduce a novel double soft-max projection mechanism to map the continuous action space into physically feasible bandwidth distributions, ensuring strict constraint adherence. Additionally, a resilient adaptive priority orchestration (RAPO) mechanism is embedded to safeguard mission-critical URLLC latency. Crucially, we establish a rigorous mathematical foundation proving that our framework ensures Lipschitz continuity and satisfies the Robbins-Monro conditions for stable asymptotic convergence. Extensive simulations under non-stationary traffic demonstrate that our RAPO-TD3 framework achieves superior performance relative to PPO, DDPG, and traditional solvers. Notably, via the RAPO mechanism, our approach maintains URLLC satisfaction levels closely approaching theoretical optima even during 500% demand surges. Furthermore, scalability evaluations indicate that sub-millisecond execution latencies strictly satisfy the 1 ms URLLC budget, demonstrating the performance efficacy of our proposed framework.

Derivative-informed training improves neural operators by directly supervising their input-output sensitivities, which is crucial when neural operators are used as differentiable surrogates for inverse problems, PDE-constrained optimization, design, and control. However, existing methods rely on offline-generated derivative labels, making data generation slow, storage-intensive, and difficult to adapt across datasets, resolutions, or perturbation bases. We propose sketched tangent consistency loss (sTCL), an on-the-fly derivative-informed training objective that, for PDEs with a known and differentiable residual, enforces sensitivity consistency directly from the governing equation without offline tangent labels or neural-operator architecture changes. sTCL uses randomly sketched input perturbations to provide a lightweight derivative-level physics constraint during training. However, raw forward-sensitivity residual penalties can fail for stiff, ill-conditioned, indefinite, or coupled saddle-point tangent operators. To address this, we introduce lightweight operator-aware loss-conditioning mechanisms selected by a simple tangent-operator decision rule. Across Helmholtz, nonlinear diffusion-reaction, Burgers, Allen-Cahn, and Navier-Stokes, with the same neural-operator backbone for all methods, the PDE-specific sTCL losses achieve solution and Jacobian accuracy comparable to offline derivative-informed training (DIFNO) while eliminating the offline derivative-data generation and storage pipeline. These results show that on-the-fly derivative-informed training need not merely amortize offline tangent-solve cost into training; with appropriate sketching and loss design, sTCL provides an effective drop-in path to derivative-informed neural operators. Code is available at https://github.com/Mou-group-UMN/Derivative-informed-training-on-the-fly.

Foundation models have recently shown strong potential for learning generalizable EEG representations, yet their effectiveness for event-related potential (ERP) analysis remains unclear. In this work, we investigate two fundamental questions: 1) can foundation-model learning benefit ERP analysis, and what limits the transfer of existing EEG foundation models to ERP tasks? 2) can the complementary advantages of single-trial and averaged-trial ERP be integrated into a unified training pipeline? To study these questions, we curate a large-scale ERP corpus comprising 1,517,157 single-trial ERPs from 3,696 subjects across 38 datasets and 18 paradigms. Leveraging this corpus, we introduce ERP-FM, to the best of our knowledge, the first foundation model specifically developed for ERP representation learning. ERP-FM uses single-channel tokenization, temporal and spatial positional embeddings, and mixed masked autoencoding for large-scale single-trial pretraining. We compare our model against 17 existing methods on 12 downstream datasets covering ERP event/condition classification and neurological disease classification. Our model achieves the best overall average rank across all evaluated methods. Furthermore, our analyses reveal that both ERP and non-ERP EEG pretraining can provide transferable representations for ERP tasks, while fine-grained temporal tokenization is critical for effectively modeling transient ERP dynamics. We further find that single-trial and averaged-trial ERP play complementary rather than competing roles. Combining single-trial pretraining with averaged-trial downstream adaptation substantially improves neurological disease analysis. Overall, these findings establish an effective foundation-model training pipeline for ERP analysis and represent significant progress toward generalizable ERP representation learning. Source code: https://github.com/DL4mHealth/ERP-FM