Papers

Tool-using LLM agents must decide not only whether additional information is needed, but also which source can resolve the uncertainty. Existing proactive approaches often specialize in either user clarification or environment verification, without explicitly determining the appropriate information source for each decision. We formulate this problem as uncertainty routing among ACT, CLARIFY, and VERIFY, and propose PROUR, a proactive uncertainty routing framework. PROUR decomposes action uncertainty into disagreement across plausible user-goal interpretations, which signals user-side ambiguity, and the entropy remaining within each interpretation, which signals missing world-side evidence. To acquire information from the routed source, a query generator is trained with a mode-conditioned information-gain reward, targeting user-goal identification under CLARIFY and next-action identification under VERIFY. On $\tau$-bench, PROUR achieves 28.17% average success rate across retail and airline, outperforming the strongest prior method by 4.57% while using 2.17 fewer interaction steps. The learned policy further generalizes to stronger task agents and transactional domains of $\tau^3$-bench without retraining, demonstrating the benefit of source-aligned uncertainty resolution for proactive agents.

Operator learning of periodic solutions requires deciding how simulation data should be recorded and represented. A natural choice is to integrate long enough for transients to decay and record a window wide enough to contain at least one full period of all trajectories. We find that these conservative choices can make the resulting trajectories difficult to learn, even when the underlying periodic orbits vary regularly with system parameters. Unaligned trajectories generalize poorly even within the training distribution. Phase alignment substantially improves in-distribution generalization, but models trained on a fixed physical-time window still have large errors on trajectories with periods outside the training range. We explain both failures through a common mechanism: frequency differences accumulate over time, so the target phase varies rapidly with the parameters. Predictors that cannot track this variation incur a population MSE floor in both settings; for fixed window prediction, we also derive a per-sample lower bound. We then study one of the simplest representations that escape these floors: learning an aligned, normalized waveform and its period separately. We establish regularity of the decoupled targets under ODE assumptions and show experimentally that this approach avoids both failures in ODE systems and a PDE case study.

Vision-language-action (VLA) models have achieved strong performance in language-conditioned manipulation, yet success under nominal evaluation does not necessarily translate into robust closed-loop behavior when executed actions are transiently corrupted. We introduce DS-VLA, a dendritic-inspired action architecture that incorporates dendritic spiking dynamics into VLA control to address this limitation. Specifically, to enable modularized feature processing and temporal information integration, DS-VLA equips action neurons with multiple sparsely connected dendritic branches, each featuring heterogeneous, learned decay factors. Furthermore, to suppress unreliable state updates while preserving task-relevant historical information, we introduce a neuron-wise inhibitory gate that adaptively regulates the admission of new multimodal evidence into dendritic states prior to somatic dynamics. We evaluate DS-VLA on all four LIBERO suites under both nominal rollouts and a unified closed-loop action-perturbation protocol. DS-VLA achieves a 91.6% average nominal success rate and an 87.35% average perturbed success rate, retaining 95.4% of its nominal performance. Under the same reported perturbation setting, OpenVLA-OFT, FAST, $\pi_0$, and GR00T achieve 39.45%, 23.90%, 28.55%, and 30.75%, respectively. A controlled ablation isolates the contribution of neuron-wise shared inhibition, while analyses of neural dynamics and post-perturbation trajectories associate robust performance with selective evidence suppression and effective behavioral recovery. Together, these results demonstrate that integrating brain-inspired computational mechanisms offers a promising architectural prior for robust embodied intelligence beyond merely scaling vision-language backbones or generative action decoders.

Acquiring data is costly: higher measurement fidelity costs power and storage and risks collecting irrelevant content, while aggressive cost reduction can discard information that later analysis needs. We address this trade-off with an information-theoretic framework that acquires data relevant to a broad set of tasks rather than to one model. A mask policy, conditioned on side information, chooses which pixels to measure so as to maximize the mutual information between a discrete image and its partial observation under a budget; since the image entropy does not depend on the mask, this is equivalent to minimizing the conditional entropy. A frozen discrete denoising diffusion model (D3PM) supplies the posterior, and we use it in two ways: as an entropy surrogate for training a one-shot mask generator, and as the criterion for sequential greedy acquisition. The one-shot generator outperforms random masks only with care, including an unbiased gradient estimator for binary masks. With sequential acquisition, on MNIST the prior makes $8\times$ fewer errors than random at a $10\%$ budget, and on CIFAR-10 it gains $0.9$–$3.4$~dB. On fastMRI, our proposed technique using a static mask outperforms the well-known methods such as variable density and LOUPE.

Chemistry's phenomenological theories multiply with its observables: the same physical reality is repeatedly named in different measurement contexts, and the relations among theories have never had an auditable carrier. Here we present PhotoLean, a machine-checked genealogy of seventeen photochemical and photophysical theories formalized in Lean 4 over a shared kernel. Every pair of theories carries either a verified relation (equivalence, implication, composition with registered premises, definitional certificate) or a registered reason for its absence, covering all 136 pairs. Three adjudications resolve inherited conflations with if-and-only-if boundaries and witnesses: the symmetry factor $\beta$ equals one-half exactly when reactant and product force constants coincide; Kasha's rule and the Kasha-Vavilov rule agree only under closed quantification with a loss channel; and intensity-only Stern-Volmer data cannot distinguish static from dynamic quenching, whereas the lifetime channel discriminates exactly. As proposition generation shifts to machines, such machine-checked relational ledgers offer a replicable audit layer for theory itself.

Sign-language interpretation in public communication relies on qualified professional interpreters and can be difficult to scale, motivating robotic signing as a complementary accessibility interface. We present RoBoSTAR, a text-conditioned sign language production (SLP) framework for generating human-centric sign motion that can be retargeted for robotic execution, with speech supported optionally through an external ASR front end. Conventional autoregressive approaches flatten motion into a single full-resolution token sequence, forcing long-range and local dependencies to be modeled at a uniform temporal granularity. RoBoSTAR instead combines part-wise Finite Scalar Quantization with next-scale autoregression, generating motion over progressively finer temporal resolutions while predicting synchronized body and hand tokens in parallel within each step. This coarse-to-fine formulation provides compact long-range context before progressively refining motion details, while self-conditioning and context corruption improve robustness to cross-scale prediction errors. The generated motion is subsequently retargeted for physical humanoid execution. Extensive qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of RoBoSTAR.

We develop entropy-stable isothermal-wall conditions for the compressible Navier–Stokes equations at continuous and semi-discrete levels. For a stationary, impermeable, no-slip wall at constant positive temperature, adding total-energy density divided by wall temperature to the canonical convex entropy cancels the wall contribution without suppressing heat transfer. This affine modification preserves the entropy Hessian, relative entropy, and volume entropy production. It is proportional to total ballistic-energy density and yields a conditional $L_2$-type bound based on the initial field under the stated assumptions. Two wall formulations use a common discontinuous Galerkin discretization with the summation-by-parts property and simultaneous approximation terms. Both give zero adapted wall contribution without a penalty and a nonpositive contribution with it. The complete-residual formulation penalizes the full wall-data residual and balances fluid energy through its complete numerical wall flux. The Fourier-energy-exact formulation combines an entropy-neutral skew correction with a momentum-projected penalty so that the complete numerical outward energy flux equals the one-sided numerical Fourier heat flux at every wall node and spatial resolution. Pointwise tests verify the local identities. Manufactured-solution studies with entropy-stable interior coupling demonstrate convergence rates consistent with order $p_s+1$ in the discrete $L_2$ norm, where $p_s$ is the solution polynomial degree. Thermal-relaxation calculations verify the semi-discrete energy and adapted-entropy balances. Three-dimensional calculations demonstrate balance closure in a closed domain, convergence of curved-wall traces, and applicability to a complex supersonic separated flow.

Large language model (LLM) leaderboards compare model capabilities by ranking models according to their mean performance on fixed benchmarks. However, variability in evaluation outcomes across runs may produce unsupported claims of model superiority on the benchmark, a risk compounded by leaderboard updates. In this paper, we propose BB-EDGE (Benchmark-Weighted and Block-Factorized e-processes for Directed Graph Evaluation), a principled framework that represents an LLM leaderboard as a directed graph whose edges certify pairwise mean-performance advantages, with anytime-valid family-wise error rate (FWER) control. Concretely, for each direction, BB-EDGE constructs an empirical-Bernstein e-process by factorizing evidence over protocol-defined blocks and assigning stakes proportional to the corresponding block weights, then applies direct e-Holm across these $e$-processes to certify directional advantages as edges. Theoretically, we characterize weight-proportional linear stakes under heterogeneous benchmark-average nulls and prove anytime FWER control under arbitrary within-block and cross-pair dependence. BB-EDGE further supports anytime-valid Top-$k$ certification and simultaneous rank intervals. Extensive experiments on synthetic data and four real-world benchmarks demonstrate that BB-EDGE maintains anytime FWER control while achieving high efficiency.

Observationally equivalent causal models can still disagree about what happens under intervention, because interventions create inputs that never occur in observational data. We introduce Interventional Separation Selection (ISS), which repeatedly queries the true system with an admissible intervention on which the surviving candidate models disagree, discards the candidates the outcome contradicts, and stops once no intervention within a cost bound separates the survivors. If the true system is among the candidates, this stopping condition certifies that every survivor agrees with it on every admissible intervention within the bound, a guarantee that no observational learner can give, however much data it sees. The stopping condition depends only on the survivors, so it can be checked without knowing the truth. For continuous variables the candidates form an infinite version space, and mixed-integer linear programs decide the stopping condition exactly over all of it, with agreement holding up to a tolerance. On a three-digit colored MNIST causal abstraction task in which ink hue tracks digit size, plain convolutional networks trained on examples reach zero held-out error, yet disagree with shape-based labels on 26% of single-digit edits, as often as hue-based labels do. Auditing the causal abstractions of networks observed only on such images, ISS certifies what each network perceives with 13.6 interventions per image on average, and each certificate, checked against every admissible intervention, holds whenever the network's true abstraction is among the candidates. When a network bypasses a unit that every candidate abstraction relies on, certificates covering interventions on that unit can be silently void, and twenty random validation interventions refute 69% of them.

Let $H$ be an infinite-dimensional Hilbert space and let $\set{x_n}\inN$ be a frame for $H$. We say that a sequence $\set{y_n}\inN$ is an alternative dual of $\set{x_n}\inN$ if $$x=\sumli\ip{x}{y_n}x_n\quad \text{for all }x\in H,$$ with the convergence of the series in the norm of $H.$ We say that a sequence $\set{z_n}\inN$ is a pseudo-synthesis dual of $\set{x_n}\inN$ if $$x=\sumli\ip{x}{x_n}z_n \quad \text{for all }x\in H,$$ with the convergence of the series in the norm of $H.$ We prove that, at every level of smoothness of the generator, there exist Gabor frames for $L^2(\R^d)$ with infinitely many alternative duals (and pseudo-synthesis duals) such that none of them is a Gabor system

Partial differential equations (PDEs) are essential for modeling complex physical systems, and neural solvers have recently emerged as powerful data-driven tools for numerically solving them. However, existing neural solvers struggle with domain-specific challenges, such as varying parameters and high-speed flows, necessitating specialized architectures. Manually designing these specialized solver architectures is a highly iterative, time-consuming process requiring deep expertise, creating a significant bottleneck in scientific discovery. We propose leveraging autonomous AI research agents to automate the synthesis of specialized solvers. To support this, we introduce AutoPDEBench, a benchmark dedicated to LLM-driven automated research for PDE solver design. The benchmark includes 25 challenging datasets featuring both novel and actively studied physical scenarios. We evaluate a suite of general-purpose models (transformer, ROM, and graph-based) alongside a multi-agent instantiation of the iterative automated research pipeline, which serves as an agentic baseline. Empirical results show that the iterative automated research system significantly outperforms the general-purpose neural solver baselines. Our findings demonstrate the viability of using AI agents to automatically design neural solvers for complex physical systems. AutoPDEBench provides a foundational testbed to accelerate agent-driven scientific discovery in physics and engineering.

Gait recognition always remains challenging due to severe overfitting and the rigid view constraints common in single-stage approaches. We propose a two-stage framework, termed Translate-First-Then-Reason (TFTR), to address these issues. In the first stage, a shallow Siamese convolutional network with triplet loss maps Gait Energy Images (GEIs) into a 128-dimensional view-specific embedding space. In the second stage, these per-view embeddings are treated as tokens and processed by a 12-layer Transformer encoder, which re-projects them into a new space with improved cosine separability. This design enables flexible fusion of an arbitrary number of views at inference, overcoming the fixed-input limitations of prior methods. Trained on the OU-MVLP dataset (6,000 subjects) and evaluated on unseen CASIA-B across normal, bag-carrying, and coat-wearing conditions, our pipeline achieves 96.91% single-view and 99.49% three-view accuracy on OU-MVLP, and attains 100% accuracy on CASIA-B with three views.

We construct a degeneration of Hitchin's non-standard minitwistor spaces associated with toric gravitational instantons of type A$_{\rm odd}$ to the minitwistor space of a simple hyperbolic orbifold. We show that the corresponding families of minitwistor lines also converge under this degeneration. Consequently, the associated non-standard Einstein–Weyl spaces converge to the hyperbolic orbifold.

Long-tailed encrypted traffic classification requires accurate recognition of infrequent classes under limited computational budgets. We propose Curv-Tail, a lightweight, end-to-end packet–byte framework trained without a separate pretraining stage. Mixed-resolution tokenization preserves exact packet-length identities within a bounded range and coarsens larger values to limit the vocabulary. An auxiliary objective predicts observed length tokens from contextual packet features before pooling, encouraging length-token retention beyond flow-level supervision. Compact temporal encoders process packet sequences and directional byte patches, and Lorentz prototypes with a shared learnable curvature magnitude classify their fused representation. On NUDT-Mobile and DataCon-Website under natural class frequencies, Curv-Tail achieves three-seed mean Tail-F1 scores of 85.70% and 46.30%, exceeding the strongest evaluated baselines by 2.91 and 1.89 percentage points, respectively. In 300-class profiling on an RTX 4090 with FP32 and batch size 256, Curv-Tail uses 98.48% fewer parameters and achieves 10.2 times the batch inference throughput of MM4Flow.

Neural image watermarks can be forged by extracting watermark-bearing residuals from released images and transferring them to unrelated content. While prior work has demonstrated this vulnerability, what makes these residuals transferable remains poorly understood. We formalize this vulnerability with residual transferability (RT), a metric that quantifies how well watermark evidence remains decodable after transfer across unrelated images. Through comparative analyses and controlled interventions, we find that common training-side variations do not account for the large RT differences across watermarking systems; instead, architectural design plays a central role. By contrasting high- and low-RT systems and validating their architectural differences through controlled interventions, we identify two mechanisms that strengthen the dependence of watermark evidence on the cover image, thereby suppressing the residual transferability. These findings provide concrete design guidance for developing more forgery-resistant watermarking architectures. Complementarily, for existing watermarking systems where architectural redesign is impractical, we introduce CoverLock, a plug-and-play strategy for existing watermarking systems that strengthens such image dependence without architectural redesign. Across representative watermarking systems exhibiting high residual transferability, CoverLock achieves a more favorable security–robustness trade-off than both traditional handcrafted defenses and learned classifier-based defenses.

A gradient descent method is arithmetically simple if the operations are limited to $+,-, \times$, and division $x/2^t$ with integer $t$. An arthmetically simple gradient method is easy to implement in chip design. We show how to transform AdaGrad, Adam, and AdamW into arithmetically simple. AdamW is based on the recursion $x_{t+1}=(1-\lambda\eta)x_t-\frac{\eta }{s}m_t$ and Adam is the special case of AdamW with $\lambda=0$. We transform them into a static case with $s=S(T)$, where $T$ is the number of iterations, and $S(T)$ is a fixed function. The convergence analysis is given for a static Adam, which is also arithmetically simple.

Federated learning offers a natural way for multiple robots to jointly improve manipulation policies without requiring centralized access to training demonstrations. However, non-IID task and environment distributions can induce representation drift and mutually incompatible robot-policy updates, making naive parameter aggregation destructive. We present FedDRMan, a federated subspace-guided distillation framework for heterogeneous robot manipulation. At each communication round, the server model provides a frozen teacher for local behavior cloning, while low-rank multimodal subspace and action-distribution distillation preserve globally useful representation geometry and policy behavior. To address heterogeneous aggregation, FedDRMan groups clients by update compatibility and maintains a persistent model for each cluster. The server then spectrally rebalances each compatible aggregate to mitigate attenuation of weaker task-relevant robot-policy update directions. Extensive experiments on LIBERO across diverse non-IID settings, heterogeneity levels, client participation variation, together with ablations and aggregation analyses, show that FedDRMan substantially improves knowledge transfer and consistently outperforms strong federated baselines achieving a peak mean success rate of 80.7%, 11.6 percentage points above the strongest evaluated federated baseline.

The internal-models approach of the Fundamental Review of the Trading Book (FRTB-IMA) determines market-risk capital at the aggregate level of a bank's approved trading desks, but it does not say how that charge should be attributed to individual trades. Risk managers, capital planners and validators often need one, and it is hard to obtain: capital passes through expected-shortfall, stress-scaling, non-modellable, default-risk, history and standardised-approach layers that are nonsmooth and depend on past positions. We present a formula-complete attribution of FRTB-IMA capital to (observation date, trade) positions that reconciles to computed capital. The calculation is written as a computational graph; after one forward evaluation, a single reverse pass propagates allocation vectors through every node by local Euler rules (expected-shortfall dual weights, active-branch weights at floors and maxima, the default-quantile scenario), avoiding one capital re-evaluation per trade. Under stated homogeneity assumptions the ledger provably sums to capital and to any desk or product grouping, and equals the Euler (gradient) allocation at smooth points; it is exact relative to the implemented calculation and this rule, not a regulatorily prescribed attribution. Its past-date entries capture capital allocated to earlier observation dates, which today's-book sensitivities miss by an exact identity at smooth points. At regulatory ties, where the marginal is not unique, we report the realisable marginal vertices, identified by exact linear-programming tests, instead of one selection. On 14 smooth 96-trade synthetic benchmark books, the median share of capital allocated to past observation dates is 61% (range 21%-99%), and ledgers reconcile to within 5.6e-16 relative error.

The fast Fourier transform (FFT) underlies radar, imaging and scientific computing. A classic rule for fast GPU FFTs is to compute the largest block that fits on chip and compose larger transforms from such blocks. We test this rule on Apple's M6 chip, whose GPU performs 29 arithmetic operations in the time it reads one byte from main memory, and which adds matrix units to both its GPU and CPU. Comparing our kernels with Apple's MPSGraph and vDSP libraries and MLX, we find that data movement, not arithmetic, sets FFT speed. Large batches run at or near the main-memory bandwidth limit in every GPU library, and benchmarks that keep data in cache overstate real throughput by up to $3.7\times$. The on-chip rule still predicts where speed collapses: MPSGraph and MLX lose half or more of their speed once a transform outgrows the GPU's 32\,KiB local memory. Keeping such transforms in registers avoids an extra trip through memory: $2.2\times$ faster than MPSGraph, and $4.4\times$ with half-precision storage. The GPU's matrix units do not help, because recasting the FFT as matrix products adds as much arithmetic as they save. The CPU's matrix unit, 47 times faster than its vector units, does: our kernel for it beats vDSP by up to $5.3\times$. End to end, a $4096\times4096$ synthetic aperture radar image takes 8.1\,ms on the GPU (6.0\,ms with half-precision intermediates), $14$–$19\times$ faster than a CPU reference. Running the CPU's matrix unit alongside the GPU gains nothing: both share one memory bandwidth.

Generative models, such as diffusion and flow-based models, have shown strong promise for robot policy learning by capturing complex and multimodal action distributions from demonstrations. However, policies trained solely with imitation learning often suffer from imperfect demonstrations and distributional shifts, while further improvement typically requires additional expert data. Reinforcement learning offers a natural solution through environment interaction, but effectively finetuning generative robot policies remains challenging due to the intractability of likelihood estimation. In this work, we propose RoboFFT, a forward-process reinforcement learning framework for finetuning generative robot policies, which applies forward noising to sampled actions and uses the weighted score / flow matching loss to construct a surrogate policy ratio for PPO-style updates. We evaluate RoboFFT with popular generative robot policies on representative simulation benchmarks, including long-horizon planning and sparse reward settings. Extensive experiments and analysis demonstrate that RoboFFT consistently improves performance while achieving better stability and training efficiency. We further integrate RoboFFT into a real world RL framework and demonstrate its effectiveness in real world tasks. Project website: https://student-of-holmes.github.io/RoboFFT/.

Large language models (LLMs) can solve every intermediate step of a multi-step math problem on its own and still fail the full problem, even when given a roadmap of the steps and all of their answers. We introduce OracleLadder, a diagnostic evaluation that locates where LLM math reasoning fails by giving the model increasing levels of oracle help. For each problem, a teacher model writes a fixed roadmap of intermediate sub-goals (milestones), and a deterministic symbolic verifier grades every answer. Testing the model with no help, with the roadmap, with the roadmap plus the milestone answers, and on each milestone alone sorts each failure into one of five reasoning gaps. On 354 NuminaMath problems and six models from 8B to 671B parameters (Qwen3, gpt-oss, Llama 3.3, DeepSeek-V3.1), the largest gap for every model is the composition gap, a stricter form of the compositionality gap. It covers 33-48% of problems, and 24-37% after removing problems that an LLM review flags as grading errors. Accuracy and milestone-help recovery rank the two strongest models differently, and two RLVR runs with similar accuracy gains move problems differently. The roadmap effect replicates on MATH500 and AIME 2024/25, per-problem recovery agrees for 83-87% of problems under an independent second teacher, and the help ladder carries over to code generation. We release the data, roadmaps, prompts, and code at https://github.com/slark-prime/OracleLadder.

Triage decides who is seen first. Building an urgency classifier for patient-voice Kinyarwanda, we found our specification could be met without producing anything it was meant to secure. We report that, and the instruments that detect it, instead of a classifier. Designed for the four languages a Rwandan health centre receives, with every instrument per-language: sentences are authored in all four arms and rows generate in one, because the frame slots those three need do not exist. Our requirement asked for one million examples; generation produced them in 130 seconds. It fails four of the nine quality gates in that specification, six when rows are attributed to their source sentence. The binding gate counts distinct authored seed phrases, not rows: at our 165, no corpus passes at any row count. Two shortfalls follow and differ: 2,835 further sentences to pass the seed-count gate, 19,835 to reach the stated million rows, because a separate gate caps a seed at 50 rows. Rows come from a machine at 7,700 per second; seeds from clinicians. A row count constrains the cheap quantity, leaves the expensive one free, and so does not constrain quality at all. Two further negatives follow. An evaluation set of 17,942 rows built from nine distinct sentences supports no verdict: our gate, which counts distinct sentences, refuses 38 of its cells and reports nothing. A model trained on a corpus of uniform surface form changes its predicted urgency for 31.5% of inputs under capitalisation and 21.0% under a single typo, reported as measurement and not attribution. A model directory shipped without its tokenizer loads without error and answers its class prior on input it cannot read, with well-formed probabilities. No figure here is evidence of model quality; the contribution is the apparatus and the negative results it produced, reproducible from a clean clone except where marked NOT REPRODUCIBLE.

We justify the vortex-wave system introduced by Marchioro and Pulvirenti in the 1990s as the vanishing-viscosity limit of the two-dimensional Navier-Stokes equations on every prescribed finite time interval. The initial vorticity consists of a point vortex and a smooth, compactly supported background that vanishes near the vortex. The regular component converges strongly to the background vorticity governed by the vortex-wave system, while the concentrated component is approximated by a Lamb-Oseen vortex centered on the limiting point-vortex trajectory. We obtain quantitative estimates for both components, with constants and a viscosity threshold depending on the chosen time interval, thereby providing a global-in-time justification of the vortex-wave system for this class of initial data.

The sudden removal of a potential barrier from a Bose-Einstein condensate (BEC) gives rise to a quantum version of a hydrodynamic dam break and leads to rich wave dynamics that have similarities to other localized defect problems such as domain wall dynamics in spin systems. Denoting $\Delta n$ as the initial difference in density between the upper $n_{1}$ and lower $n_{0}$ reservoirs on either side of the dam, we use the Gross-Pitaevskii equation to study the quasi-one dimensional case in both perturbative ($\Delta n \ll n_{0}$) and non-perturbative ($\Delta n \sim n_{1}$) regimes. In the perturbative regime a pair of outwardly propagating dispersive wavepackets forms which can be viewed as quantum versions of undular tidal bores that have analytic forms at long times in terms of the integrals of Airy functions with a wavelength that grows as $(\hbar^2 t)^{1/3}$. Airy functions are the universal wave functions that dress structurally stable fold caustics where pairs of rays coalesce, and, indeed, we show that the quantum dam break problem has the same ray structure as the naturally occurring caustic phenomenon of a double rainbow, including Alexander's dark band between the two bows where no light is scattered: we identify the intermediate density plateau in the dam break as an analogous `silent band' where only evanescent sound waves can exist. In the opposite regime of a non-perturbative dam break we show that a self-induced sonic horizon occurs when $\Delta n \geq (8/9)n_{1}$. A discussion of possible experimental schemes for amplification of quantum undulations is included as well as an alternative scheme for dispersive wave generation where a constant flow is imprinted on a BEC in box trap.

Human motion prediction requires diverse future trajectories that remain consistent with observed motion and the articulated physical structure of the body. Skeletal constraints restrict individual poses, while coordinated motion depends on spatial interactions (between connected joints) and temporal interactions (between time instants). To facilitate human motion prediction in light of these constraints and interactions, we introduce Graph Structured Flow Matching (GSFM), which transports the complete future skeletal trajectory through a single conditional velocity field. The trajectory produces a spatiotemporal skeleton graph, and spatial and temporal attention couple its evolution according to skeletal relations and physical time offsets. Bone directions lie on unit spheres relative to a root joint, and tangent evolution preserves input bone lengths throughout generation. We train a learned velocity field through conditional flow matching along geodesic paths connecting random trajectories centered on the last-observed pose to recorded future trajectories. Experiments on the Archive of Motion capture As Surface Shapes (AMASS) dataset evaluate prediction accuracy, diversity calibration, and motion statistics. We demonstrate the contributions of spatial and temporal message passing in the developed architecture through an ablation study. GSFM models trained on AMASS also perform competitively on the Human3.6M skeleton without parameter updates or retraining, demonstrating applicability to an unseen skeletal structure.

Surrogate models are commonly evaluated by how often they agree with their teacher model over an evaluation set. Local variation in this agreement is well known, but its structure and consequences are less clear. We ask whether disagreement is systematically concentrated near the teacher's decision boundary and whether retaining that structure provides information beyond a single global score. Across several datasets and surrogate model classes, we find substantially lower fidelity near teacher decision boundaries under two different methods of identifying near-boundary examples. Moreover, conditioning agreement on confidence-defined regions improves prediction of teacher–surrogate agreement when evaluation-set composition changes, relative to the global score alone. Yet surrogates that agree equally well with the teacher both globally and near the decision boundary can respond very differently to changes selected using the surrogate itself. Finally, we show that independently trained deep teachers can agree on most predictions while identifying different examples as lying near their decision boundaries, complicating the use of those boundaries as stable reference regions for evaluating surrogates. Together, these results show that surrogate fidelity depends not only on how often a surrogate agrees with its teacher, but also on where that agreement holds and, for deep models, how stable the teacher's decision boundary is across training runs.

We establish that finite expressions form a symbolic representation class capable of overcoming the curse of dimensionality for several classes of high-dimensional partial differential equations. For semilinear heat equations, we show how finite expression approximations of the terminal condition and nonlinearity can be propagated through the multilevel Picard framework to produce randomized pointwise approximations with prescribed root-mean-square accuracy. For semilinear Kolmogorov equations with Laplacian diffusion and zero drift, diagonal Black–Scholes equations, and the Laplace Dirichlet problem on a half-space, we construct deterministic finite expression approximations with arbitrarily small spatial $L^p$ error. Under suitable growth and regularity assumptions, the evaluation cost of the resulting approximants is bounded polynomially in the dimension and the reciprocal accuracy. A key ingredient in the nonlinear setting is the construction of finite expressions that approximate the PDE solution while preserving the growth and Lipschitz structures required by the stochastic solution theory. More broadly, our results show that dimension-robust approximation of high-dimensional PDEs is not restricted to conventional neural-network architectures: structured symbolic expressions generated from a fixed dictionary can achieve comparable polynomial-complexity guarantees. This provides a rigorous foundation for finite expression methods as a representation paradigm for high-dimensional scientific computing.

In self-play, a proposer generates verifiable tasks to train a solver. Proposer rewards often depend on the solver's success rate, but equally difficult tasks can differ in their training value. We introduce CompassPlay, a self-play method that rewards the proposer through gradient alignment. The reward favors tasks whose solver loss gradients align with those of reference tasks representing the target capabilities. It draws on a first-order approximation to learning progress and scores each eligible task without additional solver training. Our experiments show gains in performance and training efficiency. In coding self-play with Qwen2.5-Coder-7B, a small external reference set guides task generation. CompassPlay improves average accuracy over AZR's difficulty reward by 1.5 percentage points on in-domain coding and 2.7 on out-of-domain mathematics. In Lean4 theorem proving, CompassPlay matches the difficulty baseline's 150-iteration cumulative coverage with 40% fewer GPU-hours.

Static QA and code-generation benchmarks only partially capture the role that large language models (LLMs) now play as coding agents and research tools. We introduce OptiArena, a budget-controlled testbed for studying whether LLMs can improve executable game-playing algorithms through five rounds of code edits within a fixed minimal scaffold and under bounded evaluator feedback and fixed resource budgets. The testbed uses two optimization regimes, surface obfuscation controls, calibrated references, held-out/stress splits, and diagnostics for degradation and exceptional failures, with LLM API cost reported separately from local evaluator wall-clock. The empirical study asks three questions: whether models can close the calibrated gap between a designated weak starter and an editable competent baseline, whether they can refine editable competent baselines without damaging them, and whether gains survive surface obfuscation controls. Across twelve frontier LLMs and five games, models improve designated weak starters more consistently than they refine editable competent baselines, with substantial variation across games and models. OptiArena provides a practical testbed for measuring bounded-resource algorithm optimization within the five-edit, fixed-scaffold setting studied here. Code is available at https://github.com/WJ-Peng/OptiArena.

As optical networks continue to expand in scale, complexity, and service diversity, the implementation of automation has become essential for ensuring agility, efficiency, and reliability in lifecycle management (LCM) of optical networks. Large language model (LLM) Agent, distinguished by its progressively sophisticated capabilities in logical reasoning, adaptive decision-making, complex problem solving, and multi-task orchestration, presents great opportunities to advance network automation beyond traditional AI techniques. Nevertheless, the application of LLM Agent in optical networks remains in its early exploratory stage, challenged by the lack of multi-task coordination, high computational demands, data dependence, and reliability concerns. In this paper, we envision a conceptual roadmap toward Agentic Optical Networks (AONs) by integrating LLM Agents throughout the LCM with high-level autonomy. First, we trace the evolution from manual operations to AI-empowered frameworks and distill key technologies in Agent, providing actionable insights into leveraging its strengths for addressing practical network automation challenges. A core contribution of this paper is the proposal of a hierarchical multi-Agent framework, which is specifically developed to manage every phase in LCM of AONs, including planning, deployment, operation, maintenance, upgrade, and decommission, thereby enabling more cohesive and comprehensive automation throughout the entire lifecycle. In addition, future directions and underlying challenges are also discussed at the intersection of LLM and optical networks. By aligning the LLM Agent with the specialized requirements of AONs, this work aims to explore the potential for the evolution of optical networks moving from task-level semi-automatic execution toward lifecycle-level full autonomy.