Pathological assessment guides lung cancer diagnosis, treatment selection, and prognostic evaluation, yet current CPath approaches rely on task-specific models for isolated objectives. Although pan-cancer foundation models offer versatility, they lack subspecialty-level depth and have not been evaluated across clinical workflows or prospectively validated in real-world settings. We introduce PulmoFoundation, a multi-center, prospectively validated, randomized controlled trial (RCT)-evaluated foundation model for comprehensive lung pathology assessment across pre-operative, intra-operative, and post-operative care. Built upon Virchow2 via subspecialty-specific pretraining using ~40,000 diagnostic H&E-stained whole-slide images (WSIs), PulmoFoundation was systematically evaluated on ~26,000 WSIs across 32 clinically relevant tasks. In addition to accurately predicting molecular markers and patient survival, our model achieves clinical-grade performance in core diagnostic tasks across biopsy, frozen section, and surgical resection slides. In a registered prospective study of 1,357 patients across 11 diagnostic tasks, our model achieved an average AUC of 92.3%. Using pre-specified triage thresholds, PulmoFoundation could reduce additional second-review burden for 68.8% of biopsies and 83.0% of frozen sections, and defer 44.5% of IHC stain orders, with PPVs of 1.0, 0.991, and 0.966. Beyond prospective validation, we conducted a crossover RCT with eight pathologists, in which AI assistance improved diagnostic accuracy across 4,928 case-reader pairs (91.7% w/ AI vs. 83.8% w/o AI). AI assistance also reduced median diagnostic time by 19.6%, increased diagnostic confidence by 8.7%, and improved inter-rater agreement from moderate (kappa = 0.56) to substantial (kappa = 0.76). Together, these evaluations support PulmoFoundation as a clinically validated decision-support system for lung pathology.

The speed and accuracy of an artificial teammate fundamentally alter the failure states of Human-AI integration. While high-speed AI interventions risk inducing reflexive blind compliance, delayed interventions can induce ambiguous cognitive conflict. This study investigates how the fundamental characteristics of an in-task AI assistant, Fast/Less-Accurate (FLA-AI) versus Slow/Accurate (SA-AI) impact the synergy of Collaborative Brain-Computer Interface (cBCI) teams in a Virtual Reality drone task. Seventeen operators completed continuous search tasks under high cognitive workload while their spatial covariance was mapped using a 2D Adaptive Riemannian Oracle. The results mathematically demonstrate that AI timing dictates the mechanism of team failure. Fast AI induced instant, blind compliance; human accuracy under deception collapsed to 50.2%, and pure behavioural teams (N=8) failed to scale beyond 74.1%. In contrast, Slow AI induced delayed cognitive conflict; humans hesitated (61.1% accuracy), but N=8 behavioural teams eventually recovered to 100.0%. Crucially, the Riemannian Oracle mathematically adapted to these states: it heavily restricted temporal windows (< 0.8s) to intercept fast reflexive compliance, while widening windows (> 1.2s) to capture delayed cognitive conflict. Integrating these isolated veridical signals via Hybrid Fusion successfully rescued the Fast AI team (+7.6% at N=8) and significantly accelerated the recovery of smaller Slow AI teams (+6.9% at N=4). These findings prove that cBCI synergy is heavily contingent on the temporal dynamics of trust, providing a critical framework for designing dynamically gated Human-AI systems.

We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for choosing $k$ is largely absent, mainly due to the complex dependence between fold-wise error estimates. To obtain sharp and interpretable results, we focus on the majority algorithm in binary classification, a minimal yet nontrivial empirical risk minimization procedure. We provide a fine-grained analysis of its cross-validation behavior, showing that even this simple algorithm exhibits subtle and delicate phenomena for which existing theory provides loose and even vacuous bounds. Leveraging this analysis, we introduce a minimax framework for cross-validation risk estimation and prove that no empirical risk minimization algorithm can achieve an $O(1/n)$ minimax mean-squared error when the number of folds grows with the number of samples $n$; instead, a lower bound of order $Ω(\sqrt{k}/n)$ is unavoidable. Our results reveal fundamental limitations of cross-validation as a data-reuse strategy, clarify gaps and inaccuracies in prior theoretical work, and position the majority algorithm as a natural benchmark that any tight analysis of cross-validation should be able to explain.

Large Language Model interfaces are increasingly verbose, exposing intermediate reasoning traces alongside final answers. Traces are framed as transparency mechanisms, yet it is unclear how people use them to solve problems. We report a preregistered between-subjects study (N = 559) in which participants solved ten LSAT-style reasoning problems under one of three conditions: an Answer-only baseline, a Full-trace revealed before the answer, and a Summary-trace presented alongside the answer. Summaries preserved task performance at the no-trace baseline while significantly elevating trust and hedonic appeal, establishing that trace exposure shifts subjective appraisal of the interaction without bringing performance benefits. Under an open-weight reasoning model exposing verbose intermediate output, full traces additionally impaired performance relative to the answer-only baseline. Across all conditions, participants substantially overestimated their performance, and no trace format supported calibrated self-evaluation. Further analysis indicates that hedonic appeal, not trust, carries the indirect path to overestimation, consistent with a processing-fluency account. Reasoning traces are best understood as user-facing interface artifacts rather than transparent windows into model cognition, and calibration is unlikely to emerge from the traces themselves and may best be scaffolded by interactions that elicit users' own reasoning first.

Extracting MITRE ATT&CK techniques from cyber threat intelligence (CTI) reports is an open-set, multi-label problem requiring both high recall (not missing techniques) and high precision (not hallucinating unsupported ones). Existing methods--rule-based, supervised, and LLM-based--struggle to achieve both: rule-based and supervised approaches lack generalizability across diverse attack descriptions, while LLM-based approaches that couple candidate generation and validation within a single inference step suffer from limited recall and precision simultaneously. We propose TTPrint, which addresses this challenge through a diverge-then-converge design inspired by how human analysts work: first extracting broadly, then verifying rigorously. In the divergent phase, reports are decomposed into atomic behaviors and candidate techniques are proposed broadly. A deterministic span localization stage then anchors each candidate to a specific evidence window in the source text. A convergent verification stage retains only candidates supported by both the localized evidence and the authoritative MITRE definition. We contribute two evaluation resources--a cleaned TRAM benchmark (TRAM-Clean) and a new annotated dataset (TTPrint-Bench)--to address known annotation noise in existing benchmarks and elevate the task to document-level TTP extraction. On TRAM-Clean and TTPrint-Bench, TTPrint achieves 76.48% and 87.39% macro-F1 respectively, outperforming the leading baseline by 63.5% and 29.4%. A multi-backbone analysis across six LLMs and a threshold sensitivity study further demonstrate generalizability across model choices and provide practical guidance for parameter selection.

We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal -- a setting that arises naturally in earthquake engineering, finance, biology, and structural health monitoring, where the forcing is observed exactly once and the solver must respect the underlying physical law without recourse to an ensemble of realizations. Two ingredients are new. First, a \emph{count-sampling} construction turns the single observation into a hierarchical family of $N+1$ nested training paths on which the branched signature kernel can be evaluated; this allows the signature kernel machinery, originally designed for multi-realization regression problems, to operate on a single-trajectory observation. Second, a kernel-collocation framework places the ansatz either on the highest-order derivative of the solution (with lower derivatives recovered by integrating the kernel) or on the solution itself (after $m$-fold integration of the ODE). We prove a universal approximation theorem for the branched signature kernel, leveraging the Hairer--Kelly morphism to express branched signature evaluations through geometric signatures of time-extended paths. The offline solver is extended to a streaming Test/Train/Retrain protocol with closed-form online updates in the linear case and scalar Newton steps in the nonlinear case. Numerical experiments on six benchmarks (El-Centro earthquake displacement, the Solow capital-stock model, an fBM-driven second-order ODE, a forced Duffing oscillator, a path-dependent Arias-intensity-degraded oscillator with variable coefficients, and a noisy Kuramoto phase-oscillator system) show that the branched signature-kernel solver delivers accurate, stable predictions across all regimes.

We study counterfactual distribution learning for high-dimensional outcomes whose counterfactual law may concentrate near lower-dimensional structure. Standard isotropic smoothing treats all ambient directions equally, leading to unfavorable scaling and unstable local inference. We propose two diffusion-guided estimators based on semiparametric debiasing: diffusion-informed smoothing for counterfactual densities and diffusion-informed score smoothing for counterfactual scores. The estimators combine causal nuisance adjustment with geometry-adaptive localization driven by diffusion score information, removing first-order nuisance bias while aligning smoothing with local outcome geometry. We establish asymptotic expansions, risk bounds, and inference procedures for smoothed density and score-based targets, with ambient density inference obtained under additional approximation conditions. Under structural geometry conditions, the leading stochastic error is governed by an effective dimension induced by the diffusion-guided kernel, rather than by the ambient dimension. Semi-synthetic experiments based on CelebA show steeper error decay for geometry-adaptive methods, supporting the proposed effective-dimension theory.

In multi-stage recommender systems, reranking optimizes overall utility by capturing intra-list contextual dependencies, yet its central challenge lies in exploring optimal sequences within an exponentially large permutation space. Recent studies have shifted towards end-to-end generative frameworks, which typically leverage list-wise rewards or preference alignment to guide generator training. However, these methods still face two critical issues. First is the heuristic label bias. Existing methods often construct training targets based on simple rules, such as promoting clicked items to the top, while ignoring causal dependencies within the list context. Second is the credit assignment problem. Sparse list-level posterior rewards fail to directly guide intermediate steps in sequence generation, leading to ambiguous optimization directions. To address these issues, we propose DeGRe (Dense-supervised Generative Reranking), a generative reranking framework that bridges the gap between offline exploration and online efficiency through dense supervision. The core of DeGRe lies in its offline-online decoupled design. During the offline phase, we introduce a Lookahead Evaluator based on cumulative regression, which leverages beam search to actively mine high-value lookahead sequences in the unexposed space. During training, we transform the step-wise value estimations from the evaluator into dense supervision signals and distill them into a lightweight Online Generator. This mechanism enables the generator to internalize lookahead planning capabilities, requiring only a single efficient greedy decoding pass during online inference to approximate the global optimum. Experiments demonstrate that DeGRe outperforms baseline models on public benchmarks and industrial datasets. We have successfully deployed DeGRe on Taobao Flash Shopping, significantly improving online recommendations.

As large language model (LLM)-based multi-agent systems scale to handle increasingly complex tasks, balancing structural stability and dynamic adaptability becomes increasingly challenging. Existing systems typically adopt either structure-centric methods, committing to structures determined upfront that limit fine-grained control, or orchestration-centric methods, adapting decisions dynamically while leaving coordination structure implicit and unstable. To address this challenge, we revisit multi-agent coordination from a probabilistic perspective, casting it as posterior inference over the joint distribution of structure and orchestration. We introduce MACA, an automated coordination framework that learns a task- and budget-conditioned structural prior over agent participation and interactions. This prior guides a policy-based orchestration as an approximation to posterior inference, enabling efficient solutions with fine-grained control. Across benchmarks, MACA outperforms adaptive multi-agent baselines by an average of 8.42% while using 43.19% fewer tokens. Further investigation reveals that joint adaptation of structure and orchestration suppresses redundant interactions, converging coordination toward task-effective execution.

Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of interactions. While machine learning force fields (MLFFs) offer near-quantum accuracy, the ubiquitous message-passing layers miss long-range many-body effects. Here we introduce the Multiscale Structural Ensemble (MuSE), a hierarchical model that uses Soft Coarse-Graining Pooling to construct coarse representations from smooth fractional assignments of atoms to coarse nodes, enabling MLFF modules to operate across multiple scales. MuSE is architecture-agnostic and coupled with SO3krates, MACE, and PaiNN MLFFs for both molecules and materials. We demonstrate the power of MuSE through Hessian-based benchmarks, folding trajectories for biomolecules, and energy profiles in molecule-graphene nanostructures, where MuSE accurately captures quantum-mechanical interactions at relevant scales -- unlike other recent long-range ML models.

Large language models (LLMs) can serve as the semantic-matching engine of a content-based publish/subscribe broker for agentic AI across the edge-cloud computing continuum, bridging the vocabulary and modality gaps that defeat keyword and embedding filters. Framed as offline multi-label retrieval over three public datasets spanning social-media, legal, and smart-home sensor domains (six LLMs, seven baselines), our central contribution is a two-crossover cost-accuracy characterisation: an analytical context-window crossover below which a CoverAndMerge compression pipeline reduces LLM invocations, and an empirical discrimination-capacity crossover above which matching accuracy collapses independently of context budget, by a model-dependent factor of parameter count and training generation. Two findings carry practical weight: above the discrimination crossover, compression cannot recover accuracy and only frontier-scale models clear large subscription sets; and there backend choice dominates configuration choice, so model selection, not pipeline tuning, is the primary operator lever. We accompany this with three composable algorithms and a per-cluster Quality-of-Experience framework for autonomic LLM-tier selection.

Distributing Transformer inference across embedded edge devices can alleviate individual memory and compute constraints, yet practical benefits on real hardware remain unclear: prior work relies largely on simulations that overlook hardware-specific communication overheads. We present a hardware prototype study on NVIDIA Jetson Orin Nano devices connected over WiFi. Our key finding is that the dominant bottleneck is not just network bandwidth but also the CPU-GPU staging during communication. Because Jetson's integrated GPU architecture lacks the PCIe/NVLink pathway that NCCL requires, all inter-device data communication should be routed through GLOO and staged in CPU memory; an overhead that scales with communication data volume and makes full-tensor exchange slower than single-device inference across the batch sizes for medium sized models such as ViT. We therefore evaluate Prism by combining Segment Means compression with lightweight offline profiling to adaptively select between local and distributed execution at runtime. Experiments show that this strategy reduces latency by 65%-77% and energy consumption by 34%-52% relative to full-tensor exchange in static distributed execution setup, demonstrating that profiling-driven adaptation is essential for practical distributed Transformer inference on embedded hardware.

Security evaluations inherently depend on stable identifiers. Any finding, audit, or regulatory decision must remain attached to the specific artifact it pertains to. Continuously updated artificial intelligence systems violate this core assumption, with public model designations remaining static while underlying weights, prompts, retrieval mechanisms, misuse classifiers, inference settings, and serving infrastructures undergo unannounced modifications. Consequently, current evaluations frequently apply to superficial labels rather than identifiable and distinct systems. To resolve this, we propose referential security as a new paradigm for AI evaluation. The fundamental security question extends beyond whether a model is safe to whether subsequent parties can conclusively determine which system a specific safety claim addressed. This approach reframes model identity as an empirically verifiable property and separates referential stability from the substantive security claims it conditions. This framework brings tractability to three critical workflows that current practices handle poorly. Specifically, it enables reproducible evaluation, longitudinal audit validity, and cross-provider equivalence. By grounding these evaluations in verifiable artifacts, our approach ensures that safety audits and regulatory findings maintain their empirical utility across the operational lifecycle of dynamic systems.

AI-native software development is often evaluated at the level of individual models, prompts, or generated artifacts. This framing is insufficient for production environments where software must be continuously produced, verified, deployed, maintained, and adapted across many operational contexts and long time horizons. We present a meta-engineering harness: a software-production architecture that transforms operational and product feature requirements into explicit contracts, routes work through role-specialized AI agents, performs independent and adversarial verification, and continuously improves itself through structured failure classification and outer-loop calibration. The harness is designed for settings in which software delivery is not a one-time project but an ongoing operating function. In our motivating application, CTO-as-a-service for small service firms, the system manages websites, booking flows, payment systems, backoffice workflow automations, and AI-agent interfaces as continuously evolving technical infrastructure rather than one-off deliverables. We describe the layered architecture, including two-pass contract compilation, persistent markdown memory with specialization records, attention-based and independence-based verifications, a four-way failure arbiter, and outer-loop calibration. We report results from an early production deployment spanning 17 features over several weeks, including a detailed in-app payments case study that revealed contract incompleteness and verification-boundary issues. These observations directly drove targeted improvements to the harness. The contribution is an implemented, measurable, and extensible verification architecture for making AI-native service-as-a-software production reliable, auditable, and improvable over time.

Poor posture is a significant concern due to its detrimental effects on health and productivity. This paper presents a collar-clipped device called PostureClip, designed to restrict users from sitting and working at a bent angle, by blacking out the screen and resuming on correcting posture, thereby promoting better posture. The device integrates sensors and feedback mechanisms to provide real-time posture feedback to users. To evaluate the effectiveness of PostureClip, a controlled experiment was conducted with participants (n=165) who were working on a laptop/PC for over 6 hours per day. The participants were randomly assigned to both the intervention group (IG1,n=54 ; IG2,n=55), which used the collar-clipped device, and the control group (CG, n=56), which did not use the device. IG1 didn't get feedback while IG2 got feedback from the device by notifying and further darkening the screen. The study was conducted in the office environment of the participants, for 4 weeks, and metrics such as posture angle, duration of bent angle, and user feedback were collected. Analysis revealed significant improvements in posture angle (p<0.001) and significant reduction in bent angle duration (p<0.01) for participants' group using PostureClip with feedback and compared to the group without feedback and the control group (who were not intervened). The qualitative analysis of user feedback highlighted the device's ease of use, effectiveness in providing timely feedback, and positive impact on participants' awareness and habits regarding posture. These results indicate that PostureClip is an effective tool for promoting better posture during sedentary work.

This paper proposes StrTransformer, a source-wise structured Transformer framework for blind source recovery and branch-wise latent modeling. Instead of using an encoder to infer latent variables, StrTransformer directly optimizes the latent source matrix together with an observation-space mixer and source-wise structural Transformer branches. The mixer enforces reconstruction consistency, while each Transformer branch imposes a differentiable structural constraint on one latent source trajectory. Specifically, each source is converted into multi-scale patch tokens, randomly masked, processed by a locality-biased Transformer, and evaluated through a masked patch reconstruction energy. This energy acts as an implicit source-wise structural prior. To encourage different latent branches to specialize into different temporal regimes, StrTransformer further introduces an ordered multi-scale controller that learns branch-specific patch-scale weights, ordered scale centers, and locality attention slopes. The resulting objective combines observation reconstruction, source-wise structural regularization, and modular auxiliary penalties for separation and scale specialization. We analyze the decoupling and coupling structure of the objective, the regularized exact-reconstruction fiber, and the reduction of permutation symmetry induced by ordered branch descriptors. A controlled case study shows that the learned branches converge to distinct temporal-scale structures and recover source-aligned latent trajectories under post-hoc evaluation.

Accurate reconstruction of magnetic fields in inaccessible regions is vital for many high-precision experiments in physics. Traditional methods, such as spherical harmonic expansion, often suffer from truncation errors that limit their precision. This study proposes an advanced Physics-Informed Neural Network (PINN) framework for high-precision 3D magnetic field mapping. Unlike conventional data-driven models, the proposed PINN integrates Maxwell's equations directly into the loss function, enforcing divergence-free and curl-free conditions across the entire domain. A key innovation is the inclusion of explicit physics-residual losses at measurement locations, ensuring rigorous physical consistency beyond random collocation sampling. Validation using simulated data achieves a reconstruction accuracy of $10^{-4}$, a tenfold improvement over existing PINN benchmarks. Furthermore, experimental validation using a custom coil assembly demonstrates robust reconstruction with sub-percent relative accuracy, reaching the $10^{-3}$ level under ambient conditions. This AI-driven methodology provides a robust, high-precision solution for field monitoring and measurement in complex experimental environments where direct sensor placement is restricted.

The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates based on parameter counts and sample complexity guarantees for compositional models without incurring the curse of dimensionality (CoD). To study overparameterized regimes, where the number of parameters exceeds the sample size, we develop a framework that measures complexity via the parameter norm. Within this approach, we establish approximation rates and excess risk bounds for learning sparse compositional functions whose compositional structure is represented by directed acyclic graphs (DAGs), using Frobenius norm-constrained deep neural networks. Our results have broad applicability since every function that is efficiently Turing computable admits sparse compositional representations. In particular, we cover a range of representative models, including multi-index models, binary tree structures, and general compositional architectures. The rates we derive show that deep networks can exploit the compositional structure of the target functions, effectively avoiding the CoD through hierarchical representations.

In the past decade, numerous studies have applied deep neural networks (DNNs) to decode auditory attention (AAD) from Electroencephalogram (EEG) signals via stimulus reconstruction. However, the influence of dataset balance on the decoding performance of stimulus reconstruction-based AAD remains unexplored. In this study, three publicly available EEG-AAD datasets - KUL, DTU, and NJU cEEGrid - are used to construct both balanced and unbalanced experimental conditions. We hypothesize and demonstrate that stimulus reconstruction-based DNN decoders tend to produce overestimated decoding performance on unbalanced datasets. To address this issue, we propose a leave-one-paired-envelope-out (LOPEO) cross-validation protocol. Experimental results confirm that LOPEO effectively prevents inflated decoding accuracy on unbalanced datasets. While balanced datasets are generally preferred in experimental design, LOPEO provides a principled evaluation framework for unbalanced datasets that have already been published, filling an important gap in the field.

We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of $K$ items from a ground set of size $N$ and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a $0$-$1$ mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and characterize the induced statistical-computational trade-offs. As an application, we develop a best assortment identification algorithm for MNL bandits with linear utilities and non-uniform revenues, and prove an instance-dependent sample complexity of $\tilde{O}\big(\frac{d \log N}{Δ^2}\big)$, where $d$ is the feature dimension, $N$ is the number of arms, and $Δ$ is the minimum revenue gap.

We study nonstationary generalized linear bandits (GLBs), where the expected reward is modeled through a nonlinear link function with an unknown time-varying parameter. This framework encompasses a broad class of reward models, including linear, Bernoulli, and binomial rewards. Existing approaches are predominantly based on maximum-likelihood estimation (MLE), using sliding-window, restart, or discounting mechanisms to handle nonstationarity. Although these methods achieve statistically efficient regret guarantees, they generally require revisiting past observations at every round, which leads to computation and memory costs that grow with time; moreover, several of them rely on a non-convex projection step. In this paper, we propose DOMD-GLB, a new algorithm for nonstationary GLBs that utilizes discounted online mirror descent (DOMD) for parameter estimation, thereby incurring only $O(1)$ computation and memory costs per round. We prove dynamic regret bounds of order $\tilde{O} \big(c_μ^{-1/2} d^{3/4} P_T^{1/4} T^{3/4}\big)$ in drifting environments and $\tilde{O}\big(c_μ^{-1/3} d^{2/3} Γ_T^{1/3} T^{2/3}\big) $in piecewise-stationary environments, where $d$ denotes the feature dimension, $T$ the time horizon, $P_T$ the path length, $Γ_T$ the number of change points, and $c_μ$ a curvature parameter associated with the link function, while substantially improving computational efficiency over prior work. To the best of our knowledge, this is the first algorithm for nonstationary GLBs with per-round computation and memory costs independent of time.

Neural networks encode inputs as high-dimensional vectors, known as representations, that capture how models process data by encoding task-relevant structure and semantics. Representation alignment refers to the degree to which different models, layers, or training conditions produce similar representations for the same inputs, with important implications for model interpretation, selection, and robustness analysis. Existing approaches to measure alignment primarily rely on geometric properties, such as neighborhood and cluster similarity, offering limited insight into the global organization of representations. In this work, we present TopoAlign, a topology-aware framework for visually comparing model representations from a structural perspective. Leveraging mapper graphs from topological data analysis, TopoAlign jointly analyzes graphs constructed from representations of shared inputs across different models or layers. The framework supports a top-down comparative workflow: it first performs global structure alignment via joint force-directed optimization to produce coordinated graph layouts; it then identifies local correspondences through automated detection of structurally matching regions, visualized with Bubble Sets; and finally it enables fine-grained pattern inspection through motif-based queries and membrane-inspired visualizations. We demonstrate TopoAlign through case studies on language and multimodal models, complemented by expert feedback. Our results show that TopoAlign provides meaningful insights into representation structure and alignment from a topological perspective.

Context. Large language models (LLMs) are increasingly applied to code-generating tasks (CGTs) in software engineering. While reported results are promising, the broader effects of such application and their integration into real-world development remain insufficiently understood with existing tertiary studies provide little in this area. Objective. This tertiary study consolidates secondary evidence on LLM-based CGTs, synthesizing the publication landscape, effects, scenarios, integration challenges, and future research directions. Method. Following systematic review guidelines, we searched in related digital libraries, complemented by backward-and-forward snowballing and screening step. Study quality was assessed and extraction reliability was audited with inter-rater agreement statistics. Evidence was synthesized using SWEBOK knowledge areas and the HELM framework. Results. We identify 30 secondary studies published between 2017-2025, with rapid growth since 2023. Accuracy seems strong on benchmarks but weakly supported for real-world generalization; robustness is fragile across tasks and configurations; efficiency constraints are pervasive; toxicity and bias are under-reported. Dominant challenges concern economic feasibility, evaluation validity, and socio-technical integration. Future directions suggest domain-aware model improvement and the need for holistic, standardized evaluation. Conclusion. LLM-based CGTs represent a fast-maturing yet unevenly evaluated research area, highlighting the need for domain-aware model improvements and holistic, standardized evaluation, addressing efficiency and associated costs.

We study the geometry of determinantal point processes (DPPs) through the spectral decomposition $L=UΛU^{\top}$. The spectrum $Λ$ governs the cardinality distribution via elementary symmetric polynomials, while the eigenspace orientation $U$ governs the conditional law within each fixed-cardinality stratum. Conditioning on cardinality $k$ yields the $k$-DPP, for which the identifiability structure changes fundamentally: the spectral parameter becomes identifiable only up to a common scale, and the eigenspace rotation parameter is identifiable only through squared minors of the eigenvector matrix. We characterize the identifiability gap precisely, via three explicit invariances (scale, sign similarity, and eigenspace rotation) and a dimension-counting theorem showing the existence of additional continuous non-identifiability whenever $\binom{N}{k}<N(N+1)/2$. In contrast, for the full DPP the non-identifiability comes only from the discrete sign similarity.

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and solutions (or final states), enabling both forward simulation and inverse recovery with limited paired data. At inference, sampling is guided by a composite loss that enforces agreement with sparse measurements and reduces the PDE residual; we support deterministic, stochastic, and hybrid samplers. We provide error guarantees for these guided procedures. For the deterministic optimizer, a coercivity condition ensures trajectory boundedness and a phase-wise contraction yields logarithmic complexity in the target accuracy. For the stochastic sampler, we introduce adaptive guidance and assume dissipativity of the velocity field to obtain uniform moment bounds independent of the noise-floor parameter. This leads to polynomial-time error bounds, and a matching lower bound shows constant guidance induces an unavoidable positive bias, motivating adaptivity. A hybrid deterministic-stochastic analysis is also provided. Experiments on static and time-dependent benchmark PDEs demonstrate competitive accuracy and faster inference than diffusion-based generative models.

Generative artificial intelligence (GenAI) is the first automation wave to reach high-cognitive tasks at scale, yet its effects on intra-urban inequality remain largely unknown. Using 5 million job postings from Beijing (2018--2024), we construct a neighborhood-level GenAI Exposure Index by aggregating task-level assessments from five leading large language models. We examine the spatial, structural and causal mechanisms of this shock. We find that GenAI exposure is highly concentrated in the city's core districts, deepening the intra-urban AI divide. Since 2023, high-exposure neighborhoods have experienced wage stagnation even as they continue to attract high-skilled workers -- a "high-skill trap." This wage penalty is driven by task de-skilling and intensified labor-market crowding. A difference-in-differences design centered on ChatGPT's release supports a causal interpretation. These findings challenge the prevailing theory of skill-biased technological change and provide a basis for inclusive AI governance in global technology hubs.

Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift component using only standard PCA operations.

Large language models (LLMs) are increasingly being used for emotional support. They are also being developed for formal therapy purposes. However, LLMs like ChaptGPT or Llama are often developed with content moderation guardrails that prevent them from discussing sensitive subjects with users for both liability and safety purposes, and this inability to broach these subjects may affect their capacity as therapists. In this study, we perform an algorithm audit on three state-of-the-art moderation systems (OpenAI's moderation endpoint, Meta's Llama Guard, and Google's Shield Gemma) to investigate the extent to which these systems flag the content of real-life therapy sessions as undesirable. Our results raise implications for the limitations that users and organizations may encounter when designing LLMs to play the part of a therapist.

Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited mathematical understanding of the performance of GNNs. We discuss the various perspectives used to study statistical generalisation in GNNs. We identify three broad frameworks. The first approach, rooted in learning theory, relies on uniform convergence bounds and the complexity of the hypothesis class of specific GNN architectures. This approach also builds on the expressivity of GNNs, typically studied through the lens of graph isomorphism tests. The second principle is to simplify the neural architecture by analysing GNNs under the asymptotics of infinitely many parameters or infinite graph size. This approach approximates GNNs using Gaussian processes, neural tangent kernels or graphon neural network operators, which allow studying the generalisation or stability of trained GNNs. The third framework studies GNNs under random graph models, often the contextual stochastic block model, and derives non-asymptotic error rates using tools from high-dimensional statistics. We highlight some key theoretical results and discuss a few limitations and open research questions for each perspective.

We present a differentiable framework to automatically learn view-dependent 2D kernels in a splatting-based pipeline to improve reconstruction quality and representation efficiency for novel 3D view synthesis. Our volumetric primitive is defined as a bounding ellipsoid and a 3D-kernel latent vector. We first learn a projection network to output a 2D-kernel latent, taking the attributes of the ellipsoid and the 3D-kernel latent as input. Next, the result is sent to a decoder to produce a radially symmetric 2D kernel in terms of Mahalanobis distance, bounded by the projected ellipsoid. The neural networks along with per-primitive attributes are jointly optimized. The effectiveness of our approach is demonstrated on standard benchmarks, comparing favorably against state-of-the-art techniques on both analytical and learned kernels. Finally, we extend the idea to learn general 2D kernels for 2D splatting as well as image representation.