Papers

A persistent agent must decide both what to retain as information arrives and what to surface once a query appears, yet memory evaluations can confound these decisions by comparing methods that differ in both retention and selection. We build a streaming-recall benchmark crossing retention and selection rules and evaluate every condition on the same 300 seeded episodes. Holding access fixed, query-aware selection improves required-fact recall by 15.5 percentage points (95% CI: 12.8 to 18.2), whereas a mixed comparison that also changes history access reports a 68.7-point advantage, of which 53.2 points are attributable to access. Under bounded retention, query-aware, dense, and oracle selection reach the retention ceiling, and all 319 observed failures in the bounded recency condition are caused by eviction rather than ranking errors. Recall falls to 0% as targets recede sufficiently far into the past. Repeating the evaluation on SQuAD preserves the retention ceiling while showing that dense retrieval can outperform lexical retrieval on natural text. These results show that bounded-memory evaluations should hold access fixed and report retention and selection separately.

Recent advances in distillation and flow-map models have enabled deterministic one- or few-step generation for high-quality data, facilitating a new branch of reward alignment approaches that directly optimize the initial noise from a Gaussian distribution. However, most existing initial-noise optimization methods rely on first-order gradient information, which is either inapplicable or suffers from instability and inefficiency in black-box reward scenarios. Here, we introduce ZeNOVA, a stable and efficient initial noise alignment method in a gradient-free manner. Specifically, we address existing algorithms' major challenge in black-box scenarios through annealed soft-value guidance, manifold-constrained hyperspherical Langevin dynamics, and Metropolis-Hastings jumping. Extensive experiments on image and video generative models show that ZeNOVA outperforms all evaluated zeroth-order baselines by optimizing the initial noise toward higher rewards substantially more stably while exploiting the geometry of the Gaussian prior, demonstrating its practical applicability to various black-box reward alignment.

For a module \(M\) over a cocommutative Hopf algebra \(\mathscr A\), we define extensive amenability by amenability of its symmetric algebra as a module over \(\operatorname{Sym}(M)\#\mathscr A\). Using the author's coalgebraic rounding and quotient theorems, we prove that nonzero extensively amenable modules are amenable, that every module over an amenable Hopf algebra is extensively amenable, and that extensive amenability is preserved and reflected by short exact sequences. For permutation modules this definition agrees, over every field, with extensive amenability of group actions. A final section gives the modifications for exterior algebras and establishes the comparison between the two definitions in several cases.

Ensuring safe and reliable operation of modern railway systems increasingly relies on data-driven monitoring and intelligent fault detection. Deep learning has emerged as an effective paradigm for railway anomaly detection, driven by the growing availability of heterogeneous sensor data from rolling stock and infrastructure. This paper presents a structured survey of deep learning-based anomaly detection approaches for railway systems. The surveyed methods are organized using a unified taxonomy covering anomaly location, data representation and manifestation, sensing modality, and temporal characteristics. Existing approaches, including convolutional, recurrent and attention-based architectures, autoencoders, generative adversarial networks, and transformers, are structured into classification-based, prediction-based, reconstruction-based, and hybrid learning paradigms. The survey also examines data-centric challenges, evaluation practices, performance metrics, and practical deployment aspects, including edge-cloud architectures, computational constraints, and hardware-aware optimization. Finally, a decision-oriented framework links anomaly characteristics, data properties, and operational constraints to suitable detection paradigms and deployment configurations. This work provides a structured reference for selecting and deploying deep learning solutions for railway anomaly detection and highlights open challenges toward reliable and scalable intelligent monitoring systems.

Raedschelders, Špenko and Van den Bergh proved that the Plücker coordinate ring $C_n$ of the Grassmannian $\operatorname{Gr}(2,n)$ has finite Frobenius representation type when the characteristic $p$ satisfies $p\ge\max\{n-2,3\}$, and they determined the indecomposable summands of its Frobenius pushforwards up to nonzero multiplicity. We give nonrecursive finite formulas for every entry of the Frobenius multiplicity matrix and prove that each entry is a polynomial in $p$ of degree at most $2n-3$. Consequently the $F$-signature of $C_n$, and the asymptotic proportion of every indecomposable summand, is a single rational function of $p$ throughout the characteristic range. Its limit as $p\to\infty$ is the leading coefficient of the first free multiplicity, which we evaluate in closed form through Bernoulli numbers. For $\operatorname{Gr}(2,4)$ we find $s_p(C_4)=(13p^2+8)/(5(3p^2+2))$, and we calculate the analogous rational functions for $\operatorname{Gr}(2,5)$ and $\operatorname{Gr}(2,6)$ with computer assistance. We also construct the full characteristic polynomial from the Riemann-Roch weights and two residual matrices whose entries have degree at most $n-1$ in $p$. In the sequel, we use this work to show rank-two determinantal rings have FFRT, and to calculate their $F$-signatures.

We propose a pluripotential-theoretic framework for studying finiteness questions for polarized Calabi–Yau manifolds. The central idea is to use global \(m\)-Hessian capacities as a quantitative intermediate between complex potential theory and global geometric boundedness. We formulate a chain of uniform estimates connecting \(m\)-Hessian capacity, volume–capacity inequalities, capacity–perimeter estimates, Sobolev bounds, and non-collapsing of the associated Ricci-flat Kähler metrics. Under suitable regularity assumptions, these estimates lead to uniform diameter and curvature control and hence to metric compactness. We then describe the algebraic part of the argument. Uniform projective embeddings with bounded degree lead, through the Macaulay–Gotzmann theory, to only finitely many possible Hilbert polynomials and hence to a finite collection of Hilbert schemes. Ehresmann's fibration theorem then converts boundedness of the smooth algebraic families into finiteness of diffeomorphism and topological types. The resulting framework isolates the main analytic and algebraic bottlenecks in a potential-theoretic approach to Calabi–Yau finiteness. In particular, the capacity–perimeter estimate and the derivation of uniform algebraic embedding data from the preceding metric estimates constitute the essential steps requiring further development. Thus the paper provides a structured program linking complex Hessian potential theory with geometric and algebraic boundedness, rather than assuming that these implications are automatic.

Reinforcement learning (RL) for dexterous manipulation must discover finger-object contacts and then control the object precisely; the action noise that serves the first goal can interfere with the second. In trajectory-guided settings such as ViViDex, where RL refine hand-object trajectories from human video, our baseline PPO runs end near their initial action noise after 5M steps, motivating explicit control of exploration scale. DexPolicy makes that scale an explicit function of training steps, annealing from broad to narrow exploration while holding loss, architecture, reward, and optimizer settings fixed. We study three policy-optimization settings: PPO, critic-free GRPO continuation, and a flow-parameterized PPO variant (FPO). Across five YCB objects and three training seeds, mean deterministic Target success rises from 49.4% to 68.1% (FPO), 14.1% to 45.4% (GRPO), and 32.0% to 35.7% (PPO). On a RealMan RM75 arm with an Inspire/RH56 hand, 360 trials over three objects raise mean Target success from 25.0% to 85.0% (FPO), 10.0% to 63.3% (GRPO), and 8.3% to 43.3% (PPO), with one trained model per object-method condition. PPO component screening favors noise control over the tested optimizer contraction; the selected PPO schedule yields higher mean Target success than linear decay with the same endpoints on three tested objects. Training return, deterministic Target success, and tolerance to execution noise dissociate; schedules should therefore be judged by terminal task success under the intended execution conditions, per task and policy-optimization setting. Code: https://github.com/AIGeeksGroup/DexPolicy. Website: https://aigeeksgroup.github.io/DexPolicy.

Diffusion models with prompt and reference image-guided editing have seen rapid progress, yet they remain too coarse for pixel-level control. One promising direction is to incorporate a soft mask that specifies spatially varying edit strengths but training such fine-grained control demands expensive pixel-wise annotations, while existing zero-shot methods often yield unsatisfactory results. We introduce SoftPaint, a new zero-shot sampling method that leverages soft masks to enable a continuous spectrum of edits, from fully preserving the original content to completely re-synthesizing the masked region. Going beyond zero-shot inpainting methods, we design a Langevin-iteration-based sampler that respects per-pixel soft mask strengths, which applies universally to image and video diffusion models, enabling tasks such as video editing. The method is gradient-free, memory-efficient, and achieves smooth, pixel-level edits across multiple image and video backbones.

Let $z_1,\ldots,z_5\in\mathbb C$ satisfy $\sum_{j=1}^5|z_j|^2=5$. We prove the sharp inequality \[ \prod_{1\le i<j\le5}|z_i-z_j|^2\le 5^5, \] with equality precisely for a regular pentagon on the unit circle, up to rotation and permutation. This settles the remaining five-point case of the discriminant problem considered by Mordell in 1960. The proof first identifies a maximizer with a normalized relative equilibrium of five identical planar point vortices. We then give an independent exact classification of the corresponding stationary equations. The main algebraic step proves that every collision-free physical solution of the normalized stationary equations is reflection symmetric; it is obtained from a resultant construction and exact Gröbner-basis elimination over $\mathbb Q$. The reflection-symmetric equations have exactly five physical shapes, and an exact discriminant comparison selects the regular pentagon. All symbolic eliminations, Sturm counts, and interval inequalities are reproduced by an accompanying verification script using rational arithmetic. As consequences, the same configuration gives the Gaussian weighted Fekete set and the global mode of the five-particle complex Ginibre density after the natural rescaling.

A hidden-variable model can reproduce context-independent individual readouts while failing to preserve observable records when devices are connected or reused. We distinguish two composition requirements. For a finite family of nonnegative instrument matrices, an invariant space generated by normalization defects characterizes unit continuation mass under every finite adaptive policy. Its annihilator defines the maximal admissible positive cone closed under outcome-conditioned updates. A separate observation space characterizes indistinguishability of context-dependent hidden preparations under joint readout. A finite-state example passes every fixed sequence but fails under outcome-dependent stopping. For a wrapped-Cauchy spin source with an explicitly stipulated unchanged-source passive extension, two individually fair probes acquire a setting-dependent agreement probability with contrast $\epsilon^2\operatorname{sech}(2g)/4$. More generally, protection under one and two identical uses forces a continuous binary passive response to be constant; measurable two-valued exceptions remain possible. Exact rational calculations, exhaustive finite-policy experiments, continuous source sampling, and quadrature test the stated examples. The criteria apply to specified instrument families and accessible records; they do not construct a microscopic detector or establish consistency under unrestricted network composition.

Whether a forced-oscillation source can be uniquely localized depends jointly on the available measurements and the candidate intervention dictionary. This paper considers a single unknown constant-amplitude sinusoid acting through one of physical intervention channels. Because its amplitude and phase are unknown, each candidate harmonic response is observable only up to a nonzero complex scalar and therefore defines a projective ray in measurement space. A necessary-and-sufficient condition is derived for exact localization, together with a weighted nearest-ray locator and a deterministic recovery bound based on projective separation. The paper proposes a framework distinguishing four mechanisms of source localization failure: mechanism mismatch, feature-projection loss, structural nonidentifiability, and poor conditioning or model error. Numerical studies on the Kundur two-area system illustrate well-separated recovery, mechanism-dependent terminal decisions, measurement-induced ambiguity, and the sensitivity of nearly collinear signatures to model perturbations. Then, IEEE–NASPI Contest models are used to further examine broad candidate dictionaries, terminal-feature source coverage, and ambiguity removal through measurement augmentation. The results show that correctly locating the source bus does not by itself establish unique identification of the internal forcing channel or robustness to measurement and model uncertainty.

Efficient indoor LiDAR perception is challenging because mobile robots must understand cluttered three-dimensional environments under strict latency and memory constraints. Existing point-based and voxel-based methods often incur substantial computational overhead, whereas conventional bird's-eye-view (BEV) representations improve efficiency at the cost of discarding vertical geometric information. We present IndoorBEV, a lightweight LiDAR perception framework that mitigates this tradeoff through a height-aware BEV representation and geometry-conditioned feature fusion. IndoorBEV summarizes the vertical point distribution in each BEV cell using statistical height features and multi-frequency height encoding, allowing informative three-dimensional cues to be processed efficiently by two-dimensional convolutions. A lightweight encoder then integrates complementary geometric features with multi-scale local representations and compact global scene context. Decoupled dense prediction heads jointly produce semantic BEV maps and oriented object bounding boxes. IndoorBEV contains only 0.6M parameters and requires 2.3 MB of model storage. On an NVIDIA AGX Orin, it uses 21.52 MB of GPU memory per inference and achieves a mean latency of 169.6 ms under a 200 ms perception deadline, with a deadline miss ratio of 1.8%. Evaluations on simulated scenes, real-world robot scans, and an open-source indoor point-cloud dataset demonstrate a favorable tradeoff among perception accuracy, latency, and memory consumption. These results indicate that explicitly encoding vertical geometry within a compact BEV representation provides an effective approach to resource-efficient indoor LiDAR perception.

AI agents that control wallets read attacker-reachable content, so they can be steered into proposing harmful transactions. The usual last line of defense is a pre-signing check: a static allowlist, an LLM reviewer, or a transaction simulation. All three share a gap: the check describes the chain state at check time, but the transaction executes in a later state that an adversary can shape through front-running, contract upgrades or token-parameter changes. We call this state drift. We present Proof-Gated Signing (PGS), which simulates a proposed transaction, extracts its effects, and uses an SMT solver to check a declarative value-and-permission policy for every price in an oracle-uncertainty band. It then compiles on-chain post-conditions (wallet balance bounds, payee receipts, allowance caps and ownership) and proves that every execution satisfying them also satisfies the policy. The agent's smart-contract wallet enforces them atomically, so the guarantee applies to the executed transaction under arbitrary drift. On an open testbed of 260 scenarios (14 attack families including five drift and two adaptive families, and 12 benign families), with harm measured from attacker balances rather than from any policy, PGS prevented 93.6% of the 140 harmful scenarios and passed 97.5% of the benign ones. Simulation-only checking prevented 57.9% and a static allowlist 71.4%. None of the 50 drift scenarios produced attacker gain under PGS. The only unprevented family, an in-policy drain, was bounded by the per-session budget. We also find that giving an LLM reviewer a clean pre-drift simulation made it more likely to approve a drift attack. Overhead is about 41k gas and 0.1-0.2 s per check.

A sound judgment applies the law to established facts and weighs the circumstances in which they arose. However, existing methods swing between rigid statute matching and ungrounded discretion, benchmarks score a label or a rubric, and the experience that would supply the balance stays unverified. We formalize legal judgment as a reference-anchored task, whose object is a single decision that stays tied to the statute and to the circumstances at once. We introduce JusticeAxis, 256 real-world criminal cases from 18 countries with audio, image, and text evidence, and three lawyer-written judgments for every case: the recorded one and one for each failure. We further propose JusticeAgent, a harness whose element agents establish the facts and whose judge agent applies the law under skills carrying experience of the circumstances. Skills are distilled from execution trajectories and admitted only under Bayesian credible bounds. Experiments show that failure turns direction with scale: open-weight backbones drift to unsupported grounds, frontier models to the statutory default. We further verify that JusticeAgent, as a simple yet effective plugin, carries a frozen open-weight backbone to commercial level. Project resources are available at https://github.com/beita6969/JusticeAxis.

How much precision must be allocated, and to which uncertainty channels, to meet a prediction requirement? We formulate a minimum one-shot specification cost over initial state variables and persistent forcing parameters. The central result is that prediction accuracy can select the horizon-scaling law of this resource by activating different physical uncertainty channels. Within any common uniformly scale-separable regime with the same active channels, changing a fixed tolerance changes the required precision by only $\cO(1)$ bits. An exactly solvable multiscale toral system shows that one fixed dynamics and target can nevertheless switch from $B_N(\eps_c)=\Th(\log N)$ to $B_N(\eps_f)=\Th(N)$ when finer accuracy activates an expanding channel. A forced Lorenz–84 calculation then realizes the same channel-switching mechanism numerically over finite horizons in a single two-scale diagnostic field: a sampled post-transient eddy envelope supports a coarse branch controlled by the phase rate of a large-scale forcing, whereas finer accuracy activates exponentially sensitive atmospheric degrees of freedom and produces an approximately linear increase of the linearized one-shot cost over the resolved window. Thus accuracy can determine not only how much predictive precision is required, but which physical channel controls its growth with horizon.

Recent James Webb Space Telescope (JWST) measurements quantify the fraction of ultraviolet-selected galaxies showing detectable Lyman-alpha (Ly-$\alpha$) lines at $z \sim 6-14$. These Ly-$\alpha$ fractions are partly shaped by Ly-$\alpha$ scattering from neutral hydrogen in the surrounding intergalactic medium (IGM), and so the observed Ly-$\alpha$ fraction evolution can inform our understanding of the reionization history and the size distribution of ionized bubbles during reionization. We compare the JWST measurements with Ly-$\alpha$ transmission calculations based on both the THESAN reionization simulations and a flexible semi-analytic model. In each case, we calibrate a sub-grid model for the intrinsic Ly-$\alpha$ emission lines emerging from the interstellar medium (ISM) and circumgalactic medium (CGM) of the host galaxies using empirical estimates of the Ly-$\alpha$ equivalent width (EW) distributions at $z \sim 6$. We find that the reionization history and bubble sizes in THESAN yield good agreement with current JWST Ly-$\alpha$ fraction observations, with a reduced $\chi^2_\nu = 0.4-1.2$. Our semi-analytic models and THESAN Ly-$\alpha$ transmission calculations agree well, allowing us to explore a wide range of reionization models. We derive $1\sigma$ bounds on the average mass-weighted neutral fractions of: $\langle x_{\mathrm{HI}} \rangle$ = $0.38^{+0.14}_{-0.38}$ ($0.52^{+0.09}_{-0.21}$), $0.57^{+0.23}_{-0.57}$ ($0.68^{+0.12}_{-0.39}$), and $0.93^{+0.05}_{-0.17}$ ($0.89^{+0.11}_{-0.15}$) at $z \sim$ 7, 8, and 11, based on the Ly-$\alpha$ fraction measurements with EW $>25\,\mathring{\rm A}$ ($>10\,\mathring{\rm A}$).

We present Multimodal Flow, a fully continuous generative model of language and vision. Most unified multimodal models either model both language and quantized images as discrete tokens or combine discrete language prediction with continuous image generation. The former introduces a visual quantization bottleneck. The latter requires modality-dependent objectives and sampling procedures. Fully continuous modeling avoids these trade-offs and enables a shared generative process, but remains underexplored for multimodal pretraining. Multimodal Flow introduces a unified continuous architecture that integrates multimodal continuous representations with a shared chunk-causal flow backbone. It organizes text blocks and images as ordered continuous hyperchunks, preserving textual token order and visual spatial structure. The backbone learns a single vector field over these hyperchunks through Flow Matching. Joint attention enables cross-modal interaction, while modality-specific feed-forward networks process each modality. The model predicts multiple target chunks in parallel during training and generates hyperchunks sequentially at inference. We instantiate MF-1 and pretrain it on multimodal data. Across 0.6B, 1.2B, and 1.6B scales, continued pretraining consistently improves multimodal modeling. With only 150B pretraining tokens, MF-1 achieves an average score of 82.8 across GenEval and DPG-Bench and 75.3 across VQAv2, MMBench, and POPE, remaining competitive with unified models trained on substantially more data. Under matched data, optimization, and parameter budgets, Multimodal Flow further outperforms representative hybrid and discrete models. These results establish continuous chunk-based embedding flow modeling as a new fully continuous paradigm for unified multimodal modeling. The related code and model are publicly released at https://github.com/hustvl/Multimodal-Flow.

Multimodal large language models (MLLMs) are rapidly advancing clinical diagnosis, yet their adaptation pipelines remain anchored to accuracy-based objectives. Clinical data are heavily class-imbalanced: a constant-majority predictor can score above 90% accuracy while being clinically useless. We therefore evaluate and optimize for AUROC, a threshold-free score that ranks positives above negatives and is invariant to class balance. We focus on prompt optimization in MLLMs. Reflective methods such as GEPA use a binary scores matrix with one row per evaluation instance and one column per candidate prompt; cells record per-instance correctness, so the column average is accuracy and drives candidate selection. We introduce pair-level Pareto prompt evolution (Ranking-PE), which replaces each correctness row with a pairwise-ordering row over (positive, negative) instance pairs: the cell is 1 if the candidate scores the positive higher than the paired negative. The column average then equals empirical AUROC (by the Wilcoxon-Mann-Whitney identity). We apply this swap at all three layers the prompt evolution search reads from - the scores matrix that decides Pareto dominance, the per-example feedback to the reflection LM, and final candidate selection - at no extra model calls and with no surrogate loss. Across three diseases on MIMIC, accuracy-based prompt evolution can degrade ranking; Ranking-PE reverses this, beating the accuracy-based recipe by +5.8 AUROC pp on fine-tuned Qwen3-VL-8B and +16.2 pp on MedGemma-4B. Ablations examine each design component and show that a medical-grade visual backbone - via vision-encoder-tuned SFT or medical pretraining - is a prerequisite that prompt search cannot replace - our recipe extends reflective prompt evolution from text-only data to multimodal clinical decision-making.

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning capabilities of large language models (LLMs), yet their predictions remain sensitive to task-irrelevant prompt features. We investigate this sensitivity through semifactual prompt interventions that preserve the underlying problem and its answer. Our analysis reveals substantial variation in token-level sensitivity and shows that suppressing high-drift token candidates during decoding improves reasoning accuracy without updating model weights. These findings highlight a limitation of Group Relative Policy Optimization (GRPO), which assigns the same outcome-derived advantage to every response token and may reinforce potential spurious dependence alongside useful reasoning. Motivated by this observation, we introduce Semifactual Credit-Augmented Policy Optimization (SCAPO), a causally inspired variant of GRPO that incorporates semifactual stability into token-level credit assignment. SCAPO measures token probability drift for fixed responses under semifactual interventions and uses normalized stability scores to reduce advantages for relatively unstable tokens during early training, while granting no additional credit for stability alone. On Qwen3-4B-Base and Qwen3-1.7B-Base, SCAPO improves AIME 2024-2026 accuracy over GRPO by 5.63 and 4.17 percentage points, respectively. At both model scales, SCAPO achieves the best results on most evaluated mathematics benchmarks and all evaluated out-of-distribution benchmarks among the compared methods. These results suggest that semifactual stability provides an effective training signal for improving reasoning and generalization through finer-grained credit assignment in RLVR. The code is available at https://github.com/DtYXs/SCAPO.

We find that major reported improvements in decoding words from non-invasive brain recordings are largely reproducible without any brain data. In the influential work of d'Ascoli et al. (2025), time series of brain activity from subjects perceiving continuous speech are segmented into fixed-length windows starting at each word. A neural network then generates predictions for all of the words in a sentence together. Neighbouring windows partially overlap, implicitly revealing the interval between words. Since these intervals indicate the duration of the words spoken, and different words tend to have different durations - for example, "the" is much shorter than "supercalifragilisticexpialidocious" - the neural network can improve its predictions of words without relying on the underlying brain activity. Consistent with this, the method reaches 22.0% balanced accuracy on synthetic signals containing no brain information, compared with 22.3% on real brain recordings. To prevent the network from learning this shortcut, we make a single, simple change. Instead of jointly encoding all windows in a sentence, we process each independently. As a result, the neural network achieves better performance by learning underlying word-specific information from brain recordings. This makes two existing strategies become much more effective than before. Both aggregating predictions from distinct neural responses to the same word and using a pretrained LLM as a linguistic prior now substantially improve results. On our perceived speech benchmark, this simple recipe (SimpleB2T) achieves a word error rate of 36.6% with five observations per word, approaching past invasive speech decoding performance, albeit under different conditions. The results in this work expose an important shortcut in brain-to-text decoding and show that removing it leads to a simple and considerably more effective strategy.

Video world models are expected to predict how the physical world evolves, yet they often produce visually plausible videos that violate basic physical principles. Existing approaches commonly assume that natural language is insufficient to represent the physical knowledge required for reliable generation, and therefore introduce additional visual, latent, numerical, or planning-based signals. We revisit this assumption and introduce Physis-Lang, a self-evolving framework that treats physical language as a shared and optimizable representation across data curation, model training, and video generation. Physis-Lang represents physical processes through language that describes their relevant entities, causes, interactions, governing principles, temporal evolution, and effects. To improve this representation, we construct PhysCapBench, which decomposes physical processes into atomic assertions and evaluates captions using recall and precision. An agentic loop iteratively analyzes assertion-level errors and refines the instruction used to produce physical captions. Physis-Lang further converts model deficiencies into textual descriptions and uses language-guided retrieval to identify visually diverse videos that cover missing physical processes. Experiments on four widely used physical video benchmarks with Wan and Cosmos backbones demonstrate consistent improvements in physical plausibility. Notably, starting from open-source Cosmos3-Nano backbones, our Physis-Lang-enhanced models surpass the leading proprietary Veo 3.1 model.

Let $\Gamma<\mathrm{Isom}(\mathbb H^n)$, $n\geq2$, be a cocompact lattice containing a convex cocompact codimension-one subgroup in the sense of Sageev. We prove that every finitely supported admissible random walk on $\Gamma$ has hitting measure singular with respect to Lebesgue measure on $\partial\mathbb H^n$. The proof extends the method of Kosenko–Tiozzo, replacing Fourier analysis for a cyclic subgroup by a von Neumann dimension argument that also applies to nonabelian subgroups. As corollaries, we prove the singularity conjecture of Kaimanovich and Le Prince for cocompact hyperbolic lattices admitting a proper cocompact cubulation, cocompact Kleinian groups, and cocompact hyperbolic lattices with totally geodesic sublattices of codimension one. In particular, our result covers all cocompact hyperbolic reflection groups, cocompact arithmetic lattices of simplest type and cocompact nonarithmetic lattices arising from the hybrid and inbreeding constructions.

Recent video generation is increasingly realistic and controllable, yet video editing remains less developed, particularly for precise local edits that must preserve the original scene dynamics. Video scene text editing replaces text on scene surfaces, such as storefront signs, whiteboards, and product labels, while preserving the surrounding content, motion, and camera dynamics. Although scene text editing is well studied for images, video scene text editing that achieves high visual quality, temporal consistency, and edit locality remains underexplored. Existing resources offer limited paired real-video data, and general video-editing metrics do not directly measure whether the requested text remains correct over time. We introduce ViTeX-Bench, a benchmark suite comprising ViTeX-Dataset and a three-axis evaluation protocol. The dataset contains 387 real-world 720p videos with text-region masks and editing instructions: 230 provide reviewed, pipeline-generated paired edits for training, and 157 form a frozen evaluation split. The protocol evaluates text correctness, visual and temporal quality, and edit locality through 13 metrics, with one primary metric per axis and a Pareto comparison of their trade-offs. OCR calibration, human evaluation, and annotation-sensitivity analyses support the interpretation of these scores. Across eight baselines from four editing families, accurate text, temporal stability, and scene preservation remain difficult to achieve together. We also release ViTeX-Edit-14B, an open-source reference editor fine-tuned on the paired training split with motion-aligned glyph-video conditioning. It achieves CharAcc 0.688, the highest mean among the evaluated video-native editors, and the lowest comparable text-crop Warp among raw editor outputs. ViTeX-Bench provides a reproducible foundation for studying these trade-offs in video scene text editing.

Given multiple uses of an unknown quantum channel, we determine whether it is a specified non-mixed-unitary channel or belongs to the set of mixed-unitary channels. Formulating this as a composite channel hypothesis testing problem, we characterize the Stein exponents achievable by parallel strategies under progressively weaker restrictions on probe states and auxiliary memory. In particular, we consider block-i.i.d. probes, which allow arbitrary correlations within blocks of fixed size while remaining i.i.d. across different blocks, and derive finite-letter expressions of the corresponding Stein exponents. Varying the block size, which interpolates between fully i.i.d. and arbitrary probes, together with further restrictions on intra-block correlations and access to auxiliary memory, results in a multifaceted hierarchy. We establish several strict separations within this hierarchy. Without auxiliary memory, we prove that fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, while blocks of three product probes suffice to obtain a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, although product probes seem to be insufficient for $O(3)$-covariant channels, an entangled probe achieves a strictly positive exponent for the qutrit Werner-Holevo channel, even though every maximally entangled probe fails. In contrast, access to auxiliary memory makes fully i.i.d. probes sufficient by yielding a strictly positive exponent for every non-mixed-unitary channel, even without requiring input-reference entanglement, and this exponent admits a lower bound determined by the diamond-norm distance from the mixed-unitary set. Moreover, for odd-dimensional Werner-Holevo channels, we find that this exponent is infinite, with every full-Schmidt-rank pure state being optimal.

Optical nonlinearities arise when the response of a photonic system depends on light intensity. Radiation pressure can create such a nonlinearity by moving a mechanically compliant reflector, thereby shifting the phase of the reflected light. Based on measured properties, we predict a giant phase responsivity of 263 rad W$^{-1}$ and a device-equivalent $n_{2,\mathrm{eff}} = 5.4 \times 10^{-7}$ m$^2$ W$^{-1}$ for a silicon nitride membrane trampoline with serpentine springs. We introduce strength-range-aperture metrics for reflective phase elements. Among reported mechanical resonators compared under a common direct-reflection protocol, this trampoline is an outlier, combining high compliance, practical optical accessibility, and 99.85% retention of its small-signal phase responsivity through a full $2\pi$ reflected-phase shift. Practical implementation requires optical and thermal co-design. Our framework indicates design priorities for future mechano-optical phase elements.

The task of 3D assembly requires translating an understanding of parts and their relationships into precise spatial arrangements. Can pretrained general-purpose agents assemble objects through visual interaction without additional assembly-specific fine-tuning? To investigate this question, we introduce AssemblyWorld, an interactive 3D environment in which agents inspect rendered views and manipulate supplied rigid parts, guided by images or assembly manuals when available. Agents perceive part geometry through 2D views rather than direct access to mesh vertices or faces, while their resulting assemblies are evaluated geometrically. Building on this environment, we construct AssemblyWorldBench, comprising 100 assembly tasks across 80 objects spanning furniture, industrial assembly, and fracture reassembly. Evaluating eight agent systems reveals substantial differences in their capabilities. The strongest system achieves 80.9% part accuracy but 59.4% complete-assembly success. The evaluated open-source systems lag substantially behind their stronger closed-source peers in both execution reliability and assembly accuracy. Analyses of visual references, interaction trajectories, and failures show how agents revise assemblies while leaving residual positioning errors. AssemblyWorld provides a common setting for both assessing the capabilities of interactive assembly agents and characterizing the gap between approximate structure recovery and precise reconstruction.

We derive the half-space KPZ equation as a continuum limit from a general class of Ginzburg-Landau SPDEs under weak nonlinearity scaling. To our knowledge, this is the first half-space universality result for the KPZ equation beyond integrable models (and their perturbations).

It is well-known that every $n$-qubit unitary can be implemented by a $2^{O(n)}$-depth quantum circuit using single- and two-qubit gates. It has been open whether exponential depth is *necessary* for general unitaries, even when allowing an unlimited number of ancilla qubits. Here we show, perhaps surprisingly, that all unitaries can be implemented exactly by a circuit of one- and two-qubit gates of depth $\mathsf{poly}(n)$ with $2^{O(n)}$ ancilla qubits. In other words, every $n$-qubit unitary can be parallelized to polynomial depth. In fact, our depth bound is *linear* in $n$, which is the best possible, and an exponential improvement on the previous best bound of $2^{n/2}$ due to Rosenthal [TQC 2022, Quantum 2026]. Moreover, if we allow unbounded fan-out gates, these circuits can be further reduced to *constant* depth. Our construction takes advantage of a novel relationship connecting the unitary synthesis problem of Aaronson and Kuperberg to locally-decodable codes and private information retrieval from complexity theory and cryptography, and has a natural interpretation in bosonic quantum computation.

Pseudorandom permutations are ubiquitous in theoretical and applied cryptography. PRPs that offer security even against adversaries making quantum queries are of increasing interest, and used in applications ranging from constructing pseudorandom unitaries to separating SZK from BQP. A successful framework for constructing classically-secure PRPs is the key-alternating Even-Mansour approach, which interleaves applications of public permutations with additions of round keys. The single-round construction is already classically secure in the ideal permutation model (IPM), with added rounds offering improved concrete security. However, in the quantum-query setting, the status of this framework is presently unclear. A simple quantum-query attack based on Simon's algorithm breaks the one-round cipher. For two or more rounds, security is only known against non-adaptive adversaries who must prepare all queries in advance. In this work, we show that the two-round Even-Mansour cipher is information theoretically secure in the IPM against adversaries making polynomially-many adaptive forward and inverse quantum queries to all available oracles. Our proof uses compressed permutation oracles and a specially crafted isometry relating the ideal and real experiments. We also show that this construction is minimal, in the sense that essentially any cipher constructed via a single call to a public permutation is quantumly insecure.

A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form $G_{AB}(t-t') = \left<A(t)B(t')\right>$, where $t'$ represents the impact time and $t$ represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point $t-t'$ is calculated by a different quantum circuit, leading to at least $O(N_t)$ total shots, and at least $O(N_t^2)$ total quantum gates. Here, we provide a different approach: utilizing $O(\log N_t)$ ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only $O(\log N_t)$ times, which in total requires $O(N_t \log N_t)$ quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.