Papers

Ship structural vibrations contribute to noise, fatigue, and equipment damage, while dynamic-compliance topology optimization can produce pathological designs near resonance. This study extends neural-reparameterized topology optimization using a convolutional Kolmogorov-Arnold network (KATO) to forced-vibration design with active input power (AIP) as the objective. Applications include a 100 Hz engine-supporting deck panel and an 18 Hz thruster foundation frame. Helmholtz PDE filtering and Heaviside projection control feature sizes and manufacturing tolerance. Across both deck families, all eight optimized layouts reduce AIP relative to size-optimized references and, after finite-depth extrusion, also achieve lower static compliance. For unrestricted, manufacturing-aware, and stress-aware frame variants, KATO matches GCMMA in AIP within 0.5 dB while yielding 22-36x lower static compliance after matched-volume binary re-analysis. In a near-resonant 300 Hz case, both methods reduce initial AIP by more than 32 dB; KATO maintains a connected design, achieves 59x lower binary static compliance, and reduces maximum AIP over 1-500 Hz by 2.7 dB. KATO runs 6.4-10.4x faster than GCMMA for the implemented stress-aware formulations. The results demonstrate neural AIP-driven topology optimization as an efficient approach for designing connected, feature-size-controlled ship structures with improved forced-vibration performance.

An emergent gauge field can control boundary critical behavior without changing the bulk quantum spin liquid. We investigate the boundary criticality in $(2+1)$-dimensional $U(1)$ Dirac spin liquid, whose low-energy physics is described by massless quantum electrodynamics. Using a perturbative renormalization-group analysis in a half-space, we show that Neumann and Dirichlet boundary conditions for the emergent gauge field lead to distinct boundary universality classes. We determine the boundary scaling dimensions of the fundamental fields and gauge-invariant operators that provide observable signatures. We further propose a fermion-gauge lattice model with tunable boundary interactions as a microscopic setting for realizing and probing these boundary universality classes.

Behavior Foundation Models (BFMs) give humanoids a promptable policy over a latent behavior space, enabling one single vector to represent a motion to imitate, a pose to reach, or a reward to maximize. Forward-Backward representations successfully produce such spaces, but at the cost of hundreds of GPU-hours for a single robot. Moreover, when the training process is repeated for a second robot, it produces a second space unrelated to the first, resulting in embodiment-specific latents that do not unify or transfer. We address these problems with CrossBFM, treating the latent space as the transferable asset for various embodiments. As retargeting provides frame-level cross-embodiment correspondence, we propose a unified encoder architecture with no robot-specific parameters for distilling the behavior space to address all training embodiments simultaneously in less than a GPU-hour. Following this encoder, latent-conditioned trackers turn the distilled latent into whole-body control in a conventional PPO training manner in just 10 more GPU-hours. On three distilled humanoids, all three prompting modes transfer: motion tracking with latent-conditioned policy losing only $0.025$ rad to its joint-conditioned counterpart, smooth goal reaching between poses with no falls, and reward optimization for all $41$ reward prompts. Our experiments further reveal that 1) regressing the encoder on a quarter of the motion corpus costs only $5\%$ of tracking performance and 2) training the encoder on a subset of robots and evaluating on an unseen one recovers up to $89\%$ of the tracking performance of seen robots, demonstrating cross-embodiment generalization to morphologically similar robots. We also verify the pipeline on real robots across all three prompting modes and with flow-based generated latents. Project website: https://dotandung.github.io/crossbfm/

Active multimodal agents use visual tools to acquire task-relevant evidence while reasoning. Although reinforcement learning samples multiple interaction trajectories per input, outcome-based objectives primarily use the group to estimate scalar advantages, leaving complementary visual discoveries underused. We introduce VISTA, which internalizes collective visual experience through on-policy distillation by turning observations from same-input rollouts into shared supervision. Collective visual experience distillation (CVED) organizes these observations with their interaction context and aligns them with individual decisions, while heterogeneity-aware policy improvement (HAPI) reinforces successful trajectories and provides experience-guided distillation for unsuccessful attempts. An experience-conditioned teacher evaluates the student's sampled response prefixes, allowing discoveries from one trajectory to guide learning in another without replacing the student's original history or generating new target trajectories. The trained agent retains its visual tools and acts using its own interaction history. VISTA achieves the strongest average performance among the evaluated active multimodal agents of comparable size and consistently outperforms same-backbone training baselines across fine-grained perception and general reasoning tasks, demonstrating the value of collective experience for active multimodal learning.

Quantum algorithms are powerful tools for finding symmetries of classical objects, most famously through Shor's algorithm and the Hidden Subgroup Problem (HSP). In this work, we study quantum algorithms for learning symmetries of quantum objects. Existing work in this area centres on the recently introduced State Hidden Subgroup Problem (StateHSP), a quantum generalisation of HSP in which the task is to learn the symmetry subgroup of a quantum state. We develop efficient quantum algorithms for non-abelian StateHSP when the hidden subgroup is normal and the ambient group belongs to a broad class of non-abelian groups, extending the previous general theory beyond the abelian setting. StateHSP learns Bose symmetries, under which a state must be invariant exactly under the action of the symmetry group. In quantum mechanics, however, physically equivalent pure states are defined only up to global phase. Motivated by this, we introduce a natural notion of Anyonic state symmetry learning, based on invariance up to global phase. We give an efficient quantum algorithm by reducing the problem to StateHSP, where the reduction rests on a new correspondence between linearisations of projective representations and linear error-correcting codes. As an application, we obtain an improved algorithm for learning stabiliser groups of mixed qudit states of arbitrary local dimension. Finally, we introduce symmetry learning problems for other quantum objects, including unitaries, Hamiltonians, and finite collections of states, and give efficient algorithms for them by reduction to state symmetry learning. Together, these results broaden the scope of state symmetry learning as a common algorithmic primitive for learning quantum symmetries.

Unit interval graphs admit a classical Catalan encoding by area sequences, or equivalently by Dyck paths. We introduce a new statistic on these graphs, called peak-nesting, defined as the largest number of peak-cliques containing a common vertex. Through the correspondence with area sequences, peak-nesting also defines a new statistic on Dyck paths. We construct a bijection between Dyck paths and bicolored Motzkin paths which simultaneously records peak-nesting and the number of peaks. This yields a refinement of Touchard's identity, coefficient formulas involving Dyck paths of given height, and new combinatorial interpretations for several sequences recorded in the OEIS. We study the peak and peak-nesting polynomials over all unit interval graphs and over the subclasses of connected, Abelian, $2$-nested, and reduced unit interval graphs. For these families we obtain closed formulas, recurrences, and, for the symmetric cases, nonnegative expansions in the gamma-basis with explicit combinatorial interpretations. We also investigate questions regarding the location of zeros and the log-concavity of the corresponding coefficient sequences: some of the polynomial families form generalized Sturm sequences, whereas others fail to be real-rooted but appear nevertheless to have log-concave coefficients. Finally, we relate the peak-clique presentation of a unit interval graph to lattice path matroids.

We show that the optimal commuting operator correlation for a variant of Coladangelo's two-player generalized nonlocal game, based on the embezzlement of entanglement, is a commuting operator self-test. Our result gives the first correlation self-test for an exact entanglement embezzlement protocol in the commuting operator framework. Because the unique optimal correlation necessitates the exact embezzlement of entanglement, the correlation is unrealizable using quantum tensor-product models, even if the local spaces are allowed to be infinite dimensional. As such, our result provides an example of a commuting operator self-test where the Hilbert space shared by the two parties cannot be factored into a tensor-product of local spaces that is compatible with the local measurement operators. Our main proof technique relies on Harris' unique abstract state characterization of exact embezzlement of entanglement involving Cuntz algebras.

We study the deterministic query complexity of finding approximate Goldstein stationary points of globally Lipschitz functions that may be nonsmooth and nonconvex. Under prescribed bounds on the Lipschitz constant and on the difference between the initial function value and the infimum, we prove a lower bound on the worst-case number of oracle calls that is exponential in the dimension at fixed sufficiently small accuracy parameters. The result holds for a local oracle and gives explicit dependence on the accuracy parameters. A complementary deterministic algorithm using only function values gives an exponential upper bound, establishing the exponential order in the dimension in this regime. For a coarser stationarity requirement, we also give a deterministic first-order algorithm with a dimension-free query bound. Thus, the dimension dependence differs between the two accuracy regimes.

On a single task, deep networks can learn many solutions, depending on their optimizer, training data, architecture, and hyperparameters. Many of these solutions are mode-connected: rather than isolated points in weight space, they are connected by low-loss regions. Yet how their internal computation varies within these regions is unknown. A parallel line of work has identified the degeneracy of neural representations: many networks reach similar training loss with distinct internal structures. However, it is unclear how these solutions are related in weight space. We unify these subfields and show for the first time that many different internal mechanisms exist within a local mode-connected region in weight space. To do so, we introduce Hessian Null Space Continuation (HNC), a scalable method that uses local curvature to traverse regions of weight space that preserve network function, and can be steered toward solutions with specified properties. In RNNs trained on a memory task, HNC reaches drastically different representations and dynamics with maintained behavior. In ImageNet-trained Vision Transformers, HNC finds representations that differ more from the original network than any independently trained model with a different architecture or objective. In reinforcement-learning agents, HNC uncovers a distinct navigation strategy at comparable return and exposes reward hacking in an AI Safety Gridworld. Finally, HNC measures the local geometry of the solution set, showing how model size and task complexity shape its dimension and functional sensitivity. Our results show that a surprisingly large amount of representational diversity exists near a single trained solution, unseen by standard gradient-based optimization. HNC identifies and quantifies this diversity, opening new possibilities for mechanistic understanding of solution spaces and for model merging, editing, and fine-tuning.

The escape of ionizing photons from galaxies during the Epoch of Reionization is often inferred indirectly because the intervening neutral hydrogen in the intergalactic medium (IGM) is expected to absorb all flux blueward of Lyman-$\alpha$ at these redshifts. However, in this work, we report the significant detection ($\approx7\sigma$) of flux blueward of Ly$\alpha$ in a massive ($M_{\ast}\approx10^{9.1}\ M_{\odot}$) star-forming galaxy at $z\approx7.57$, JADES-GS-z7-LAF, using JWST/NIRSpec PRISM spectroscopy. We independently confirm this detection of the Ly$\alpha$ forest (LAF) using JWST/NIRCam F090W imaging ($\approx10\sigma$). The blueward flux in F090W is spatially coincident with the galaxy and emerges $\approx0.4$ pkpc from its UV centroid at $\lambda_{\mathrm{rest}}\approx1500\ \mathrm{\mathring{A}}$. We find no evidence for a foreground interloper producing the observed flux, although we cannot formally reject this interpretation with the existing data. The transmitted flux implies an extraordinarily transparent sightline ($x_{\mathrm{HI}}\ll0.1\%$) through the IGM at $z \approx 5.5-7.5$, a sightline that is spatially and kinematically coincident with numerous high-redshift galaxy overdensities, which possibly explains the emergence of this flux. We observe a smooth and gradual turnover around the Ly$\alpha$ break that is either consistent with an extreme damping-wing ($N_{\mathrm{HI}}\approx10^{23.3}\ \mathrm{cm}^{-2}$) or a strong nebular continuum (contributing $\approx60-70\%$ of the flux at $\lambda_{\mathrm{rest}}=1500\ \mathrm{\mathring{A}}$). JADES-GS-z7-LAF is far more luminous ($M_{\mathrm{UV}}\approx-21.5$, similar to GN-z11) than the faint sources usually invoked as the drivers of cosmic reionization. If such systems are common in the early Universe, massive galaxies may contribute more to the ionizing photon budget than suggested by other indirect constraints.

Training a model to generate visual content can encourage it to learn rich perceptual capabilities related to geometry, spatial relationships, and objectness; yet, its benefits for visual understanding remain unclear. We ask: when and how does visual generation supervision improve visual understanding? We study controlled pairs of image-to-image (I2I) generation and image-to-text (I2T) understanding tasks that express the same underlying problem in different output modalities. We find that under the correct recipe, I2I training improves downstream I2T performance, with larger gains as the amount of I2I training data increases. We next ask which generation tasks benefit which understanding capabilities. To study transfer beyond paired tasks, we introduce OmniTaskonomy, a unified taxonomy spanning 19 I2I generation tasks and 25 I2T understanding capabilities. The resulting transfer map reveals selective, task-dependent benefits. Some follow intuitive correspondences, e.g., depth prediction improving metric 3D reasoning, object pointing improving counting, and jigsaw reconstruction improving 2D ordering. Interestingly, we also uncover surprising connections: 2.5D segmentation improving category recognition and Z-depth prediction improving localization. To probe these patterns, we analyze gradient alignment between generation and understanding tasks and find that stronger alignment is associated with larger downstream transfer gains. Together, our results highlight visual generation as a rich source of supervision for visual understanding and provide a roadmap for unlocking its benefits through the right training curriculum and task selection. Project page: https://omni-taskonomy.github.io/.

Vision-language-action (VLA) models have advanced robotic manipulation, but their zero-shot generalization in new tasks and environments remains limited, and their reliance on specialized training keeps them from benefiting directly from rapidly advancing general-purpose vision-language models (VLMs). In parallel, recent agentic robotic systems leverage VLMs for high-level reasoning or coding agents for robot control, but often depend on extensive external models and tools, introducing additional complexity and cost. This motivates us to ask: Can a general-purpose VLM itself operate a robot more like the human teleoperator by reasoning directly from observations, issuing actions, and continuously adapting to execution feedback, without relying on external models such as learned action experts, coding agents or grounding tools like SAM3? In this work, we introduce MotorMind, a robot manipulation harness that connects VLM-proposed mid-level actions to deterministic robot control and feedback, with asynchronous monitoring and background memory updates. Without task-specific policy training, coding agents, or additional grounding tools such as SAM3, MotorMind achieves 66.7% success on the base LIBERO-PRO suites and 53.8% under perturbations, compared with at most 13.3% and 19.2%, respectively, for the prior zero-shot methods we evaluate. The same interface reaches 95% average success on a real xArm6 robot across direct manipulation and human-perturbation settings. Replacing the backbone with a stronger VLM further improves performance, while the remaining failures - primarily due to visual grounding, embodied reasoning, and action knowledge - decrease as VLM capability improves. These results show that a general-purpose VLM, when equipped with an appropriate mid-level action representation and asynchronous execution harness, can perform effective zero-shot robotic manipulation.

Interactive panoramic video generation aims to synthesize immersive 360\textdegree{} videos that remain visually coherent while following user-specified camera trajectories during exploration. However, progress is limited by a coupled data-and-model gap: existing panoramic video datasets are often short, weakly annotated, or lack camera trajectories, while existing camera-controlled video generation models are designed for perspective videos and do not directly support panoramic geometry. In this paper, we introduce MUGEN and Wan360 to address these limitations. MUGEN is a large-scale real-world panoramic video dataset tailored to interactive 360-degree world exploration, comprising over 1,300 hours of at least 4K panoramic videos with rich semantic and geometric annotations. Built on MUGEN, we further present Wan360, a camera-controllable interactive panoramic video generation model. Panoramic videos are commonly represented by EquiRectangular Projection (ERP), which unfolds a spherical 360-degree view into a rectangular frame with cyclic longitude seams and pole distortions. To this end, Wan360 introduces three parameter-free ERP-aware components: periodic longitude RoPE for seam-consistent positional encoding, ERP-aware padding for reducing boundary artifacts, and random roll yaw for consistent learning. For camera control, Wan360 uses a panoramic Plücker embedding that represents camera motion with ERP rays rather than perspective pinhole rays. Experiments show that MUGEN serves as a data foundation for panoramic world exploration, and that Wan360 enables high-quality, temporally coherent, camera-controllable 360-degree video generation.

Given integers $k,\ell \geq 2$, define the Erdős–Selfridge curve \begin{align*} \mathcal{C}_{k,\ell} : y^\ell = x(x+1)\cdots (x+k-1). \end{align*} Bennett and Siksek proved that if $(x,y)$ is a rational point on $\mathcal{C}_{k,\ell}$ with $\ell$ a prime and $y \neq 0$, then $\ell$ is bounded (doubly-exponentially) in terms of $k$. We improve this bound on $\ell$ when $k$ is sufficiently large. Our method uses combinatorial and sieve-theoretic arguments, as well as results on solutions to generalized Fermat equations.

For every odd prime power $q$ and $D=q+1$, we construct an infinite family of Ramanujan quantum expanders of degree $D$. The construction transfers Morgenstern's Ramanujan Cayley graphs on $\operatorname{PSL}_2(\mathbb{F}_{p})$ for $p$ which is an even power of $q$, through the odd irreducible subrepresentation of the Weil representation of $\operatorname{SL}_2(\mathbb{F}_{p})$. For a quantum expander of dimension $N$, our implementation uses $O(\log^2 N)$ elementary gates, and $O(\log N)$ ancilla qudits, using a fixed finite gate set depending on $q$. An advantage compared to the previous work of Iyer, Jain, Jordan, and Somma (FOCS 2026) is that assuming the quantum circuit is implemented exactly, we satisfy the $2\sqrt{D-1}/D$ singular value bound exactly without any additive error.

We review mathematical results about the spectrum of spin-$s$ chains with a nearest neighbor interaction given by the projection onto the singlet state of two spin-$s$ degrees of freedom. Up to normalization, these interaction terms generate a Temperley-Lieb algebra at loop parameter $d=2s+1$. We also present several new results. First, we prove a ferromagnetic ordering of energy levels across symmetry sectors of the model, thus generalizing a previous result of Nachtergaele, Spitzer and Starr (2004) for the spin-$\tfrac12$ $XXZ$ chain. This enables us to determine a uniform lower bound on the finite volume spectral gap for these spin chains. By combining a variational estimate with Knabe's finite size criterion, we show that the exact spectral gap of the GNS Hamiltonian of the fully polarized state is $1-2/d$. Furthermore, this value serves as a lower bound for the gap of the maximally mixed ground state. Finally, we show that the ground state projectors on open chains satisfy the Jones-Wenzl recursion, thereby recovering a known result that the degeneracies are the quantum integers $[L+1]_q$ for $q+q^{-1}=d$. We discuss how the high degeneracy of the ground states allows the model to break a continuous symmetry while remaining gapped, and renders that gap unstable.

We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=\Omega\!\left(\frac{\mathsf{Q}(\mathcal C)^3\log N}{\log \mathsf{Q}(\mathcal C)}\right) \qquad\text{and}\qquad \mathsf{D}(\mathcal C')=\Omega(\mathsf{Q}(\mathcal C')^3\log N). \] The first bound matches the upper bound of Arunachalam et al.~[Quantum'21] up to constant factors, while the second matches the upper bound of Servedio and Gortler~[SICOMP'04]. In particular, this shows that the saving in the randomized upper bound of Arunachalam et al. fundamentally relies on randomness. Apart from characterizing the optimal relationship between classical and quantum query complexity, our results are the first to show that quantum speedups for learning can go beyond the Grover and Bernstein-Vazirani paradigms.

Ultra-high-resolution (UHR) remote sensing visual question answering (VQA) requires models to resolve small visual evidence within extremely large images. Existing approaches typically rely on token pruning, visual search, or tool-augmented reasoning at inference time. We instead investigate whether the benefit of zoom-in visual privilege can be internalized into the model. We introduce RS-OPSD, a reliable privileged on-policy self-distillation (OPSD) framework for UHR remote sensing VQA. To provide high-quality privileged information with explicit question-relevant evidence, we construct GeoEvidence-6K, containing 6,750 VQA samples across seven task categories with evidence-region annotations, and develop Human Feedback-Guided Skill Refinement (HF-SR) for scalable annotation. To address context loss from tight crops and conflicting signals from imperfect teachers, RS-OPSD introduces Context-Preserving Visual Privilege (CPVP) and Correctness-Aligned Distillation (CAD). Without any additional visual search or tool calls at inference time, RS-OPSD achieves state-of-the-art (SOTA) performance on XLRS-Bench, MME-RealWorld-RS, and LRS-VQA, outperforming previous SOTA models of comparable scale by an average of 4.0 percentage points. Moreover, our 2B variant, RS-OPD-Lite, surpasses most 8B-scale models while achieving the fastest measured inference speed. Our Code, GeoEvidence-6K, and the model weights for RS-OPSD and RS-OPD-Lite are publicly available.

The kagome metal CsV$_3$Sb$_5$ exhibits charge density wave (CDW) and superconducting transitions, both of which are substantially affected by pressure. Recent x-ray diffraction experiments identify a new charge-ordered phase at a pressure coinciding with the dip of the superconducting dome. This CDW phase displays a distinctive wavevector $\mathbf{Q} = (3/8, 0, 1/2)$ and monoclinic symmetry, in contrast to the $2\times2\times 2$ and $2\times2\times 4$ orders reported at ambient pressure. In this letter, we show that density functional perturbation theory (DFPT) calculations on a fine reciprocal-space grid predict the leading lattice instability of CsV$_3$Sb$_5$ to be at this wavevector. Finite-displacement calculations reveal that while anharmonic effects stabilize the conventional $L_2^-$ CDW at ambient pressure, the competing $3/8$ instability becomes energetically favorable above $\sim$1 GPa, consistent with experimental observations. Interestingly, the nesting function displays a peak at the same wavevector. A Landau free energy analysis explains the emergence of the monoclinic distortion observed in x-ray diffraction, in addition to several bond-ordering patterns that may be relevant to the observed trends in the superconducting $T_c$.

As the chain-of-thought reasoning capabilities of large language models improve, evaluating and calibrating their reasoning confidence is becoming increasingly important for quantifying the uncertainty of their answers. Current methods for estimating the confidence of large language models are generally based on probabilities of selected key tokens, but the underlying mechanism remains unclear. Our pilot study finds that replacing selected token probabilities with coarse substitutes can also improve calibration, motivating us to further explore effective signals of model confidence. We introduce Divergent Token Confidence (DTC), a framework that estimates confidence by counting tokens at which two models strongly disagree during decoding. DTC identifies these divergent tokens using the Jensen-Shannon divergence between next-token distributions evaluated along the same reasoning trajectory. We find that their count is almost negatively associated with answer accuracy, thereby serving as a simple yet effective signal for uncertainty quantification. DTC supports both white-box and black-box evaluation using auxiliary models, without explicit training and affecting the generation process. Experiments across multiple model families and six mathematical benchmarks demonstrate improved calibration over probability-based and verbalized baselines. Under white-box evaluation, the count-only estimator achieves an average expected calibration error of 13.0%, compared with 32.7%-42.4% for standard full-sequence confidence methods. In black-box settings, it also improves calibration over the original verbalized scores. For example, mean expected calibration error falls from 32.1%-40.2% to 13.7%-16.3% on DeepSeek-V3.2. These findings provide new insights for improving reasoning uncertainty quantification in large language models. The code is released at https://github.com/szu-tera/DTC.git.

We propose a continuous-time algorithm for zeroth-order global optimization of smooth functions on compact manifolds that synthesizes Riemannian gradient dynamics using only objective measurements, without evaluating gradients. The algorithm is formulated as an ordinary differential equation driven by piecewise-smooth McShane-type approximations of the Wiener process, with a geometric compensation term that depends only on the actuation frame and not on the objective function. Our main result establishes infinite-horizon practical probabilistic guarantees for fixed approximation parameters. To this end, we show that the algorithm's trajectories approximate, in the mean-square sense, a Riemannian Langevin diffusion whose unique invariant Gibbs measure concentrates on the set of global minimizers. We exploit this approximation to establish finite-horizon probabilistic convergence guarantees and directly analyze the algorithm's long-time behavior to obtain the infinite-horizon result.

We classify the deep points of cluster varieties of cluster algebras of punctured marked surfaces with boundary.

Scientific foundation models are commonly evaluated after heterogeneous physical problems have already been translated into a compatible gridded, tokenized or symbolic representation. This leaves the scientific interface outside both the pretrained model and the audit of what is actually reused. We study the complementary setting in which boundary histories, sparse monitor records and loading histories retain their native inference classes and their outputs remain on Cartesian, latitude-longitude and unstructured domains. GEODE couples task-specific scientific interfaces to a shared routed library of wavelet operators. A single jointly pretrained model represents cavity flow, radiation dose and elastoplastic stress, then acquires a heat exchanger and a reactor subchannel by training a private interface containing 2.1% of its parameters. Earlier predictions remain unchanged by parameter isolation, whereas unrestricted fine-tuning degrades them by factors of 14-29. Crucially, preservation alone does not establish reuse: norm-matched randomized-library controls show that the contribution of pretrained computation is conditional on the task and data regime. A separate decomposition shows that full-field relative L2 error can substantially understate error relative to spatial variation when field level dominates the norm. Task-specific operators remain more accurate on three of the five problems. These results distinguish multi-task coverage, preservation and pretrained reuse as separate properties that must be tested independently when scientific foundation models span heterogeneous interfaces.

Discrete diffusion language models can generate multiple tokens in parallel, but reducing the number of denoising steps can lead to inconsistent predictions. Standard cross-entropy training fits conditional token marginals, whereas parallel generation requires consistent joint predictions. We introduce Alpha Diffusion Language Models (AlphaDLM), trained with a sequence-level alpha loss that recovers cross-entropy in the limit of vanishing alpha and has a joint-mode optimum at alpha one. Our analysis characterizes how the objective and factorization jointly determine the fitted distribution. We identify conditions under which intermediate alpha preserves multiple valid completions while excluding invalid token combinations. Trained on TinyGSM, our method achieves 34.6% accuracy on GSM8K with only four model evaluations. We further scale the method to SDAR-1.7B and evaluate it on code and mathematics benchmarks. These results show that changing the training objective can improve the accuracy-computation trade-off of factorized diffusion language models.

Training agents to follow arbitrary instructions is an important goal of multi-task reinforcement learning (RL). Linear temporal logic (LTL) provides a precise and structured formalism for specifying instructions to agents, and has been successfully adopted for training generalist multi-task policies. However, differences in implementations, task distributions, and evaluation protocols make existing methods difficult to compare, while high computational costs limit the scale and statistical reliability of experiments. We introduce Jaxolotl, a unified high-performance benchmark suite for multi-task LTL-RL to address these concerns. Jaxolotl provides a modular, end-to-end JAX implementation of six representative algorithms and four environments, together with newly curated task suites and a standardised, statistically robust evaluation protocol. By precompiling symbolic task representations into static arrays, Jaxolotl enables fully JIT-compiled training and evaluation, achieving end-to-end speedups of up to $220\times$ and supporting controlled comparisons at substantially greater experimental scale. We use this framework to systematically evaluate existing approaches, revealing complementary strengths and limitations: general methods capable of non-myopic reasoning struggle as the number of propositions grows, while methods with stronger scaling rely on environment-specific assumptions and suffer from myopia.

We study the effective potentials for various probe D-branes surrounding AdS$_5$ black holes in consistent truncations of type IIB supergravity on Sasaki-Einstein 5-manifolds $Y^{p,q}$, focusing in particular on the conifold base $T^{1,1}$. The probes are either dual Giant Gravitons having support on AdS spacetime dimensions or D3 probe branes wrapped on non-contractible cycles of the internal manifold, which then appear "point-like" in the AdS spacetime. The non-contractible cycles of $T^{1,1}$ and $Y^{p,q}$ topologically stabilize the branes at a finite size, and we find stable supersymmetric wrapped D3 branes on Gutowski-Reall black holes, effectively providing a stable BPS composite system in AdS$_5$ made by a black hole surrounded by a baryonic condensate. We show that the onset of superradiance in the black hole backgrounds matches the emergence of stable minima in the probe effective potentials, extending the constructions of Dual Dressed Black Holes and the Grey Galaxies. We comment on the relevance of this result for recent studies concerning the classical cohomology problem and the associated fortuitous states in the dual Klebanov-Witten theory.

A simple model gives good agreement between observed emissions of CO2 into the atmosphere from the combustion of fossil fuels and observed increases of the atmospheric concentrations C of CO2 and decreases of the isotope delta value delta13C. If fossil fuel emissions were to cease the model predicts that: (1) the difference between the CO2 concentration C and the preindustrial value, Co = 280 ppm, would decay exponentially with time constant of 60 y; (2) the difference between the concentration-delta-value product C x delta13C and the preindustrial value Co x delta13Co = (280 ppm) x (-6.5%%), would decay exponentially with a time constant of 8 y. The decay times are different because of isotopic exchange, largely driven by photosynthesis and respiration on the land.

We report the experimental observation of the $^{\text{133}}$Cs 6S$_{\text{1/2}}$ to 6D$_{\text{5/2}}$ single-frequency two-photon transition at low excitation power using an optical nanofiber embedded in a cold atom cloud. We investigate the 917 nm fluorescence spectra modified by the surface-induced interaction of the nanofiber, which exhibits a pronounced asymmetric broadening with a distinct red-shifted tail. We present a systematic theoretical description of the two-photon transition process of atoms near a nanofiber surface, considering atomic angular momentum coupling, guided-mode decay rate, and surface-induced van der Waals interactions. Owing to the tight spatial confinement provided by the guided evanescent field, efficient nonlinear excitation is realized at excitation powers down to tens of microwatts, corresponding to a reduction of approximately four orders of magnitude relative to typical free-space implementations. Our work reveals the interplay among waveguide-modified radiative dynamics, surface-induced interactions, and the spatial distribution of atoms around the nanofiber, and provides insights into further studies on nonlinear optical transitions and surface-mediated atomic dynamics in waveguide quantum electrodynamics systems.

We are interested in the molecule reduction algorithm used by Deng, Hani and Ma. This algorithm allows them to establish a rigidity theorem, which plays a central role in the long-time derivation of the Boltzmann equation using the hard-sphere dynamics. In the present article, we show that this algorithm is a graph traversal algorithm of Kruskal type, and we prove that it constructs a Kruskal spanning tree of the input molecule.

Computational self-testing gives a classical verifier command over the quantum register of a single computationally bounded prover. We use this framework to construct the first argument system for BQP with quasilinear total resource requirements in the circuit model. Our argument system is based on the learning with errors (LWE) assumption and requires total resources of $O(\mathrm{poly}(\lambda, \log g)\cdot g)$ for delegating a circuit with $g$ gates, where $\lambda$ is the LWE security parameter. This is achieved by constructing a new computational self-test for certifying the prover's quantum state and using it to dequantize the efficient verification protocol of Broadbent (ToC 2018). Specifically, this self-test enables the verifiable, random remote state preparation of tensor product states of the single-qubit Clifford observables $\sigma_X, \sigma_Y, \sigma_Z, (\sigma_Y-\sigma_X)/\sqrt{2}$ and $(\sigma_Y+\sigma_X)/\sqrt{2}$, with constant robustness: the verification error is independent of the number of prepared qubits. This approach was first proposed by Coladangelo et al. (ToC 2024) in the multi-prover setting. We replicate their result in the single-prover setting by applying the compiler proposed by Kalai et al. (STOC 2023)—which turns any nonlocal game into a single-prover argument system—to a modified version of their self-test.