Sparse-view 3D reconstruction is increasingly addressed with feed-forward splatting networks that predict explicit primitives directly from images. Yet most existing methods remain centered on Gaussian primitives and expose surfaces only indirectly: extracting a usable mesh for downstream simulation, physics reasoning, or embodied interaction still requires expensive post-hoc steps that break the feed-forward promise. This limitation is especially pronounced in pose-free settings, where scene structure and camera parameters must be estimated jointly from sparse observations. We present TriSplat, a feed-forward reconstruction network that represents scenes with oriented triangle primitives and directly exports simulation-ready mesh scenes from a single forward pass. Given input images, the network predicts local 3D point maps, triangle attributes, camera poses, and optional intrinsics. Rather than regressing triangle orientation as an unconstrained latent variable, our approach constructs geometry normals from the predicted point maps, refines them with an image-conditioned normal head, and converts them into stable local frames for triangle parameterization. A mono-normal bootstrap schedule further stabilizes early training, while opacity and blur scheduling progressively sharpens the learned surface representation for direct mesh extraction. Experiments on RealEstate10K and DL3DV show that this representation produces more geometry-faithful reconstructions than Gaussian feed-forward baselines while maintaining competitive novel-view rendering quality. Because the rendering primitives are themselves surface triangles, the output can be directly ingested by physics engines, collision detectors, and standard rendering pipelines without any conversion, making it a practical simulation-ready solution for feed-forward 3D scene reconstruction.

Generating high-fidelity and controllable synthetic data is critical for advancing end-to-end autonomous driving, particularly for addressing the long tail of rare safety-critical scenarios. Existing occupancy-guided methods typically rely on shallow conditioning mechanisms and reference-frame-dependent video synthesis, which limits fine-grained controllability from arbitrary BEV layouts and restricts their applicability for scalable simulation. In this paper, we propose AnyScene, a unified occupancy-centric framework for driving scene generation. AnyScene generates semantic occupancy sequences from BEV layouts through a Spatial-Temporal Occupancy Diffusion Transformer that jointly tokenizes BEV and occupancy features in an autoregressive manner. This design enables precise controllability from cross-dataset and user-defined BEV inputs while naturally supporting long-horizon generation. Building upon the generated occupancy, a Geometry-Grounded View Expansion module treats occupancy as the canonical spatial representation and synthesizes temporally consistent multi-view driving videos in a reference-free and autoregressive fashion, supporting flexible camera configurations at inference time. Extensive experiments demonstrate that AnyScene achieves state-of-the-art performance in both occupancy and video generation. It exhibits strong generalization to unseen and customized layouts, and provides measurable benefits for downstream tasks such as sparse-view 3D reconstruction.

This paper studies the next major bottleneck in agentic AI as system scaling, not only model scaling: the design of auditable, persistent, modular, and verifiable architectures around foundation models. We refer to this shift as scaling the harness: treating the structured execution layer around a foundation model as a first-class object of design, evaluation, and optimization. Although recent large language models enable agents to use tools, retrieve information, maintain memory, and execute long-horizon workflows, evaluation remains largely model-centric, often reducing agents to final-task success while treating memory, retrieval, tool use, orchestration, verification, and governance as secondary implementation details. This framing is increasingly inadequate because agent performance emerges from the interaction among the foundation model, memory substrate, context constructor, skill-routing layer, orchestration loop, and verification-and-governance layer. Together, these components form the agent harness, which translates model capability into long-horizon agent behavior. We study scaling the harness through three core bottlenecks: context governance, trustworthy memory, and dynamic skill routing, together with the orchestration and governance mechanisms that coordinate and constrain them. We further outline a research agenda for harness-level benchmarks that go beyond one-shot task success to measure trajectory quality, memory hygiene, context efficiency, communication fidelity, verification cost, and safe evolution over time. To make the discussion concrete, we develop CheetahClaws: https://github.com/SafeRL-Lab/cheetahclaws, a Python-native reference harness, and compare it with Claude Code and OpenClaw. Our main claim is that future progress in agentic AI will depend as much on system design as on stronger foundation models.

Subject-driven image generation aims to synthesize new images that preserve the identity of the given subject while following textual instructions. Existing approaches often encode text and reference images separately. This limits cross-modal reasoning abilities and causes copy-paste artifacts. Recent frameworks that connect multimodal models and diffusion models improve instruction following, but largely overlook identity preservation. To address these limitations, we condition diffusion models on Multimodal Large Language Models (MLLMs) that jointly encode text and reference images, and augment it with VAE-based identity conditioning. A novel Dual Layer Aggregation (DLA) module is designed to aggregate multi-level MLLM features for optimal conditioning, and a multi-stage denoising strategy is applied to progressively balance the semantic information from MLLM and fine-detail identity from VAE during inference. Extensive experiments demonstrate that our approach harmonizes multimodal understanding with identity preservation, mitigates copy-paste issues, and achieves superior performance regarding human preference on subject-driven image generation. Our project website is available at https://zsh2000.github.io/squeeze-mllm-subject-gen/.

Multimodal Large Language Models (MLLMs) achieve versatility by reformulating diverse tasks into a unified instruction-following framework via instruction tuning. However, real-world deployment requires continuous adaptation to emerging tasks, motivating Multimodal Continual Instruction Tuning (MCIT). Despite its growing importance, current MCIT research is hindered by severe engineering bottlenecks. Existing methods are typically implemented by directly modifying the base MLLM codebase, which imposes substantial implementation overhead and yields method-specific architectures that severely limit code reuse and fair comparison. To address this, we introduce Prism, a plug-in reproducible codebase specifically designed for scalable MCIT research. It separates algorithmic development from the backbone implementation via a lightweight plugin registration mechanism, enabling new strategies to be integrated as independent plugins without modifying the underlying MLLM codebase, thereby eliminating structural fragmentation and accelerating method development. Prism natively supports widely used large-scale training pipeline, thereby enabling reproducible and scalable MCIT experimentation. Code is available at https://github.com/LAMDA-CL/Prism.

Current video-to-4D methods struggle with complex topology changes, transparent materials, thin structures, and inner surfaces. We present Helix4D, a dynamic mesh generation framework by inheriting the expressive representation of Trellis2, adapting it from image-to-3D to video-conditioned 4D generation. Our design arises from two key questions: (a) how to enable Trellis2's frame-local attention to share information across frames while preserving its pretrained quality on rare cases such as transparent objects and inner surfaces, and (b) how to inject temporal information into a purely 3D positional encoding without breaking pretrained capabilities. We address (a) with a sliding-window cross-frame attention and anchor on the first frame. The first frame is generated by the base Trellis2 model and injected into our model, letting it inherit Trellis2's quality in rare cases through cross-frame attention. We address (b) with a 4D temporal encoding that repurposes redundant low-frequency spatial RoPE bands for time, extending the encoding from 3D with no additional parameters. Extensive experiments show the effectiveness of Helix4D for high-quality dynamic mesh generation on ActionBench and our own challenging complex dynamics set.

For the independent reference model with popularity vector $p\inΔ_N^\circ$, let $H_C(p)$ denote the exact stationary hit rate of an LRU cache of capacity $C$. We prove that, for every $1\le C<N$, the uniform popularity vector is the unique global minimizer of $H_C$ on the interior simplex. More sharply, along every nonconstant segment from the uniform vector to an interior point, the LRU hit rate is strictly increasing. The proof uses the standard exponential-age representation of the stationary LRU cache and gives an explicit positive pair-square formula for the radial derivative. Equivalently, for the move-to-front rule, the stationary search-cost distribution improves strictly in the usual stochastic order along every nonconstant ray away from uniform. This proves the radial restriction of the Fill--Holst Schur-concavity conjecture for move-to-front search-cost tails. In particular, all LRU miss probabilities and all nonconstant nondecreasing stack-depth costs decrease strictly along such rays. The result is radial rather than Schur-convex: full majorization monotonicity for LRU is known to fail, and the proof identifies the special positivity that survives on rays from the uniform vector.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models for language modeling, yet the effective design of transformer architectures for MDMs remains underexplored. In this paper, we show that selectively looping the early-middle transformer layers significantly improves both training efficiency and model performance in MDMs. We call this approach LoopMDM(Looped Masked Diffusion Model), which brings two key benefits: looping layers at training-time yields a depth-scaling effect without adding parameters, while varying the number of loops at inference-time enables flexible compute scaling. Despite the simplicity, the results are striking: across multiple pre-training corpora, LoopMDM matches the performance of same-size MDMs with up to 3.3 fewer training FLOPs, while its final performance outperforms them on various reasoning benchmarks, including up to 8.5 points on GSM8K. It even surpasses deeper non-looped MDMs trained with comparable per-step compute, indicating that selective looping is more effective than naive depth scaling. Furthermore, LoopMDM can scale inference-time compute by increasing the number of loops. Adaptively adjusting the number of loops throughout the sampling process further yields additional gains in compute efficiency while maintaining performance. Lastly, with attention analysis, we provide evidence that looping is effective in MDMs by promoting interactions among masked positions. Our code and weights will be publicly released.

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.

Fine-tuning MLLMs for Video Temporal Grounding (VTG) often improves in-domain performance but degrades sharply under domain shift. In this work, we find that this failure is primarily driven not just by unseen query concepts, but by visual domain shift, which prevents the model from coupling its learned temporal localization knowledge with its inherent entity-attention capability. To address this, we introduce EVIDENT, a parameter-efficient adaptation framework that anchors temporal grounding in the inherent entity-attention of pre-trained MLLMs by routing VTG adaptation through explicit visual entity evidence. EVIDENT consists of three components: (i) an Entity Bottleneck Adapter that transforms dense visual tokens into compact entity-level slots, (ii) an Entity-Binding Distillation loss that instills objectness priors into the semantically unstructured MLLM visual space, guiding each slot to bind to a coherent entity, and (iii) an Entity-to-eVidence gating mechanism that leverages the captured entities as evidence, steering the model to localize moments containing query-relevant entities. Together, these components enable VTG fine-tuning to rely on entity-grounded evidence rather than brittle dataset shortcuts. Experiments on cross-domain VTG benchmarks show that EVIDENT consistently improves out-of-domain robustness while preserving competitive in-domain performance with modest parameter overhead. These results suggest that entity-level grounding is an effective inductive bias for generalizable temporal localization.

Code review is a critical practice in software engineering, yet the growing scale and frequency of code patches in modern projects, together with the widespread adoption of AI code assistants, make manual review increasingly challenging. Identifying the types of changes within a patch, such as renames, moves, or logic modifications, can substantially improve review efficiency by enabling prioritization, filtering, and automation. However, existing LLM-based approaches to code review have largely focused on summarization and comment generation, leaving structured code reviews underexplored. In this paper, we present a systematic study of using large language models (LLMs) for taxonomy-based labeling of code changes in a code patch. We introduce a two-stage pipeline that assigns labels to diff hunks and then refines them to capture structural relationships and semantic attributes, such as rename propagation and type changes. Our approach employs few-shot prompting to produce language-agnostic and customizable labels, without the engineering overhead of traditional static-analysis pipelines. We evaluate four LLMs across multiple context configurations on a manually curated benchmark of natural and synthetic patches. Our best configuration achieves up to $84\%$ recall and $81\%$ precision, with high accuracy in extracting relational and attribute metadata. These results suggest that LLM-based labeling can effectively complement static analysis by enabling flexible, multilingual, and automation-friendly code review workflows.

Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.

Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical Hamiltonians are rarely exactly commuting, which naturally motivates the study of almost commuting Hamiltonians. Despite their relevance, the implications of approximate commutation are only poorly understood. In this work, we show how to efficiently approximate any almost commuting $2$-local qubit Hamiltonian by a commuting one: we give a locality-preserving algorithmic rounding technique that maps any $2$-local Hamiltonian $H=\sum_{i=1}^m h_i$ with $\|[h_i,h_j]\| \leq ε$ to a nearby Hamiltonian $\hat{H}$ whose terms pair-wise commute, and which is within overall distance $\|H-\hat{H}\| = O(m\,ε^{1/6})$. As a consequence, we show that $δ$-approximations to the ground energy for $ε$-almost commuting $2$-local qubit Hamiltonians lie in $\mathsf{NP}$ when $δ\gg mε^{1/6}$, extending the classical containment well beyond the commuting setting. Finally, we present two applications of our rounding framework: Gibbs sampling and fast Hamiltonian simulation for almost commuting systems.

Automated pavement distress assessment requires more than image-level classification or coarse bounding box detection, demanding precise localization of thin, branching, and irregular cracks to achieve the geometric precision necessary for maintenance-relevant quantification. This paper presents a vision-based pavement distress analysis system based on Mask R-CNN instance segmentation and evaluates it on UWGB-StreetCrack, a custom field-collected roadway image dataset acquired with a vehicle-mounted smartphone and manually annotated with polygon labels for longitudinal cracks, transverse cracks, alligator cracks, and potholes. Five Detectron2-based Mask R-CNN backbone variants were considered under a consistent fine-tuning protocol. The best-performing model, Mask R-CNN with a ResNet-101 FPN backbone, achieved 84.23% precision, 90.04% recall, and an F1 score of 87.04% under the project-specific bounding-box matching protocol. The same model produced an aggregate predicted crack-area fraction of 2.164%, closely matching the 2.170% ground-truth crack-area fraction. To contextualize the segmentation system against a detector-oriented alternative, a CSPDarknet53-based YOLO detector was also adapted and retrained on the dataset, reaching 27.5% precision and 20.7% recall on the validation protocol. The results show that instance segmentation is a practical direction for field pavement imagery and aggregate crack-area estimation, while also exposing open challenges in annotation consistency, class imbalance, confounder rejection, and mask-level benchmarking.

Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions, as only specific parameter directions relevant to the objective truly matter. We propose GoBOED, a goal-driven BOED framework that directly optimizes experimental designs for a specified decision-making objective. GoBOED combines an amortized variational posterior surrogate with a differentiable convex decision layer, enabling gradient-based design optimization that is fully decision-focused. We theoretically show that GoBOED gradients are insensitive to parameter directions irrelevant to the decision objective, providing a formal justification for why goal-driven design achieves equivalent decision quality over a wider set of experimental designs than information-gain maximization. Empirically, across source localization, epidemic management, and pharmacokinetic control, GoBOED identifies designs that better align with downstream decision objectives and reveals that near-optimal design windows are substantially wider than those predicted by goal-agnostic BOED approaches.

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be inverted is a decisive parameter. A well known classical, and now quantum, remedy is to precondition the linear system $A x = b$ by premultiplying it by a matrix $H$ in such a way that the condition number of $HA$ is significantly smaller than the condition number of $A$. In this work, we focus on a family of preconditioners called domain decomposition. First, we prove that it is feasible to apply quantum domain decomposition. We provide upper bounds for the block-encoding parameters of the Poisson problem discretized by the finite element method and preconditioned by the two-level Additive Schwarz preconditioner (one of the most fundamental domain decomposition techniques). From these bounds, we deduce the complexity of the quantum linear system solver. Second, we focus on a particular choice of local solver within the domain decomposition preconditioner by applying recent work by [Deiml and Peterseim, \textit{Math. Comput.}, 2025] on the Bramble--Pasciak--Xu (BPX) preconditioner. Finally, we provide details on how the operators are implemented.

Frontier LLMs now perform strongly across a wide range of physics evaluations, but it is hard to disentangle genuine reasoning from recall of established science. We introduce DiscoverPhysics, an interactive benchmark that asks a LLM agent to discover the laws of motion of a simulated world whose physics deliberately deviates from our own. We construct 22 worlds governed by, among others, screened and fractional-power gravity, multi-species couplings, hidden dark-matter-like particles, non-coordinate-free physics, and time-varying interactions. Each world is generated on demand by an N-body simulator, for which the agent proposes several rounds of experiments, observes raw trajectory data, and ultimately submits both a natural-language explanation of the world's physics and a Python implementation of the inferred law. Because solving a world requires the agent to design informative experiments and revise its hypotheses, the benchmark probes long-horizon reasoning over an experimental history. We evaluate submissions along two complementary axes: trajectory MSE on held-out particles and an LLM-judged explanation score following an expert-written rubric assessing conceptual understanding of each world. Across eleven frontier models, we find that the strongest agents pass only half of the worlds and consistently fail on those where latent structure must be uncovered. Open-source models lag substantially behind commercial models, both in their ability to design informative experiments and in extracting conclusions from the data. We further find that good predictive accuracy does not guarantee high explanation quality and that conceptual understanding depends on hypothesis refinement through well-chosen experiments.

Large language model agents are increasingly envisioned as always-on personal assistants with access to anything relevant in the user's digital world. Yet current systems operate over only narrow slices of that world, limiting context-sensitive reasoning and effective assistance. Existing benchmarks similarly provide only partial user state and therefore fail to capture performance in such a broad, always-on setting. To address this gap, we introduce Claw-Anything, a benchmark that expands agent context along three dimensions: long-horizon activity histories, interdependent backend services, and integrated GUI and CLI interaction across multiple devices. To instantiate this setting, we simulate months of user activity through multi-round event injection, producing complex world states and realistic noise, including irrelevant events and conflicting signals. Agents must reason over rich contextual environments while remaining robust to such noise. This expanded scope also enables the evaluation of proactive assistance, requiring agents to anticipate user needs and deliver timely recommendations. Experiments show that GPT-5.5 achieves only 34.5% pass@1, substantially below prior benchmarks, underscoring a gap between current agent capabilities and the demands of always-on personal assistance. Alongside the benchmark, we release an automated data-generation pipeline that yields 2,000 training environments and improves the base model by 23.7%, demonstrating its utility of scalable data infrastructure.

The concept of 'undone science' emerged in the 2010s in research in social sciences at the intersection of studies on social movements and of science and technology studies. It refers to research questions that are neglected, ignored, or left unfunded, even though they deserve to be explored. The aim of this special issue is to apply this concept to computer science, by examining whether the way this discipline is structured (including its sociological, economic, and political dimensions), as well as the paradigms that shape it, make it possible to identify epistemological and ethical questions that are crucial for its development and conception.

Deep research agents face vast, interdependent, and pervasively uncertain information. Existing systems explore what evolving intermediate representations should look like, but leave their evolution to the LLM's implicit reasoning. Without explicit regulation, the intermediate layer is easily contaminated by mixed-quality information and propagates errors along its dependencies, so model scale often ends up substituting for absent regulation. We argue that an agent's mental model should instead evolve through explicit feedback that continuously aligns task understanding with reality, and identify three regulatory loops: interpretive update, deviation feedback, and schema revision. We realise this in VeriTrace, a cognitive-graph framework that explicitly implements the three loops. Using matched Qwen3.5-27B backbones, VeriTrace improves over the strongest matched baseline by 4.22 pp on DeepResearch Bench (DRB) Insight (1.49 pp Overall) and by 5.9 pp Overall win rate on DeepConsult. With Config-DeepSeek, it achieves the strongest reproducible open-source result on DRB.

The integration of Artificial Intelligence into sustainable finance represents a transformative paradigm shift in how Environmental, Social, and Governance factors are analyzed, predicted, and incorporated into investment decisions. This review provides a comprehensive taxonomy of AI approaches applicable to sustainable investment decision-making, categorizing methodologies based on their underlying algorithms and their impact on ESG-related financial processes. The proposed AI Taxonomy includes machine learning paradigms -- including supervised, unsupervised, and reinforcement learning -- as well as natural language processing techniques and optimization algorithms, examining their specific applications in ESG score prediction, controversy detection, portfolio management, and sustainability report analysis. By synthesizing findings from the recent literature, a framework emerges on AI-powered sustainable finance that identifies technological applications to overcome ESG data barriers.

Existing financial NLP benchmarks often rely on labels supplied by outside observers, measuring how language is perceived rather than what speakers have committed to in the market. We introduce StakeBench, an evaluation framework for language understanding grounded in market commitment. StakeBench links 560,876 comments from 2,261 resolved markets to verified position, action, and market-odds records across Polymarket and Manifold. Supervision is derived from observable market behavior. Position sides, post-comment trading actions, and market-odds trajectories replace human annotation. Four diagnostic tasks test whether models detect market commitment, identify the revealed side, anticipate future action, and perform collective odds projection. Three commitment-aware metrics measure alignment with revealed preferences rather than perceived sentiment. Validity audits and explicit interpretation boundaries help distinguish observable commitment signals from latent belief and causal market-odds impact. Across 15 LLMs and 18 topics and platform settings, models partially recover position-side signals, with Directed Accuracy from 0.506 to 0.599, but show structural failures on later tasks. Ten of the fifteen models collapse to one or two action labels in future action anticipation, and no model consistently improves on the naive odds-direction baseline in collective odds projection. Model scale is not correlated with performance, finance-domain tuning does not improve revealed-side identification, and platform incentives strongly shape higher-order results. StakeBench is packaged with evaluation code and dataset under CC-BY 4.0.

Efficient learning of user preferences is crucial for many modern decision making systems but typically requires costly labeled data. Active learning reduces this cost, yet standard methods are computationally expensive due to pool-based evaluation. Further, most methods assume all query feedback is equally reliable, ignoring that pairwise queries between nearly identical or entirely dissimilar items yield ambiguous, low-confidence responses. To address the issue of feedback reliability, we introduce a novel confidence aware response model that explicitly accounts for these ambiguous comparisons. To overcome the computational bottleneck of pool-based evaluation, we propose an active query synthesis framework, Info-Synth that generates optimal queries by maximizing a mutual information-based objective within a continuous space. Moreover, we propose two strategies, Pair M-dist and Pair Opt-dist, that extend Info-Synth to select effective queries even when restricted to finite query pools. We demonstrate our framework's versatility and performance across synthetic preference learning, constrained text summary datasets, and subjective, continuous-space controller gain tuning for a simulated mobile robot.

Annotating speaker attributes from text is inherently ambiguous, particularly in multilingual settings where demographic and social cues are implicit and culturally variable. We propose a human-large language model (LLM) collaborative re-annotation framework for stabilizing multilingual speaker-attribute labels under practical resource constraints. Starting from a noisy corpus, we use LLMs to surface recurring annotation rationales through iterative interaction with experts, and apply disagreement-focused sampling for targeted re-annotation. Using this framework, we construct WhoSaidIt, a multilingual dataset covering nine speaker-attribute labels. We quantify divergence between original and revised annotations, benchmark recent LLMs, and analyze the effect of explicit rationales on model behavior. Our results reveal substantial cross-lingual differences in annotation decisions and demonstrate both the strengths and limitations of LLMs in speaker-attribute classification.

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method -- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR -- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by $\mathcal{F}$, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by $\mathcal{O}(1/\sqrt{N})$, where $N$ is the sample size and the hidden constant depends on the class $\mathcal{F}$ and the input distribution. This reduction enables us to analyze conditional KRR in the case where $K$ is positive definite and $\mathcal{F}$ is given by the first $k$ principal eigenfunctions in the Mercer decomposition of $K$. We also consider the setting where $\mathcal{F}$ consists of $k$ random features from a random feature representation of $K$. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the $\mathcal{F}$-component of the regression function is more pronounced than the residual part.

Digital twins are evolving into self-learning, autonomous systems that link models, data, and human interaction. Realizing their full potential depends on interoperability, standardization, and the integration of artificial intelligence and advanced computational reasoning across sectors.

We present CrossLift, a technique for computing cross fields on meshes guided by visual features in images. We leverage powerful text-to-image priors that are capable of synthesizing images of feature-aligned quad meshes in 2D. We extract this signal as explicit per-pixel directions in the 2D images, which we then back-project to the mesh surface. We aggregate these candidate surface directions by performing two smooth interpolations on the mesh surface (first within each view and second across multiple views). We propose custom confidence-based weights for the candidate directions in each interpolation that allow us to resolve conflicts between candidates on the same face and smoothly interpolate our field to occluded faces. Our method is modular and can be used with many different 2D visual priors. We show additional applications to texture-aligned quad meshing as well as interactive cross-field design using coarse, user-drawn lines as signal. We demonstrate the effectiveness of CrossLift on a diverse set of both organic and mechanical shapes and produce quad meshes that exhibit superior semantic alignment as compared to existing methods. Project page at: https://crosslift.github.io/

Reliable quantification of uncertainty estimates in continuous-time (CT) representation learning remains nascent, particularly within CT attention architectures. We introduce the Neuronal Stochastic Attention Circuit (NSAC), a novel biologically-inspired CT attention architecture that reformulates attention logit computation as the solution of an Ornstein-Uhlenbeck stochastic differential equation modulated by input-dependent, nonlinear interlinked gates derived from repurposed C.elegans Neuronal Circuit Policies (NCPs) wiring mechanism. It induces Gaussian distribution over logits that propagates principled stochasticity through logistic-normal distribution over attention weights to yield probabilistic output. A two-term objective function combining Gaussian negative log-likelihood with an epistemic-separation regularizer enforces higher predictive variance and enables joint quantification of aleatoric and epistemic uncertainty. Empirically, we implement NSAC in a diverse set of learning tasks including: (i) irregular CT function approximation; (ii) multivariate regression; (iii) long-range forecasting; (iv) Industry 4.0; and (v) the lane-keeping of autonomous vehicles. We observe that the NSAC remains competitive against several baselines in terms of accuracy and produces reasonably well-calibrated uncertainty estimates while being interpretable at the neuronal cell level.

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited by the cost of repeated high-fidelity simulations required for gradient-based Markov chain Monte Carlo (MCMC) sampling. While surrogate models are commonly proposed to reduce this cost, their effect on posterior geometry and uncertainty, especially for shock-dominated flows, remains poorly understood. In this work, we demonstrate that neural operator surrogates can be embedded directly within the MCMC inference loop while preserving posterior structure. Using a fully Bayesian inverse formulation of quasi-one-dimensional nozzle flow, we demonstrate that geometry parameterization plays a decisive role in identifiability and posterior conditioning, with cubic B-splines yielding stable and physically meaningful uncertainty estimates. Building on this formulation, a Deep Operator Network trained on CFD-generated data is substituted for the CFD solver within a No-U-Turn Sampler, while keeping the likelihood model, priors, and sampling configuration unchanged. Across sparse to fully observed regimes, surrogate-based inference reproduces the posterior geometry and uncertainty trends of the CFD reference. As a result of surrogate integration, total inference time is reduced to under one second, corresponding to a speedup exceeding three orders of magnitude. In addition, a direct inverse neural operator is examined as a deterministic alternative for inverse design, enabling single-shot geometry reconstruction without posterior sampling. These results demonstrate that neural operator-accelerated Bayesian inference enables practical, uncertainty-aware inverse design workflows for aerodynamic applications.

Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximation is challenging because the variable-order fractional derivative generates time-dependent history weights and therefore lacks the standard time-translation-invariant convolution structure of constant-order fractional operators. In this paper, we develop and analyze a fully discrete energy-based discontinuous Galerkin (DG) method for wave equations with a Caputo-type variable-order time-fractional derivative. The equation is reformulated as a reduced first-order-in-time system, discretized in space by an energy-based DG method, and advanced in time using a second-order approximation of the variable-order Caputo derivative at a specially chosen point in each time interval. The main analytical novelty is a cumulative weight-variation estimate for the variable-order memory weights, which requires only that the variable order $α:[0,T] \rightarrow (0,1)$ be Lipschitz continuous. Based on this estimate, we establish energy stability of the fully discrete scheme and derive second-order temporal convergence together with energy-norm spatial error estimates. The analysis gives suboptimal convergence on general affine simplicial or tensor-product meshes and optimal convergence under additional Cartesian and flux assumptions. Numerical experiments in one and two dimensions validate the theoretical findings.