Papers

Self-distillation is an emerging approach that trains a model to imitate its own predictions when conditioned on privileged information, such as correct answers or environmental feedback. Recent methods have reported better sample efficiency and generalization than reinforcement learning (RL), but it remains unclear whether these gains extend beyond in-distribution evaluations and whether they stem from privileged distillation. In this paper, we revisit two representative methods, Self-Distillation Policy Optimization (SDPO) and On-Policy Self-Distillation (OPSD), across code, science, tool use, and math reasoning tasks. We find that their reported gains do not consistently generalize to unseen problems and are largely explained by overfitting or transferring existing reasoning behavior, rather than effectively using privileged information. Moreover, self-distillation gradients show weak alignment with policy gradients that directly optimize expected reward, questioning whether they provide an effective direction for policy improvement. Our experiments across Qwen3 models (1.7B-14B) and OLMo-3-7B suggest that effectively leveraging privileged information to improve reasoning remains an open challenge. Our code is available at https://github.com/sleepypandu/does-sd-improve-reasoning

System One models such as Jev change how software makes decisions by mapping open-ended semantic contexts into structured judgments that directly drive program execution. However, this paradigm introduces a new security risk, which we term Jev Program Decision Hijacking (JPDH): attacker-controlled contexts can redirect program decisions through schema-valid Jev judgments. Existing evaluations focus primarily on model-level attacks or predefined injection channels, leaving attack reachability and downstream security consequences in real-world Jev applications underexplored. In this paper, we present JevProbe, the first automated framework to evaluate JPDH by tracing adversarial influence from reachable context surfaces through program-consumed decisions to downstream security consequences in real-world Jev applications. Our key insight is that application logic maps diverse Jev judgments to observable decisions, enabling systematic, program-grounded attack evaluation. Across 228 popular real-world Jev applications and 2,273 test cases, 81.5% exhibit decision flips, of which 98.6% lead to potential downstream security impacts. Compared with the strongest adapted baseline, JevProbe improves macro-average Decision Flip Rate (DFR) by 50.4 percentage points, while existing defenses offer limited protection. We further construct JevProbeBench to support systematic evaluation of JPDH in real-world Jev applications. We have responsibly disclosed our findings to Jev application maintainers, pending their responses. The source code of JevProbe and the JevProbeBench dataset are publicly available on GitHub (https://github.com/xiaoxiaohg8d/JevProbe-).

Legal question answering requires answers that are not only plausible, but also grounded in legally valid and citable evidence. Standard retrieval-augmented generation often relies on one-shot semantic matching, which is insufficient when legal evidence must be selected according to authority, applicability, and diversity across heterogeneous sources. We introduce Legal-R1, an agentic retrieval framework for evidence-based legal reasoning. Legal-R1 decomposes legal reasoning into a multi-agent workflow, where a Lawyer agent learns when to retrieve, which legal source to query, what evidence to seek, and when the collected evidence is sufficient. A Legal Assistant agent retrieves from normative legal sources and precedent cases with authority-aware and diversity-aware selection, while a Judge agent generates the final answer from the complete evidence trajectory. We post-train only the Lawyer agent with masked supervised fine-tuning and trajectory-aware reinforcement learning. Experiments on multiple Chinese legal benchmarks show that Legal-R1 improves over general-purpose, legal-specific, and retrieval-augmented baselines.

Dialogue and collaborative assistants repeatedly judge what a partner knows, believes, or intends. Typed decision models offer a potential alternative to generative large language models for bounded Theory of Mind (ToM) selection. We present Jev-ToM, comparing five typed decision models and seven generative baselines on 11,117 English text questions from nine ToM benchmarks across six capability groups. TypeSafe Jev reaches 73.2% source-balanced accuracy including native controls and ranks first or second across all six capabilities, leading beliefs, goals/desires/intentions, and emotions. Other typed models show distinct strengths across tasks. Separate resource comparisons suggest that Jev could reduce the cost and waiting time of repeated ToM selection. Confidence-based selection remains benchmark-dependent, and supplied reasons can repair errors or overturn correct answers depending on their attachment. Candidate expansion reveals distinct selection and output-validity problems. Related-question cues account for most of Jev's downstream gains, with task-dependent effects from predicted states. The findings motivate testing Jev as a ToM selection component in assistants, with task-specific confidence calibration, candidate design, and output validation as integration priorities.

Direct Preference Optimization (DPO) has become a widely adopted approach for aligning vision-language models (VLMs), yet the security of multimodal preference data remains largely unexplored. Existing preference poisoning attacks either corrupt explicit supervision signals or require visible triggers, making them detectable under human inspection. We introduce DPOison-VL, the first clean preference poisoning attack against VLM-DPO, which manipulates model alignment solely through imperceptible perturbations on a small fraction of training images, while leaving all prompts, responses, and preference annotations semantically intact. We formulate poison construction as a bilevel optimization and derive a gradient alignment surrogate that efficiently steers image perturbations toward the attacker-specified preference. We further introduce a preference displacement score for principled poison selection with provable first-order optimality under a fixed poison budget, and derive a sufficient condition for preference inversion. Extensive experiments across diverse attack tasks, different VLM architectures and scales, and baseline comparisons demonstrate that DPOison-VL achieves up to 98% ASR with only 2% poisoned data and exhibits cross-model transferability, while largely preserving clean accuracy and general utility. Our findings reveal a critical vulnerability in VLM-DPO, where imperceptible image perturbations in preference training data can silently redirect alignment.

A closed subspace $E$ of a Banach space $F$ is \emph{$L$-embedded in $F$} if there is a projection $P\colon F\to E$ such that $\|x\|=\|Px\|+\|x-Px\|$ for all $x\in F$. We show that if $X$ is a proper, geodesic metric space with locally finite $\H^1$-measure, then its Lipschitz-free space, denoted by $\F(X)$, is $L$-embedded in its bidual. We also extend an argument by Cúth, Kalenda, and Kaplický, to show that if $E$ is a finite dimensional normed space and $C\ge 1$ is such that every subspace of $E$ is $C$-complemented in $E$, then $\cal F(E)$ is $C$-complemented in its bidual. In particular, for every two-dimensional normed space $E$, $\cal F(E)$ is $1$-complemented in its bidual.

Pretrained diffusion models provide powerful generative priors for extreme image compression, but their stochastic, iterative generation processes are not designed to decode compressed representations directly. We present PrismCodec, which recasts a pretrained Diffusion Transformer (DiT) as a bitstream-grounded one-step generative decoder. PrismCodec uses the decoded representation in two complementary roles: a projected codec state defines the starting state for generation, while hierarchical visual priors derived from the same decoded latent provide semantic and structural guidance. To bridge the gap between stochastic, iterative generation and deterministic one-step decoding, we develop a progressive adaptation strategy. We first learn codec-conditioned transport from a noisy neighborhood centered on the codec state, distill it into a one-step mapping, and finally anneal the source perturbation to zero during end-to-end optimization. The resulting decoder reconstructs deterministically from the received representation without additional conditioning bits. Across Kodak, CLIC, and DIV2K, PrismCodec consistently improves rate-perception performance over prior generative codecs, achieving BD-rate reductions of 70-75% in LPIPS and 75-81% in DISTS over StableCodec. Code will be released upon acceptance.

Large language models increasingly tackle tasks that require multi-step reasoning, where errors in intermediate claims can affect the final answer. Self-consistency (SC) improves reasoning by voting over sampled final answers, but its vote leaves intermediate disagreements unresolved. To address this problem, we introduce DDRG (Disagreement-Driven Verification Guided by Reasoning Graphs), a framework for selective correction from a frozen bank of reasoning traces. Our insight is that graph alignment can expose claim-level disagreements and provide correction evidence without expanding the sampled trace bank. DDRG builds source-grounded claim graphs and sends localized conflicts to an answer-blind verifier. A verifier-supported refutation that reaches the majority answer's supporting path triggers one focused repair; otherwise, DDRG returns the exact SC vote. Experimental results across five benchmarks show that native zero-shot DDRG improves macro-average accuracy over direct answering by 8.65 and 15.83 percentage points for Qwen2.5-7B and Llama3.1-8B. It also exceeds CoT, the evaluated GoT and GoV question-answering adaptations, and SC on this macro metric. DDRG links local verification to selective correction without enlarging the initial candidate bank.

Large language models (LLMs) often diagnose full sight, static clinical cases well yet struggle in foresight, dynamic diagnosis. Prior work has improved this limitation by quantifying the information models acquire and by developing stronger follow-up strategies to improve diagnostic accuracy. In contrast, we introduce a distinctive hindsight to systematically dissect why LLMs fail to acquire diagnostically critical evidence, tracing the failure from evidence identification, utilization and downstream diagnostic updating through not only diagnostic accuracy, but also evidence coverage, trajectory dynamics, and elicited probability and information entropy. Starting experiments from the breakdown at the level of capabilities, to the diagnosis of the pre-event state before the evidence arrives, and to the post-event state transition after the evidence arrives, our research has revealed the profound limitations and internal causes existing in the dynamic diagnostic process. At the same time, we have also conducted sufficient verification and generalization experiments to prove that these limitations are widespread. Together, these findings shift the central challenge from whether LLMs possess relevant clinical knowledge to whether they can identify, acquire, and effectively use the right evidence under clinical diagnosis and conduct a more detailed mechanism analysis to identify the exact location of the capability gap.

3D part assembly aims to reconstruct a complete shape from a set of unassembled parts by predicting a rigid SE(3) transformation for each part. Because the placement of a part is rarely determined by its own geometry, the task demands reasoning over the entire part set, and existing methods, which rely on pairwise relations or iterative generation and verification, scale poorly to objects with many parts. We present LLM2R, which casts part assembly as sequence modeling with a pretrained decoder-only large language model (LLM): a Point-BERT encoder and a Q-Former compress each part into a block of geometric tokens, the blocks of all parts are concatenated, and a causal LLM adapted with Low-Rank Adaptation (LoRA) processes the sequence in one forward pass. Causal attention, however, lets the hidden states of a part observe only the parts that precede it. LLM2R therefore appends a block of learnable summary tokens after the last part: these tokens follow every part, so their states aggregate the whole assembly at a constant token cost, and a part-aware pose head fuses each part's states with them before predicting its rotation and translation. One architecture thus handles semantic and geometric assembly and predicts all poses in a single non-autoregressive pass. LLM2R achieves the highest part accuracy and success rate on all three PartNet categories, the best rotation error, translation error, and part accuracy on PartNeXt, and the lowest translation error and fastest inference on Breaking Bad, where only a fracture-specialized method is more accurate. Its advantage grows with the number of parts: at 100 parts it exceeds GARF by 33.5 points in part accuracy on Breaking Bad and Assembler by 29.1 points on PartNet, and it transfers zero-shot to unseen categories with more than 16 points higher part accuracy than the strongest of three baselines.

Benchmarks report what an Artificial Intelligence (AI) agent can do on a task suite, but not whether one released version has been engineered with the controls that make it reliable, safe and observable, or how strongly that is shown. This paper proposes AgentStripes, an evidence-graded maturity model for AI agents. It defines levels (0 to 7 stripes), process areas (12 areas holding 40 capabilities), three gates (basic, safety, proof) that hold an agent at a level however high its score, and evidence grades E0 to E5. Each applicable capability receives a rating from 0 to 3 and a separate evidence level; these are combined into a credit, aggregated into a severity-weighted score and converted into stripes that the gates limit. Instruments gather evidence, language-model judges interpret it under explicit criteria, and the arithmetic is deterministic. The model is compared with standards at topic level without a claim of conformance, and an unexecuted validation protocol is specified. An empirical evaluation (exploratory, non-confirmatory) of 30 public Python agent repositories, with static evidence only, is a demonstration and not a validation: static evidence caps every final stripe at 2, 26 repositories end at one stripe and 4 at two, and this distinction is unreliable, since re-judging changed the final stripe of 4 of 22 repositories (engine, dossier and panel changed), whereas none of 8 panel-only repeats, all at stripe 1, changed. The parameters are expert conventions without outcome based calibration, and the stripes have not been shown to predict reliability or safety.

Point-in-time (PIT) agents can recall post-cutoff facts even when their external evidence respects a historical cutoff. We examine whether this access predicts evidence gathering in 48 historical company-comparison tasks. Independent closed-book revenue probes identify the better-remembered company for each model on tasks with unequal recall, fixing the predicted direction before agent runs. We then compare paired runs with real or anonymized company identities while keeping external evidence PIT-valid. Both Qwen and DeepSeek recalled future facts, but neither supported the prespecified shift toward the better-remembered company. Qwen's four allocation estimates on 28 unequal-recall tasks were negative, with descriptive intervals spanning zero. A prospective DeepSeek replication showed an inverse pattern across all four metrics on 20 such tasks, with intervals below zero. These estimates remained negative after each company, pair, and future-fact omission, and all four post-hoc max-T-adjusted sign-flip p-values were below .05. In a prospectively specified follow-up, explicit future facts produced small estimated shifts away from the supplied-fact company, with intervals spanning zero, while final choices shifted toward it. The mechanism behind the natural inverse pattern remains unresolved. These findings support separate assessments of memory accessibility, search allocation, and final outputs alongside cutoff checks on external evidence.

Dormant black holes (dormant BHs, i.e., X-ray quiet binaries comprising a BH and a companion star) are probes of the effect of cluster dynamics and binary stellar evolution on compact-object binaries. A dozen dormant BH binaries are known, a number that will increase substantially with the upcoming Gaia Data Release 4 (DR4). Their origin is uncertain, and dynamical formation is proposed as one possible channel. Here, we study the formation of dormant BHs in low-mass star clusters, accounting for the interplay of binary stellar evolution and cluster dynamics. We present new simulations with the $N$-body code PeTar, interfaced with the population synthesis code SEVN for single and binary star evolution. Our grid spans a range of cluster masses ($300-4800\,$M$_\odot$), metallicities ($1.4\times10^{-2}$, $1.4\times10^{-4}$), and natal kick models (with and without fallback). We find that almost all dormant BH binaries escape the parent cluster within $\sim1\,$Gyr ($\sim10\,$Myr) when assuming weak (strong) natal kicks. Most ($73\%$) dormant BHs form via the exchange of a BH (or its progenitor star) into a stellar binary, or of a star into a binary with a BH. Dormant BHs in low-mass clusters have a wide orbital period distribution (from a few hours to $10^8\,$d), with an upper limit set by natal kicks, a bimodal eccentricity distribution (a first peak at zero eccentricity for circularised systems and a second at high eccentricity), and stellar masses that follow the (evolved) initial mass function. Large BH masses are a smoking gun of dynamical formation, via exchanges and stellar collisions. We expect Gaia DR4 to contain $\sim1-64$ high-metallicity and $\sim0.4-48$ low-metallicity dormant BHs, with a period distribution peaking at $\sim10^3\,$d, $\gtrsim90\%$ of them with eccentricity $e>0.1$, and $\sim20\%$ with large BH masses ($m_{\rm BH} \gtrsim 30\,$M$_\odot$).

We consider a natural extension of the classical saturation problem to oriented graphs, defined as the minimum number of edges in an oriented graph $H$ on $n$ vertices that avoids a fixed oriented graph $G$, but adding any missing edge to $H$ creates a copy of $G$. Our main result shows that saturation functions of oriented graphs attain at least four distinct orders of magnitude. In particular, if $G$ is acyclic, then its saturation function is bounded if and only if $G$ contains an isolated edge; otherwise, it is linear. Certain tournaments together with an isolated edge give further infinite examples of bounded and linear saturation functions. Two additional orders of magnitude are $\Theta(n \sqrt{\log n})$ and $\Theta(n \log n)$. For these two, the lower bounds are obtained by adapting a recently developed approach for the saturation problem in edge-ordered graphs, while the matching upper bounds are constructive. Finally, we study the semisaturation problem, in which we require only that adding any missing edge to $H$ creates a copy of $G$. We completely characterize the possible orders of magnitude: the semisaturation function is either bounded, linear, or $\Theta(n \log n)$.

We establish a Weyl law for the codimension-one anisotropic volume spectrum on compact Riemannian manifolds. We then use this law to obtain equidistribution in the full Grassmannian bundle while keeping the ambient metric fixed. More precisely, on every closed connected smooth Riemannian manifold of dimension three through six, we construct smooth, embedded hypersurfaces stationary for anisotropies smoothly converging to area. The cumulative sum of their area measures, when lifted to the Grassmannian bundle, converges to the uniform measure.

Multimodal LLMs are typically trained by first aligning a vision encoder with a language model via projector training on large image-caption datasets, followed by joint training of the full multimodal model. Despite its widespread use, the role of the projector training stage remains poorly understood. We find that (i) using only $10$ to $20\%$ of the data for training the projector already recovers most downstream performance gains, and (ii) projectors trained on different datasets can be linearly interpolated while largely preserving performance. These results suggest that projector training mainly performs a coarse alignment, which many different projectors achieve equally well. Motivated by these findings, we propose PORTAL, a training-free projector initialization that requires neither paired image-caption data nor gradient-based optimization, but only per-modality summary statistics. PORTAL computes an optimal-transport-based map between Gaussian approximations of the vision and language feature distributions on a shared principal subspace, so that the projector training stage can be skipped entirely. Without any paired data, PORTAL matches the standard pipeline trained on 558k image-caption pairs across six LLM backbones, two vision encoders, and 16 benchmarks. It outperforms that pipeline in $3$ of $7$ (vision encoder, LLM) settings and reaches an average $98\%$ of its score across the other four.

Physical properties provide intuitive controls for sounds made by interacting objects. The challenge is to make a generative model respond predictably to these controls, both individually and in combination. We present \method\ (PXS), trained on simulated contact sounds with 15 material, geometry and contact parameters. Two separately trained variants accept direct parameter inputs or numerical captions. PXS controls hardness, size, speed and damping, supports room descriptions and produces spectrally distinct outputs at fixed targets. When controlling damping and size together, specifying thickness improves frequency accuracy and joint target delivery. Measurements from real recordings define effective-damping targets, which simulator inversion maps to generation inputs without real-audio fine-tuning. Across 18 impact classes from five real-audio datasets, PXS-Physical follows these targets with mean grouped Spearman correlation $\rho=0.976$ and class-median error 0.094 dex (a factor of 1.24).

Reinforcement learning (RL) post-training improves robot foundation models (RFMs) beyond their demonstrations, but real-world deployment demands more: learning new tasks efficiently while retaining previously acquired behaviors. Existing continual RL methods on top of VLAs mitigate forgetting but rely on on-policy updates with limited forward transfer, whereas off-policy methods improve single-task sample efficiency without addressing learner persistence across tasks. We propose ACCRUE, a continual off-policy RL framework that carries lightweight actor and critic networks across tasks, allowing each stage to reuse behavioral and value knowledge acquired through prior RL. The inherited critic adapts only on current-task transitions and guides current-task actor learning, while prior behavior is preserved by distilling the actor toward cached targets on a small number of retained episodes. Fixed visual features keep the inherited learner and its replay compatible with base-policy updates. Across contact-rich assembly sequences in simulation and on real-robot hardware, ACCRUE accelerates subsequent-task learning with near-zero forgetting and significantly reduces real-robot training time by 31.0% to 68.5%.

We establish a Bogomolov–Gieseker-type inequality for tilt-semistable objects on smooth projective varieties of dimension $\geq 3$, in the spirit of the Bayer–Macrì–Toda conjecture. A key ingredient is an analysis of the action of the Frobenius morphism on tilt-semistable objects. As an application, we prove the Castelnuovo Bound Conjecture, up to an explicit constant term. Combining our results with work of Feyzbakhsh and Thomas, we further show that on a Calabi–Yau threefold, arbitrary rank Donaldson–Thomas invariants of semistable sheaves are determined by rank one invariants, and hence are symplectic invariants.

This paper proposes an Autonomous Cyber Operations (ACO) gym, a unified framework integrating high-fidelity network emulation, realistic user behaviour modelling for benign network traffic and adversarial profiles, and the generation of cybersecurity scenarios through open toolkits. By supporting live and deferred feature extraction at the packet and flow levels, the gym facilitates the creation of labelled synthetic datasets for training Deep Neural Network (DNN)-based Intrusion Detection Systems (IDSs), as well as developing and evaluating modular components for autonomous defence agents through emulated interactions. While evaluation of a DNN classifier within the gym shows high in-domain performance, achieving near-perfect recall on adversarial network flows, our experiments reveal a significant sensitivity to domain shift, showing that even minor changes in network composition, such as variations in traffic protocol distribution, can lead to a catastrophic collapse in model transferability and detection performance.

Fairness constraints in predict-then-optimize pipelines are necessarily enforced on predicted outcomes $\hat{y}$, since true outcomes $y$ are unobserved at decision time. We study whether a demographic parity constraint enforced this way continues to hold against $y$, and how the resulting violation scales with prediction error. Using a budget-constrained allocation problem solved as a linear program, we show empirically that the true-outcome fairness gap grows with prediction error $\sigma$ and saturates, well fit by $c(1 - e^{-\sigma/\tau})$ with $c = 0.1545 \pm 0.0103$ and $\tau = 3.9045 \pm 0.3745$; its mean is invariant to sample size while its variance decays at the standard $O(1/\sqrt{n})$ rate. We derive a two-part theoretical bound: a closed-form local sensitivity result showing the gap's first-order response to prediction error depends on only two individuals per group, validated against the solver to within three significant figures; and a universal, error-independent ceiling following from the boundedness of the decision variable, confirmed consistent with but looser than the empirical saturation level. On US Census income data, enforcing demographic parity on a trained predictor's output reduces an unconstrained disparity in true income to roughly one-third of its original size, leaving 34.4% $\pm$ 3.3% (California) and 35.7% $\pm$ 1.8% (Texas) of the disparity intact and undetectable from the predictions alone – consistent not only in mechanism but in approximate magnitude across two states with different demographics and income distributions, and stable across ten independent train/test splits in each. A fairness constraint that appears fully satisfied at decision time can mask a substantial, systematic violation of the outcome it was meant to protect.

Every October, the Nobel Prizes in Physics, Chemistry, Physiology or Medicine and Economic Sciences are announced, with one to three prizes in each discipline. Of the 769 Laureates (since 1901) in these four disciplines only 4% are women (30 Laureates). In 2026, there are eight Laureates within these disciplines and they are all men. Based on historical data across four fields and a Bayesian hierarchical model, we update the 8 year old model on bias in Nobel Prizes and confirm the gender gap, with exceedingly large confidence.

We study aspects of the Euclidean partition function of the $\frac{SL(2,\mathbb R)\times U(1)}{U(1)}$ gauged WZW model. The target space geometry is either a smooth horizonless geometry with a linear-dilaton asymptotic region, or the Horne–Horowitz black string, depending on which circles we unwind as the time-direction. We first study the worldsheet spectrum and obtain the character decomposition via the holonomy integrals. Next, we obtain the spacetime spectrum of the horizonless geometry by directly performing the unfolded modular integrals, and recover the Maldacena-Ooguri-Son spectrum in the ungauged limit. When the chirally charged three-dimensional black string is dimensionally reduced, the target space is instead a two-dimensional charged black hole. We study the near extremal regime of the black hole and black string. For the two dimensional black hole, we propose two candidate towers of states that produce the expected $\frac{3}{2}\log T$ of the AdS$_2$ throat from the worldsheet discrete series representation. These towers appear only below the temperature at which the full amplitude becomes divergent. We comment on the contribution of these states in the near-extremal limit of the full partition function.

In this paper, we introduce a new class of data-driven ambiguity sets for distributionally robust optimization (DRO) that aim to enhance the local inference accuracy of an unknown distribution. Building on optimal transport-based discrepancy measures, we depart from the conventional paradigm of monolithic ambiguity balls, which rely on a single global transport budget to capture distributional uncertainty. Instead, we introduce local-discrepancy ambiguity sets, where the support of the distribution is partitioned into predefined regions and transport cost constraints are imposed locally to each region. This added flexibility allows for a more refined characterization of plausible distributions by preventing highly imbalanced transport across regions. As a result, the proposed approach can yield less conservative and more robust decisions, particularly in settings where decisions depend on the local properties of the sample space. We further derive tractable reformulations of the resulting DRO problems and demonstrate through simulations that our method can outperform traditional Wasserstein ambiguity sets in terms of decision quality.

We construct Clifford+$T$ circuits implementing arbitrary $n$-qubit unitaries with worst-case $T$-count $\widetilde{O}(N^{8/7})$ at constant operator-norm error, where $N=2^n$, improving the previous exponent $5/4$. The construction uses $\widetilde{O}(N^{6/7})$ clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error $\epsilon\in(0,1/2)$, let $L=\log_2(N/\epsilon)$, the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using $\widetilde{O}(N^{8/7}L^{3/7}+NL)$ $T$ gates and $\widetilde{O}(N)$ clean ancillas whenever $L\le N$. We also prove that, at constant precision, the exponent $8/7$ is optimal within a sequential block-SELECT model.

Annotator disagreement is increasingly recognized as a meaningful property of subjective tasks, rather than merely noise to be removed. Predicting which items are likely to be contested could help allocate annotation effort and route difficult cases to human review. We propose predicting disagreement from interpretable semantic properties of the text. An LLM answers a set of binary questions covering harmful-content characteristics, disagreement-related cues such as borderline severity and missing context, and language-sensitive cues such as local slurs. A classifier predicts disagreement from these answers, and we analyze which questions contribute most to the predictions. Across four datasets in English, German, and Turkish and three open-weight LLMs, our structured question features outperform direct prompting by 10.5 ROC-AUC points and the strongest text-based baselines by 5.0 points. A compact subset of eight questions performs within 1.5 ROC-AUC points of the full twenty-question set. In leave-one-dataset-out evaluation, models retain roughly 90-95% of their in-domain ROC-AUC. Across models and datasets, questions about derogation, missing context, and decision boundaries serve as the strongest predictors, suggesting that what makes harmful content contested is partly observable in the text.

Multimodal Emotion Recognition (MER) aims to understand human emotions by integrating information from multiple modalities such as speech and text. Psychological studies suggest that emotions exhibit latent hierarchical structured relationships in their semantic representations. However, most MER approaches rely on Euclidean representations, which capture fine-grained cross-modal interactions but do not explicitly provide a geometric prior for organizing hierarchical emotional structures. To mitigate this gap, we propose GeoMER, a joint Euclidean-Hyperbolic modeling framework that introduces hyperbolic emotion-core routing to capture higher-level, abstract emotional representations for MER. The proposed framework jointly models token-level cross-modal semantic interactions and latent emotion representations in two complementary geometric spaces. Specifically, GeoMER consists of a Euclidean Multimodal Fusion Module (EuclFusion) for multimodal representation fusion and a Hyperbolic Geometric Core Routing (HypGeoRoute) module that performs geometry-aware core assignment and aggregation in a hyperbolic manifold to capture more abstract feature representations. The HypGeoRoute module complements the Euclidean token-level modeling. We experiment on the IEMOCAP multimodal MER benchmark and demonstrate that the proposed method achieves the best performance, with 83.54% weighted accuracy and 83.35% unweighted accuracy, outperforming Euclidean baselines, including MemoCMT.

The Klein-Gordon equation is a second order differential equation that appears in a variety of applications in mathematics, physics and engineering. This equation is often solved using numerical methods, since a general analytical solution is unattainable. However, one can find very useful analytical solutions for some special cases. In cosmology, the Klein-Gordon equation of a field can explain the physics of inflation and has important consequences on understanding the origin and evolution of the universe. An analytical solution to the Klein-Gordon equation in cosmology has been obtained in the small-field excursion approximation, and it turns out that the solution can be written in terms of the confluent hypergeometric limit function. In this work, we derive this result again while showing the details of the calculations and then generalize to the case of two coupled Klein-Gordon equations. We show that the solution of this coupled system can be written in terms of Kummer's hypergeometric limit function while considering minimal assumptions. We carry out a full numerical calculation of the coupled system and compare it to the results from the analytical expressions.

JavaScript vulnerabilities in npm packages pose a significant risk to the Node$.$js ecosystem, and a growing body of work aims to detect, exploit, and mitigate them. Studying and evaluating this work requires up-to-date collections of real vulnerabilities, yet the most commonly used datasets stop recording vulnerabilities in 2022. We present X$.$js, a live benchmark of real-world Node$.$js taint-style vulnerabilities covering code and command injection, prototype pollution, and path traversal. Built from 1,738 advisories collected through mid-2026, primarily from the GitHub Advisory Database, X$.$js pairs each vulnerability with precise source and sink locations, a validated executable exploit and its execution trace, and, when available, a patched version of the package. X$.$js supports long-term reproducibility and growth: dependencies are mirrored in a self-hosted registry to guard against package removal from the ecosystem, and dedicated infrastructure generates and validates exploits for newly reported vulnerabilities. The current release contains 1,159 validated exploits for 965 packages. Using X$.$js, we characterize how the frequency, structure, and complexity of Node$.$js taint-style vulnerabilities have evolved over time. We find that these vulnerabilities are increasingly reported in large packages: the median vulnerable package grew from roughly 250 LoC in 2021–2022 to 6,100 LoC in 2026.

For $f(X)=X^r(X^s+a)\in\mathbb F_{p^m}[X]$, with $m,r,s\geqslant1$ and $a\in\mathbb F_{p^m}^\times$, put $g=\gcd(s,p^m-1)$. We prove that, for each fixed $g$, only finitely many prime characteristics $p$ admit such permutation binomials, even as $m,r,s,a$ vary. If $6\nmid g$, every such $p$ divides Wendt's determinant $W_g=\operatorname{Res}_X(X^g-1,(X+1)^g-1)$, which is nonzero. When $6\mid g$, this determinant vanishes; inverse power sums and iterated resultants yield an explicit nonzero integer divisible by every such $p>2g+1$. We determine the exact admissible characteristics for $1\leqslant g\leqslant10$, obtain a further divisibility condition over prime fields, and show that in prime fields $g=11$ occurs precisely when $p=23$.