Papers

Diffusion-based unsupervised domain adaptation (UDA) improves cross-domain transfer by generating target-specific synthetic data for downstream adaptation. Existing methods are largely designed for single-target adaptation: when a model trained on one labeled source domain must be adapted to multiple unlabeled target domains, they typically require separate diffusion fine-tuning for each source–target pair, causing training, storage, and deployment costs to grow with the number of targets. In this paper, we study multi-target data generation for diffusion-based UDA, where a single source-guided diffusion fine-tuning process is reused to generate target-specific synthetic data for multiple target domains. We propose MUSE (Multi-target UDA-oriented Synthesis with Efficient diffusion fine-tuning), a decoupled adaptation framework that separates source-supervised semantic adaptation from target-specific style adaptation. MUSE uses a shared semantic branch updated by labeled source data and target-private style branches specialized to individual target domains, enabling target-specific generation while avoiding repeated source-guided fine-tuning for each target. Experiments on standard UDA benchmarks show that MUSE achieves a stronger accuracy–efficiency trade-off than repeated per-target diffusion adaptation, reducing diffusion fine-tuning cost while improving average target-domain accuracy. The project page is available at https://xuanqi99.github.io/MUSE/.

Accurate numerical solutions of partial differential equations (PDEs) are crucial in numerous science and engineering applications. In this work, we introduce a novel neural PDE solver named AFDONet, which incorporates neural operator learning and adaptive Fourier decomposition (AFD) theory for the first time into a specifically designed variational autoencoder (VAE) structure, to solve a general class of nonlinear PDEs on smooth manifolds. AFDONet is the first neural PDE solver whose architectural and component design is fully guided by an established mathematical framework (in this case, AFD theory), turning neural operator design from an art to a science. Thus, AFDONet also exhibits exceptional mathematical explainability and groundness, and enjoys several desired properties. Furthermore, AFDONet achieves outstanding solution accuracy and competitive computational efficiency in several benchmark problems. In particular, thanks to its deep connections with AFD theory, AFDONet shows superior performance in solving PDEs on i) arbitrary (Riemannian) manifolds, and ii) datasets with sharp gradients. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

The negatively charged boron vacancy is an optically addressable spin centre in hexagonal boron nitride (hBN), but bringing two vacancies together introduces electronic interactions absent from the isolated-defect picture. Here we use density-functional theory at total charge q = -2 to show that atomic-scale placement reverses the preferred collinear spin alignment in monolayer hBN. Among seven configurations, the closest pair, separated by 4.3 angstrom, favours parallel alignment by 27.6 meV within the semilocal approximation. Moving one vacancy by a single lattice vector reverses the preference, and a 7.5 angstrom pair favours antiparallel alignment by 50.7 meV. Numerical controls change these two reference splittings by less than 1 meV; hybrid-functional calculations retain their signs while substantially changing their magnitudes. Local distortions connect the antiparallel preference at 7.5 angstrom to changes in vacancy-state hybridization along an intervening atomic chain. The closest pair instead exhibits a contact-localized spin-density contrast and constrained angular energies that depart from the bilinear Heisenberg form. These results identify a placement-sensitive regime of interacting defects and provide a microscopic foundation for investigating coupled spin centres in atomically thin materials.

Adapting general-purpose multimodal large language models (MLLMs) to specialized domains requires learning domain-specific decision criteria, which often hinge on subtle visual distinctions between otherwise plausible answers. Rationale augmentation aims to expose such evidence through additional observations or inter-sample comparisons, yet a visually valid cue is not necessarily decision-relevant: it may describe how samples differ without changing the model's relative preference between competing answers. We therefore introduce BIRD, a self-improving Boundary-Informed Rationale Distillation framework that uses model-specific confusions to locate unresolved local decision boundaries and distills the evidence that resolves these confusions into rationales. For each sample, BIRD retrieves candidate neighbors from the target MLLM's own representation space and selects the most confusable one according to its answer preferences. It then generates answer-blind candidate evidence from their visual differences and functionally verifies which evidence most effectively strengthens the model's preference for the correct answer while avoiding inappropriate transfer across the pair. The verified evidence is then distilled into a single-sample rationale for standard supervised fine-tuning. Experiments on medical and chart VQA show that BIRD outperforms competing rationale-augmentation methods across two target MLLMs, while further analyses demonstrate clearer separation of confusable answers and stronger gains from model-matched supervision.

Coding agents can now change code for developers, who describe goals, supply context, and respond to the agent's work. Yet prompts, screen activity, and task success each tell only part of this story. We present Say, Do, Understand, an end-to-end workflow for analyzing what developers write to an agent, what they do while it works, and what they can explain afterwards. The workflow has five stages (Capture, Prepare, Analyze, Integrate, and Interpret) and three instruments: a prompt codebook, a scheme for coding screen-recorded activities and events, and separate rubrics for explaining the process and the solution. We applied it in an observational study of ten experienced developers who used GitHub Copilot on an unfamiliar codebase. Crossing task performance with understanding produced four personas. The two measures agreed for eight developers but split for two: one passed most tests but could not explain the solution, and another passed few tests but explained it well. In this sample, the personas that most often asked the agent to check its work spent the least time testing on their own. These patterns are descriptive and do not generalize beyond the sample. We recommend the workflow to computing educators, industry practitioners, and researchers to adapt and evaluate human–AI communication in software engineering.

On-policy distillation (OPD) trains a student on its own responses with token-level feedback from a stronger teacher, yet the teacher can fail on questions the student already answers correctly, and how often each model succeeds varies across tasks. OPD ignores these outcomes and, on average, pushes down even the student's correct responses; gating feedback by student correctness fixes the direction but uses the teacher in the same way whether or not it succeeded. We introduce DuoOPD, in which the student's outcome sets the direction of feedback and the joint teacher-student outcome decides how the teacher supports it: when only the teacher succeeds, its verified answer becomes context for scoring the student's failed response, and when only the student succeeds, a weight shared within the task reinforces the whole response. A single rule covers all four outcome combinations without task-specific settings. Across Qwen3 and Llama, DuoOPD outperforms all five baselines in mean macro accuracy, improving over OPD by 2.58 and 5.98 percentage points, and it also leads on two further task mixtures spanning scientific calculation, instruction following, and code generation. Ablations show that outcome-based direction alone stays near the gated baseline, while the joint-outcome designs supply most of the gain.

We introduce the analogue, for invariant jet differentials, of the principal symbol of a differential operator: the component of maximal degree in the highest derivative. The top symbol identifies a canonical quotient bundle of the Demailly–Semple bundle $E_{k,m}T^*_X$, with values in jet differentials of lower order, and together with the Brückmann–Rackwitz vanishing theorem it gives a non-ampleness criterion for $E_{k,m}T^*_Z$ on complete intersections $Z\subset\PP^N$. On the Demailly–Semple tower the top symbol is the restriction to a thickening of the vertical divisor, inside the singular jets. The criterion applies in orders $3$ and $4$: $E_{3,5q}T^*_X$ is not ample on any smooth hypersurface $X\subset\PP^4$, and $E_{4,m}T^*_X$ is not ample for $m\ge7$ with $m\equiv0,1,2\pmod 7$ on any smooth hypersurface $X\subset\PP^5$ of degree at least $2$. This contradicts the Diverio–Trapani conjecture at its own threshold.

Recent advances in speech deepfake detection (SDD) have leveraged the Mixture of Experts (MoE) to enhance generalization capacity. However, existing gating networks often overlook the acoustic and temporal cues of deepfakes. In this work, we propose a novel domain-adaptive dual-gating MoE (DADGMoE) framework for SDD under unseen attack types and acoustic conditions. Our innovative dual-gating mechanism leverages Sinc-layer-based filters to process both low-level acoustic signals (raw waveforms) and high-level speech representations from a large self-supervised learning (SSL) model. It further incorporates domain prototypes to guide expert routing based on implicit deepfake patterns. The lightweight affine experts process the routed inputs. Experiments show that our DADGMoE significantly outperforms the baseline, achieving up to a 40.8% relative EER reduction on challenging out-of-dataset benchmarks. This framework demonstrates superior generalization capabilities and efficient design.

How does compositional reasoning emerge during learning? We address this question by mathematically analyzing the learning dynamics of deep linear networks. We train these networks in structured synthetic environments and derive a theory linking the structure of experience to compositional learning. Our theory predicts when compositional inferences emerge, whether they are identifiable from the available evidence, and how new linking evidence can rapidly unlock previously unavailable inferences. These results provide a qualitative explanation for several phenomena observed in human cognition. They account for why a composition can fail despite knowing its premises, why similar compositions can emerge at different times, and how a single linking fact can suddenly enable many new inferences. Taken together, these findings establish a mathematical link between the statistical structure of experience and the development of compositional reasoning.

Vision-language-action (VLA) models adapt pretrained vision-language models (VLMs) for closed-loop robot control, transferring their perceptual and semantic capabilities to action prediction. Despite strong in-distribution performance, however, VLAs often degrade under deployment shifts. Adversarial training (AT) offers a model-adaptive approach to robustness without explicitly anticipating individual shifts, but its effect on natural distribution-shift generalization in multi-view VLAs remains unclear. We study this question using a multi-view VLA directly adapted from a pretrained VLM and evaluate generalization across seven LIBERO-Plus shift axes. Direct AT substantially improves Camera Viewpoint and Sensor Noise, the two shifts affecting only the third-person view, yet produces mixed or negative effects on other shifts. Controlled view interventions reveal a surprising failure mode that we term view collapse: Direct AT can shift cross-view reliance so strongly that the policy becomes dominated by the wrist view. This exposes a robustness shortcut: apparent robustness to a shifted view can arise from reduced use of that view rather than more robust perception of it. This motivates a distinction between robust perception, extracting reliable information under within-view shifts, and robust fusion, adapting reliance across views according to their reliability. To reduce fixed view reliance, we use a simple View Swap intervention and then re-evaluate AT. With View Swap, AT further improves Camera Viewpoint, Sensor Noise, and Robot Initial State, while its effects remain mixed on other shifts. Our results show that multi-view robustness requires separating improved perception from changes in cross-view reliance, and that AT provides selective rather than generic distribution-shift benefits.

Speech deepfake detection faces significant challenges due to domain shifts. Domain generalization (DG), particularly meta-learning for domain generalization (MLDG), offers a promising solution by simulating and mitigating domain shifts. However, MLDG is often hindered by conflicting gradients between its meta-train and meta-test objectives, leading to suboptimal performance. To address this problem, we propose domain gradient surgery (DGS), a meta-learning method that resolves conflicts through an asymmetric projection strategy. DGS removes the destructive component from the meta-test gradient, ensuring a conflict-free optimization trajectory versus the meta-train gradient. Furthermore, we introduce layer-wise DGS (LW-DGS), an efficient variant of DGS that dynamically identifies and intervenes only conflict-prone layers. Extensive experiments on challenging benchmarks demonstrate that DGS-MLDG and LW-DGS-MLDG achieve an average relative EER reduction of 5.29% and 4.04%, respectively.

A class of graphs is monadically dependent if one cannot encode all graphs in coloured graphs from the class using a fixed first-order formula, and monadically stable if one cannot even encode arbitrarily long linear orders. Bonnet et al. (ICALP 2025) characterised monadic dependence by flip-separability: for every vertex weighting, boundedly many flips - complementations of the adjacency relation within a vertex subset - make every ball of radius $r$ carry at most an $\varepsilon$-fraction of the weight, so that every set carrying an $\varepsilon$-fraction has two elements pulled apart. We introduce flip-packability: boundedly many graphs, each obtained from the input by boundedly many flips and all determined by the weighting before any set is presented, such that every set carrying an $\varepsilon$-fraction of the weight has $m$ elements pairwise far apart in one of them. The number of flips producing each graph depends on the radius alone; only the number of graphs depends on $\varepsilon$ and $m$. We prove that a class of graphs is flip-packable if and only if it is monadically stable, and $2$-flip-packable, that is, flip-packable with $m=2$, if and only if it is monadically dependent. The passage from two scattered elements to $m$ is thus exactly what separates the two notions. For monadically stable classes we show that the flipped graphs can be computed from the weighting in cubic time. Varying the three parameters of the definition - the sparsifying operation, the radius, and the number $m$ of elements scattered - produces eight known characterisations of sparse and dense graph classes from the same template. In each case $m$ separates a depth-like notion from its width-like relaxation: treedepth from treewidth, shrubdepth from cliquewidth, and monadic stability from monadic dependence.

Graph learning from edge-detecting queries concerns the reconstruction of an unknown edge set on a known vertex set. Each query reports whether a specified vertex subset contains at least one edge. We study non-adaptive schemes, in which all queries are fixed before any outcomes are observed, with the goal of achieving exact recovery using few queries and fast decoding. For general graphs on $n$ vertices with at most $k$ edges, non-adaptive recovery requires $\Omega(\min\{k^2\log n,n^2\})$ queries in the worst case, even when a small error probability is allowed. In this paper, we consider Erdős–Rényi ($\mathrm{ER}$) graphs $G\sim \mathrm{ER}(n,q)$, with expected edge count $\bar{k}=q\binom{n}{2}$. Our scheme uses $O(\bar{k}\log n)$ queries and achieves exact recovery in $O(\bar{k}\log n)$ decoding time with probability tending to one throughout the regime $\bar{k}\to\infty$ and $\bar{k}=o(n^2)$. This improves the previous $O(\bar{k}^{1+\delta}\log n)$ decoding guarantee for any fixed $\delta>0$, while maintaining the same query order. The guarantee also extends beyond the previously studied regime $\bar{k}=\Theta(n^{2\theta})$ with fixed $\theta\in(0,1)$. Our approach builds on the binary splitting method used in prior work, which organizes vertices into a hierarchy of successively smaller groups. We introduce three main changes: (i) we use random affine hash functions over a finite field to process each candidate pair in constant time; (ii) we apply the splitting procedure directly to the full graph, avoiding the need to combine solutions to multiple smaller graph-learning subproblems; and (iii) we bound the total decoding workload directly rather than deriving separate high-probability bounds on candidate counts at each level.

For $d\ge2$ the $q$-deformed modular group specialized at a primitive $d$-th root of unity is the triangle group of type $(2,3,d)$. Using this we determine the fractions $r/s$ for which the $d$-th cyclotomic polynomial divides the denominator $S_{r/s}(q)$ of the $q$-deformed rational number $[r/s]_q$. They form the orbit of $\infty$ under the normal closure of the translation $z\mapsto z+d$ in $\mathrm{PSL}(2,\mathbb{Z})$. This proves a conjecture of Byakuno, Ren and Yanagawa, and shows that the congruences $s\equiv0$ and $r\equiv\pm1$ modulo $d$ characterize the divisibility exactly for $d\le5$. For $a\in\{2,3,4,6\}$ and $n>5a^2$ prime to $a$ we show that $S_{a/n}(q)$ is irreducible up to cyclotomic factors. Together with a computer check for small primes, this confirms a conjecture of Kogiso, Ren, Wakui, Yanagawa and the author for every prime $p$ and every $r$ prime to $p$ with $r\equiv\pm a$ or $ar\equiv\pm1\pmod p$.

Natural Language Autoencoders (NLAs) produce unsupervised text explanations of a model's activations: a verbalizer describes an activation and a reconstructor learns to recover it from this text. Under the established point-reconstruction NLA training recipe, explanations become more useful for predicting model behavior while also increasingly introducing unsupported details and exhibiting writing defects. To assess these changes separately, we introduce a standardized evaluation framework for unstructured NLA explanations, measuring information recoverable from explanations, contextual support for their claims, and writing quality. To address confabulation and writing defects, we move beyond predicting a single activation: explanations can distinguish distributions of possible activations even when their means and optimal point-reconstruction rewards are identical. We introduce Flow-NLA, which models the distribution of activations compatible with an explanation and trains the verbalizer using a diffusion likelihood bound. Across Qwen, Gemma, and Apertus, this richer signal retains the utility gains of point reconstruction while curbing the growth of confabulation and writing defects, opening up a direction for improving activation-derived training to encourage more informative, supported, and readable explanations. Code and evaluation prompts will be made publicly available upon acceptance.

Pretrained biomedical vision-language models achieve strong zero-shot performance in biomedical image classification. However, downstream biomedical classification often depends on subtle visual differences between classes that may not be fully captured by pretrained representations. Few-shot adaptation addresses this mismatch by optimizing a task-specific predictor on a small labeled support set. Because the selected examples capture only part of the visual variation within the target classes, the adapted predictions can depend strongly on their composition. We propose Prompt-Anchored Residual Adaptation (PARA), which retains the frozen prompt prediction as a support-invariant semantic anchor and incorporates a visual prediction learned from the support set through an anchor-relative residual. The residual step is computed in a closed form from frozen support embeddings using anchor discrepancy and support agreement. Support-set dependence also limits evaluation: comparisons are fair within a shared draw but remain conditional on its composition. To obtain more reliable comparisons, we introduce a repeated-support protocol that separates support-selection variation from optimization randomness and reports both average and worst-20% performance. PARA achieves state-of-the-art performance in both few-shot classification and base-to-novel generalization.

Quantum physics-informed neural networks (QPINNs) solve partial differential equations (PDEs) by training parameterized quantum circuits against physics-based residuals, yet the role of the embedding that maps coordinates into quantum states remains insufficiently understood. In this research, we introduce a unified embedding framework that formulates embedding as a functional transformation shaping the feature representation available to the variational circuit, and we propose two embeddings within it. The Linear Quantum Neural Network Trainable Embedding QPINN (LQNN-TE-QPINN) generates data-dependent features with an auxiliary quantum circuit and adds them to the input coordinates, instead of multiplying them as in our previous formulation. The adaptive-frequency QPINN (AdaFreq-QPINN) promotes the frequency-scaling factors of an arccos-Chebyshev encoding to trainable parameters. We evaluate both against direct and fixed analytical frequency encodings and alternative hybrid architectures on one- and two-dimensional Burgers equations. In one dimension, LQNN-TE-QPINN achieves a relative $L_2$ error of 0.0916 with 720 trainable parameters, compared with 0.4501 for direct-encoding QPINN and 0.1233 for a locally adaptive classical physics-informed neural network with approximately eleven times more parameters, while AdaFreq-QPINN attains the lowest error among the analytical embeddings with only four additional parameters. In two dimensions, LQNN-TE-QPINN attains the lowest training objective, although its solution error is not clearly separated from that of a data re-uploading QPINN. Under simulated hardware noise, LQNN-TE-QPINN retains the lowest absolute derivative error while degrading most relative to its noiseless baseline. These results demonstrate that embedding design substantially influences the approximation and optimization behavior of QPINNs.

Existing benchmarks for large language models (LLMs) in hardware design evaluate downstream artifacts such as generated RTL, assertions, or testbenches. When a model fails such a benchmark, the failure is ambiguous: it may have misread the specification, or it may have understood the specification and failed to write the code. We present SpecRead, a benchmark that isolates specification comprehension from generation ability. SpecRead v2.1 contains 385 questions over 10 open-source OpenTitan IP blocks: exact retrieval, cross-section reasoning, contradiction detection in mutated specifications, and spec-RTL consistency checking, plus 82 controls (41 distractor, 41 consistent-RTL). Type-4 items are built from real RTL mutations; we retain only mutations that Icarus Verilog simulation shows to change observable behavior. A with-spec vs. without-spec ablation suggests the questions require the excerpt, not training recall alone (without-spec accuracy 3/20 on the t1/t2 subset), though memorization of the source text may still help spot mutations. As an initial characterization with a small model, Ministral-3B scores 33.2% overall (128/385; macro average 39.0%): 55.2% on retrieval, 51.7% on cross-section reasoning. On the two contradiction-focused types, the verdict-plus-location measure gives 48.0% (t3) and 63.3% (t4), with a 51.2% false-positive rate on distractors and 100% on consistent-RTL controls. Layered scoring shows the model locates contradictions well (78.9-81.6% location accuracy) but scores lower on their category (43.9-49.7%). A structured "rule-table" prompting intervention lowers accuracy on every question type except t2 (tied). SpecRead is automatically scorable by deterministic checks, with gray-zone cases counted wrong under the conservative main scoring. The benchmark is regenerable for type-3 items via mutation injection, and built exclusively from public sources.

Most continuous diffusion language models process one latent position per token at each sampling step, making generation expensive. Two-stage methods lower the cost by reducing the latent length, but they fix the compressed embedding space before training the diffusion model. Embeddings from the fixed space can be difficult to model with diffusion and decode reliably into tokens, which limits generation quality after compression. To address this problem, we introduce JPEG-DLM (Joint-embedding Prediction for Efficient Generation with Diffusion Language Model), which jointly trains a compressor, a flow matching model and a decoding module. With joint-embedding prediction, JPEG-DLM learns compressed embeddings that are more structured, easier to model with diffusion and reliably decodable into tokens. JPEG-DLM achieves the lowest mean Gen-PPL and highest throughput among recent diffusion and flow models on LM1B and OWT. At a compression rate of 0.5 on OWT, it reaches a Gen-PPL of 34.52 and approximately 2.3 times ELF's throughput. These results suggest that jointly learning compressed embeddings offers a promising path toward efficient diffusion language modeling. Code will be released soon.

We develop positivity certificates for polynomials that are affine in auxiliary parameters, with sum-of-squares multipliers depending only on the principal variables. Under a restricted Archimedean order-unit condition, every strictly positive scalar polynomial admits such a certificate. We construct a convergent restricted moment-SOS hierarchy for polynomial optimization problems with affine parameters and establish a flatness criterion for global optimality detection and global minimizer recovery. The scalar theorem extends to polynomial-matrix constraints with any number of affine parameters. For matrix-valued objectives, pointwise positivity is sufficient with one parameter but can fail with two or more parameters; uniform free positivity provides a general sufficient replacement. Applications include robust linear programming, robust Lyapunov design, min-max polynomial optimization, analysis and control of input-affine dynamical systems. Numerical experiments show that the proposed approach substantially reduces semidefinite block sizes and solution times while incurring little or no degradation in bound quality for most test cases.

We prove the $L^p(\mathbb R^n\times\mathbb R^m)$ boundedness of the rough product singular integral $T_\Omega$, its maximal truncation $T_\Omega^*$, and the product Marcinkiewicz integral $\mu_\Omega$ for $1<p<\infty$, assuming that $\Omega\in H^1(S^{n-1}\times S^{m-1})$ satisfies separate cancellation. These results include kernels in $H^1(S^{n-1}\times S^{m-1})$ that lie outside the Orlicz classes required in earlier work. We also obtain equivalent characterizations of the product Hardy space in terms of restricted, conjugate, and spectral Riesz transforms, together with radial maximal functions, non-tangential maximal functions, and area integrals associated with the spectral and ball Poisson extensions. The operator bounds are proved using restricted Riesz transforms and the Calderón–Zygmund rotation method. For the Marcinkiewicz integral, we further establish integrable bounds for the radial profiles of the transformed kernels.

Decoding signals over unknown channels with minimal pilot overhead is a critical challenge in next-generation communications. Existing deep learning approaches typically rely on generic encoders that struggle to model long-range temporal dependencies or efficiently capture the channel's physical properties from scarce data. We argue that standard architectures suffer from agnostic estimation gaps, as they must implicitly learn the constellation geometry that is already known. We introduce the Constellation-Aware Transformer (CAT), a novel architecture that explicitly injects geometric inductive biases into the equalization process. CAT is composed of a stack of custom TransFIRmer blocks, which use an "early interaction" paradigm to co-process received signals and ideal constellation symbols. Each block features a split Feed-Forward Network that applies a Finite Impulse Response (FIR)-inspired filter for deconvolution and a parallel MLP for geometric refinement. We show that this design is structurally aligned with the optimal linear (MIMO Wiener) receiver: its attention can implement a matched-filter bank, and its bidirectional FIR branch provides the non-causal filtering that block MMSE equalization requires. In the semi-supervised setting, CAT needs fewer pilots than VAE and standard Transformer baselines: on two of our three ISI channels, it reaches a lower SER with 64 pilots than they do with 128.

Vision-language models (VLMs) answer visual questions by combining visual information extraction with downstream problem solving. We investigate a fundamental question: Does an incorrect answer necessarily reflect a failure in visual extraction or problem solving? A model may succeed at both abilities when tested separately yet still fail on the original multimodal question, a distinction that overall answer accuracy cannot reveal. To study this, we perform a question-level empirical analysis across multiple VLMs and visual domains. We define an exactly scorable task state (i.e., the visual information sufficient to solve a question) and use it to test whether the same model can extract the required state, solve the question from the ground-truth state, and answer the original multimodal question. We find that composition failures, where extraction and solving both succeed but direct answering fails, account for 17.7% to 75.6% of direct-answering errors across multiple VLMs and datasets. To address this failure mode, we introduce a simple yet effective method, termed State Realization Tuning (SRT). SRT fine-tunes LoRA adapters attached to the language-model layers while keeping the pretrained VLM weights frozen. It trains the model to output the ground-truth task state before the final answer in a single autoregressive response. SRT improves over standard supervised fine-tuning by 1.7 to 14.1 percentage points and repairs 92.5% to 98.1% of diagnosed composition failures. A single LoRA adapter trained with SRT also improves performance across substantially different task-state structures. Our work shows that having both visual extraction and problem-solving capabilities does not guarantee correct multimodal answering. Requiring the model to first output the visual information needed to solve the question can help bridge this gap.

Learning PDE operators on complex domains requires capturing interactions among fields on vertices, edges, and faces, alongside global responses shaped by topology. Existing neural operators accommodate irregular geometries but often overlook these distinct field supports or their condition-dependent coupling. We introduce the Dynamic Kuramoto–Hodge Operator (DKHO), which combines topology-constrained interactions with learned coordination. DKHO encodes conditions on their native cochain supports, evolves Kuramoto-inspired relation states through the boundary and coboundary operators that compose the Dirac operator, and decodes non-harmonic and harmonic responses in orthogonal Hodge subspaces. Topology thus determines where information can flow, while learned dynamics adapts how it is exchanged to each PDE instance. Across porous-medium Darcy flow, torus transport–diffusion, and cavity magnetostatics, DKHO-large reduces prediction error by approximately 61% on average over leading baselines, while DKHO-small remains competitive using only 11.5–24.3% as many parameters. These results suggest that coupling topological structure with adaptive dynamics provides an effective inductive bias for accurate and parameter-efficient PDE operator learning on complex geometries and topologies.

Assuming a suitably uniform Hardy–Littlewood prime tuples hypothesis, we obtain a second-order asymptotic for the proportion of short intervals containing a prescribed number of primes, when the interval length is comparable to the average prime spacing. The leading term is Poisson, but the arithmetic correction differs from the binomial correction in Cramér's independent model and predicts a stronger bias toward counts near the mean. The proof combines inclusion–exclusion with singular-series estimates of Montgomery and Soundararajan and a finite-sieve argument that controls the required alternating sums as the truncation order grows. We also give a refined random model that reproduces the correction and numerical comparisons that support the prediction.

Classical texts aligned with their translations support machine translation, retrieval and computational research, but evidence comparing alignment workflows is scattered. This study compares seven systems on 452 texts in Pali, Sanskrit, Mishnaic Hebrew and Tibetan, comprising 9,833 human-aligned units: four embedding pipelines, a direct LLM call, an autonomous agent, and the agent revised by an independent auditor. Generative workflows recover 93-94% of reference correspondences, against at most 77% for embeddings. A ceiling analysis shows that sentence boundaries make some references unrepresentable by the embedding pipelines. Reference recovery is similar across generative workflows: the agent's advantage is 0.5 percentage points (95% CI -0.02 to 1.17), and auditing adds no established benefit. Agents nevertheless produce structurally valid output for all 452 texts, against 437 for direct calls. A blinded three-LLM panel assesses every generative mismatch against the source and human reference. Most mismatches are labelled defensible editorial variation; consensus major-error labels cover only 0.06-0.14% of units. The panel labels significantly fewer residual defects for agents than direct calls (0.7% versus 1.4%), suggesting that reference recovery alone understates alignment quality. On ten long Pali discourses taken as published online, agents and audited agents raise recovery from the direct call's 71% to 84% and 92%. Identical reference-located chunks bring all three to 93%. Agents thus improve structural reliability and reduce judged defects on short passages, while their large recovery advantage on long documents disappears after chunking. In this setting, independent auditing offers little measurable additional benefit on prepared passages.

The renormalization of asymptotically AdS spacetimes in New Massive Gravity is studied using boundary terms constructed with the extrinsic curvature. For generic values of the theory couplings, a single extrinsic boundary term produces a consistent holographic description, as the variation of the total action is finite and expressible in terms of the holographic source. This prescription applies to constant-curvature geometries and non-Einstein solutions with Brown-Henneaux asymptotic conditions. A suitable asymptotic expansion shows the agreement of the resulting holographic stress tensor with the one obtained from the auxiliary-field formulation. At the degenerate point, where the two maximally symmetric vacua coalesce, the Fefferman-Graham expansion admits an additional mode associated with relaxed AdS boundary conditions. A quadratic extrinsic counterterm removes the new divergences and leads naturally to a holographic picture with two independent sources. The corresponding responses obey a modified holographic Ward identity and determine finite conserved charges. Finally, the proper use of the Noether-Wald formalism reproduces the correct charges of the BTZ black hole, non-Einstein AdS waves, and the rotating hairy black hole.

This paper presents a theory-driven characterization of type-safe decision frameworks for the agentic control of 5G networks, where every decision must be an element of a declared option set rather than free text. Three design points are evaluated on an Open5GS/UERANSIM testbed with a closed core-policy loop, namely a hosted typed model (Jev), an open fine-tunable typed encoder (Laya), and a zero-label retrofit of a general language model (AnyJev). The proposed theoretical framework turns timeliness, type conformance, certification cost and cardinality into checkable applicability predicates, supported by an optimal act/escalate/abstain gate, an escalation-feasibility floor, a co-location stability condition, per-type conformal risk control with a certification label floor, and a type-mismatch bound. Measuring every predicate yields an applicability map from framework to 5G decision class. Type safety removes format failures but not the question: the fine-tuned typed encoder returned its training answer for 98-99.5% of changed questions, and its calibrated gate then acted wrongly on up to 80% of them, whereas the question-reading frameworks acted wrongly on at most 0.143 (Jev) and 0.137 (AnyJev) of any changed question, but were either hosted and 11-29 times slower (Jev) or reliant on an 8B language model (AnyJev).

Deep learning has emerged as an efficient alternative for predicting high-performance material distributions in topology optimization. Existing methods struggle to accurately capture load-transfer information, limiting out-of-distribution generalization, while their model architectures often incur high computational costs. To address these challenges, this paper proposes TopoMamba, a topology prediction framework incorporating a load-support relation-guided multi-directional state-space model. Coupling physical fields with load-support relations enables more effective modeling of mechanical dependencies. A load-support relation-guided spatially adaptive fusion mechanism dynamically adjusts multi-directional scan features according to spatial conditions. Mamba is coupled with the solid isotropic material with penalty method to enhance structural mechanical performance while maintaining computational efficiency. Results on two-dimensional topology optimization benchmarks demonstrate that TopoMamba achieves superior topology prediction accuracy, out-of-distribution generalization, and computational efficiency over state-of-the-art models. The proposed load-support physics-guided framework enables efficient optimization of more complex structural systems.

Onboard satellite models often require frequent updates, but the weights adapted to earlier data distributions can quickly become outdated. However, updating large-scale model parameters in orbit presents significant challenges due to the limited uplink bandwidth of Low Earth Orbit (LEO) satellite systems, particularly for hyperspectral satellite imagery, where high-dimensional spectral-spatial inputs lead to increased model size and update costs. Existing full fine-tuning methods are thus expensive to retrain and difficult to deploy under strict communication constraints. To address this challenge, we propose NE-LoRA, a parameter-efficient adaptation framework for bandwidth-constrained onboard hyperspectral model updates. NE-LoRA combines a primary low-rank branch with a nonlinear auxiliary branch to capture both global update trends and complex spectral-spatial variations. Additionally, we introduce a differentiated training strategy for multi-matrix adapters, motivated by the asymmetric initialization and gradient dynamics of different adapter matrices. Experiments on four hyperspectral datasets and three representative backbone models demonstrate that NE-LoRA consistently outperforms LoRA-based baselines and remains competitive with, and in several cases superior to, full fine-tuning. Across the evaluated settings, NE-LoRA updates only a small fraction of the total parameters on average while preserving low deployment overhead, offering a favorable accuracy-communication trade-off for onboard hyperspectral adaptation.