Papers

We interpret the $248~\mathrm{keV_{nr}}$ nuclear-recoil candidate reported by LZ through elastic dark matter scattering mediated by a light Majoron. The Majoron provides a natural origin for the required pseudoscalar interaction: it is the pseudo Nambu-Goldstone boson associated with spontaneous lepton number breaking, directly connecting the recoil signal to neutrino mass generation. After a model independent analysis of this idea, we present a concrete realization in a scotogenic ultraviolet completion in which the lightest singlet Majorana fermion is dark matter and acquires both its mass and Majoron coupling from the symmetry breaking dynamics. A vector like up type quark and a type-I Dirac seesaw in quark sector communicate the Majoron interaction to the up quark. At low energies, the resulting portal generates the nonrelativistic operator $\mathcal O_6$, whose momentum dependence reproduces the high-recoil event without overpopulating the lower energy bins. Its spin structure removes the dominant heavy element solar capture channels, while capture on hydrogen is suppressed by poor kinematic matching and small momentum transfer. This construction simultaneously reproduces the LZ recoil spectrum and the observed thermal relic abundance while strongly suppressing solar capture.

Given a large language model (LLM), can whoever holds the weights name a semantic target (e.g., the model's identity), locate the model components that produce it, and edit them so that the target no longer appears while other capability is preserved? We call such an edit on a trained model a post-edit. We present L2W (latents to wires), a framework that performs surgical post-edits for named semantic targets. For localization, L2W uses Jacobian lens (J-lens) attribution to score components against the semantic target. For surgical removal, because LLM mechanisms are redundant (i.e., a semantic target may have multiple components producing it), L2W runs Counterexample-Guided Causal Cut (CGCC) until the target no longer appears. CGCC first cumulatively closes model components, treating each surviving expression of the target as a counterexample that exposes the next components to close, and then reopens some of them to preserve capability. In a controlled experiment with an implanted behavioural watermark, L2W removes the watermark, and its localization lands on the model region the implant changed. Across three model configurations, L2W removes model-metadata (e.g., identity) self-claims in all nine runs, and adult-content refusal in all three, with no held-out target residual. L2W further composes two post-edits on a text-to-image model: one removes the refusal of requested nudity, and a second removes the nude rendering the first exposes. The results support post-editing as a complement to post-training: post-training installs preferred behaviours, and post-editing removes named unwanted ones.

Feedback-based ALgorithm for Quantum OptimizatioN (FALQON) is a hybrid quantum-classical algorithm for solving combinatorial optimization problems, which circumvents classical parameter optimization but requires a deep quantum circuit. To reduce circuit depth, Arai et al. proposed second-order FALQON (SO-FALQON), achieving the best depth reduction among existing approaches. However, SO-FALQON brings a 2.3 times per-step measurement overhead, as it needs to calculate an additional second-order control coefficient. In this paper, inspired by the Backtracking Line Search (BLS) theory, we propose another method called BLS-FALQON, which not only reduces circuit depth to a comparable extent, but also achieves fewer measurements than SO-FALQON. Numerical simulations on max-cut problem with 8 to 20 vertices demonstrate that BLS-FALQON reduces the total measurement count by 37.7% compared to SO-FALQON, while maintaining a comparable circuit depth. Furthermore, we conduct real quantum hardware experiments on the Tianyan-176 quantum computer, which uses the zuchongzhi2 superconducting quantum processor, confirming that BLS-FALQON remains effective under real quantum hardware conditions.

Flow matching and diffusion can be trained to predict different quantities, most commonly the data $x_1$, the source noise $x_0$, or the velocity~$v$. Although theoretically equivalent, these can lead to substantially different performances. We identify two main drivers for these differences: the source–data signal-to-noise ratio, and the information bottleneck induced by the neural architecture. We show that, beyond intrinsic data dimension, the factor affecting the optimal parametrization the most is a certain signal-to-noise ratio in each data covariance direction. From this analysis, we introduce new spectral hybrid parameterizations that adapt across time and data covariance directions; we show that these are optimal for Gaussian data. We also show that architecture-induced compression changes which parameterization is easier to learn, with $v$-prediction being more sensitive to discarded directions than $x_1$-prediction. Experiments across architectures and source scales show that our spectral parameterizations are robust across regimes, can substantially accelerate optimization, while incurring essentially no additional training cost compared with standard parameterizations.

Large language models provide a practical way to generate augmented data for logical reasoning at scale, but a larger generation volume does not guarantee semantic, label, or logical reliability. Existing work has improved generation quality through generation constraints, candidate validation, filtering, and feedback-based revision; however, once a quality judgment is available, deciding whether a candidate should be retained, filtered, or repaired remains an important control problem. We propose DualGuard, a dual-mode quality-control framework for logic-preserving data augmentation. The first mode uses the current instance and candidate batch for selective retention, filtering, attribution, and targeted feedback. The second mode accumulates cross-instance execution records of augmentation actions on top of per-sample diagnosis and attribution, compares new executions against each action's own historical behavior, and supports retrospective anomaly inspection, targeted rollback, and bounded repair. Both modes share semantic verification and additionally use symbolic verification when a reliable logical form is available. Across seven downstream tasks in the Two-Stage Transfer setting, DualGuard achieves the highest Accuracy on five tasks and outperforms the no-augmentation BERT baseline on all seven. Controlled ablations further show complementary roles for Memory, Z3, and history-aware anomaly control.

LLMs enable multi-agent systems (MAS) to tackle complex tasks, but manually designing agent roles, prompts, and communication structures requires substantial expertise and effort. This motivates learning policies that construct query-specific MAS from execution reward. Existing approaches typically train these policies by repeatedly traversing a fixed set of training queries and assigning rewards at the workflow level. However, this overlooks differences in queries' evolving learning potential and obscures which substructures improve solution quality. In this paper, we propose Active Substructure-aware Policy Optimization (ASPO), a RL framework for query-level MAS search. ASPO introduces an Adaptive Query-Selection Mechanism (AQSM) that focuses training on queries at the policy's competence boundary: those it can solve but not yet reliably. A complementary discovery mechanism widens architectural exploration for hard queries, helping distinguish insufficient exploration from operator capability limits. Beyond query selection, ASPO introduces substructure-level rewards that measure output-quality gains within each action's descendant subgraph. These rewards guide proximal policy optimization to reinforce useful architectural refinements and discourage redundant or harmful computation. Together, these mechanisms prioritize learnable queries and provide fine-grained feedback for learning effective MASs. Across six benchmarks spanning mathematical reasoning, general question answering, and code generation, ASPO ranks first on every benchmark against twelve baselines.

Smaller activation outliers do not necessarily imply better low-bit quantization: their alignment with the quantizer matters. We introduce PrismQuant, a quantizer-aware rotation framework that aligns the leading activation eigenspace with the constant group subspace of asymmetric grouped INT4. The affine offsets represent the energy in this subspace without widening the range within the group. We formulate rotation design as a Ky Fan trace maximization and derive a closed-form solution that is provably optimal for this alignment objective. Compact Householder transformations and their compact-WY representation enable gradient-free construction and efficient application at both foldable and online sites. A predictive range law further connects unaligned activation energy and group size to quantization-relevant variation. Experiments on Llama, Qwen, and Mistral span dense models up to 70B parameters and a 30B mixture-of-experts model. Under W4A4KV4, PrismQuant sets the state of the art on Llama-3.2-3B among the compared methods in both perplexity and accuracy. On Llama-3.1-70B, it attains 3.85 perplexity and 72.46% average zero-shot accuracy, only 0.22 percentage points below full precision. In the deployment study on Llama-3.1-8B, our optimized implementation achieves 1.51x prefill and 1.22x CUDA Graph decode speedups over matched FP16 baselines, with 56.34% lower decode peak memory and only 2.35% additional Graph decode latency over Hadamard. Code and models are available at https://github.com/ForeverBlue816/PrismQuant and https://huggingface.co/collections/ForeverBlue/prsimquant.

Tool-using large language model (LLM) agents increasingly perform state-changing actions that require user authorization. Yet existing approaches do not provide a principled mechanism for selectively updating prior authorization when only part of an instruction changes. To this end, we propose an Authorization-Closure-Graph (ACG)-based framework that represents authorization and its dependencies as an evolving, versioned state. ACG selectively invalidates authority affected by a revision while preserving unaffected portions of the authorization state, and computes a minimal repair that identifies only the missing evidence or authority required for execution. This enables agents to adapt to revised instructions while avoiding stale authority and unnecessary authorization requests. We evaluate ACG across three advanced LLMs in two natural tasks, and ACG consistently improves action safety rate and task success rate. Code is available at https://github.com/weiliang822/ACG.

CityToolVQA addresses the weak performance of Vision-Language Models (VLMs) on quantitative tasks in urban low-altitude visual question answering. We divide the seven tasks into qualitative and quantitative groups: qualitative questions are answered directly by the VLM, whereas quantitative questions are handled by an external visual-geometric toolchain that performs object grounding, segmentation, depth back-projection, and spatial computation. The toolchain can be attached to different VLMs in a zero-shot manner; a Depth-Assisted Prompt Inference (DAPI) fallback is triggered when the main-chain detection is invalid or unreliable, and CityToolVQA-SFT adapts the 8B backbone to tool-conditioned inputs. On the 73,324-question Open3D-VQA-v2 test set, CityToolVQA-SFT (Qwen3-VL-8B) reaches 67.6% overall accuracy, and attaching the toolchain to ten open-source VLMs improves quantitative-task accuracy by 12.7-36.9 percentage points. These results indicate that externalizing explicit 3D geometric computation effectively complements the limited ability of RGB-only VLMs to estimate metric distances and object sizes.

For graph node classification, calibrated class probabilities are needed when confidence scores, usually the maximum predicted class probability, are used to rank predictions, defer uncertain nodes to human review, or control risk. Existing post-hoc calibrators either apply one global temperature or use graph-aware modules without a principled structural form. We study how local graph structure should enter node-level calibration. Our first results show that a logit-only temperature rule is insufficient when nodes with identical logits but different local homophily require different optimal temperatures. We then analyze a population-concentration contextual stochastic block model with Gaussian features and a one-layer linear GCN. Under equidistant class means, the Bayes posterior over class-template scores is a temperature-scaled softmax whose inverse-temperature is governed by a homophily-dependent signal strength. In the positive-signal homophilic regime, the resulting temperature decreases approximately inversely with normalized local homophily. This law motivates Homophily-aware Temperature Scaling (HoTS), a simple post-hoc calibrator that assigns each node a positive scalar temperature from entropy-based logit concentration and estimated local homophily. HoTS has three temperature parameters, preserves the predicted class, and learns the strength of the structural correction from calibration data. Across 18 node-classification benchmarks, two GNN backbones, and eight calibration baselines, HoTS achieves the best mean Expected Calibration Error (ECE) of 4.79%, the best average rank, and the most reliable confidence ranking in selective classification. Code is available at https://github.com/inu0104/HoTS.

We construct Laurent phenomenon structures on reductive branching algebras. For $A_{2n-1}\downarrow C_{n}$, $n\ge 2$, and the exceptional inclusions $D_4\downarrow G_2$, $E_6\downarrow F_4$, and $F_4\downarrow B_4$, we identify the branching algebras with upper Laurent phenomenon algebras, keeping the frozen coefficients polynomial. Degree-fibred categories of projective presentations give a common construction. It also gives cluster seeds of type $A_1$ for $B_3 \downarrow G_2$ and $G_2\downarrow A_2$. We give uniform sufficient conditions identifying a specialized Keel–Yu mirror algebra with an upper Laurent phenomenon algebra admitting a suitable binomial seed. The resulting theta basis is simultaneously adapted to the frozen boundary valuations. For $A_{2n-1}\downarrow C_{n}$ with $2\le n\le5$ and for the other exceptional inclusions, we obtain homogeneous theta bases parametrized by lattice points of explicit rational polyhedral cones, whose weight fibres compute every branching multiplicity. We also prove mutation invariance of finite upper bounds for LP patterns over a UFD.

Large language model agents have demonstrated promising capabilities in cybersecurity tasks, yet their ability to reconstruct complete Advanced Persistent Threat attack campaigns from complex security logs remains largely unexplored. Existing cybersecurity benchmarks for agents mainly focus on vulnerability discovery, exploitation, and security analysis tasks, leaving the evaluation of attack chain provenance under realistic security logs insufficiently studied. To address this gap, we introduce CyberClear, a benchmark for evaluating LLM agents and advanced agent systems on APT attack chain provenance from long-context security logs. CyberClear covers both single-step attacks and multi-stage attack chains, requiring agents to identify attack evidence, infer attack progression, and generate provenance graphs containing entities, causal relationships, MITRE ATT&CK techniques, and forensic evidence. To enable comprehensive evaluation, we develop an evaluation method tailored to APT attack chain provenance. Unlike conventional text similarity metrics that focus on surface-level matching, our evaluation examines whether reconstructed graphs preserve the semantics of attack chains across single-step behavior correctness, multi-step behavior identification, temporal and causal consistency, entity and relationship fidelity, and overall attack narrative consistency. Advanced multi-agent systems powered by state-of-the-art LLMs still struggle on CyberClear, motivating us to propose CyberProvenance, an agent cyber harness designed for multi-agents that augments LLM agents with evidence accumulation, execution-based validation, and feedback-guided refinement mechanisms for reliable attack-chain provenance. Extensive evaluations on CyberClear demonstrate the effectiveness of CyberProvenance in improving evidence reasoning, execution-grounded validation, and complete APT attack chain reconstruction.

The harness surrounding a language model is a central determinant of agent performance. Recent methods optimize harnesses by searching over complete programs, where individual mechanisms are difficult to isolate and reuse. We introduce PluginRSI, which represents a harness as a composition of atomized plugins and organizes harness evolution around these plugins. Individual plugins are improved independently and accumulated in a shared library, then recombined into new harnesses at each iteration. PluginRSI improves over existing harness optimization methods across software engineering, command-line interaction, and question-answering tasks. The resulting harnesses retain their advantage when transferred to other solver models without further optimization. The evolved plugin library accelerates subsequent optimization from the initial harness, which helps faster and higher convergence on unseen tasks. These results show that accumulating reusable mechanisms provides an effective basis for continued harness improvement.

Model merging consolidates task-specialized experts into a single deployable model. However, we show that such capability consolidation incurs a merging tax of increased hallucination: across 8 model-merging methods, every merged checkpoint exhibits a higher hallucination rate than the average of its constituent experts. An intuitive approach is to adapt existing hallucination-mitigation methods to the post-merge model, yet this unconstrained adaptation disrupts inherited capabilities, creating a tension between hallucination mitigation and expertise retention. To tackle this challenge, we introduce MergeHEIR, a post-merge adaptation framework designed to reduce this merging tax while preserving expertise inherited from initial experts. Using small expert-task calibration sets, MergeHEIR constructs layer-wise null-space projectors via SVD from task-specific activations collected from the merged checkpoint, and periodically projects the accumulated post-merge displacement onto the resulting null spaces to preserve inherited expertise. Theoretically, we establish minimum-distortion and maximum-dimensionality guarantees, characterize the threshold-controlled adaptation-retention trade-off, and extend perturbation guarantees beyond finite calibration data. Across 24 paired comparisons spanning three MLLM configurations and 8 model-merging methods, MergeHEIR consistently mitigates hallucination while largely preserving inherited expertise, demonstrating a more favorable hallucination-retention trade-off.

We prove that the strong spherical maximal operator in $\mathbb{R}^n$ is bounded on $L^p$ for $n\geq4$ and $p>(n+1)/(n-1)$. This establishes the conjecture of Hickman and Zahl in the remaining dimensions. The main ingredient is a local $L^2$ estimate for the pieces obtained by a dyadic decomposition in the normal variable. After squaring one input coordinate, we reduce this estimate to a $TT^*$ argument for diagonal quadratic phases.

Video diffusion transformers produce high-quality videos, yet iterative denoising incurs substantial inference latency, limiting interactive and large-scale serving. Most existing acceleration methods focus on individual requests, thereby restricting efficiency gains to redundancy within a single generation trajectory. Recent cross-request reuse offers an additional source of savings, but existing approaches often infer reusability from coarse semantic similarity. This conflates semantic relatedness with generation-level computational compatibility, so aggressive reuse may accept incompatible historical computation while conservative reuse leaves substantial acceleration unrealized. We present Carnator, a cross-request acceleration framework that addresses this challenge by extracting and using generation-native compatibility evidence directly from the model's evolving internal states. Specifically, Carnator performs a lightweight early probe to construct an Early Signature from internal diffusion states, assessing reuse validity through risk-aware compatibility decisions. The same evidence characterizes reuse scope by localizing target-specific computation and guiding joint reuse of historical latent trajectories and sparse attention connectivity. Across three text-to-video backbones, Carnator consistently achieves higher cache-hit end-to-end acceleration than the evaluated cross-request baselines despite more selective cache acceptance, reaching up to 2.17$\times$ speedup while maintaining competitive generation quality.

We study the entanglement structure of $\Omega^-\bar{\Omega}^+$ pairs produced in $e^+e^-\to\psi(3686)$, focusing on whether the entanglement requires the full four-dimensional spin space of each spin-$3/2$ baryon. Beam polarization controls the parent-state populations and coherence, thereby modifying helicity interference. Using the negativity criterion $\Neg>1$ and the measured BESIII helicity parameters, we find critical polarizations of about $0.65$ per beam for equal transverse polarization and $0.57$ per beam for equal-and-opposite longitudinal polarization. Full transverse polarization gives a near-maximal peak negativity, $\Neg_{\rm peak}\simeq1.50$, with a production-rate-weighted angular fraction of $0.60$ satisfying the witness. At the optimal production directions, destructive interference removes the unequal-helicity channels, while the near equality of the relevant equal-helicity amplitudes yields nearly equal Schmidt coefficients. Constituent-quark benchmarks further show that the angular extent of the witness is more sensitive to relative phases than the peak negativity. These results link polarization-controlled helicity interference to four-dimensional entanglement in high-spin baryon production.

The oscillation spectra of rapidly rotating $\delta$ Scuti stars are difficult to interpret because rotation modifies both the frequencies and spatial structure of the modes. Although theoretical studies predict that acoustic modes should organize into approximately equally spaced frequency sequences, systematic searches for such patterns have been limited by the absence of scalable, statistically robust detection methods. We present an automated statistical framework for identifying approximately equally spaced mode sequences in stellar oscillation spectra while quantifying the significance of each candidate detection. We apply this method to oscillation spectra of 4,681 $\delta$ Scuti stars observed by the Transiting Exoplanet Survey Satellite (TESS). The analysis identifies regular mode sequences in a large number of stars and, in many cases, reveals multiple independent regular frequency spacings within the same oscillation spectrum. While the existence of regular sequences is broadly consistent with theoretical expectations for rapidly rotating acoustic modes, the occurrence of multiple dissimilar spacings is not readily explained by current models. Differences in acoustic travel times between known island-mode families appear insufficient to account for the observed diversity of spacings, suggesting that additional mode families or other physical effects contribute to the organization of oscillation spectra of $\delta$ Scuti stars. Our results provide a scalable framework for studying regular mode sequences in large stellar surveys and new observational constraints on oscillations in rapidly rotating stars.

This paper is concerned with the maximal regularity theory for non-autonomous stochastic evolution equations with a generalized fractional derivative in UMD spaces. The generalized time-fractional derivative provides a unified framework covering both the classical Riemann-Liouville and Caputo fractional derivatives, which accommodates a wider class of anomalous diffusion processes with intermediate memory effects. Based on the singularities of the initial term and the stochastic convolution kernel, a time-weighted space and a regular-singular decomposition are used to obtain the well-posedness, space-time regularity, and stochastic maximal $L^p$-regularity results. Our results are applied to non-autonomous stochastic diffusion equation and stochastic fractional reaction-diffusion SIR model.

Code-as-Policy agents accomplish long-horizon embodied tasks by generating and executing code, yet continually improving them with teachers that are stronger but not globally reliable remains a key challenge. Existing distillation methods typically treat the teacher's complete behavior as the supervision target and thus misassign training credit on states where the teacher fails. We propose RE-0, a recursively verified policy improvement framework: rather than assuming that the teacher globally outperforms the student, RE-0 requests local corrections from the teacher on the student's own failure histories and checks in the environment whether each correction is genuinely beneficial; verified corrections yield immediate improvement. Building on this, we propose RE-OPD, which turns verified interventions into supervision for on-policy distillation. Only counterfactually verified teacher interventions provide distribution-level supervision, weighted by their measured local benefit, and the improvement they induce is projected back into the standalone student, so both where supervision is applied and how much credit the teacher receives co-evolve with the student policy. We further prove that the student's per-round gain is lower-bounded by its verified intervention gain up to verification and projection error terms. Experiments across multiple Code-as-Policy embodied tasks show that RE-0 improves both teacher-assisted execution and the standalone student, and generalizes to novel robots and scenes.

Diffusion Transformers (DiTs) have become the standard backbone for high-quality generative modeling, yet deploying them in conditional generation tasks remains computationally prohibitive because bidirectional joint attention repeatedly processes large reference streams. While existing optimization schemes mitigate generic temporal redundancy, they typically rely on coarse-grained static reuse and overlook the distinct dynamics of references and targets. Specifically, we observe that reference representations often evolve slowly along the generation trajectory, while the target often assigns little attention mass to them; reference drift and this target-to-reference exposure jointly shape how strongly stale reference states affect the target. To exploit these patterns, we introduce \RefAdapt, a training-free framework for adaptive control of joint attention between references and targets. Instead of rigid static strategies, \RefAdapt combines consecutive target-Q change with previously observed target-to-reference attention mass to control reference computation adaptively at block granularity. Under ultra-few-step settings, \RefAdapt enables speedups of up to $2.097\times$ on 4-step MiniMax H3 and $3.54\times$ on 8-step Qwen Image Edit, while maintaining comparable visual quality.

Context. AI tools for software development have progressed from code completion to autonomous agents, yet evidence on their effects on DORA performance is mixed, mostly cross-sectional, and often conflates AI-generated code (AGC) with agentic AI (AGT). Objective. We examine how AGC and AGT, separately and jointly, affect deployment frequency, lead time, change failure rate, recovery time, and deployment rework rate. Method. We audit the evidence, formalise a two-construct model with four capability moderators, and implement a discrete-event simulation of a delivery pipeline. Six experiments include a factorial design, Shapley decompositions, sensitivity analysis over 600 parameter draws, a fixed-demand robustness test, and a staggered-adoption panel of 5,000 simulated teams with counterfactuals. Results. AGC increased failure rate, rework, and recovery time in both capability profiles. When AI increased change volume, AGC shortened lead time only where review capacity was spare (-13%) and lengthened it once review saturated; in the low-capability team, its deployment-frequency gain came entirely from unplanned rework. AGT improved deployment frequency (+31% to +34%), lead time (-8% to -22%), and recovery time (-29% to -38%), but its stability effect depended on autonomous CI repair masking defects, and escaped defects increased in the high-capability team. Capability reduced AGC's absolute failure-rate penalty (7.9 vs. 1.5 points) but not its relative penalty (+34% vs. +84%). Two-way fixed effects underestimated adoption effects by 8-16%; detecting the modelled stability effect required about 50 teams, and its capability moderation about 400. Conclusions. Within the model, DORA metrics respond to AI through queueing, batching, and oversight, not only code quality. We derive measurement rules, guardrails for agentic remediation, and a sample-size-informed field-validation protocol.

Interactive chart code generation requires models to reproduce a reference chart's appearance and underlying data and correctly implement the state changes triggered by specified user interactions. Existing chart-to-code benchmarks focus on static outputs and lack task representations or evaluation protocols for interaction specification, browser execution, and post-interaction verification. We introduce IChart2Code, a benchmark comprising 377 tasks across 20 chart forms and 13 data families, with 1209 interaction requirements in six families. Each task provides a reference screenshot, task-local data, and natural-language interaction requirements, with executable HTML/JavaScript code as the target output. We further develop a browser-based evaluation protocol with an Executability gate and three rubric-guided dimensions: Data Fidelity, Static Visual Correctness, and Interaction Correctness. The protocol tests runtime viability, consistency with task-local data, fidelity of the initial rendering to the reference screenshot, and interaction-induced state changes in a sandboxed browser. A rubric-guided MLLM judge evaluates task-specific items for the three scored dimensions using the collected browser observations and achieves an overall item-level F1 score of 0.8844 against adjudicated human labels. We also propose TRAIL, a trajectory-guided dual-agent framework for interactive chart code generation. An Inspector derives task-specific inspection checks, executes them in the browser, and uses the resulting trajectories to diagnose failures and produce structured repair feedback. Averaged across four MLLMs, TRAIL improves the four evaluation dimensions over direct prompting by 7.89, 4.98, 3.45, and 4.47 percentage points, respectively.

The gravitational-wave (GW) memory effect is a prediction of general relativity, characterized by a permanent change in spacetime geometry. Although it has not yet been observed, next-generation detectors such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA) are expected to provide the sensitivity required for its first detection. GW memory comprises two distinct contributions: the nonlinear memory, generated by the self-interaction of GWs, and the linear memory, originating from the anisotropic emission of matter and radiation associated with astrophysical transients. In this work, we quantify both nonlinear and linear memory contributions produced during binary neutron star mergers (BNSs), including those associated with GWs, gamma-ray bursts (GRBs), afterglows, neutrinos, dynamical and disk-wind ejecta, and kilonova emission. We evaluate the detectability of the resulting memory signals with ET and LISA through two applications. First, we apply our analysis to the multi-messenger event GW170817 - GRB 170817A - AT2017gfo. We find that the combined memory signal from this event would have been detectable by ET with a signal-to-noise ratio of 10.7 dominated by the nonlinear memory. We also assess the detectability of the GRB memory across a synthetic population of GRBs, and find that only extreme-energy and jointly favorable configurations could produce a detectable signal in ET. Together, these results demonstrate that while next-generation detectors will probe nonlinear memory, observing linear memory from BNS counterparts will remain elusive except in the most favorable scenarios.

Bayesian state estimation for high-dimensional nonlinear dynamical systems entails a fundamental tension between statistical fidelity and computational tractability, as particle weights can collapse, while Gaussian ensemble updates can miss non-Gaussian posterior structure. Score-based diffusion filters offer a sampling-based alternative, but existing training-free score filters often rely on heuristic likelihood corrections, which can compromise posterior accuracy by neglecting uncertainty about the system state associated with each noisy reverse particle. To address these issues, we propose AECSF, a training-free adaptive ensemble conditional score filter. AECSF constructs an analytically tractable score estimator from the conditional Tweedie identity, which recasts noisy posterior score estimation as estimating the conditional mean of the system state given a noisy reverse particle and the observation. To estimate these conditional means efficiently, AECSF employs a shared adaptive weighted proposal ensemble, while particle-specific conditional weights yield an estimate for each noisy reverse particle without separate proposal sampling. The proposal ensemble is updated using reverse-particle information within the same reverse-diffusion run to improve conditional-mean estimation. Theoretically, we characterize when a fixed weighted proposal measure yields the exact noisy posterior score. Under stated assumptions, we establish a bound relating conditional-mean estimation errors to reverse-sampling endpoint error. Numerical experiments demonstrate that AECSF improves the accuracy of posterior sampling and nonlinear filtering in high-dimensional problems with limited forecast ensembles.

Finite-difference discretizations of Laplace operators yield discrete Laplacians whose spectral properties are closely tied to the stability, convergence, and physical fidelity of numerical solvers. While symmetric discretizations are well understood, many high-order finite-difference schemes produce nonsymmetric matrices for which rigorous spectral analysis is overlooked. Surprisingly, we prove that two fourth-order schemes with Dirichlet boundary conditions yield nonsymmetric discrete Laplacians whose spectra are purely real and strictly positive. Computer-assisted computations show that this property does not hold for higher-order extensions of these schemes in general.

Amortized neural likelihoods enable computationally expensive inference for models with analytically intractable or unspecified likelihoods, but their black-box nature limits interpretability. We introduce a symbolic distillation pipeline that converts trained neural likelihoods into explicit, interpretable expressions optimized for efficient parameter estimation. Our approach uses a recovery-directed objective to guide symbolic regression toward expressions that preserve parameter-recovery accuracy rather than merely approximating the likelihood function. Candidate expressions are evaluated on held-out datasets and selected using a criterion that jointly accounts for expression complexity, parameter-recovery performance, and distributional distance from the learned likelihood. We evaluate the pipeline on the diffusion decision model, a classical cognitive model, whose analytically tractable likelihood provides ground truth for controlled evaluation. The proposed recovery-directed objective improves parameter recovery over standard symbolic-regression objectives. The resulting symbolic likelihoods enable over 100 times faster parameter evaluation than both neural likelihoods and, when available, the exact likelihood, while maintaining a manageable loss in precision. We further demonstrate these computational benefits in Bayesian hierarchical inference on empirical data. Our pipeline provides a lightweight interface for integrating symbolic distillation with existing neural-likelihood estimation methods and can be adapted to a range of simulation-based inference settings.

The rapid advancement of Artificial Intelligence (AI) and Natural Language Processing (NLP) has revolutionized the way humans interact with machines. Among the most impactful developments is Automatic Speech Recognition (ASR), which enables computers to convert spoken language into text. Systems such as those built on deep neural networks, transformer architectures, and self-supervised learning have achieved near-human performance for well-resourced languages such as English and French. Yet, these advances have disproportionately benefited a small fraction of the world's languages.

LLM judges are widely used to evaluate model outputs, but their verdicts can be unreliable: a judge may favor the worse answer for its position, length, or other surface features. When a judge is wrong, is the information needed to judge correctly absent from the model, or present in its internal representations but not reflected in the output? We study this across 64 open-weight evaluators and 14 datasets, including causal interventions on 41 judges (editing activations mid-run to see whether the verdict changes). On LLMBar, built so the superficially better answer is the worse one, the verdicts of 50 judges agree with human labels only 0.456 of the time, even after averaging both answer orders. Yet a small probe on the same judges' activations, with no weight updates, reaches 0.846, and 0.686 once surface features such as length and position are residualized out (0.507 with shuffled labels). The gap holds across eight benchmarks and model families, but is not universal: a score of how well surface features alone predict the human label, computed before any probe is trained, predicts the size of the gain (Spearman rho = 0.90). On rubric tasks that score one answer at a time, leaving no surface cue to exploit, reading the internals gives no advantage. The interventions also show that editing activations mid-network already changes the verdict, before it can be read off directly, and locate the pathways carrying position and length bias. At the same label budget, the recovered signal lets a judge flag cases where it is likely wrong and yields better labels for preference learning. A wrong verdict, then, does not mean the judge lacks the information, and a simple diagnostic shows when it is worth recovering.

We develop a structure-preserving locally optimal block preconditioned conjugate gradient(LOBPCG) method for computing several of the largest positive generalized singular values of a matrix pair \((A, B)\), where \(B\) has full column rank, together with the associated generalized singular vectors. The method is derived from the Hermitian-definite Jordan–Wielandt pencil and therefore avoids explicitly forming the normal-equation matrices. By exploiting the block structure and spectral symmetry of this pencil, we construct separate search subspaces for the left and right generalized singular vectors. The resulting Rayleigh–Ritz procedure requires only a singular value decomposition of a small projected cross matrix. We adapt the improved Hetmaniuk–Lehoucq (IHL) trick to construct stable conjugate search directions in the two component spaces. We also establish an explicit correspondence between the coefficient matrices produced by the componentwise and augmented Rayleigh–Ritz procedures. This correspondence permits the componentwise IHL construction to be used in an augmented, structure-preserving LOBPCG formulation without explicitly assembling the augmented basis. Numerical experiments demonstrate the computational advantages of the proposed method over unstructured and Gram-matrix-based LOBPCG implementations.