Papers

Marine litter is a growing threat to the underwater ecosystem, driving demand for autonomous survey methods that can locate debris efficiently over large areas. Existing survey methods typically follow predefined paths or operate with a single sensing modality, typically a camera (with image quality suffering in poor-visibility conditions) or sonar (usually noisy and low-resolution). We present an active mapping framework in which a forward-looking sonar and a camera both feed into a shared Bayesian occupancy map, and an optimization problem is solved at each step to decide on the next best view. Candidate viewpoints are scored by a two-term utility that balances exploration of uncertain regions via voxel entropy against exploitation of likely objects. Each sensor is characterized by range- and bearing-dependent detection and false-alarm probability tables determined from data. We evaluate the approach in a realistic underwater simulator, demonstrating that active mapping finds objects faster than a lawnmower coverage pattern, and that the dual-sensor approach works better than using either of the individual sensors.

We compute the first-order incoherent backscattering cross-section of a rough surface over a half-space with randomly fluctuating permittivity, when the two random fields are correlated, so that surface and volume scattering are not additive. A non-orthogonal coordinate transformation flattens the rough boundary and turns the geometric roughness into volume sources of the same Helmholtz equation as the dielectric fluctuations, propagated by the same Green's function: both mechanisms and their interference follow from one calculation, with no equivalent surface currents and no prescription for the field discontinuity. The geometric part of the amplitude reproduces the small-perturbation kernel exactly, for any incidence angle, permittivity and profile function. The interference term is obtained for both co-polarized channels, with an explicit surface-dielectric correlation coefficient. The departure from additivity reaches twenty percent at full correlation, changes sign with that coefficient, and is governed by a balance condition and a coherence condition on the depth of the correlated layer. It carries no angular signature and shifts the co-polarized ratio by less than a tenth of a decibel, so an additive inversion absorbs it, biasing the retrieved amplitude of the dielectric fluctuations by tens of percent.

Let $B$ and $D$ be both algebras and coalgebras in a braided monoidal category $\mathcal{C}$. In the literature, there are equivalent conditions for $(B,D)$ to form a generalized smash biproduct (or cross product) denoted by $B\times D$, which were mainly given by Bespalov and Drabant in 1999 as well as by Bulacu, Caenepeel and Torrecillas in 2013. This paper is devoted to constructing another biproduct $D\times B^\ast$ when $B$ has a left dual object $B^\ast$ in $\mathcal{C}$. As results, we show that $B\times D$ is left smash over $D\times B^\ast$, and establish a specific isomorphism ${}_{B\times D}\mathfrak{YD}(\mathcal{C})^{B\times D}\cong{}_{D\times B^\ast}\mathfrak{YD}(\mathcal{C})^{D\times B^\ast}$ between the categories of the (left-right) Yetter-Drinfeld modules in $\mathcal{C}$. The constructions and results are provided in three levels: (1) $B\times D$ is an algebra and a coalgebra; (2) $B\times D$ is a bialgebra; (3) $B\times D$ is a Hopf algebra.

How much unknown process noise can a bounded experiment tolerate while still establishing that the plant can be stabilized? We answer this question for scalar discrete-time systems with bounded inputs, exact state measurements, and a disturbance-energy budget proportional to the experiment length. We distinguish individual stabilizability of every consistent model, stabilization by one common gain, and a common quadratic certificate. We determine their exact noise ceilings for every drift. The last two requirements coincide; individual stabilizability generally tolerates more noise. Bounded periodic inputs approach the ceilings, while adversarial disturbances prevent their attainment. We also determine the long-horizon limits. For unstable plants, a short experiment can establish individual stabilizability at noise levels where every sufficiently long experiment fails. The same obstruction yields upper bounds for multidimensional systems with real eigenvalues. Input design may use plant knowledge, but certification uses only the recorded data and noise bound. The results therefore provide fundamental robustness benchmarks for unknown-plant designs.

Different from natural videos, Screen Content Videos (SCVs) are characterized by abrupt motion, scene switches, and high-frequency details such as text and graphics. Conventional video enhancement methods, which rely heavily on temporal continuity, often suffer from performance degradation when processing SCVs due to the disruption of temporal correlations. To address these challenges, we propose the Spatial-Temporal Multi-scale Network (STM-Net), a novel framework specifically tailored for compressed SCV enhancement. Our approach integrates three complementary components: a Prior-Guided Spatio-Temporal Dispatcher (PG-STD) that routes input into three parallel streams to avoid feature contamination, a Bidirectional Temporal Feature Extraction (BTFE) module that adaptively handles abrupt transitions without explicit detection, and a Cascaded Multi-scale Feature Distillation (CMFD) module that preserves critical high-frequency details. Experimental results demonstrate that STM-Net outperforms state-of-the-art methods in both objective metrics and subjective visual quality, providing a robust solution for screen content artifacts. Code is available at https://github.com/HUANGZiyin1/STM-Net.

We derive a closed expression for the $1/c_{M}$ correction to highest-weight BMS$_3$ blocks with four light external primaries of generic weights and non-vacuum exchange. With $c_L$ and all operator weights held fixed, we prove that the global sector and descendants containing exactly one non-global generator $L_{-n}$ or $M_{-n}$ with $n\geq2$ suffice through this order. This truncation reduces the intrinsic calculation to global blocks and their derivatives, whose contributions we resum for nonzero exchanged boost weight $\xi_{p}$. For pairwise identical external operators, we independently reproduce the correction through the introduction of boundary gravitons in the normalized three-point functions in the shadow representation, while keeping the exchanged two-point function fixed. The analogous prescription also reproduces the known non-vacuum Virasoro correction at order $1/c$. For the same external configuration, a formal ultra-relativistic contraction of Virasoro blocks with one flipped chiral representation provides a further check: it yields the same correction, and we prove that contraction commutes with extraction of the $1/c_{M}$ coefficient at each fixed descendant level. The degenerate exchange with $\xi_{p}=0$ requires a separate quotient construction and is not obtained as a smooth limit of the generic block, which we discuss in the appendix.

Looped Transformers repeatedly apply the same set of Transformer layers, giving them a recurrent architecture for latent computation. Their strong performance on iterative reasoning and length-generalization tasks suggests an appealing explanation: recurrence may provide an inductive bias that lets the model reuse a learned algorithm across loops. However, weight sharing alone does not imply that every loop performs the same operation. This raises a basic question: is each loop actually repeating the same computation, and if not, what routes the shared parameters to different operations? We study this question using graph walks as a test case. In the model's native trajectories, decoded predictions can advance by different numbers of graph steps or remain at a reached target, showing that recurrent progress need not follow a fixed one-loop-one-step pattern. We then show that a frozen loop can be steered toward different transitions by modifying its entering hidden state: a learned linear layer $J$ selects the desired transition without changing the shared Transformer layers. To test how this steering works, we use activation patching and find that attention patterns can recover its effects and switch the selected transition. Across five matched pairs of graph models, changing intermediate supervision during backbone training changes which transitions $J$ can induce. This suggests that $J$ selects computations learned by the backbone rather than creating new algorithms. Together, these results show that the hidden state can control shared computation, with attention routing as a causal pathway.

We consider a strongly dispersive Boussinesq-type system arising as a model for the propagation of weakly nonlinear water waves. The system is characterized by a nonlinearity parameter $0<\epsilon\le 1$ and a shallow water parameter $0<\mu\le 1$. In the Boussinesq regime $\mu \sim \epsilon$, Saut, Wang and Xu \cite{SWX2017} used a hyperbolic approach to prove the well-posedness of the system on a time scale of order $1/\epsilon$, in both one and two dimensions, under a non-cavitation condition. In this paper, we establish well-posedness on a time scale of order $ ( \mu^{ 1/4} \epsilon^{-1} h_0 )^{4/3}$ in one dimension and of order $(\mu^{ 1/4}\epsilon^{-1} h_0)^{2-}$ in two dimensions, assuming a non-cavitation condition with a parameter $h_0>0$. Our results show quantitatively how the lifespan depends on the balance between nonlinearity and dispersion in the regimes $\epsilon\lesssim \mu$ and $\mu\ll\epsilon$. They also make explicit how the existence time deteriorates as $h_0\to0$, that is, as the wave approaches cavitation. Our proofs combine dispersive and Strichartz estimates with energy estimates.

Routing unknown quantum information across distributed communication networks requires autonomous, measurement-free mechanisms to prevent wave-function collapse. Szegedy quantum walks provide a mechanism for spatial state transport. The conventional walks on unweighted graphs suffer from severe back-reflection, spatial dispersion, and channel crosstalk. In this paper, we introduce a deterministic topological quantum routing architecture based on coined Szegedy quantum walks on edge-duplicated signed graphs. By treating edge signs as localized phase shifts within a balanced coin reflection, we enforce an exact zero back-scattering condition across routing nodes. We demonstrate deterministic Perfect State Transfer (PST) with unit fidelity at exact arrival times across fundamental archetypes, including the signed dumbbell switch $D_{2m,0,2n}$ and scalable glued binary trees. Furthermore, we analyse routing performance under realistic open-system amplitude and phase damping noise channels.

Sokoban, a puzzle game in which an agent pushes boxes onto unlabelled target locations in a grid world, is a long-standing benchmark planning problem. While it is easy to see the connection to practical applications such as warehouse logistics with autonomous forklifts, its multi-agent counterpart has remained underdeveloped. This is because Multi-Agent Sokoban is substantially more difficult due to factors specific to multi-agent planning, such as the rapidly growing branching factor as the number of agents grows and the need to handle integrated task assignment and collision-free pathfinding. In this paper, we show that a scalable planner for Multi-Agent Sokoban can be designed by leveraging recent advances in multi-agent pathfinding (MAPF). Specifically, our Sokoban-LaCAM efficiently solves instances involving tens of agents and boxes while preserving both completeness and eventual optimality guarantees. This provides evidence that MAPF can serve as a powerful primitive for solving broader collective automation problems.

Neural trajectory predictors can reach low prediction error while violating dynamics, actuator limits, or state constraints, especially when controls are unobserved and dynamics are partially specified. We introduce the Markovian Dynamics Enforcer (MaDE), a time-invariant post-hoc operator mapping state-transition proposals onto a learned feasible dynamics manifold, trained on feasible states without ground-truth controls. For each transition it infers a control and recomputes the state through a completion model of known physics plus a learned residual. It then corrects that control by gradient-based inequality reduction, so inequality satisfaction is best-effort within an iteration budget. Since every correction iterate re-enters the completion model, the returned state is dynamically consistent by construction relative to that model and the supplied previous-state anchor. MaDE drives dynamics residuals to essentially zero on fully specified simulated systems, and on an underspecified system leaves a smaller true-dynamics residual than the baselines. Designed to attach to arbitrary predictors, the frozen operator is evaluated downstream of recurrent, structured state-space, and transformer predictors. On recorded vehicle trajectories the one-step residual against a kinematic bicycle model is 0.0071 to 0.0072 for MaDE and 0.1703 to 0.1714 for raw predictors. MaDE raises average displacement error by a factor of 1.57 to 1.83.

Prophet Inequalities for online auctions, as many classical auction settings, traditionally consider agents who strive to maximize quasi-linear utility, i.e. their obtained value minus the price paid. This simplified view of the agents' objectives does not capture real-world settings where agents are almost always constrained by budgets, and can have different objectives altogether (e.g., very prominently, value maximizers in autobidding). We generalize classic prophet inequality auction settings to accommodate unknown, varying types of agent objectives and budgets, modeling them as stochastic input similar to the traditional valuation distributions. In this new model, we analyze (anonymous) posted-price mechanisms, one main category of which are the balanced prices central to many auction results in the prophet inequality model. We demonstrate both the resilience and limits of balanced price mechanisms for generalized prophet inequalities with stochastic agent objectives, budgets and valuations: our generalization of the balanced prices framework incorporates budget constraints and mixed objectives. We show constant competitive ratios for some the most central settings, spanning all the way up to agents with subadditive valuation functions. On the way, we establish trade-offs between competitive ratio and agents' price-sensitivity, and give a general reduction from the budgeted setting to budget-free value maximizers.

We investigate the chiral separation effect (CSE) and the axial-partner susceptibility splittings within the three-flavor Nambu–Jona-Lasinio (NJL) model, providing two complementary aspects of axial dynamics in hot and dense magnetized matter. We compare a field-dependent scalar coupling, which leads to inverse magnetic catalysis (IMC), with a constant coupling, which exhibits magnetic catalysis (MC). In the weak-field limit, the CSE conductivity is suppressed at low temperature and approaches its chiral-limit value as the temperature increases. Its magnetic-field dependence is reversed between the IMC and MC scenarios. On the other hand, the susceptibility splittings $\Delta_A = \chi_{\pi^0} - \chi_{\delta^0}$ and $\Delta\chi = \chi_{\pi^0} -\chi_{\sigma_l}$ are suppressed at high temperature or density, reflecting the substantial restoration of axial symmetries. Their difference develops a pronounced peak near the cross-over or first-order transition, implying that the $U(1)_A^{(0)}$ and $U(1)_A^{(3)}$ symmetries are restored at different temperatures or chemical potentials. Both the weak-field CSE and the IMC susceptibility splittings at vanishing chemical potential agree qualitatively with lattice-QCD calculations. We also provide model predictions for the susceptibility splittings at finite density.

The efficacy of advanced cycling helmet technologies under youth-specific impact conditions remains unclear. We evaluated how helmet technologies affect head kinematics and concussion risk and whether helmet deformation and helmet-headform relative rotation contribute to protection. Six youth bicycle helmet technologies were tested, including two conventional EPS controls (FOAM-A, FOAM-B) and four advanced technologies (CELL, SLIP, SLIDE, HYDRAULIC). Helmeted headforms were impacted at three locations using a 25 degree anvil at 2.9 m/s, and a 45 degree anvil at 5.2 m/s. Peak linear acceleration (PLA), peak rotational acceleration (PRA), and YGAMBIT-predicted concussion risk were quantified. Stereo high-speed videography measured anvil-normal headform displacement to approximate helmet deformation, and helmet-headform relative rotation. Helmet technology significantly affected predicted concussion risk under both conditions. At 2.9 m/s, all advanced technologies reduced risk relative to FOAM-A, while only SLIDE and HYDRAULIC reduced risk relative to FOAM-B. At 5.2 m/s, all advanced technologies reduced risk relative to both foam controls. HYDRAULIC produced the lowest risk in both conditions, reducing mean risk by 94-95% and 77-78% relative to the foam controls at 2.9 and 5.2 m/s, respectively. CELL, SLIP, and SLIDE significantly reduced PRA across both conditions, whereas HYDRAULIC significantly reduced both PLA and PRA. Greater anvil-normal headform displacement was associated with lower PLA, and greater relative rotation with lower PRA; both independently contributed to lower predicted concussion risk. Advanced technologies in youth cycling helmets can reduce youth concussion risk, but effectiveness depends on impact condition and mitigation mechanism. Designs maximizing controlled helmet deformation and rotational decoupling may provide robust protection in youth-relevant impacts.

Role prompting elicits specialized behavior from large language models through an expert identity, offering a lightweight way to guide reasoning on demanding tasks. However, evaluating or distilling complete role-prompted answers can miss useful next-token preferences when the sampled solution remains incorrect. Transferring these preferences also requires an objective that reaches alternatives the student rarely predicts. We introduce OPSRD, which uses a fixed expert role as privileged teaching context for on-policy self-distillation without reference solutions. A role-free student generates a trajectory, and a frozen instance of the same base model supplies role-conditioned distributions on its exact prefixes, exposing alternatives beyond the sampled continuation. Teacher-weighted forward KL targets alternatives the student underestimates, with clipping to limit individual vocabulary contributions. Supervision is restricted to the highest-entropy half of student positions, concentrating learning where predictions are uncertain. Experiments on three competition-math benchmarks with Qwen3-1.7B, 4B, and 8B show improvements over the base models without role prompts at inference. Forward KL achieves the highest macro-averaged accuracy among the three evaluated divergences at every scale. Code is available at https://github.com/zhansan114514/OPSRD.

Video temporal grounding supports applications such as video search, content review, and automated editing by localizing events described in natural language. Yet existing generative models typically output timestamps without explicit interval-level confidence scores to guide candidate selection. We separate candidate generation from acceptance by scoring individual intervals within the original decoding pass. A lightweight confidence head reads pooled decoder states, providing an explicit score trained for interval selection. Offline verifier scores supervise the head on fixed candidate sequences, and temporal-overlap labels adapt it to current rollouts during reinforcement learning. GT-anchored candidate-pool supervision and set-level optimization train the generator. The resulting scores support ranking, threshold-based selection, and rejection without invoking an external verifier at inference. On a fixed OMTG-Bench candidate pool, confidence raises query-macro Recall@0.5 from 9.95% to 14.42% over generation order at a 10% global return budget, and from 26.48% to 31.12% at a 25% budget. The continuous scores let downstream applications adjust return budgets or acceptance thresholds to match their precision-recall preferences, without regenerating candidate intervals. Code is available at https://github.com/Alibaba-VELLDEPTH/Grounding-with-Confidence.

Pre-training equips large language models (LLMs) with a broad repertoire of behavioral patterns associated with roles, styles, values, and goals. Post-training teaches conditional enactment and makes a helpful Assistant the default, but it does not erase alternative modes from the weights; explicit prompts can therefore elicit personas that repeatedly shape judgment, language, and action. In open-weight settings, runtime controls can be removed, motivating persona unlearning: a weight-level edit that makes a designated persona difficult to elicit and enact on unseen contexts. We introduce PersonaUnlearnBench, a model-specific paired benchmark spanning six LLMs from three families and five personas, with aligned forget/retain sets, held-out instruction paraphrases, and four-axis evaluation. The benchmark shows that standard unlearning methods cannot reliably erase the target persona without sacrificing meaningful generation or general utility. We therefore propose PaCE, which compares target and desirable responses to the same questions to locate an internal behavior direction, then trains target-prompt states away from the target mode and toward the matched desirable response. Experiments show that PaCE consistently suppresses target personas with high response quality and useful counterpart behavior, at moderate utility cost. These results establish persona unlearning as a distinct behavior-level editing problem and a practical route toward persistent control of latent LLM response policies.

Radiative proton capture on ${}^{12}\mathrm{C}$ to the ground state of ${}^{13}\mathrm{N}$ is calculated in cluster effective field theory through next-to-leading order. At low energy the reaction is dominated by $s_{1/2}\to p_{1/2}$ $E1$ capture, which we treat in the long-wavelength limit. Its amplitude is strongly hindered by destructive interference between the contribution fixed by gauge invariance and a counter-term $E1$ current, making the capture particularly sensitive to subleading terms. We fit the recent data below $0.95$~MeV, determining the $E1$ transition counter-term coefficients together with the ground-state asymptotic normalization coefficient and the $\frac{1}{2}^+$ resonance and shape parameters. We obtain $S(0)=1.34\pm0.07$~keV\,b and $S(25~\mathrm{keV})=1.43\pm0.07$~keV\,b, the latter in agreement with recent $R$-matrix extrapolations. We also estimate the effects of the omitted $p$-wave $M1$ capture and $\frac{3}{2}^-$ resonance tail, and find that the fitted asymptotic normalization coefficient moves substantially while the $S$ factors remain almost unchanged.

Passwords remain the dominant online authentication mechanism, and understanding how humans choose them is essential for defensive strength estimation and attack simulation alike. Recent learning-based approaches such as PassGAN and PassGPT have shown that deep generative models can learn password structure directly from leaked corpora. However, both train from random initialization on password data alone. The role of linguistic prior knowledge in password modeling, and what it reveals about how humans create secrets, remains largely underexplored. Here, we address this gap with PassGPT+, which adapts the linguistic prior of GPT-2 to password observations through character-aware tokenization. We also introduce PassDiffusion, the first absorbing-state discrete diffusion model for password generation, as a probe of whether non-autoregressive approaches are competitive. On the RockYou benchmark, PassGPT+ recovers 22.53% of held-out passwords at 108 guesses, a 16% relative gain over PassGPT, and retains 79% of this match rate when transferred without retraining to a disjoint 2020 leak dataset, demonstrating that linguistic priors capture persistent regularities of human password generation. PassDiffusion underperforms by two to three orders of magnitude, indicating that autoregressive modeling is substantially better matched than iterative denoising to the discrete, exact-match nature of password generation.

We introduce a classification of quantum phases of mixed states based on the ability to preserve and fault tolerantly transfer information. We formulate phase equivalence between sets of states that encode logical quantum information and are connected by shallow local channel circuits assisted by local measurements and global classical communication of measurement outcomes, where all quantum operations, including measurements, must be robust to noise. We show that the existence of a recovery threshold for local noise is a property of an entire phase. We prove that any two sets of states with nonzero thresholds that are related by finite-depth local channel circuits belong to the same fault tolerant phase. Our approach leads to a classification of subsystem codes without favoring any state of the gauge subsystem, and we demonstrate phase equivalence between 2D and 3D color codes using dimensional jumps within the 3D gauge color code. Lastly, we study how syndrome structure affects fault tolerance in circuits with measurements. We show that qudit stabilizer codes with extended syndromes permit single-shot state preparation, whereas a broad class of shallow circuits measuring point-like syndromes, including state preparation for 2D topological codes and non-Abelian topological orders with solvable anyon theories, is not fault tolerant.

Two-dimensional materials are promising candidates for electronic applications beyond the operating limits of conventional semiconductor technologies. Within this class, transition-metal dichalcogenides offer attractive properties for field-effect transistor operation, with tungsten disulphide (WS$_2$) emerging as a particularly promising material for operation at cryogenic temperatures. Here, we investigate the electrical performance of a back-gated multilayer WS$_2$ transistor at deep cryogenic temperature, down to 20 mK. The device remains strongly gate-tunable throughout the cryogenic regime, with an effective on/off current ratio exceeding $10^{5}$. Most notably, the low-temperature turn-on characteristics exhibit reproducible shoulder-like features, which we describe using a phenomenological model comprising multiple effective conduction branches operating in parallel.

Algorithmic recourse provides individuals who have received undesirable outcomes from machine learning models with suggestions for minimum-cost improvements to achieve the desired outcome. A central assumption when computing recourse is that the decision rule remains fixed throughout the recourse implementation phase. We challenge this assumption in settings where individuals compete for limited resources. In such settings, widespread recourse implementation can change the acceptance threshold even when the scoring model that is used to evaluate individuals remains the same. This change in acceptance threshold can, in turn, invalidate the original recourse recommendations (i.e., following the recourse may not lead to the desired outcome). To address this problem, we introduce a framework called recourse under competition that jointly optimizes for recommendation recipients and the recommended score target they need to satisfy to balance the recourse cost and post-shift validity among initially rejected individuals. We develop an algorithm based on the Implicit Function Theorem and empirically analyze its performance. Experiments on synthetic and real datasets show that personalized score targets can achieve higher validity, albeit at a higher cost. In contrast, common score targets generally offer favorable cost-validity trade-offs for lower to medium validity values.

Let $q$ be an odd prime power and $m\geq 1$. Let $Q$ be a nondegenerate quadratic form on $\mathbb F_q^{2m}$. For every sphere $S_j=\{Q=j\}$ with $j\in \mathbb F_q^\times$, we prove the sharp extension estimate $R_{S_j}^*(2\to r)\lesssim_m1$ for $r\ge 2(m+1)/m$, uniformly in $q$, $Q$, and $j$. As an application, we show that if $E\subseteq\mathbb F_q^{2m}$ satisfies $|E|/q^{m+1/3}\to\infty$, then almost every pin $y\in E$ determines $(1-o(1))q$ values of $Q(x-y)$. The proof combines two arithmetic Hecke operator estimates with an induction in the dimension, a centered sphere–cone estimate, and an orthogonal decomposition.

In this paper, we determine the set of Euler classes of all taut foliations for a family of closed graph manifolds. As a consequence, for any closed aspherical graph manifold $Y$, every integral class in the closed dual Thurston unit ball can be virtually realized as the Euler class of some taut foliation. In particular, $Y$ virtually admits a taut foliation with vanishing Euler class. We present examples of graph manifolds with arbitrarily large first Betti number, which admit no taut foliations with vanishing real Euler classes. This shows that the virtual requirement is necessary. We also provide examples of graph manifolds with arbitrarily large first Betti number, for which every taut foliation has vanishing real Euler class, but none has vanishing integral Euler class. This illustrates the subtle difference between real Euler class zero and integral Euler class zero.

Reconfigurable atom arrays provide a promising platform for high-rate quantum low-density parity-check codes, but their computational advantage depends on whether logical operations can be implemented without incurring prohibitive shuttling and space overheads. We introduce algebraic surgery for lifted product codes, co-designing the logical measurements, auxiliary codes, and atom shuttling to enable hardware-efficient Pauli-product measurements. These protocols provide flexible logical addressability subject to the cyclic-symmetry constraint, enabling a broad class of parallel logical measurements, including canonical logical operators with heavily overlapping physical supports and joint measurements within or between code blocks even with different lift sizes, while achieving constant shuttling depth on neutral-atom processors under explicit layout assumptions. In a representative hardware-model benchmark, a cycle supporting 33 parallel canonical logical measurements is about $2\times$ faster than the compared single-observable graph-based surgery schedules, with competitive qubit overhead. These shuttling and circuit-level simulations confirm that the algebraic structure of quantum low-density parity-check codes can be used not only to reduce space overhead, but also to simplify physical implementation and expand the set of efficiently accessible logical operations on neutral-atom processors.

World action models (WAMs) are large embodied policies that jointly predict future video and the actions to execute, emitting a fixed-length action chunk per inference call. Such a policy allocates its computational budget uniformly in time, unable to execute for longer over free-space motion or to spend more inference on contact-rich manipulation, which limits the throughput a WAM can reach when served in the cloud. We present SplineWAM, which adaptively compresses the action trajectory into a fixed-size window of cubic B-spline parameters, fitting the knot times to the characteristics of the motion. One parameter budget then decodes into chunks of varying temporal resolution and duration, and both the executed span and the interval until the next policy call follow from the prediction itself. Aligning the video supervision to the fitted knot times of the demonstration rather than to a uniform grid concentrates the supervised frames where the action trajectory is complex. For asynchronous deployment we introduce Jacobian-Pullback Real-Time Chunking (JP-RTC), which imposes chunk continuity on the decoded raw actions the robot executes rather than on the spline parameters, and corrects the parameters through the decoder so that the executed prefix agrees with the actions already committed. On LIBERO-Plus and RoboCasa, SplineWAM improves success rate over an action chunking WAM by $8.2$ and $4.4$ points while cutting policy calls per episode by 22% and 26%. On three bimanual real-robot tasks under asynchronous execution, it leads or matches the baseline while decoding 1.2 to 1.6 times as much executed motion per call.

We consider the 653 equational laws of order up to 4 for an associative binary operation, and all of their conjunctions. We determine that there are only 456 equivalence classes of such conjunctions (associative equational theories), and find all implications between them. The conjunction operation makes this set of theories into a semi-lattice. These results are formalized in Lean. This is a semigroup analogue of the Equational Theories Project, but extended to conjunctions of equations.

Hyperspectral remote sensing has advanced across diverse deep learning paradigms, including spectral spatial CNNs, Vision Transformers, Mamba, graph neural networks, Kolmogorov Arnold networks, and self supervised masked autoencoding. Yet progress remains hindered by fragmented repositories, incompatible tensor conventions, and non standardized evaluation. Hyperspectral Image Models addresses these challenges through a modular framework unifying 55 representative models across six paradigms with a common registry, automatic 4D/5D tensor adaptation, and standardized constructors. It integrates 24 benchmark scenes from Airborne, Spaceborne, UAV, and Mars CRISM sensors, with caching, label remapping, PCA, explicit band selection or raw spectra, optional spatial max pooling, and arbitrary PxP patch extraction. To prevent inflated accuracy from overlapping windows, it supports class balanced random partitioning and spatially disjoint regional blocking with Chebyshev guard bands that eliminate train test pixel overlap. Experiments use a single config with deterministic seeds and complete provenance, generating LaTeX benchmark tables and classification maps. Across 1,320 model scene evaluations and 6,600 seeded runs, scene difficulty dominates architecture, with mean accuracy ranging from 96.40% on Botswana to 56.70% on Houston 2018, versus a 15 point spread across paradigm means. No paradigm universally dominates, while sub 1 M parameter models can match architectures two orders of magnitude larger. Code is publicly available at https://github.com/Tanishq251/Hyperspectral-Image-Models.

World-action models (WAMs) augment robot policies with action-conditioned environment dynamics, yet existing approaches largely rely on future observation reconstruction or generic latent prediction and lack structured, control-oriented world representations tightly coupled with action generation. We introduce Magic-W0, a world-action foundation model that jointly models structured physical state evolution and continuous actions. Magic-W0 represents interaction as a Structured World Transition consisting of Current State, Transition, and Future State. Current State combines vision-language context with Current 3D Geometry; Transition is represented by 3D Motion capturing action-induced three-dimensional changes; and Future State is represented by Future Semantics describing task-relevant outcomes. To couple prediction and control, we propose a layer-aligned world-action interaction architecture in which evolving action hypotheses condition world-transition prediction, while predicted world representations continuously inform action generation. Magic-W0 is pre-trained on large-scale egocentric human manipulation, UMI, real-robot, and simulation data, with latent supervision for geometry, 3D motion, and future semantics from pre-trained visual models. Inference-time interventions show that structured world representations respond systematically to changes in candidate actions and that action-related information propagates through shared 3D representations into future semantic predictions. On RoboDojo-Sim, Magic-W0 achieves an average Score of 27.10, the highest among the compared WAMs. Across multiple real-robot tasks, it also demonstrates strong downstream performance after fine-tuning with limited downstream data, supporting generalization and rapid adaptation.

Grammar-constrained generation guarantees syntactic validity, but can substantially degrade semantic quality when the model's preferred outputs are poorly aligned with the imposed grammar. This trade-off is particularly severe when the prompt is underspecified or the model has limited instruction-following ability. Beam search can partially mitigate these failures by exploring multiple valid sequences, but its computational cost grows with beam width, while sequence-level probability is only an imperfect proxy for semantic quality. We introduce GrammarRL, a label-free reinforcement learning method that adapts language models to grammar constraints without requiring annotated data. GrammarRL optimizes the model using two complementary self-supervised rewards derived from its own likelihoods: a direct reward, measuring how likely the constrained output is given the input, and a reverse reward, measuring how well the input can be reconstructed from the generated output. We optimize these rewards with a Reinforce Leave-One-Out (RLOO) objective over groups of grammar-constrained rollouts, augmented with the top-1 beam-search hypothesis and regularized towards a frozen base model. We evaluate GrammarRL on sign language gloss translation, hierarchical text classification, and named entity recognition using Llama models ranging from 1B to 8B parameters. GrammarRL consistently outperforms constrained greedy decoding, with an average improvement of 9.8 points and gains of up to 22.8 BLEU. It matches or outperforms beam search on two of the three tasks while preserving greedy-decoding inference cost. Ablations further show that the two rewards are complementary: either reward alone can underperform the untrained baseline, whereas their combination consistently improves upon it.