We provide sharp estimates on the number of vertices needed to approximate the Euclidean unit ball $B_d\subset\mathbb R^d$ with relative symmetric-difference volume error at most $\varepsilon\in(0,1)$. We show that the minimum vertex budget $N_\varepsilon(d)$ satisfies $$\log N_\varepsilon(d)\asymp d\log\left(1+\frac1{\varepsilon\sqrt d}\right).$$ In particular, $\exp(O(\sqrt d/\varepsilon))$ vertices suffice for every $\varepsilon\in(0,1)$ and all sufficiently large $d$. We also prove that achieving a fixed error $\varepsilon\in(0,1)$ requires at least $\Omega\bigl((\tfrac{1+\varepsilon}{2\sqrt\varepsilon})^{d-1}\bigr)$ facets, an exponential number in $d$. We extend our vertex approximation result to Gaussian symmetric-difference error, and give a positive answer to the question of De, Nadimpalli, and Servedio about subexponential vertex complexity for approximating Euclidean balls. We also disprove a Macbeath-type extremality principle for unrestricted vertex approximation. Whereas the ball uniformly maximizes the inscribed approximation error among all convex bodies (Macbeath, 1951), we show that approximating the hypercube $[-1,1]^d$ to relative error $\varepsilon$, with $\delta:=1-\varepsilon$, requires $N\ge\frac{\delta}{2}\exp(\Omega(\delta^2d/\log^2(2/\delta)))$ vertices whenever $d\ge16\log(2/\delta)$. Thus, when $d$ is large, the cube is harder to approximate than the ball in this sense. Finally, we determine the sharp dimensional order of the classical Laguerre-Delone triangulation number, showing that $\mathrm{ldel}_{d-1}=\Theta(d^{-1/2})$ as $d\to\infty$. This improves both the upper bound of Ludwig, Sch\"utt, and Werner and the lower bound of B\"or\"oczky by a factor of order $\sqrt d$. By classical asymptotic approximation theorems (Ludwig, 1999), this improvement applies to every convex body in $\mathbb R^d$ with $C^2$ boundary and positive Gaussian curvature.
Statistics are often the only evidence of whether a text in an unread script records a language, but meaningless text shares many of them. A test means little until it is run on texts whose answer is known. We build such tests and apply them to the Voynich manuscript, whose text may be meaningless copying or a language hidden by a cipher. We write both accounts as programs, fit them with the same search budget and check them on held-out statistics. The copying process of Timm and Schinner predicts these statistics better than any cipher with one key, but ciphers with two keys, or that encode only the word classes of a real text, do equally well. A trace of language that needs no decipherment says more. In 28 texts in 16 natural languages the same word pairs keep sharing a line, and the manuscript shows this at half the strength of the weakest. Word codes fall to this level only with heavy miscopying or a plaintext whose word pairs recur weakly, such as abbreviated Latin. Solvers that read enciphered controls find nothing readable in the manuscript under letter ciphers, word codes or codes with one word per letter or syllable. One cipher remains, a nomenclator with two keys, which writes frequent words whole and spells the rest, and whose scribe miscopies more than half of the words. Our tests exclude it in all languages but Arabic and Hebrew. Planted messages show that a short message could still hide.
Computer-using agents are increasingly capable of performing complex tasks in the digital world. To advance such agents, supervised learning on annotated interaction trajectories has become a common approach to improving their task-solving capabilities. However, high-quality interaction trajectories remain scarce for specialized desktop applications, where limited application knowledge, complex GUI workflows, and incomplete exploration hinder automated collection. To address these challenges, we introduce \aks{}, a knowledge-guided automated trajectory collection framework. It combines tutorial-guided exploration with a hybrid GUI--Code action space, providing application-specific knowledge and simplifying GUI workflows through direct execution of application-native commands. The framework also checkpoints and revisits pivotal states during tree exploration to explore alternative workflows, complementing linear rollouts for broader coverage. We collect 10.9K automatically validated trajectories and use them to fine-tune open-source base models. The resulting model achieves 64.1\% accuracy on a benchmark of specialized desktop workflows, improving performance by 58.2 percentage points, establishing a new state of the art. The fine-tuned model also improves performance on general desktop workflows using GUI actions only, suggesting that the collected supervision benefits general desktop tasks as well. Comparative experiments and ablations demonstrate the efficiency of our collection framework and the value of code actions in specialized workflows.
Zero-shot detection of machine-generated text is vital for mitigating the risks of large language models (LLMs) misuse. While the state-of-the-art dual-model detectors and resampling-based detectors outperform single-model statistical detectors on unprompted continuations, they suffer a catastrophic breakdown on instruction-conditioned text in the black-box setting, where the source model is unknown. We analyze this failure and trace it to poor prompt conditioning for resampling-based methods and diminished cross-model discrepancy for dual-model detectors. Motivated by recent studies that human writing maintains a steady, uniform information flow, whereas machine-generated text exhibits sharp, localized entropy fluctuations, we propose a new metric, the Relative Peak Prominence Rate (RelPPR) to capture this structural contrast along the entropy trajectory and further leverage it as a signal for LLM-generated text detection. Extensive evaluations across diverse model families and datasets demonstrate that RelPPR achieves state-of-the-art black-box detection performance and remains the most reliable detector under various practical situations. Our code is available at https://github.com/brushing-git/entropy-llm-detector.
Content moderation compresses a graded, contested human judgment into a binary act (leave up / take down) over billions of items, at a scale where running a frontier LLM on every post is uneconomical. A new class of frozen "System One" models returns typed, calibrated decisions instead of text at ~USD 0.000025 per call and ~100 ms. We run the first independent audit of one such model on 142,658 human-labeled comments, and benchmark it against 14 frontier reasoning models (the GPT-5.x, Claude, Gemini 3, and Grok families) on a shared probe set. Two findings stand out. First, the cheap model is accuracy-competitive: its zero-shot classification AUROC (0.83) is not statistically separable (paired bootstrap, n=56; a failure to reject parity, not proof of equivalence) from 13 of the 14 frontier systems while costing 1-3 orders of magnitude less, and it is no worse calibrated than several of them. Second, "confidence" conflates two uncertainties that come apart: human disagreement (where annotators split on satire and coded language) and decision risk (where the automatic action is costly-wrong). Under an asymmetric moderation loss these call for opposite escalation signals, so no single confidence number serves both. Because the model prices extra questions at nearly zero, decomposing the judgment into parallel sub-questions and reading their spread recovers a human-disagreement signal that the model's native confidence misses -- but this remedy is specific: it helps the weakest, disagreement-blind models and only when the decomposition aligns with the sources of disagreement; a specialist toxicity model and the strongest LLMs do not need it, and the effect is distribution-sensitive. We will release the instrument, the cached runs, and the analysis.
How can a language model know whether it has enough evidence to answer? Language models tend to answer even when the evidence they have is insufficient. Deciding whether to answer or gather more evidence requires a calibrated estimate of how likely an answer is to be correct with the available evidence. However, most calibration work treats the input as fixed, without asking how this estimate should change with the evidence. We introduce evidence-state calibration, which requires a model's confidence before answering to match its probability of answering correctly and to change accordingly whenever the evidence changes this probability. We propose SuffiCE (Sufficiency Confidence Estimation), which fine-tunes the confidence already present in a model's next-token distribution to match how often the model answers correctly from each evidence state. Across clinical diagnosis and multi-hop question answering with four models from two families, SuffiCE reduces the Brier score by up to 60% and increases AUROC by up to 0.16. Its confidence matches the empirical success rate and responds not only to the amount of evidence but also to which evidence is present, showing that models can learn to judge whether their current evidence is enough to answer.
Current sign language recognition and translation benchmarks are commonly collected in controlled settings using fixed or studio-style cameras, particularly limiting their ability to reflect how signers communicate in everyday mobile scenarios. As such, this gap becomes increasingly evident when considering the Arabic Sign Language (ArSL), which is a primary sign language used across Arab countries. In this work, we introduce Isharah-Selfie, a large-scale ArSL dataset collected entirely using front-facing smartphone cameras under unconstrained selfie conditions. The dataset comprises 8,997 video clips performed by 16 signers across 1,493 unique sentences, covering several domains such as healthcare, education, and transportation. Unlike conventional datasets dominated by fixed-camera, two-handed signing, Isharah-Selfie captures realistic mobile communication characterized by one-handed signing, close-range viewpoints, partial body visibility, camera motion, unconstrained environments, and heterogeneous device resolutions. Each video is annotated with both gloss sequences for continuous sign language recognition (CSLR) and Arabic sentence translations for sign language translation (SLT). Moreover, we define signer-independent and unseen-sentences evaluation protocols to assess generalization across unseen signers and novel sentence compositions. Extensive benchmarks using RGB-based and pose-based data show that current CSLR and SLT methods remain challenged by selfie-style signing conditions, particularly under unseen-sentence evaluation, where compositional generalization remains weak. By releasing Isharah-Selfie, we aim to support research toward robust, user-centered sign language technologies that operate reliably in realistic smartphone-based communication settings. The Isharah-Selfie dataset is available on https://isharah-selfie.github.io/.
We present HyScale, a long-context training system for learned sparse attention. Learned sparse attention is a promising architecture for million-token contexts, widely adopted in production since DeepSeek-V3.2. Selection, however, grows into the training bottleneck. For each query, it scores every previous token whereas sparse attention reads only $k$; worse, current systems materialize a full score table and repeat selection during recomputation. Our key insight is that the output of selection is not an activation, but rather a set of indices. Building on it, HyScale introduces FlashTopK and selection replay. FlashTopK finds each query's exact top-$k$ on the fly without a score table, while selection replay reuses forward-pass selection in recomputation. Together with holistic system optimizations tackling end-to-end challenges, HyScale speeds up GLM-5.1 training on 1M-token sequences by $2.07\times$ over Megatron-LM on 512 H20 GPUs. It also speeds up the CSA layers of DeepSeek-V4-Flash and the QSA layers of Qwen3.8-Flash-Next by $2.01\times$ and $1.57\times$ at 1M tokens on 32 H800 GPUs.
Temporary traffic control redirects vehicles through work zones, requiring automated vehicles to connect an interpretation of the visible devices to a continuous passing path. Geometric predictors provide several plausible paths, yet selecting the one consistent with the temporary control remains difficult. We propose SAGE (Semantic-to-Action Grounded Execution), a read-decide-execute-check framework that separates path construction, path preference, and control compliance within a shared candidate space. The central idea is to use a vision-language model's (VLM's) trajectory as a preference over intact geometric candidates. A role-decoupled generator constructs the candidates, and rank fusion combines each candidate's geometric score with its agreement with the VLM trajectory. Supervision structured around the Manual on Uniform Traffic Control Devices (MUTCD) trains SAGE-VLM to state the lane status and hazard side before its passage decision and trajectory. The predicted hazard side enters image-space predicates derived from MUTCD provisions, which support a final intervention bounded in score and displacement. On 2,306 real-world ROADWork validation episodes, the candidates include a path within 10 px of the human demonstration in 87% of episodes, yet selection regret accounts for 53% of the geometric ranker's error. SAGE reduces average and final displacement errors by 8.3% and 12.0% relative to the ranker and hard-constraint violations by 37%. The trajectory opinion improves all four tested generator-selector combinations. SAGE is comparable to state-of-the-art VLM modules in accuracy, with a faster-responding VLM, and outperforms four other adapted driving VLMs in displacement error and safety measures. Project page: https://hhjj233.github.io/SAGE-page/.
Humanoid loco-manipulation in dynamic scenes is non-Markovian: cues vanish as objects change or are hidden, or leave the view as the robot turns and walks, yet whole-body vision-language-action (VLA) policies see only the present. We present WholeBodyMem, an object-guided perceptual memory that keeps the pre-history of object events seen before the robot acts on its goal. SAM3 tracks the task objects, and their events causally select key frames within an adaptive budget, which the action expert reads by cross-attention together with object tokens encoding appearance, geometry and time. We also contribute HuMeGo, a humanoid memory benchmark with six simulated and six real-world Unitree G1 tasks. Keeping the right frames rather than more frames, WholeBodyMem surpasses memoryless and uniform-memory baselines, raising its base policy's success from 29.1% to 72.6% in simulation and from 36.7% to 88.3% on the real robot, while also improving the standard SIMPLE tasks (70.2% to 86.9%).
Sequential decision-making under partial observability is difficult because agents must explore to infer hidden, task-relevant information before acting effectively. Learning such information-gathering behaviors tabula rasa via online reinforcement learning is sample-inefficient, whereas offline imitation averages expert actions across hidden states and fails to learn exploration. In this work, we propose ASTEROID, a simple and effective student--teacher supervised learning framework that can learn test-time exploration. Although a privileged expert never needs to explore, we demonstrate that a history-conditioned student can learn to do so when trained with on-policy contexts: the student first collects on-policy context under partial observability, and then imitates the privileged expert conditioned on that context. By distilling expert actions directly conditioned on the student's on-policy history, the student learns to systematically resolve partial observability, i.e., search while uncertain and exploit once the hidden state is revealed. This enables efficient test-time exploration (similar to Bayesian posterior sampling) without incurring the impractical training-data costs of reinforcement learning. Across a diverse range of eleven different environments, including discrete exploration benchmarks, robotic manipulation, navigation, and Procgen environments, ASTEROID achieves ~2x higher returns under fixed exploration budgets, uses ~100x fewer interactions than RL baselines, and outperforms frontier models at exploration. Finally, our method transfers policies trained in simulation to vision-denied real-world robot manipulation, exhibiting efficient exploration and increasing success by +40% over standard distillation. Overall, it provides a simple yet surprisingly effective framework to learn efficient test-time exploration.
Generative models propose crystalline materials by learning composition and geometry, but unconditional sampling gives no direct control over the space group, which constrains whether responses such as piezoelectricity are symmetry-allowed. We present Orbitol, a crystal generator built on the Crystalite diffusion Transformer that replaces atom tokens with Wyckoff-orbit tokens. Given a space group and a collection of occupied Wyckoff positions, Orbitol generates the atom type and free coordinates of each orbit together with a compatible lattice, so every valid structure is invariant under the operations of the requested group. It generates structures two to three orders of magnitude faster than the symmetry-aware baselines at the evaluated settings. On MP-20, 13.8% of Orbitol's attempts yielded stable or metastable, unique and novel structures that retained the requested space group after relaxation, compared with 10.8% for SGFM, the next best model. We also introduce SPARC, a score that combines retention of the raw detected space group with agreement between the retained-group and training distributions. Finally, we used Orbitol to generate candidates in piezoelectric crystal classes. Of the structures selected by internal screening, 89% passed our density functional theory checks, and 79% also matched no Materials Project or Alexandria entry with the same space group. Their median figure of merit was nine times that of the piezoelectric materials computed in the Materials Project, and 24% of the new candidates ranked in that set's top 10%.
The development of embodied models of animal behavior is a major goal of the neuro-AI community. Embodied models will enhance our ability to make direct comparisons between biological and artificial agents. To make such comparisons effective, though, we need embodied models that actually move like animals. Previous work has developed virtual animal bodies and techniques for training realistic motion through imitation. However, to date, there is no system for embodied animal modeling that produces natural movements both during trained goal-directed behavior, and during exploration driven by random generation. Here, we introduce Simulated Control via Augmented Motor Priors for Embodied Reinforcement learning (SCAMPER), a system for training an embodied virtual rat model, enabling natural movements during both goal-directed behavior and random exploration. SCAMPER uses a variational architecture with two distinct priors, a motion prior for control and a behavior prior for exploration. We show that combining both of these priors allows SCAMPER to generate realistic behavior during exploration and exploit the task structure effectively. SCAMPER can also learn from sparse rewards as a result of the diverse movements induced by the behavior prior, allowing the system to model realistic sparse-reward tasks from experimental neuroscience. Altogether, SCAMPER provides the neuro-AI community with an effective new system for training embodied models of rodents on realistic tasks.
When given an image and a text prompt, vision-language models (VLMs) can produce seemingly sophisticated text responses. However, they are also prone to hallucinate objects in their output, which can have detrimental consequences in safety-critical applications. To detect these hallucinations, certain methods interestingly leverage internal signals from the VLM as it generates the text response; potentially, these methods use the same signals that led to a hallucination to detect it. We conduct an in-depth analysis to understand the robustness of these detection methods. First, we show that a naive baseline of a generated word's token position in the VLM text response achieves competitive performance. Further, we reveal how some detection methods rely on token position and use this heuristic as a shortcut. Second, we explore detection methods' sensitivity to language and vision modalities. Our experiments suggest that strong detection performance is often driven by detecting language-based hallucinations, and when methods rely on token position, they tend to be less visually grounded and exhibit reduced robustness when hallucinations occur earlier in a text response. Lastly, we demonstrate that different detection methods can carry complementary signals; when ensembling methods together, adding weaker methods to an ensemble of higher performing ones still offers performance improvements. Altogether, while there may be useful internal VLM signals to detect hallucinations, our investigation reveals important limitations of the current methods that try to leverage them.
Turning a moving-camera perspective video into a 360{\deg} video means generating content outside the input frame under several constraints: observations revealed over time must be preserved, unseen regions plausibly completed, and the resulting scene kept consistent as the camera viewpoint changes. Existing methods assign these different requirements to a single conditional video model, requiring them to be jointly learned from panoramic video data. We instead present a modular, 3D-driven framework that distributes these three responsibilities across specialized components, all connected through a shared scene representation. Input observations are reconstructed explicitly in 3D, while a pretrained panoramic image model completes unobserved content from a selected panoramic render. This generated content is lifted into the shared 3D scene, where it remains spatially anchored across camera viewpoints. Without requiring any additional panoramic-video training, our framework achieves state-of-the-art input-view fidelity, perceptual quality, and geometric consistency on a static-scene subset of the Argus evaluation set. These results support our decomposed, 3D-driven formulation as a promising alternative to direct video generation in this setting.
High-definition maps provide critical structural information for downstream autonomous driving tasks. Recent methods increasingly rely on external priors to improve prediction accuracy and robustness. Yet, existing prior representations expose a trade-off: dense rasters are easy to integrate but ignore certain map geometric properties, while sparse vectors preserve geometric structure but require dedicated encoders and are difficult to plug into existing architectures. Moreover, external priors can be inaccurate, costly to acquire, or difficult to maintain, motivating a structural representation that can provide geometric guidance while remaining learnable and broadly applicable. We address this limitation with the Lane Field, a dense BEV-aligned geometric representation that encodes local lane structure at each spatial location and can be either predicted from onboard observations or constructed from external map priors. Building on this representation, we introduce a plug-and-play framework that enhances online HD mapping through two complementary mechanisms: BEV feature modulation, which injects lane-structured cues into latent BEV features, and deformable attention guidance, which steers query sampling toward the underlying lane geometry. We primarily evaluate our method on OpenLane-V2, showing that conditioning BEV features and guiding deformable attention with local lane geometry enables our framework to consistently improve existing methods and achieve state-of-the-art performance on lane segment perception. Project page: https://andberto.github.io/LaneField/
Mathematical problem solving and autonomous agents are increasingly important applications of language models, demanding stronger reasoning capabilities. Computational depth is a key resource for such reasoning, but adding model layers increases both training and inference costs, while test-time scaling incurs substantial additional inference computation. We introduce P2N (Previous to Next), which reuses the previous token's deep representations, already available during generation, to increase effective computational depth with negligible decoding overhead. Specifically, P2N adds the previous token's deep hidden state to the current token's shallow representation, allowing subsequent layers to build on previously completed deep computation. This recurrence extends effective computational depth across tokens, while introducing only a single vector addition per decoding step. We train the recurrence using parallel Jacobi updates restricted to a middle-layer core. Experiments with Qwen-style models show that, at 1.5B parameters, P2N improves GSM8K accuracy by over 10 percentage points under both zero-shot and few-shot prompting, with nearly unchanged decoding latency. The benefits also extend to language modeling and average performance on general downstream benchmarks. on general downstream benchmarks.
Linear sketches estimate properties of high-dimensional inputs from a fixed low-dimensional projection. At constant accuracy, randomized Euclidean-norm sketches, notably the Johnson-Lindenstrauss transform, support exponentially many nonadaptive queries in sketch dimension $k$. For adaptive black-box queries, known privacy-based defenses guarantee $\widetilde{\Omega}(k^2)$ and it remained open whether stronger guarantees were possible. Prior attacks used more queries, restricted the responder, or provided weaker failure guarantees. We show that the quadratic guarantee is optimal up to logarithmic factors, even with a computationally unbounded responder that knows the matrix, attack algorithm, history, and query distributions and may change its randomized rule after every query. For every fixed hidden $A\in\mathbb{R}^{k\times n}$ with $n>40k$ and target accuracy $\alpha \in (0,1]$, our black-box attack uses $O(k+\alpha^2k^2\log(2+\alpha^2k))$ queries in $\widetilde{O}(1+\alpha^2k)$ adaptive rounds to force, with constant probability, a round in which a constant fraction of answers have $\Omega(\alpha)$ relative error. This fraction can be taken arbitrarily close to one half. Our results clarify the limits of defending a fixed compressive linear representation by adapting the prediction rule.
Sky-image irradiance forecasting is dominated by a two-stage design: a video-prediction model forecasts future sky frames, and a separately trained regressor maps those frames to irradiance. We propose a single-stage alternative that co-denoises the future sky-image and clear-sky-index sequences in one diffusion process, with an irradiance head that reads a denoised preview of the future sky rather than the noised diffusion state. The forecaster needs no regression stage and runs from sky images and deterministic covariates alone, with no measured irradiance at its input --- the situation at a site with a camera but no pyranometer. On 2023 SIRTA data the model reaches a pooled RMSE of $104.1$~W\,m$^{-2}$ and a skill score of $+0.34$ on the continuous ranked probability score (CRPS) against smart persistence, higher than any of twelve baseline configurations, and retains that skill when retrained on 2021--2022. On the model's own generated frames, a separately trained regressor reaches $150.6$~W\,m$^{-2}$ against the joint head's $104.1$: roughly $46$~W\,m$^{-2}$ that joint training recovers and a cascade discards. Point accuracy is competitive but not best: a deterministic network that also reads measured irradiance attains $97.6$~W\,m$^{-2}$. The model's CRPS skill leads that network's in every sky-condition tertile, by $0.26$ to $0.30$.
Diffusion models achieve strong performance in text-to-image generation, but they can still produce unsafe content. Training-free safety guidance offers a practical inference-time alternative that intervenes during sampling without modifying model weights. However, many existing safeguards still rely on a coupled safety-control chain. In this chain, the same unsafe condition simultaneously specifies what should be avoided, indicates the current unsafe signal, constructs the intervention, and determines when that intervention remains active. This coupling can work when unsafe factors are explicit, but becomes less reliable once harmful and benign semantics are entangled in the current generation state, often leaving residual unsafe content or unnecessarily degrading benign-generation quality or prompt fidelity. We address this problem with Decoupled Safety Control (DSC), a plug-in safety-control algorithm for training-free safety guidance. DSC reformulates training-free safety guidance as an explicit state-dependent control process, so the executed intervention is determined from the current generation state rather than inherited directly from a single unsafe condition. Experiments on standard safety benchmarks show that DSC improves representative latent- and text-space safeguards, achieving stronger unsafe-content suppression while preserving benign-generation quality and maintaining efficient inference.