Papers

Long-horizon agents require context compression to manage growing interaction histories. Compression quality, however, is ultimately determined by downstream execution. Existing prompt-adaptation methods infer compression errors by comparing full-context and compressed trajectories. Such comparisons cannot isolate individual compressions and are confounded by agent stochasticity. We first find that compression degrades reliability before solvability. Using matched counterfactual continuations that compare execution from the same agent state with versus without compression, we further show that severe degradation concentrates at isolated compression events. Motivated by this finding, we propose PAIR (Prompt Adaptation using Interventional Rollouts) for adapting structured compression prompts. PAIR identifies individual compressions that degrade subsequent execution, diagnoses their effects, and revises the relevant sections of a fixed compression template. PAIR achieves the strongest cross-run reliability among compressed methods in every main benchmark-scope combination, consistently exceeding the competing prompt-adaptation baseline. Without modifying the downstream agent, PAIR brings compressed execution close to the no-compression baseline and sometimes numerically exceeds it.

Distributed inference has become an indispensable part of deploying medical models under practical latency, memory, and throughput constraints. Although modern frameworks improve serving efficiency through tensor parallelism, mixed precision, kernel fusion, and multi-device communication, they are generally assumed to preserve the behavior observed during centralized HuggingFace evaluation. This assumption creates an evaluation-deployment mismatch: a model may pass offline evaluation but produce a different output after the execution stack changes. To address this mismatch, we propose a testing framework and an improved, distributed-execution-sensitive medical-model benchmark that evaluates the same checkpoint and input under a centralized HuggingFace reference and matched distributed deployments. Extensive experiments across language, vision, and multimodal medical models show that execution changes can produce measurable output disagreements. Across supported visual settings, the test success rate ranges from 0.21 to 0.43 for single-modality models and from 0.32 to 0.98 for multimodal models. The benchmark is aimed at extending medical-model evaluation from capability and security to evaluation-deployment consistency.

We investigate the problem of which multisets of integer entries yield integer eigenvalues in every square matrix arrangement? Combining module reduction with a dyadic criterion for complete splitting of cubic polynomials, we first show that if the multiset has at least one zero entry, the only possibilities have either at most one nonzero entry or exactly two whose product is a perfect square. We then apply block embedding to extend it to higher dimensions, by obtaining a linear threshold on the number of zeros. For any multiset close to a nonzero constant, we use rank reduction to derive an exact criterion for one exceptional entry, thus yielding nonconstant examples in infinitely many dimensions, and to also derive an exact reduction for two distinct exceptional entries in dimension three. The general fully nonzero three-dimensional case remains open.

Extracting the intrinsic transverse-momentum structure of quarks from deep-inelastic scattering data requires separating nonperturbative effects from perturbative radiation, which broadens the measured transverse-momentum distributions. We address this problem in electron–proton scattering, $ep\to eX$, by introducing the fiducial imbalance $\boldsymbol{q}_T$, defined as the vector sum of the scattered electron's transverse momentum and all hadronic transverse momenta within a specified rapidity window. This construction reduces radiative recoil without requiring jet reconstruction or an explicit jet veto. We account for non-global logarithms (NGLs) arising from correlated soft emissions across the acceptance boundary. The azimuthally averaged NGL contribution is resummed to all orders at leading-logarithmic accuracy in the large-$N_c$ limit using Banfi–Marchesini–Smye evolution, while the leading NGL correction to the first azimuthal harmonic is included at $\mathcal{O}(\alpha_s^2)$. For the EIC and EicC kinematics considered, widening the rapidity window increases the cross section at low $q_T$, a region particularly sensitive to nonperturbative transverse dynamics, and reduces the dilution of spin asymmetries by azimuthally symmetric soft recoil. Both the Sivers single-spin asymmetry $A_{UT}$ and the worm-gear double-spin asymmetry $A_{LT}$ increase in magnitude, while the $\boldsymbol{q}_T$ integrated cross section remains unchanged. The unpolarized $\cos\phi$ moment generated by soft gluon radiation is sensitive to NGL effects, with its ratio definition reducing common normalization uncertainties. The absence of jet reconstruction makes this observable particularly relevant at the lower collision energies of EicC, providing a way to study nonperturbative spin–momentum correlations by varying the fiducial acceptance.

Diffusion models have achieved remarkable success in generative tasks, but their inherently sequential sampling process introduces a severe computational bottleneck. Recent Parallel-in-Time (PinT) solvers attempt to mitigate this by parallelizing generation across a sliding window of timesteps, advancing the window only when step-wise changes stabilize. However, this overlapping window mechanism forces the network to repeatedly evaluate the same timesteps. When the input variations between iterations are minimal, these redundant evaluations lead to significant computational waste. To address this inefficiency, we propose ParaAnya, an output cache mechanism agnostic to the parallel sampling algorithm that can reduce the number of function evaluations (NFE). ParaAnya caches input-output pairs of diffusion models and reuses the cached output at overlapping timesteps. By dispatching only cache-miss timesteps to GPU workers, our approach eliminates redundant computation while preserving the structure of the underlying algorithms' update rules. We integrate ParaAnya into four representative parallel sampling algorithms and evaluate its performance on Stable Diffusion v1.5. Across four parallel samplers evaluated with DDIM on eight GPUs, ParaAnya provides $1.30$–$2.43\times$ speedups over their uncached counterparts and reduces NFE by up to 70.1%, reaching up to a $5.62\times$ speedup over single-GPU serial sampling while maintaining comparable CLIP scores.

Physical-field reconstruction and forecasting depend on both measurement density and spatial layout, yet evaluation under a single observation pattern does not characterize performance when that pattern changes. We introduce PDE-OBS, an integrated benchmarking platform spanning numerical data generation, model training, and inference and evaluation under varying observation conditions. It combines 560,000 fields and trajectories from seven partial differential equation families with configurable observation operators and seven adapted baseline methods for stationary reconstruction and short-horizon forecasting. Separating observation construction from physical records allows users to specify parameterized patterns and deterministic mixtures for training and testing while preserving prediction targets and data splits. The evaluation protocol uses references trained for each test pattern to compare models on identical test observations and targets, alongside equal-count groups for spatial-layout comparisons. On a 14,000-record subset, we evaluate 441 trained models under nine test patterns, yielding 3,969 evaluations. Mean cross-pattern error exceeds mean matched-pattern error in all 49 PDE-method pairs, and this finding persists in a configuration-matched subset of 117 models. Denser test observations do not consistently reduce error for a fixed model. Mixed-pattern training on five completed pairs reduces large single-pattern transfer errors, although destination-trained references usually remain more accurate. Together, the benchmark and findings support systematic evaluation of observation-pattern sensitivity and provide a reusable workflow for developing methods under changing measurement conditions. Code: https://github.com/ru1ch3n/PDE-OBS.

RGB-only end-to-end visual navigation policies remain vulnerable to collisions in real-world dynamic environments, motivating a dedicated safety layer. Existing visual Control Barrier Function (CBF) approaches seek to provide safety from RGB observations, but often rely on real-time rendering or explicit scene reconstruction and are primarily designed for static scenes, limiting their practicality for onboard deployment. We propose a teacher-student visual distillation framework that transfers the safety behavior of a privileged CBF teacher to an RGB-only student filter for dynamic environments. The student maps a short RGB history, robot velocity, and a nominal control action directly to a safe action, while the teacher uses ground-truth robot and obstacle states in a real-to-sim dynamic Gaussian Splatting environment. To reduce the teacher-student information gap, the teacher constructs safety constraints only from obstacles observable within the student's RGB history. It also accounts for obstacle-velocity uncertainty to improve robustness to motion variations, while action augmentation exposes the student to diverse safe and unsafe nominal actions to better capture the safety boundary. At deployment, the student requires only RGB observations and robot velocity, without explicit 3D reconstruction or online rendering. Experiments show that the proposed method outperforms visual CBF baselines and improves the safety of RGB-based navigation policies under dynamic obstacle motion. Project page: https://syeon-yoo.github.io/distill-cbf-site/.

In this note, we provide an estimate for the Willmore energy of Klein bottles in $\mathbb R^N$, building on the ideas of Li-Yau and Montiel-Ros for $2$-tori. In particular, we prove that the Willmore energy $\mathcal{W}(\phi)> 6\pi$ for any conformal branched immersion $\phi:\mathbb{K}^2_b\rightarrow \mathbb R^N$, where $\mathbb{K}^2_b$ is a flat Klein bottle with $0.350\lesssim b \lesssim 0.755$. This confirms partially a conjecture of Kusner. Moreover, for a flat immersion $\psi:\mathbb{K}^2_b\rightarrow \mathbb R^N$, we derive a lower bound of $\mathcal{W}(\psi)$, which confirms a conjecture of Hirsch-Mäder-Baumdicker for flat Klein bottles in $\mathbb R^N$. We also construct a smooth family of flat Klein bottles in $\mathbb R^5$, with Willmore energy between $6.912\pi$ and $8\pi$.

Robots must often continue a task after a target moves, the viewpoint shifts, or an obstacle appears, even though their earlier observations and committed actions reflect the previous scene. Many simulation robustness benchmarks fix external conditions at reset, leaving this temporal challenge underexamined. We introduce LIBERO-MAX, a benchmark of 8,000 paired cases spanning eight types of changes to geometry, observations, appearance, clutter, and paths. Each pair compares task execution with and without a mid-task event, holding the task, initial state, policy seed, and pre-event action sequence fixed. This controlled comparison distinguishes event-associated regressions from failures already present without the change. Across fourteen current VLA, hybrid, and world-action policies, events reduce success by 11.0-25.7 percentage points. Event profiles reveal shared vulnerabilities to geometry and observation changes, while policy-family rankings interleave. Camera controls show that robustness reflects both competence under the changed conditions and the trajectory from which they are encountered; varying query cadence does not eliminate the gap. Together, the paired protocol and temporal diagnostics establish LIBERO-MAX as a reproducible testbed for diagnosing failures under mid-execution changes and measuring progress toward robot policies that remain effective as the world changes.

Let $\Omega\subset\mathbb{R}^2$ be a bounded planar set that is star-shaped with respect to the origin, and let $A,B,C,D$ be independent random points uniformly distributed on $\Omega$. We consider the random segments $S_{AB}$ and $S_{CD}$ and study the distribution of the smaller angle $\Theta\in[0,\pi/2]$ formed by them, conditional on the event that they intersect. Using the radial function of $\Omega$, together with a parametrization of each segment in terms of its supporting line and the positions of its endpoints along that line, we derive an integral representation for the conditional distribution \[ \Pr\{\Theta\leq\theta | S_{AB}\cap S_{CD}\neq\varnothing\}. \] The resulting expression makes explicit how the geometry of the boundary of $\Omega$ determines the angular distribution. The probability of intersection appears naturally as the normalizing constant and is related to the probabilistic version of Sylvester's four-point problem.

Let \[ M_{k,\ell}=[z^k-w^\ell]\subset H^2(\mathbb D^2), \qquad k,\ell\in\mathbb N,\quad k\ne\ell . \] We study the large-index asymptotics of Yang's numerical invariants and the boundary structure of their generating function. Starting from the exact staircase formula obtained in our preceding work, we prove that \[ \Sigma_j(M_{k,\ell}) = \frac{C_{k,\ell}}{j} + O(j^{-2}), \] where \[ C_{k,\ell} = \int_0^\infty \frac{x^2} {(x+1/k)^2(x+1/\ell)^2}\,dx . \] The first strict descent together with $C_{k,\ell}$ recovers the unordered pair $\{k,\ell\}$, yielding an asymptotic rigidity principle. At the next order we obtain a periodic correction \[ \Sigma_j(M_{k,\ell}) = \frac{C_{k,\ell}}{j} + \frac{\Psi_{k,\ell}(j)}{j^2} + O(j^{-3}), \] whose least period is \(\operatorname{lcm}(k,\ell)\), and we determine the leading amplitudes of the strict drops. For Yang's generating function \[ \mathcal P_{k,\ell}(t) = \sum_{j=0}^{\infty}\Sigma_j(M_{k,\ell})t^j, \] we prove that it has radius of convergence one and a logarithmic singularity at $t=1$; hence it is never a polynomial for $k\ne\ell$, giving a negative answer to Yang's polynomiality question within this quasi-homogeneous family. The periodic higher-order corrections generate root-of-unity polylogarithmic boundary modes. The leading logarithmic coefficient together with the second-order boundary support determines the unordered pair $\{k,\ell\}$, while successive renormalized boundary limits recover the Fourier coefficients of every finite-order periodic asymptotic term.

A common assumption in language model development is that cognitive abilities are organized around a general, domain-free intelligence factor, like fluid intelligence in humans. This assumption is rarely tested directly, and prior attempts have done so only at a much smaller scale. We take a latent variable approach to intelligence in language models, similar to how psychometricians study psychological constructs. Performance in every specific problem set is influenced by a domain-specific and a domain-agnostic latent factor. Using factor analysis as a dimension-reduction technique, we analyzed 13,251 published evaluation scores covering 1,618 language models across 456 different text-only benchmarks. Due to the super-sparse nature of the dataset, we triangulate our analysis across different data densifiers and imputation methods. A robust pattern across different modes of bias is that 1. A general intelligence factor accounts for 70.8% of variance in model performance at our most generous estimate, and far less than that in most of our solutions, 2. Content-similar benchmarks do not necessarily cluster together, and 3. The $g$ factor is not dominated by any common theme, and there is a lack of evidence that it is well-proxied by standard "intelligence" benchmarks. Our findings go against current endeavors of defining, identifying, and targeting general intelligence as a tangible construct in language model development. This leaves the strategy of targeting a single conceptual ability without support, since the first-order abilities it would have to reach are often partially idiosyncratic and not identifiable in practice.

Precision stellar astrometry near the Sun can constrain the parametrized post-Newtonian (PPN) parameter gamma through gravitational light deflection. This study develops ECLIPSE-X, a localized multi-frame estimation architecture in which one persistent relativistic parameter is estimated simultaneously with frame-dependent spacecraft line-of-sight and roll states, separated by their differing spatial signatures and by the persistence of gamma across frames. The aim is not a competitive determination of gamma, but an assessment of whether such a joint solution and its formal covariance stay statistically valid under realistic astrometric model error. A synthetic field of 250 stars spanning 1.22-8 apparent solar radii is observed over 40 frames at 5-s cadence; weighted least squares estimates gamma with three navigation states per frame, and Schur-complement marginalization gives the formal uncertainty in gamma after navigation coupling. The nominal solution recovers gamma = 1.0001198167 with sigma_gamma = 3.075104e-4, and a 1000-realization ensemble confirms calibration. Perturbations unknown to the estimator identify plate-scale mismatch as the dominant failure mechanism: a 300-ppm scale error alone inflates the empirical-to-formal uncertainty ratio to 7126.6 with zero 1-sigma and 2-sigma coverage, against 2.18 for catalog-coordinate mismatch and 1.12 for a frame-coherent radial perturbation, while every realization converges numerically: convergence does not guarantee statistical validity. Augmenting the state with a plate-scale parameter restores consistency, at a fixed 21.2% cost in the precision of gamma set by the correlation between the two persistent parameters. A calibration sweep shows the unaugmented estimator is covariance-consistent only below sigma_p = 2.7884e-8, so the augmented state is a requirement, not a refinement, for near-Sun relativistic astrometric estimators.

Given $n$ points in a metric space, Max-Min diversification asks for a subset of $k$ points maximizing the minimum pairwise distance between the selected points. This is arguably the most fundamental notion of diversity with applications across a wide range of domains. We consider this problem under partition constraints, previously studied as Fair Max-Min Diversification (FMMD). Here, each point has a color in $[m]$, and a feasible solution must contain exactly $k_i$ points of color $i$, where $k_1,\ldots,k_m$ are prescribed parameters satisfying $\sum_i k_i=k$. We give the first constant factor approximation for the problem using local search, that runs in time $f(m)\cdot \operatorname{poly}(n)$, in which all constraints are satisfied exactly. All previously known algorithms either provided an $\widetilde \Theta(m)$ approximation factor, had running times exponential in the solution size $k$, or satisfied the fairness constraints only approximately or in expectation. We further generalize our result to the problem where each point may belong to an arbitrary subset of colors. Given lower and upper bounds $\ell_i$ and $u_i$ for every color $i$, the goal is to find $k$ points whose color counts satisfy all these bounds while maximizing their diversity.

Data lakes store large amounts of telemetry, with logs from network sensors, hosts, and applications containing possibly hundreds of fields for every event. Large enterprises are then left with data lakes that cannot be analyzed efficiently with AI. Aggregate analysis looks at persistent shifts in behavior over time. Many of the fields and columns in data lakes are not useful as they do not contain information that is sufficiently diverse or concentrated to support AI analysis. SAIVE is a simple method for examining a few rows in a large table and applies a histogram of histograms filtering criterion to select the fields that for AI analysis is more likely to yield useful results. This paper provides a principled foundation for the SAIVE heuristics by assuming of a Zipf-Mandelbrot power-law distribution of the underlying data. Constraining the Zipf-Mandelbrot exponent alpha to a reasonable range provides a a practical, cheap, expert-free filter for selecting AI valuable entities in large data sets.

We construct a supersymmetric factorization for generalized driven anisotropic Rabi–Stark Hamiltonians using an affine factor $\hat{A}=\hat{C}+\hat{a}\hat{D}$ in an inhomogeneous orthosymplectic superalgebra, with two real invertible spin matrices $\hat{C}$ and $\hat{D}$. The six real pencil parameters constrain nine Hamiltonian frequencies and one energy offset up to an overall frequency scale. The normal product $\hat{A}^{\dagger}\hat{A}$ has an exact zero-energy ground doublet and, with its antinormal partner $\hat{A}\hat{A}^{\dagger}$, gives a Witten index of two. For distinct pencil roots with finite baseline slopes, coherent gauges define a Bargmann hierarchy and endpoint conditions for exceptional finite-polynomial states. The spin grading organizes four limiting cases, comprising two driven-oscillator families with every baseline exact and the constrained anisotropic-Rabi and Rabi–Stark sheets, which meet at the degenerate-qubit isotropic Rabi model. An aligned interior example adds direct and longitudinal drives, Stark deformation, and intensity-dependent coupling while retaining the factorization.

Grid planning and operation under increasingly variable operating conditions require fast and accurate AC power flow (AC-PF) contingency analysis for numerous line outages. While ML models can accelerate these computations, existing approaches often require either training separate models for different contingencies or a single model using data from multiple topologies. Both approaches incur substantial offline data generation and training costs. To address this gap, this work proposes a fixed-point framework that reuses a single ML model trained exclusively on basecase topology data to predict post-contingency AC-PF states under any non-critical single-line outage. We analyze the proposed method's convergence under the DC model approximation and derive its convergence rate in terms of network parameters. As a side result, we show that power transfer distribution factors (PTDFs) for non-critical lines have magnitudes less than one. We further characterize the ML training region to accommodate PF specifications encountered during fixed-point iterations and derive bounds on ML prediction errors for post-contingency state estimates. Numerical tests on a 6,717-bus synthetic Texas system demonstrate convergence across all non-critical single-line outages, with prediction errors remaining close to those of basecase. The proposed framework offers a favorable tradeoff between the speed of DC solvers and Newton-Raphson accuracy.

We prove that the negative $r$-spin tautological relations of Chidambaram–Garcia-Failde–Giacchetto are a consequence of Pixton's $3$-spin relations, for every $r\ge2$, and deduce that they hold in the tautological Chow ring of $\overline{\mathcal{M}}_{g,n}$. In particular, our result for $r=2$ implies that Kazarian–Norbury $K$-relations hold in Chow. The proof factors through two essential parts. The first part shows that the tautological relations arising from Chiodo's class imply the negative $r$-spin relations. This requires an intricate study of limiting behavior of the Givental–Teleman graph contributions. In the second part, we show that the Chiodo relations are a consequence of Pixton's $3$-spin relations as an application of a generalization of Janda's work on tautological relations from CohFTs.

The Unanimous Vote problem is to determine a fixed order in which to flip each of $n$ biased coins, where each coin can be flipped only once, such that the expected number of flips until seeing both a head and a tail (or flipping all coins) is minimized. Duman Keles et al. (arXiv:2510.16678 [cs.DS]) gave an $\mathcal{O}(n \log n)$-time algorithm for this problem. Extensions of the Unanimous Vote problem are a rich source of stochastic optimization problems. We focus on three: (1) a variant in which each coin can be flipped arbitrarily many times (a solution is thus an infinite sequence of coin choices), (2) a generalization with $d$-sided dice, that can each be rolled once, where dice must be rolled until two different outcomes are observed (or all dice have been rolled), and (3) a different generalization with $d$-sided dice, where dice must be rolled until all $d$ outcomes have been observed. For (1), we show that there is an optimal sequence which follows a simple greedy rule; the same rule only gives a 1-additive approximation for the original problem (arXiv:2510.16678 [cs.DS]). The rule also yields a correspondence between a particular optimal sequence and a related mechanical word, which we exploit to characterize the conditions under which this optimal sequence is periodic. We establish tight multiplicative and additive adaptivity gaps for this variant. For (2), we show that two different generalizations of the greedy rule from (arXiv:2510.16678 [cs.DS]) can be combined to obtain a PTAS. For (3), we give an $\mathcal{O}(\log d)$-approximation algorithm by reducing the problem to Submodular Ranking (arXiv:1007.2503 [cs.DS]); the same reduction technique can be used to yield approximation algorithms for other stochastic probing problems. Finally, we pose a number of related open questions.

Hospice quality should be interpreted in relation to both provider organization and the local conditions under which care is delivered. This study develops a provider-county performance assessment framework by linking national Centers for Medicare & Medicaid Services (CMS) hospice data and Consumer Assessment of Healthcare Providers and Systems (CAHPS) Hospice Survey outcomes with county measures of rurality, social vulnerability, health burden, and workforce and health-resource context. The adjusted analysis includes 2,928 providers in 1,078 counties and combines geographic mapping, blockwise regression, six secondary CAHPS outcomes, and eight sensitivity analyses. Adding county context increased adjusted R-squared from 0.077 to 0.202. After full adjustment, for-profit hospices had overall caregiver ratings 3.832 percentage points lower than nonprofit hospices. This negative association appeared across all six secondary CAHPS domains and remained significant in every sensitivity specification. Higher county social vulnerability was also associated with poorer caregiver experience, although its magnitude depended partly on the specification of community health burden. These findings show that county context materially improves hospice performance assessment but does not eliminate the ownership difference. The framework supports context-aware monitoring, peer comparison, and targeted quality improvement.

The storage and recovery of a vector of length \(2^d\) can become prohibitively expensive as \(d\) grows, a manifestation of the curse of dimensionality. For certain structured functions and multiscale quantities, the resulting discretized vectors admit compact quantized tensor train (QTT) representations after binary tensorization: a length-\(2^d\) vector is reshaped into a \(d\)-way binary tensor with low tensor-train (TT) rank. Motivated by this construction, we study compressed sensing of tensorized signals that combine bounded TT rank with sparse low-order interaction structure, using randomly sampled Walsh–Hadamard measurements. For this structured model class, we establish a uniform restricted isometry property and derive a measurement condition guaranteeing uniqueness of noiseless recovery. We also propose a structure-aware initializer for the alternating linear scheme (ALS), obtained by projecting the adjoint backprojection onto the low-order interaction space before applying TT-SVD. We prove a uniform initialization error bound whose measurement requirement, for fixed structural parameters, grows polynomially with the tensor order \(d\) rather than with the ambient dimension \(2^d\). Numerical experiments support the predicted RIP and initialization scaling and demonstrate more reliable ALS recovery.

Agentic reinforcement learning (ARL) with verifiable rewards improves the ability of large language models (LLMs) to tackle knowledge-intensive tasks by learning to interleave search and reasoning. However, most existing ARL methods optimize only LLM-generated tokens and treat retrieved evidence as environment observations. This creates an information-credit gap: failures caused by missing or misleading evidence are attributed to the LLM policy rather than to the retriever, which motivates training the LLM and the retriever jointly. In this paper, we show that retrieval and LLM policy learning are order-sensitive: adapting the retriever before optimizing the policy yields a larger reward gain than the reverse order. To preserve this hierarchy while allowing both components to co-adapt, we formulate retrieval-augmented agentic RL as a bilevel optimization problem. To solve it efficiently, we introduce BRIDGE, a memory-efficient first-order bilevel method motivated by a loss-landscape analysis of the RL and retrieval objectives. Across seven open-domain QA benchmarks, BRIDGE achieves the highest average accuracy with both 3B and 7B backbones, improving the multi-hop average over the strongest baseline by 9.6 and 3.4 EM points, respectively. It also achieves the best averaged answer accuracy and reasoning quality across medical QA benchmarks.

Accurate prediction of three-dimensional (3D) microstructure evolution remains computationally demanding because high-fidelity phase-field simulations require repeated numerical integration over large volumetric domains and long temporal horizons. This study develops an efficient and scalable physics-guided fully convolutional spatiotemporal framework for direct multi-frame prediction of complete 3D microstructure sequences. The model combines shared 3D spatial encoding and decoding with a factorized latent translator that integrates temporal, local 3D spatial, and channel interactions. A discrete Cahn–Hilliard (CH) residual is incorporated during training to regularize the learned evolution toward the governing dynamics without altering the inference pathway. The framework is evaluated on high-resolution 3D spinodal-decomposition trajectories under nominal, long-horizon, and reduced-temporal-context forecasting. Under full temporal context, the model accurately reproduces volumetric evolution, with average 3D structural similarity remaining above 0.97 over the nominal prediction horizon. Physics guidance becomes increasingly beneficial as temporal information is reduced, improving predictive robustness and preservation of interface-level morphology. The framework also achieves more than a 30-fold wall-clock speedup relative to the reference spectral phase-field solver, while physics guidance introduces no additional inference cost. These results establish direct multi-frame, physics-guided fully convolutional learning as a high-throughput surrogate strategy for dense 3D phase-field dynamics and repeated microstructure forecasting.

Adding or removing a sounding object requires coordinated changes to visual content and sound while preserving the surrounding scene. Yet paired supervision for localized non-speech audiovisual editing remains limited, as visual and acoustic edits must target the same object and isolate its sound from overlapping sources. To address this gap, we introduce AVIOBench, a dataset comprising 37.9 hours of paired audiovisual examples spanning 1{,}878 target-object names. AVIOBench links the visual presence and acoustic contribution of each target object through a shared identity and visual mask. Our automated pipeline uses visual grounding and cross-modal consistency to select target-sound removal candidates, then jointly refines the audiovisual pairs to improve perceptual quality and cross-modal consistency. Building on this dataset, we propose AVIO, which adapts a pretrained text-to audiovisual generation model through source-conditioned feature modulation to jointly learn object addition and removal. A reference-frame curriculum gradually reduces reference conditioning during training, enabling one model to perform instruction-only editing with optional visual guidance. Quantitative and qualitative evaluations demonstrate effective audiovisual object removal and addition, with optional reference guidance providing appearance and placement control for addition.

Past research using log data has faced the "learning system wall," whereby few methods exist for generalizing models of student learning across platforms. Increasingly, online learning is captured by richer forms of data, including dialog and video, with new affordances. An example of this is remote tutoring programs, where human tutors support students who use learning systems while video conferencing. Toward better platform-general modeling of learning, we introduce an AI-driven multimodal transcription system that processes screen-recording videos into unified screenplay-style transcripts containing audio dialogue and annotated learning log actions. We describe a planned method for temporally aligning AI-generated multimodal transcripts with MATHia learning logs and for identifying and classifying student learning processes to align with MATHia logs. Lastly, we highlight challenges and potential solutions in capturing learning processes in one system, offering initial steps towards generalizing log data across diverse systems.

We show that for a horizontally stretched Bunimovich billiard, for almost every stretching parameter, there exists a sequence of eigenfunctions concentrating in the rectangular part. Thanks to the work of Markarian–Oliffson Kamphorst–Pinto de Carvalho, we know that for an open set of parameters such billiards are ergodic. The proof is a result of interaction with ChatGPT 6: we were curious if it could establish the existence of bouncing ball modes for Bunimovich or Sinai billiards. That was not successful until we suggested varying the wings. That produced an essentially complete argument for the existence of quasimodes. We then suggested using Hassell's parameter-variation argument which led to the result about eigenfunctions. The argument was then significantly simplified and clarified by the authors.

Speaker verification systems encounter combinations of noise, channel distortion, and changes in speech. Evaluating each condition separately does not establish whether their effects add. InterBias-SV organises this question around a four-term comparison: joint error, two marginal errors, and a common reference. Its results artefact contains 4,068 scored records across 17 experiments, 12 encoder labels, and six speech corpora, totalling 12 million trial evaluations. Three experiment families contain the same-corpus terms needed to compute additive contrasts. For labels assigned to speaker-trained encoders, their mean contrasts are +0.0026, +0.0088, and +0.0024 in equal error rate (EER), with larger variation across settings. These descriptive averages do not establish equivalence to additivity: trial matching, checkpoint identity, and parts of the condition metadata remain unverified. We also examine two interpretation problems. Near-chance EER can make additive predictions difficult to interpret, but chance performance is not a hard EER ceiling, and correlation with the prediction does not identify a saturation mechanism. Ratios of demographic gaps are unstable when their clean reference is near zero; absolute gaps provide a more direct summary. The benchmark provides condition definitions, analysis scripts, and explicit requirements for interpretable compound-condition comparisons, while separating recomputable summaries from claims that require further experimental validation.

We explicitly investigate Gorenstein projective, injective and flat modules over the $n$-trivial extension $R\ltimes_{n}M$ of a ring $R$ by an $R$-bimodule $M$. Assume that $fd(M^{\otimes_{R}i}_{R})<\infty$ and $pd(_{R}M^{\otimes_{R}i})<\infty$ for any $1\leq i\leq n$, $fd(\textbf{Z}(R)_{R\ltimes_{n}M})<\infty$ and $pd(_{R\ltimes_{n}M}\textbf{Z}(R))<\infty$. It is proven that a left $R\ltimes_{n}M$-module $(X,f)$ is Gorenstein projective if and only if the sequence $M^{\otimes_{R}n+1}\otimes_{R} X\stackrel{(M\otimes f) \cdots(M^{\otimes_{R}n}\otimes f)}\longrightarrow M\otimes_{R} X\stackrel{f}\longrightarrow X$ is exact and coker$(f)$ is a Gorenstein projective left $R$-module. As a consequence, we characterize Gorenstein projective, injective and flat modules over tensor rings.

Discrete fair division is the problem of dividing a discrete set of goods among agents in a fair manner. In this setting, one of the most sought-after notions of fairness is envy-freeness up to any good (EFX). In 2023, Christodoulou, Fiat, Koutsoupias, and Sgouritsa introduced the idea of a graphical valuation, where the fair division problem is represented by a simple graph where vertices are the agents and the edges are the goods, and each vertex only values incident edges. They showed that an EFX allocation always exists, while determining the existence of an EFX orientation is NP-hard. They posed a open question of determining which graphs always admit an EFX orientation regardless of valuation. These graphs, called strongly EFX orientable graphs, were first studied by Zeng and Mehta in 2025, who demonstrated that all such graphs have chromatic number at most 3, and bipartite graphs always admit an EFX orientation regardless of valuation. In this manuscript, we finish resolving this question by giving a polynomial time characterization of strongly EFX orientable graphs. In particular, we show that a connected graph $G$ is strongly EFX orientable if and only if either of the following is true: (1) $G$ is bipartite, or (2) the block decomposition of $G$ contains exactly one nonbipartite block $B$, and there exists a vertex $v \in B$ such that the degree of $v$ within $B$ is 2 and $G-v$ is bipartite. This proof was discovered by AI, with human intervention to break the problem into the appropriate subproblems.

We compute the evanescent-wave Johnson noise (EWJN) in the vacuum half-space above a superconductor, and the resulting relaxation time ($T_1$) of spin and charge qubits placed at nanometer distances from the surface. The electromagnetic response is described by a single microscopic transverse current-response kernel $Q(q, \omega)$ for a BCS superconductor. This is computed for varying densities of both non-magnetic impurities and magnetic impurities, for arbitrary frequency and temperature and for wave vectors $q \ll k_F$ (the Fermi wavevector). When combined with the fluctuation-dissipation theorem and the nonlocal surface impedances of the half-space, this yields the magnetic and electric field noise at any distance $z \gg k_F^{-1}$ from the surface, from which we obtain $T_1$. Just below $T_c$ the magnetic noise is enhanced relative to the normal state by the coherence (Hebel-Slichter-type) peak of the dissipative conductivity and drops exponentially at lower temperatures; the electric noise shows no coherence peak. The theory predicts that there is a zero-temperature noise floor induced by magnetic impurities. In the gapless regime produced by pair breaking, the finite subgap density of states $\nu(0)$ yields a temperature-independent noise spectral density and a relaxation rate bounded by $T_1^{-1}(T)\le[\nu(0)/\nu_F]^{2}\,T_{1,N}^{-1}(T)$ for $T\ll T_c$, with equality in the extreme nonlocal regime. Here $\nu(0)$ and $\nu_F$ are the superconducting and normal-state densities of states at the Fermi energy, and $T_{1,N}(T)$ is the relaxation time the same electrode would produce in its normal state at the same temperature.