Papers

This paper investigates the construction of full-systematic permutation codes capable of correcting multiple deletions under two complementary models, namely symbol-invariant deletions (SIDs), where surviving symbol values are preserved, and permutation-invariant deletions (PIDs), where the surviving sequence is standardized to a permutation. For any fixed integer $t \ge 1$ and all sufficiently large message lengths $n$, our proposed encoders map any message permutation of length $n$ to a codeword by inserting distinct redundancy symbols while strictly preserving the sequence order of the original message symbols. The proposed constructions correct up to $t$ deletions using $7t-1$ redundancy markers for PIDs and $4t$ redundancy markers for SIDs, achieving redundancies of $(7t-1)\log n + O_t(1)$ bits and $4t\log n + O_t(1)$ bits, respectively. Both code families are uniformly constructible, encodable, and decodable in $n^{O(t)}$ time. The underlying framework stores an inner deletion-correcting syndrome in the relative positions of redundancy markers via an algebraic outer code based on integer moments and residual graph coloring. We further extend this framework to fixed-composition and strictly $\lambda$-regular multipermutations, proving that the PID and SID channels coincide whenever the common multiplicity satisfies $\lambda > t$.

Large Language Model judges are widely used to rank texts and text-generating systems through pairwise comparison, and their reliability is typically assessed via three proxies: position bias, transitivity, and pairwise agreement (self- or human-labeled). Because these proxies drive judge selection and benchmarking, a substantial literature reporting that judges perform poorly on them risks steering practitioners away from otherwise capable evaluators. We argue this assessment is misleading. Under the Bradley–Terry geometry underlying pairwise aggregation, each proxy is dominated by close-rank-gap pairs, where inconsistency is expected and errors cost little aggregate ranking accuracy; far-gap pairs determine the ranking accuracy but barely move the proxies. We formalize this argument and validate it in a controlled simulation and on two human-rated corpora: the proxies correlate only weakly with ranking accuracy against gold, and their predictive component concentrates in the far-gap regime. Judges should therefore be assessed on rank-gap-conditional metrics, ideally against human rankings. Code at https://github.com/brunobrocai/PairDifficulty

With the rapid advancement of text-to-image (T2I) generation, robust evaluation becomes critical yet challenging, as traditional metrics fail to capture fine-grained alignment and generative artifacts. While large multimodal models (LMMs) are increasingly adopted as evaluators, existing benchmarks typically study semantic understanding, quality perception, and authenticity identification in isolation, while largely neglecting responsibility detection. This leaves a gap in unified and comprehensive validation. To bridge this gap, we introduce SQUARE-Bench, a comprehensive benchmark that systematically evaluates LMM capabilities as evaluators of AI-generated images across four aspects: Semantics, Quality, Authenticity, and Responsibility. SQUARE-Bench introduces a granular taxonomy of 38 sub-dimensions to evaluate nearly 10K AI-generated images sampled from 22 diverse models, ranging from legacy to state-of-the-art generators, complemented by over 3K real-world images. The images are annotated with curated question-answering pairs. Extensive experiments on 23 LMMs reveal that top proprietary models, such as Gemini-3-Pro, already outperform the individual human expert baseline. However, the performance gap between models remains significant, exhibiting notable disparities in fine-grained inference and domain-specific robustness. Beyond benchmarking, we conduct a proof-of-concept study of LMM-guided iterative editing, in which dimension-specific LMMs provide diagnostic feedback to fixed image editors. The resulting guided system yields selective improvements in semantics, authenticity, and responsibility, while exhibiting a consistent visual-quality trade-off. SQUARE-Bench can serve as both a diagnostic tool for characterizing LMM evaluator capabilities and studying their use in T2I generation refinement. The benchmark and dataset will be released upon publication.

We argue that dividing codec design into Coding for Machines (CfM) and Coding for Humans (CfH) is a misleading distinction for deciding what information a codec may discard. Receiver identity does not determine admissible information loss. The required rate depends on task scope, including the predictions to support, their losses and tolerated risks, the encoder observation, and the permitted decoding procedures. Notably, a machine task may have a higher minimum rate than a restricted human decision. Rate savings on selected machine tasks apply only to the stated requirements, not to an intrinsic ordering by receiver type. We extend source and feature coding to finite task families, derive when restricting the encoder observation preserves the minimum rate, and show that equality between source and split-feature coding rates can no longer hold as the task scope expands.

Large Language Models (LLMs) are increasingly used to enrich user queries in information retrieval (IR) so that a standard retriever such as BM25 can bridge vocabulary gaps with the target corpus. Any single LLM, however, is limited by its training data and architectural biases, and its enrichment behavior depends on hand-crafted prompts that must be re-engineered for each new model – an expensive and poorly scalable process. We present MERGE (Multi-LLM Ensemble for Retrieval via Generative Enrichment), a two-stage framework: three heterogeneous 7-8B open-source LLMs independently produce candidate expansions, and a larger LLM generatively synthesizes them into a single query. To make prompt engineering scalable across the ensemble, we integrate a task-grounded Automatic Prompt Optimization (APO) loop into both stages. Unlike APO methods that judge candidates with an LLM evaluator, our loop scores each candidate by its downstream retrieval performance and runs a small tournament between the current champion prompt and optimizer-proposed drafts, terminating once the champion survives two consecutive rounds; a history-augmented variant additionally feeds the recent tournament trajectory back to the optimizer. MERGE is retriever-agnostic and issues a single BM25 pass with no rank fusion, no supervised document expansion, and no re-indexing. On five BEIR benchmarks (NQ, SciFact, FiQA, Touche-2020, DBPedia), MERGE improves BM25 nDCG@10 over the original queries by +2.1 to +14.9 points and matches or outperforms strong LLM-based query-expansion baselines despite using only compact open-source models. Ablations confirm that the Stage-2 ensemble beats any single Stage-1 LLM, and that task-grounded APO converts large seed-prompt regressions into consistent gains without hand-tuning.

This work aims to investigate the long-time asymptotic behavior of solutions to the Cauchy problem for the Heisenberg ferromagnet equation with the Schwartz initial data. Utilizing the gauge transformations, spectral analysis and the inverse scattering method, we prove that the solutions to the Heisenberg ferromagnet equation can be expressed in terms of the solutions to a matrix Riemann-Hilbert problem formulated in the complex $k$-plane. Various Deift-Zhou contour deformations and the motivation behind them are given. By applying the nonlinear steepest descent method to the associated matrix-valued Riemann-Hilbert problem, we obtain the exact leading-order asymptotic formulas and uniform error estimates for solutions to the Cauchy problem of the Heisenberg ferromagnet equation.

Asset names influence market behavior, yet standardized name measurement remains lacking. Existing processing fluency measures focus mainly on alphabetic languages and are unsuitable for Chinese names. Cultural meanings usually require manual coding, limiting large-scale analysis, while name competition through reuse and semantic crowding remains underexplored. This study constructs a dataset of 513,647 naming attempts from the Four token launchpad on BNB Chain between February and June 2026 and proposes a three-layer framework for name measurement. The form layer measures linguistic fluency using 38 Chinese-oriented features. The reference layer captures cultural meanings through human coding and large language model expansion with reliability evaluation. The relation layer measures name reuse, semantic crowding, and lexical variation. The three layers are largely independent, with correlations below 0.11. Census analysis reveals that name diversity follows Heaps' law, new-name adoption declines over time, name reuse shows heavy-tailed patterns, and repeated naming occurs at distinct creator-level and cross-creator time scales. Cultural events also trigger rapid naming responses. The framework, annotated dataset, and code are released to support scalable analysis of naming behavior in digital markets and other naming environments.

Machine-learning (ML) corrections to density functional approximations (DFAs) offer a route to improving electronic-structure predictions while retaining the efficiency of semilocal functionals. An important question is whether such corrections learn transferable improvements or instead compensate for errors specific to the parent functional. Here, we address this question by applying the semilocal ML correction of Wang et al. [J.~Chem.~Phys.~158, 154107 (2023)] to PBE, B3LYP, SCAN, and r$^2$SCAN, while keeping the network architecture, loss function, training set, and optimization protocol unchanged. We find that the learned correction develops a systematic size-dependent contribution to atomization energies for all four parents, with $|r|\geq0.9999$ along the $n$-alkane series, where r is the Pearson coefficient of the linear fit. Its magnitude and sign depend systematically on the parent: the correction partially compensates the size-dependent errors of PBE and B3LYP, but introduces substantial size-dependent contributions for SCAN and r$^2$SCAN, whose parent errors show little size dependence. In contrast, ionization potentials, electron affinities, and isomerization energies are largely unaffected. Spatial decomposition further reveals distinct origins of this extensive contribution, with bonding regions dominating for B3LYP, SCAN, and r$^2$SCAN and core regions dominating for PBE. These results show that the global-energy ML correction is strongly dependent on the error structure of its parent DFA, highlighting size-dependent error accumulation as a critical consideration in the assessment and development of ML-enhanced density functionals.

We show that inflation with a large number of fields, as predicted by concrete ultraviolet embeddings, generically produces almost-local cosmological collider signals in the bispectrum squeezed limit. We construct the most general boost-breaking mixings between the curvature perturbation and $N_{\rm f}$ additional fields, and extract the late-time scaling dimensions that dictate the soft limits of cosmological correlators. For a handful of fields, an enhanced squeezed limit (with potential oscillations) is a fine-tuned signal. At large $N_{\rm f}\sim100$, however, mixings generically drive the scaling dimensions toward the unitarity boundary. We show that this is a direct consequence of extreme value statistics and random-matrix universality, turning an almost-local bispectrum shape into a generic prediction for almost any masses and mixings.

Rendering accurate Chinese text remains challenging for text-to-image models. Existing OCR-based reinforcement-learning rewards compare decoded transcripts with target strings. Such rewards overlook the compositional nature of Chinese writing: an ideograph consists of reusable components arranged through explicit spatial relations, yet OCR evaluates it as an atomic character. Consequently, visually different radical-level errors may receive equally coarse feedback, encouraging glyphs that merely resemble the target instead of faithfully reproducing its internal structure. We employ Ideographic Description Sequences (IDS), which comprise spatial operators and character components, and train an expert IDS recognizer to transcribe rendered Chinese text into this representation. Building on this recognizer, we introduce IDSpect, which deterministically decomposes the target text into IDS tokens and aligns crop-level visual IDS predictions with the target sequence. Globally unique token credit makes this comparison robust to the order of detected text regions. Combined with a whole-character semantic reward, IDSpect supplies fine-grained credit with component and spatial-relation without changing the image generator or adding inference-time cost. Experiments with GRPO post-training of Qwen-Image demonstrate that IDSpect achieves leading structural quality and semantic alignment on LongText and GenTextEval.

Audio-visual large language models (AVLLMs) have made remarkable progress in multimodal understanding and reasoning through interactions among visual, auditory, and linguistic information. However, recent studies show that AVLLMs face a critical challenge: $\textbf{source-confused grounding hallucination}$, where cues from the unused modality induce responses that the required modality does not support, undermining reliability in real-world applications. Existing methods have made progress in mitigating this failure, yet how it arises from internal cross-modal interactions remains insufficiently understood. To address this gap, we conduct path-intervention and representation analyses, revealing a $\textbf{question-relay}$ mechanism: question states carry interfering cues alongside required-source evidence, undermining grounding in required-modality evidence. Cutting pathways from interfering modality to question states yields greater correct-answer logit recovery than cutting those to the generation position. Motivated by these findings, we propose $\textbf{SECRET}$ ($\textbf{S}$ourc$\textbf{E}$-$\textbf{C}$onditioned $\textbf{RE}$lay s$\textbf{T}$eering), a training-free method that mitigates cross-modal interference at the question relay. Using contrasting question representations elicited through different modality-pathway interventions, SECRET steers the original question states toward required-source evidence. Experiments on two widely adopted benchmarks CMM and AVHBench across three AVLLMs show that SECRET consistently outperforms prior training-free methods, substantially mitigating source-confused grounding hallucinations (e.g., up to +18.0 and +7.1 percentage points over base models). Modality-specific captioning further demonstrates its generalizability to open-ended generation.

Driven by the rapid advancement of large language models (LLMs), LLM-based multi-agent systems (MAS) have emerged as a powerful paradigm for collaborative reasoning over complex tasks. A key design element of MAS is the communication topology, which governs information flow among agents and often encodes proprietary knowledge about the system architecture. However, recent work has shown that such topologies can be inferred even in black-box settings by exploiting semantic dependencies in observable reasoning traces, posing significant risks of intellectual property leakage and exposure of system vulnerabilities. To address this threat, we propose MIRAGE, a topology-concealment framework that preserves the genuine communication topology for task execution while shaping adversary-facing semantic evidence toward a carefully constructed phantom topology. Specifically, MIRAGE operates in three stages: (1) phantom topology synthesis, (2) semantic edge realization, and (3) protected MAS execution. It constructs a phantom topology structurally distinct from the genuine one, materializes phantom edges as plausible semantic dependencies, and suppresses source-specific cues that could reveal genuine edges absent from the phantom topology. Extensive experiments across three topology optimization frameworks and four benchmark datasets demonstrate that MIRAGE substantially reduces the effectiveness of topology inference attacks while largely preserving the task utility of the protected MAS.

A message drawn from a small alphabet helps a teammate only if it keeps the distinctions that change that teammate's next decision. We show that scoring messages by action values averaged over the receiver's situation can erase exactly these distinctions, and we propose RAVEN (Receiver-conditioned Action-Value ENcoding), which trains a four-symbol, one-step-delayed channel to preserve each receiver's centered action-value profile within the receiver's own context. The sender never needs to know that context: the receiver decodes every symbol with its private information. We give two estimators of this target. With a teacher, offline RAVEN selects the codebook that exactly minimizes an empirical conditional distortion and distills it into a frozen sender; we bound the resulting codebook-selection error and one-step decision loss. Without a teacher, online RAVEN aligns, inside a QMIX learner, the deployed symbol pathway with a training-only continuous reference that shares its routing. Against five recent communication methods on eight navigation settings, offline RAVEN attains the highest return in seven, and removing receiver conditioning forfeits 83% of its communication gain. Online RAVEN raises predator-prey capture success from 53.2% to 96.0% over the same QMIX backbone without communication, and on SMAC and MPE it attains the best mean normalized score of 14 methods, including methods that exchange kilobit messages. Every RAVEN message costs 2 bits, 12-1,024x fewer than those of NDQ, CACOM and ExpoComm on navigation.

Deep learning surrogates can produce high-resolution coastal flood maps orders of magnitude faster than physics-based hydrodynamic simulators, yet transferring them to new coastal regions remains costly, since generating target-region data for fine-tuning typically requires numerous time-consuming simulations. To tackle this bottleneck, we introduce the Physics Adapter (PA), a compact, architecture-agnostic adaptation interface that enables efficient few-shot transfer of flood prediction models across diverse coastal regions. PA predicts peak water level through a differentiable wet/dry response that compares terrain elevation against a learned water level, and blends this physics-structured prediction with a data-driven branch through a learned gate. Unlike physics-informed formulations, PA imposes no PDE-residual or conservation losses and instead exploits elevation as an architectural inductive bias, adding a negligible number of trainable parameters. We integrate PA into 12 heterogeneous models, and evaluate them on two coastal regions with markedly distinct geometries, topographies, and shoreline protection configurations. The performance of PA is benchmarked against a no-physics baseline, full fine-tuning, and standard parameter-efficient fine-tuning (PEFT) methods, considering both within-region generalization to unseen sea level rise values and between-region transfer. In low-shot regime (K=3), and averaged over all backbones and transfer settings, adding PA reduces root mean square error by 11.5% when only the output head is adapted on a frozen backbone, by 15.4% when combined with PEFT methods, and by 22.9% under full fine-tuning, compared to matched configurations without PA. Taken together, the findings of this work offer practitioners a concrete recipe for extending DL-based coastal flood predictors to new, data-scarce regions.

Merging pretrained models has emerged as an effective approach for consolidating diverse capabilities into a single unified model. However, prevailing merging methods typically treat each task vector as an indivisible merging unit, overlooking the heterogeneous geometric changes encoded within it. This treatment can induce cross-component coupling: when merging decisions are derived from statistics of the complete task vector, the geometric characteristics of one component may influence how another is selected, weighted, or combined, potentially degrading the quality of the merged model. To address this issue, we propose DiGA, a Disentangled Geometry-Aware model merging framework. Using the pretrained weights as a shared geometric reference, DiGA orthogonally decomposes each task vector into components corresponding to distinct geometric attributes. Rather than merging the task vectors as a whole, DiGA aggregates corresponding components independently within their respective subspaces and subsequently recombines them into a unified update. This component-wise formulation preserves the geometric identity of each component and prevents the characteristics of one component from interfering with the aggregation of another. Furthermore, DiGA can be incorporated into a broad range of existing model merging methods. Extensive experiments across diverse models, tasks, and merging methods demonstrate that DiGA improves merged-model performance and reduces capability degradation. Our repository is on https://github.com/wzj1718/DiGA.

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop pure-singlet contribution to the quark-to-quark splitting function in perturbative QCD. Together with the known non-singlet contribution, our result completes the quark-to-quark splitting function at this order. We confirm previous partial results and obtain, for the first time, a fully analytic expression valid for all momentum fractions. We examine its behavior at small momentum fractions and provide precise numerical representations suitable for parton evolution.

For every integer $n\ge2$, we prove that every countable group embeds in a group of type $\mathrm{FP}_n$. We also construct a group of type $\mathrm{F}_n$ containing a copy of every recursively presented group. Consequently, a finitely generated group embeds in a group of type $\mathrm{F}_n$ if and only if it is recursively presented. This answers questions of Fournier-Facio and Zaremsky, and confirms a suggestion of Gromov. An appendix combines the construction with the controlled-filling argument in a subsequently released OpenAI preprint to prove that every countable group embeds in a two-generator group of type $\mathrm{FP}_\infty$.

The LUX-ZEPLIN (LZ) experiment has reported a single nuclear-recoil candidate at $248\pm23\,(\mathrm{stat})\pm23\,(\mathrm{sys})$ keV. We suggest that it comes from a GeV-scale dark state $\chi_1$ that downscatters exothermically, $\chi_1A\to\chi_2A$, and is continuously replenished in the halo by the slow decay $\chi_0\to\chi_1\chi_1$ of a long-lived parent. Because the recoil energy is supplied by the mass splitting rather than by the halo velocity, the event is a narrow line with no low-energy tail. Kinematics requires $m_{\chi_1}\gtrsim247$ MeV and fixes the splitting for each $m_{\chi_1}$. The same line should appear at 700$-$810 keV in argon for $m_{\chi_1}=0.3-10$ GeV. Normalizing to one LZ event also fixes the local rate of the radiative decay $\chi_1\to\chi_2\gamma\gamma$, up to the mediator's photon coupling. A rough $\gamma$-ray estimate then requires this coupling to be $\lesssim10^{-2}$ of a proton-loop reference at $m_{\chi_1}=10$ GeV, but $\lesssim10^{-9}$ at 0.3 GeV, which favours daughters near 10 GeV.

Grinding and sanding are fundamental processes in industrial robotic surface finishing. However, physical trials are expensive and consume workpieces, making reproducible experiments difficult. We present RoboFin3D, a sim-to-real platform built on Isaac Sim and the Newton physics engine, that provides physics-based grinding and sanding simulation for cheap and repeatable robotic surface finishing experiments. RoboFin3D utilizes a signed distance field (SDF) to model the changing geometry of the workpiece, enabling contact computation, live updates and rendering without an intermediate mesh. It additionally uses a separate surface field to model progressive surface appearance change during sanding. We also introduce WeldGen, a weld sampling module, to generate weld beads on 8,918 real-world workpiece meshes for providing diverse simulation assets. The simulation parameters are calibrated on real experimental results and our evaluation demonstrates our simulation's fidelity against the real world. We also demonstrate that simulation-generated data can be used to improve the performance of perception models. Simulation-only fine-tuning of SAM2 improves IoU for segmentation of unsanded regions from 77.15% to 84.47%, while combined synthetic and real training reaches 97.41%.

To serve as real-world personal assistants, streaming video models need persistent memory that retains past experiences for later use. Yet existing streaming benchmarks and methods often focus on individual continuous videos or short clips, overlooking that real-world interactions are often intermittent and require memory to persist across interruptions. To fill this gap, we introduce APM-Bench, which reformulates real-world streaming interaction as multi-session life trajectories. It contains 549 sessions, 104 trajectories, and 2,719 candidates, spanning both objective and open-ended questions. Each session is a video with fine-grained annotations, and sessions within a trajectory revolve around related activities. Models then use persistent memory to answer questions about past sessions and provide proactive responses while maintaining real-time interaction. This raises challenges: persistent memory must be storable, selectively retain information, be injected at the right time, and remain efficient. Moreover, finite storage may leave required evidence unavailable, so assistants should recognize missing evidence. Therefore, we systematically evaluate general video models under different memory protocols and diverse specialized streaming memory systems, and test whether models acknowledge insufficient evidence. Our evaluation reveals a clear utility–latency–storage trade-off: existing methods still struggle to simultaneously achieve reliable long-term recall, low overhead, and effective proactive assistance across sessions. APM-Bench provides a comprehensive testbed for developing and comparing persistent memory systems under realistic streaming conditions. We hope it encourages future work that jointly considers utility, latency, and storage toward more practical persistent memory for real-world streaming assistants.

We construct a correspondence between ordinary irreducible characters of height zero above the generalized Dade-Glauberman-Nagao correspondence for blocks with central defect. The correspondence is equivariant under group and Galois automorphisms and satisfies a block relation between $\mathcal{H}$-triples. For each pair of corresponding characters, one pair of associated projective representations realizes matching factor sets, equal central scalars, synchronized mixed comparison functions and compatible block correspondences for every intermediate group. The construction uses the multiplicity algebra over the group algebra of the central defect subgroup, a normalized integral lift of a residual semilinear realization, and a graded corner isomorphism. It treats all central-character fibers, including those with nontrivial central character. We also obtain a form suited to normal $p$-sections in an Alperin-McKay-Navarro reduction.

Accurate models of programmable metasurfaces based on multiport-network theory (MNT) account for mutual coupling (MC) through a configuration-dependent matrix inversion. The latter's high computational cost during gradient-based optimization (GBO) can be alleviated via a finite-order Neumann approximation. We show that the accuracy of this approximation depends strongly on the (tacitly) chosen MNT parametrization. For 1-bit-programmable meta-elements (e.g., meta-elements based on PIN diodes), we identify a closed-form Möbius reparametrization that depends only on the meta-element's two load states and requires neither training data nor numerical optimization. For an experimentally estimated proxy MNT model of a fabricated 96-element 19-GHz dynamic metasurface antenna with strong MC, a second-order Neumann approximation with our reparametrization achieves forward and control-gradient accuracies of 21.68 and 21.70 dB, respectively. Relative to the full proxy MNT, it reduces the runtime of a combined forward and control-gradient evaluation by a third and the saved-tensor memory by a factor of ten. In a prototypical GBO problem of end-to-end optimization for DMA-based scene classification, it achieves 94.97% test accuracy vs. 95.57% with the full model. We further note that MC-strength metrics and MC-unaware benchmarks should be parametrization-invariant, motivating, for instance, definitions based on the best directly fitted zeroth-order model.

Renormalisation-group evolution enters PDF determinations through the running coupling and the splitting functions. At fixed perturbative order, the solution of the evolution equations is not unique beyond the nominal accuracy, and this residual freedom can be probed through resummation-scale variations. This contribution summarises an NNLO study of this effect in inclusive HERA DIS fits performed with the xFitter fitting framework. The induced shifts are sizeable in a low-scale baseline fit, especially for the gluon and sea PDFs, and can affect LHC and FCC top-quark pair predictions at the few-percent level. Raising the PDF starting scale and applying a higher DIS virtuality cut considerably reduces the effect, a conclusion also supported by treating the resummation scale as a free parameter constrained directly by the data.

Drug discovery is a costly and high-risk process, where toxicity-related failures remain a major cause of attrition in both preclinical and clinical stages. As a result, accurate early prediction of chemical toxicity is essential to reduce downstream costs and improve compound prioritization. In this context, graph deep learning (GDL) has emerged as a powerful paradigm for toxicity prediction, leveraging molecular graph representations to learn directly from chemical structure with improved expressivity over traditional approaches. Despite the growing number of proposed models, current literature-based comparisons are often difficult to interpret due to inconsistencies in datasets, preprocessing pipelines, and evaluation protocols. To address this limitation, we introduce a unified and standardized benchmarking framework for GDL-based toxicity prediction. We systematically evaluate more than 20 representative approaches under consistent experimental conditions and across multiple datasets and partitioning strategies, enabling a fair and reproducible comparison of model performance. In addition, we complement this empirical study with a structured literature analysis to contextualize existing methodological trends and performance claims. Our results provide a clearer and more reliable assessment of the current state of the field, highlighting both the strengths and limitations of existing graph-based approaches. To support transparency and reproducibility, we release our benchmarking framework as open-source software https://gitlab.citius.gal/noel.suarez/benchtox, allowing the community to evaluate and compare models under consistent conditions.

Large language models (LLMs) are increasingly used as high-level planners in robot navigation, but their outputs may become unreliable when instructions are ambiguous, unsupported by the environment, or semantically inconsistent. This paper presents a Risk-Aware Semantic Grounding framework for trustworthy LLM-based robot planning. Unlike existing LLM-based planners that primarily optimize plan generation, we formulate semantic grounding reliability as a multi-dimensional risk estimation problem. The proposed architecture explicitly models grounding uncertainty through ambiguity, hallucination and semantic-conflict risks before planning occurs, enabling the system to decide whether to execute the instruction, request clarification, or reject it. To evaluate the approach, we introduce TRUST-NAV, a benchmark containing both standard navigation tasks and risk-inducing instruction scenarios. Experimental results show that while conventional LLM planners achieve strong performance on valid navigation tasks, the proposed framework substantially improves ambiguity detection and semantic conflict rejection. These findings suggest that trustworthy robot planning should be evaluated not only by task completion, but also by the ability to recognize when execution should not occur.

In this paper, we first construct two graphs $\mathcal{F}(l,m,t,s)$ and $\mathcal{G}_4(l,m,t,s)$. Then we introduce the graph $\mathcal{F}_n(l,m,t,s)$ and the operator $E_{\mathcal{G}_4(l,m,t,s)}$, where $\mathcal{F}_n(l,m,t,s)$ is defined by identifying the vertex $c$ of $n$ copies of $\mathcal{F}(l,m,t,s)$, and $E_{\mathcal{G}_4(l,m,t,s)}$ is defined by replacing each edge of $G$ with $\mathcal{G}_4(l,m,t,s)$, for any simple finite undirected graph $G$. By using the theory of Lorentzian polynomials, we prove that the independence polynomials of the graphs $\mathcal{F}_n(l,m,t,s)$ and the image graphs of $E_{\mathcal{G}_4(l,m,t,s)}$ are log-concave, respectively. As applications, our results not only make progress on the conjecture of Alavi, Malde, Schwenk and Erdős, but also generalize the results of Bendjeddou and Hardiman.

While contact-rich manipulation requires deliberate regulation of interaction forces, recent approaches to robot manipulation learning predominantly represent actions as target positions or poses. Even methods that incorporate force sensing either use it solely as an observation or, when predicting forces as part of the output, rely on a hybrid force controller. In this paper, we propose an imitation learning policy that predicts wrenches as its sole action output for direct use by a pure force controller. Our studies suggest that force-domain imitation learning depends critically on data collection, with force-feedback teleoperation improving policy performance by capturing the operator's deliberate force regulation. Using Action Chunking with Transformers (ACT) as the base architecture, we train single-task models on bilateral wrench demonstrations and evaluate them on five contact-rich manipulation tasks. The wrench policy matches or outperforms position-based baselines across all tasks, with gains varying according to the degree of deliberate force regulation each task requires. Cross-condition ablations show that the bilateral data collection interface and the wrench action space each contribute independently to performance. To support further research, we will release over 1000 wrench-action demonstrations spanning these tasks on a companion website upon publication.

Emerging optical-network applications increasingly use received data for inference and control rather than exact source reproduction, creating an opportunity to trade bit-level fidelity for greater transmission reach and efficiency. We propose an end-to-end optical semantic communication system for joint image classification and reconstruction over a nonlinear wavelength-division multiplexed (WDM) fiber channel. The system maps each image directly into a fixed-length sequence of channel symbols that preserves task-relevant information, without explicit source compression or channel coding. Experiments on the MNIST dataset cover launch powers from -9 to +3 dBm, fiber lengths up to 800 km, and 16-, 64-, and 256-Quadrature Amplitude Modulation (QAM) formats. At 0 dBm, classification accuracy remains between 98.92% and 99.31% across all tested link lengths and modulation orders, while requiring fewer transmitted symbols than a Low-Density Parity-Check (LDPC)-coded JPEG baseline at every tested modulation order. These results show that semantic communication can simultaneously extend optical reach and reduce transmission resources by conveying only task-relevant information.

Large-scale models have permeated the molecular sciences, yet what makes a model 'foundational' in this domain remains poorly defined. This paper proposes three testable criteria for assessing the foundational nature of molecular models: (i) generality across molecular entities, properties, and tasks; (ii) transferability to new applications with no or minimal task-specific retraining; and (iii) generalization beyond the training distribution. Applying these criteria to the state of the art reveals promising progress, particularly visible in biomolecular structure prediction and machine-learned interatomic potentials, although none of the approaches examined fully satisfies all three. Success is concentrated in domains where target properties are consistently defined and training data are abundant, with low label noise relative to physically meaningful variation. More broadly, progress in the molecular sciences appears to depend less on model scale alone than on the quality and structure of available data, as well as the incorporation of prior knowledge into models, prediction tasks, or downstream applications. This work shifts the notion of a molecular foundation model from a descriptive label to a testable hypothesis, offering a framework for assessing current models and guiding future developments.

We prove Petrunin's smoothing conjecture in all dimensions: every compact Euclidean polyhedral space without boundary and with nonnegative Alexandrov curvature is a Gromov-Hausdorff limit of smooth Riemannian orbifolds with geometrically nonnegative curvature. More strongly, the approximating metrics are positive-time slices of a single orbifold Ricci flow whose metric initial condition is the given polyhedral space. The proof rests on a new short-time existence and regularization theory for Ricci flow that, under two-sided volume bounds and a generalized segment inequality, replaces pointwise lower curvature control by small scale-invariant integral control of the defect from a preserved curvature cone. Although it allows arbitrarily large pointwise violations, this theory yields an existence time and positive-time curvature estimates independent of the initial upper curvature bound. As a further application, it gives rigidity consequences for manifolds with small integral curvature defect.