Papers

We study retrieval-augmented generation (RAG) for questions about French PDF documents when both the answer and its supporting document pages are evaluated. Five system variants add dense retrieval, rank fusion, reranking, and query decomposition to a BM25 baseline. On 595 challenge questions, the complete system scores 0.4450 MRR@10 and 0.4013 Recall@10, compared with 0.3430 and 0.2994 for BM25. Dense retrieval alone and a simple lexical–dense fusion both underperform BM25. Reranking improves the hybrid system, whereas adding query decomposition produces the largest further gain, with higher latency and more detected output artifacts. The complete system slightly exceeds the reported anonymous overall mean on two answer metrics but falls below it on most page-retrieval metrics. These results identify accurate page selection, rather than semantic retrieval in isolation, as the main opportunity for improvement in this setting.

A graph $G$ is point determining, if no two vertices have the same neighborhoods. In this paper, we show that this property is recognizable from the deck of cards of a graph.

The motional modes of trapped ions are promising candidates for continuous-variable (CV) quantum computation and simulation. However, to achieve a universal gate set for CV quantum computation, anharmonic nonlinear unitaries are required. Here, we experimentally demonstrate a protocol that allows us to approximate the cubic phase gate. By numerically optimizing the phase angles and amplitudes of a set of state-dependent force pulses, we demonstrate the cubic phase gate for both vacuum and low-$\alpha$ coherent state inputs and verify its performance. Our protocol can also be extended to approximate other nonlinear unitaries.

We study Bregman proximal gradient (BPG) algorithms under relative smoothness for convex, relatively strongly convex, and nonconvex objectives. Existing accelerated BPG algorithms for convex objectives typically require additional assumptions on Bregman divergences, most notably triangle-scaling conditions, which can lead to slower convergence rates. We propose a family of geometry-accelerated BPG algorithms that exploit Bregman geometry in both proximal-gradient and mirror-space updates, without imposing additional geometric conditions such as triangle-scaling conditions. Our methods adapt the stepsizes and mirror-space updates through local backtracking and computable acceptance criteria, without a global relative-smoothness constant as input. We derive convergence bounds in terms of the parameters accepted during the iterations. These bounds yield an $\O(k^{-2})$ rate for convex objectives and a linear rate for relatively strongly convex objectives when the geometry-acceleration parameters remain uniformly bounded. For nonconvex objectives, we establish an $\O(k^{-1})$ rate for a stationarity measure without requiring a lower Bregman bound or a full-domain Bregman divergence. Numerical experiments on inverse problems, entropy-regularized least squares, D-optimal design, and nonnegative matrix factorization demonstrate faster practical convergence than established Bregman baselines.

Multimodal diffusion language models generate responses by iteratively unmasking tokens, making each answer the endpoint of a multi-step trajectory rather than an immediate commitment. Hallucination benchmarks built for autoregressive models evaluate only the final output, and therefore cannot determine whether an unsupported claim in diffusion VLMs appears late or has already stabilized before any answer token is revealed. We introduce DynaHall, a trajectory-level benchmark of annotation-backed binary visual propositions covering object existence, counting, attributes, and relations, with controlled hard negatives graded by visual prior. DynaHall is paired with a commitment-aware protocol that records the intermediate answer tendency at every unmasking step alongside the committed output. Across five diffusion VLMs from three architecture families, visual hallucination is settled before commitment: an unsupported answer is already the preferred state while the answer position is still masked, and later unmasking steps rarely reverse it, so the failure is not introduced at the write step. This holds across decoding schedules, answer formats, and open-ended generation. DynaHall also exposes failures hidden by final-output metrics, including counting and relation collapse, prior-driven false positives, and attribute errors whose direction changes by type. Guided by this diagnosis, PGS (Pre-commitment Gradient Steering) edits still-masked answer states to reduce false positives, bringing the affirmation rate close to balance, and transfers to another architecture without degrading general ability. DynaHall and PGS suggest that hallucination should be measured and mitigated along the generation trajectory of diffusion VLMs, not only at the final answer.

Reliable AI safeguards require both control mechanisms that reduce unsafe behavior and monitoring mechanisms that detect safety risks during model interactions. Established behavioral safeguards include alignment methods that optimize model outputs and text monitors that assess interaction text. Representation engineering instead reads or modifies internal model states, but the relative strengths of these approaches remain unclear because they are often evaluated under different settings. We present a matched evaluation across two tracks. For safety control, we compare DPO, a behavioral alignment method, with three representation steering methods across robustness, practicality, and granularity. DPO provides the strongest overall control and generally improves with increasing training data, although its safety can degrade after subsequent benign fine-tuning. Representation steering remains competitive primarily in low-data settings, particularly with high-quality contrastive data. For safety monitoring, we compare representation probes with fine-tuned and open-weight text monitors across full-response detection, early detection, and computational cost. Specialized text monitors achieve the strongest overall detection accuracy, while representation probes remain competitive at substantially lower marginal cost. Finally, monitor-guided interventions recover much of the safety lost by DPO after benign fine-tuning, with little additional over-refusal. Overall, representation engineering does not generally replace behavioral safeguards, but offers practical advantages under specific conditions and can provide complementary safety benefits.

Instruction-following machine translation (IF-MT) requires respecting prompt-level rules on terminology, formatting, and register. Rule compliance typically trades off against translation quality, a tension that general-purpose IF data augmentation methods do not address. We propose Reference-Grounded Data Curation, a two-phase pipeline that extracts every supervised constraint from a reference translation that already satisfies it, ensuring feasibility by construction. Phase 1 applies Instruction-Following Difficulty (IFD) scoring to retain the hardest-but-learnable instances from an English-Thai parallel pool. Phase 2 extracts constraints from each reference target and keeps only generations satisfying every constraint, yielding the 1.97M-record Grounded dataset. We fine-tune open-weight bases on Grounded to produce ChindaMT, a Thai-English translation family at 4B, 2B, and 0.8B parameters. Under length-controlled pairwise judging, ChindaMT outperforms or matches every same-size baseline at every tier on both plain translation and under explicit rules, reaching up to a 68.4% win rate against the strongest baseline. The recipe transfers cleanly across Qwen generations. We release model weights, the Grounded dataset, and evaluation suites.

GUI agents need long-horizon visual reasoning: they must interpret a changing interface while keeping a multi-step plan viable as earlier actions constrain later ones. Existing benchmarks evaluate grounding, computer use, and game play, but rarely test whether agents stay coherent across long chains of coupled decisions. Long-horizon visual puzzles expose this capability directly: a legal move that looks like progress can make the puzzle unsolvable, and the loss shows only several moves later. We introduce LongPuzzleBench, 114 levels in six puzzle games played through native GUI actions, where one objective can take a human over a thousand actions on persistent boards and dead ends go unannounced. With Native GUI Actions alone, the strongest agents solve most objectives, but success falls sharply on harder, longer boards: seven of ten general-purpose agents solve nothing harder than Medium, and none completes Bolt Unscrew Hard, which a human solves along with every other objective. Code Execution CUA does not close this gap, and its scores mix visual solving with algorithmic search. Controlled diagnostics trace these failures to one limitation that neither rules, state hints, nor failure memory removes: agents judge each move by the visible progress it makes, not by the future options it leaves.

Millimeter-wave (mmWave) radar enables privacy-preserving human perception, but the extreme sparsity of point clouds from commercial single-chip sensors (mean ~6.5 points/frame; ~28% empty frames) has confined prior art to body-part keypoints or discrete action classification. We present a cross-modal teacher-student framework that lifts commercial radar to full-body, per-frame, metric 3D mesh reconstruction with per-joint uncertainty. Three innovations: (1) a mesh-foundation-model teacher - SAM 3D Body produces whole-body MHR ground truth (70 joints, 18,439 mesh vertices) from a single RGB frame with zero training, slashing annotation cost by orders of magnitude; (2) StudentPoseFormer - set encoding with masked attention pooling, a temporal Transformer, and a CVAE multi-hypothesis head that outputs both the pose mean and per-joint variance, honestly reporting where the radar cannot see; and (3) a multi-stage ground-truth quality pipeline (confidence gating, depth validation, temporal smoothing, bone-length consistency, bad-frame rejection) plus systematic information-lever ablations. On the public MM-Fi benchmark (same TI IWR6843 sensor, cross-subject), our full configuration reaches 7.45 cm 12-joint MPJPE, with ablations proving the causal value of point accumulation (k = 3, -0.34 cm), Doppler (-0.85 cm; -2 cm at the wrist on fast actions), and velocity loss (-0.27 cm). On our own synchronized radar + RGB-D corpus with block-level held-out splits, the pipeline achieves 21.47 cm end-to-end (per-joint hierarchy from 4.8 cm at the hip to 34.7 cm at the wrist - matching physical information limits), could be improved to 15 cm with ~30k diverse samples, and a scaling law shows sample diversity, not volume, is the binding constraint. Deployment inference is radar-only - no camera, no image.

We study the localization properties of 1D and 2D tight-binding models with power-law distributed couplings by comparing the spectrum and the localization properties of the eigenmodes of the Laplacian and the adjacency matrix, using numerical diagonalization of these matrices for different system sizes and connectivities. These two matrices are relevant for different types of dynamical processes. While all eigenmodes of the adjacency matrix are localized for sufficiently large system sizes, the Laplacian matrix always leads to a small proportion of system-spanning modes due to a conservation law, and therefore to power-law tails in the probability distribution of the participation ratio and its relation to the eigenvalues. In one dimension, the exponent of these power laws change continuously with the exponent that characterizes the distribution of couplings. In two dimensions, the modes with the largest relaxation times change from system-spanning to localized when the exponent of the distribution of couplings becomes larger than 0.75. We provide phenomenological explanations for all these findings.

A compact formulation of magnetostatics is presented. Without using constitutive relations, including the aether relations, an expression is proposed for the potential energy of a region carrying a distribution of magnetic dipoles under a vector potential field, where the dipole distribution is specified by a current density potential field. Assuming that during a virtual motion of the dipole distribution the virtual work expended by the field is equal to minus the time derivative of the potential energy, an expression for the mechanical force functional is derived. In addition to the Lorentz and Kelvin force densities, the force functional contains an asymmetric active stress field, the skew-symmetric part of which is the mechanical couple density, and a pressure term.

Post-training quantization (PTQ) enables efficient deployment of large vision-language models (LVLMs), but is typically calibrated on a small set while expected to generalize across diverse downstream tasks. Although recent PTQ methods for LVLMs incorporate sensitivity signals, they still minimize reconstruction loss with respect to the full-precision model, potentially over-preserving FP behavior and calibration-specific bias. Rather than treating quantization solely as an error to be minimized, we observe that it can also provide beneficial regularization for certain layers and modalities. Motivated by this observation, we propose Balanced Fitting, a quantization effect-based framework that balances precision and regularization beyond reconstruction-based optimization. By measuring layer- and component-wise quantization effects for weights, vision activations, and text activations, Balanced Fitting combines fine-grained fitting for sensitive components with coarser fitting to exploit potential regularization benefits. Experiments on multiple LVLMs show that our method consistently outperforms prior PTQ approaches under both weight-only and weight-activation quantization, while lower reconstruction loss does not reliably translate into better downstream performance. The source code is publicly available at https://github.com/kmc3661/BFQ

Multimodal data analysis, which answers questions over relational tables, text, and images, has attracted growing attention in the data management community. Large language models (LLMs) enable such analysis in natural language by generating analysis plans over relational and semantic operators. However, LLM-generated plans are error-prone: a plan may silently compute something other than what was asked, fail during execution, or return a result that misses the question. This paper presents WeaveData, a multimodal data analysis system with self-critiquing and self-evolving LLM plans. First, WeaveData generates a typed logical plan for each question and critiques it step by step before execution, and it checks the executed result against the question afterwards. Second, WeaveData evolves a plan that fails or misses the question: it diagnoses the failure with the actual data, reuses the results that remain valid, and accumulates planning experience for later questions. Third, WeaveData grounds planning in a metadata knowledge graph of all modalities, clarifies ambiguous questions with the user, and backs every model judgment with evidence in an interactive notebook. We demonstrate WeaveData on two public multimodal datasets.

This paper focuses on robust beamforming for orthogonal time frequency space (OTFS)-enabled massive multiple-input multiple-output (MIMO) systems under channel state information (CSI) uncertainty. In high-mobility satellite communications, uncertain CSI severely degrades beamforming accuracy and poses a major challenge to meeting users' quality of service (QoS) requirements. To address this challenge, we first formulate a chance-constrained optimization problem aiming to minimize the total transmit power while guaranteeing a predefined outage probability. Building on a 3D delay-Doppler-angle (DDA) channel representation, we propose a data-driven approach using support vector clustering (SVC) to model the uncertain CSI as an asymmetric uncertainty set. We then derive a robust counterpart that reformulates the intractable chance constraints into a deterministic semidefinite program. Finally, we design a graphics processing unit (GPU)-accelerated parallelizable alternating direction method of multipliers (ADMM) algorithm to address the computational complexity of large-scale antenna arrays. Simulation results show that the proposed SVC-based design reduces transmit power compared with conventional beamforming schemes, and that the GPU-accelerated ADMM achieves a speedup. These results confirm that the proposed framework achieves improved robustness, energy efficiency, and efficient computation in dynamic massive MIMO networks.

Data analytics offer a great opportunity for organizations within the cold-chain industry to become more sustainable and reduce their environmental footprint. Yet, despite recent progress in data sciences, they still face challenges to ensure data quality and streamline data processes through adapted full-scale ecosystems, limiting their ability to perform sustainable analytics. Most data techniques and tools stem from the data-science community and are not always suitably adapted to domain specificities. For instance, nearly all data-quality frameworks are designed to individually consider entities, i.e. representations of real-world elements. However, achieving environmental impact reduction in industrial settings, particularly within the cold-chain sector, often requires modelling and studying entire systems comprised of multiple interdependent entities. This publication challenges the application of conventional data science and engineering concepts in data ecosystems within the cold-chain sector and proposes an alternative approach to sustainably address prevalent challenges and thus optimize analytical processes.

Positron forming a bound state with molecules is an area of meticulous research and remains open to simpler techniques for estimating the binding energy. Correlation between the incoming positron and the molecular electrons plays a crucial role even for polar molecules, where binding is also possible at the static-potential level. In this work, we have used a model correlation potential, which accounts for the virtual positronium formation, in the single-center expansion scattering calculations for polar oxygen-containing molecules. The thus determined S-matrix is continued into the complex momentum plane by fitting it to the Pade approximant. The positron bound state is estimated using the calculated pole position of the S-matrix. The results, compared with the latest experimental and ab initio findings, look quite promising.

In this short communication we answer negatively to a question posed by the authors in their work \cite[Section 1.4]{Brue2022} about the complex interpolation nature of the spaces $BV^{s}(\R^n)$, introduced by G.E. Comi and G. Stefani in \cite{ComiStefani2019}.

Recent vision-language models (VLMs) have advanced vision-and-language navigation (VLN), enabling models to predict navigation actions from visual observations and language instructions. In this work, we explore VLN with panoramic observations and introduce PanoVLN. The motivation is straightforward: more complete visual context should enable better-informed navigation decisions. For example, a panorama can reveal a passage outside a perspective camera's field of view, allowing the model to identify the intended route without additional exploration. However, we find that simply replacing perspective images with panoramas yields only limited gains. Our diagnosis suggests that fully exploiting wider visibility requires modifications to action prediction, training supervision, and visual representation. First, wider visibility supports longer-horizon action planning. We make the model predict longer action sequences, enabling larger turns and subsequent movement from a single panorama. Specifically, we introduce a confidence-guided execution (CGE) strategy that dynamically determines how many predicted actions to execute before replanning. Second, wider visibility also brings more complex route choices. We therefore construct training routes with frequent branching points and clear instructions to provide targeted supervision for route selection. Third, panoramic navigation requires understanding spatial relationships across viewing directions, beyond recognizing individual landmarks. We combine semantic and geometric features from RGB panoramas to capture both scene content and spatial layout without adding visual tokens. With a 4B backbone and RGB-only input, PanoVLN surpasses the previous SOTA by 11.9% and 8.7% in success rate on R2R-CE and RxR-CE Val-Unseen. Real-world experiments on a quadruped further demonstrate faster navigation with fewer pauses than prior VLN methods.

Energetic electrons dominate the energy precipitated into Jupiter's auroral regions, but protons precipitate along the same field lines, with a contribution that remains poorly constrained. We statistically compare the precipitating energy flux of protons and electrons in two of Jupiter's auroral sub-regions, the polar (PE) and main (ME) emission regions. We use Juno/JEDI data from PJ3 to PJ66. The magnetic footprint of the spacecraft, computed with the JRM33 and CON2020 field models, is assigned to one of the two sub-regions, and the precipitating energy flux of each species is obtained by integrating over the loss cone the mean differential intensity measured within it. In both sub-regions, the median proton energy flux is 52 to 223 times lower than that of the electrons, and the total precipitated proton power is less than 2% of the electron power. Proton fluxes are broadly distributed across the sub-regions, with higher values in the ME than in the PE. Protons play a secondary role in Jupiter's auroral energy budget, radiating an estimated 5 to 9 GW in the UV per sub-region, pending a dedicated proton transport modelling. Their Doppler signature in the red wing of the Lyman-$\alpha$ line, undetected by HST and difficult to access with Juno/UVS, is a key observable for the upcoming Juice and Europa Clipper missions.

We study the maximum likelihood estimation of the coefficient {\beta} in well-specified Poisson regression. Using tools from empirical process theory and random conic geometry, we show that the probability of existence of the maximum likelihood estimator (MLE) exhibits a sharp phase transition at the threshold n > d. We then determine a minimum threshold exponential in the norm of {\beta} on the sample size n to guarantee with high probability an excess risk of the asymptotic order d/n. We reveal the existence of an intermediate regime in Poisson regression, when n is larger than d but smaller than this exponential threshold, where the MLE exists but does not achieve the optimal rate d/n. We close the gap between the two regimes up to a d^{1+\epsilon} term with {\epsilon} \in (0, 1) by providing an upper bound on the distance between the MLE and {\beta} whenever n > d^{1+\epsilon}. Along the way, we provide two generalizations of well-known PAC-Bayes inequalities regarding sub-Gamma random vectors and sub-Gamma random matrices that are of independent interest and that we use extensively to prove the main results of the present paper.

Adapting pretrained models to downstream tasks with limited data has become a central paradigm in modern deep learning. Yet, despite its widespread practical success, how fine-tuning leverages information from pretraining remains poorly understood theoretically. We study fine-tuning from pretrained weights through the lens of sparse linear regression and two-layer diagonal linear networks. In our setting, pretraining provides information through the support (and signs) of the initialization predictor, which may contain coordinates relevant to the downstream task. We show how pretrained information reshapes the implicit bias and training dynamics, and can thereby reduce the sample complexity of recovering the target parameters and support. In particular, for a clean initialization with correctly inherited signs, we show that the required sample size is comparable to that of a weighted Lasso estimator that explicitly exploits the pretrained support through a suitably chosen regularizer. Our results thus show how information encoded in pretrained weights can be implicitly exploited by gradient-based fine-tuning, reducing the amount of data needed to recover a downstream task.

Many process engineering applications hold a gas-liquid interface stationary inside a structured solid by a controlled pressure difference. Gas diffusion electrodes (GDEs) are one such case, where the interface separates the liquid electrolyte from the gaseous reactant. Maintaining it is particularly challenging in organic electrosynthesis, where low surface tensions lower the admissible pressures throughout and small contact angles leave the electrode with little margin against flooding. Here, we quantify how the shape, wettability, and three-dimensional topology of a structured medium set this window, using phase-field simulations of the Cahn-Hilliard-Navier-Stokes equations. Each geometry is characterised by its Laplace pressure curve, which yields both the maximum admissible pressure difference and the stiffness of the interface against pressure fluctuations. For single flat orifices at constant open area, elongating the opening from an aspect ratio of one to six raises the admissible pressure difference by 40 % and the stiffness by a factor of 3.3. Comparison with slits of equal width shows that this gain originates entirely from the reduced opening width. Sheared, diamond shaped openings are markedly less effective. In woven meshes, the wettability displaces the operating window several times as far as it stretches it. A less wetting surface therefore buys flooding margin largely at the expense of breakthrough margin, whereas the geometric route, established here for flat openings, widens the window itself. From these results we derive design rules for structured gas-liquid contactors and improved GDE architectures for organic electrosynthesis.

Latent communication passes internal states between language models instead of decoded text, but higher receiver accuracy does not show that the receiver used the message content. Across five method-dataset pairs, replacing each message with one from an unrelated question changes accuracy by at most 0.60 points, even when communication adds 15.44 points over the receiver alone. Thus the interface can supply the gain while making the sharer dispensable. Draft-KV instead sends the key-value states formed while the sharer drafts an answer to the current question. Linear projections place these states in a side memory read through a gated attention branch, and progressive training moves from message reconstruction to answer supervision under a guard on harm from mismatched messages. Both models remain frozen and the interface trains 1.05M parameters, 348x fewer than C2C. With a Qwen3-8B sharer, a frozen Qwen2.5-0.5B-Instruct receiver reaches 78.04% on MMLU-Redux, versus 37.45% alone and 36.40% with reassigned messages. At fixed interface size, scaling the sharer from 0.6B to 8B raises accuracy from 46.11% to 78.04%; communication also transfers to held-out tasks and can exceed both models when each holds different evidence.

The development of round elimination into a general-purpose technique [PODC 2019] marked a turning point in our understanding of the hardness of many graph problems in the distributed setting and led to several breakthrough results. However, the round elimination technique seems unable to yield randomized lower bounds of $\omega(\log \log n)$ rounds as a function of the number $n$ of nodes. Very recently, Khoury and Schild [FOCS 2025] introduced a new technique called round elimination via self-reduction, which bypasses the limitations of classical round elimination. Using this approach, the authors show that any randomized algorithm for maximal matching requires $\Omega(\sqrt{\log n})$ rounds in the LOCAL model. Their elegant technique is, in some respects, similar to classical round elimination while being fundamentally different in others. However, it is tailored specifically to maximal matching rather than being applicable to a broad class of problems. In this paper, we show that self-reduction is, in fact, a special case of classical round elimination, thereby turning it into a general-purpose approach. In particular, we introduce a new way to measure the error of an algorithm and show that, under this new measure, classical round elimination can indeed yield $\omega(\log \log n)$ randomized lower bounds. More specifically, we identify a large class of problems for which this improvement is entirely black-box: once a problem is shown to belong to the class, stronger randomized lower bounds follow automatically from the classical round-elimination framework. As an application, we prove $\Omega(\sqrt{\log n})$ randomized lower bounds for a range of graph problems, namely, maximal matching on regular $2$-colored graphs, $\frac{1}{k}$-integral matching, and maximal $H$-packing.

Reproduction test generation translates a natural-language issue description into executable tests that fail on the original code and pass after the issue is resolved, providing executable evidence for verifying candidate patches. Existing benchmarks are constructed for individual programming languages, preventing a unified evaluation across diverse programming ecosystems. To address this limitation, we introduce MULTI-SWT-BENCH, a multilingual benchmark for reproduction test generation consisting of 1,963 instances across eight programming languages: Python, Java, TypeScript, JavaScript, Go, Rust, C, and C++. Using this benchmark, we conduct an empirical study of state-of-the-art LLMs with four representative methods (MSWE-agent, MOpenHands, Codex, and Claude Code) and perform a failure analysis across programming languages. Our evaluation reveals a systematic language gap. Across every evaluated method and LLM, the success rate on Python exceeds the aggregate success rate across all languages, while C++ exhibits particularly low success rates. Our failure analysis identifies both language-specific challenges arising from repository testing conventions and cross-language challenges in inferring implicit setup requirements and preserving the target behavior through iterative revisions. These findings demonstrate the importance of multilingual evaluation and provide actionable directions for developing reproduction test generation methods that generalize across software ecosystems and reliably capture issue-specific behavior.

We solve the asymptotic Plateau problem in hyperbolic space for the curvature given by the normalized geometric mean of the $p$-fold sums of the principal curvatures. For every $n\ge3$, $2\le p\le n-1$, and $\sigma\in(0,1)$, each bounded domain $\Omega\subset\mathbb{R}^n$ with smooth mean-convex boundary admits a unique complete admissible vertical graph with prescribed curvature $\sigma$ and asymptotic boundary $\partial\Omega\times\{0\}$. The result extends the known cases $(n,p)=(3,2)$ and $(4,3)$ to the stated range. The key curvature estimate is uniform with respect to the positive boundary height in the approximating Dirichlet problems. The proof establishes two lower bounds for the full third-derivative quadratic form under the linearized constraints: a sharp universal bound with coefficient $2/p$ and a stronger direction-dependent bound when the relevant principal curvature lies in a specified range.

Concept-based explanations describe neural network predictions through human-understandable properties of inputs called concepts. The field encompasses approaches that differ in how they define and represent concepts and connect them to model predictions. We introduce a theoretical framework that describes these approaches in a common mathematical language and supports a shared analysis of their properties. For concept discovery, which identifies concepts automatically within a latent space of a trained model, we employ a concept autoencoder view. An encoder extracts concept representations from the model's latent space, and a decoder uses them to reconstruct the original latent representation. The autoencoder's reconstruction error measures how accurately its decoder recovers the original latent representation. We revisit model completeness: how well the concepts can reproduce the model's outputs. We show that model incompleteness of the concepts can be bounded by the autoencoder's reconstruction error. The autoencoder view also provides a common way to define individual concept attributions, which measure each concept's contribution to a prediction. We establish when these attributions sum to the model's prediction, and bound the discrepancy otherwise, thus providing attribution completeness guarantees.

Real-world driving is inherently multi-agent, yet most existing driving world models generate observations from a single ego vehicle. Independently extending them to multiple vehicles does not ensure that different agents observe a consistent shared world. We present CoDrive, a cross-vehicle, multi-view driving video generation framework that jointly generates observations of vehicles sharing the same dynamic scene with precise camera-trajectory control. CoDrive interleaves local self-attention, which models spatiotemporal dependencies among the views of each vehicle, with global self-attention, which enables information exchange and consistency modeling across vehicles. To explicitly encode their spatial relationships, all camera trajectories are represented in a shared world coordinate system and injected into the attention layers through projective relative positional encoding. We further adopt a progressive mixed-task training strategy that combines large-scale real-world single-agent data with synthetic cross-agent interaction data, allowing the model to benefit from real-world appearance distributions while learning cross-agent consistency from simulation. For systematic evaluation, we introduce CoDrive-Bench, a benchmark covering real and synthetic multi-vehicle scenarios and evaluating trajectory controllability, scene geometry consistency, and instance-level consistency. Experiments show that CoDrive improves trajectory controllability and cross-agent geometric and instance consistency while maintaining competitive visual quality.

In this paper, we formulate a general differencing framework for variance estimation across a range of settings. We demonstrate that conventional difference-based noise variance estimators cannot achieve the desired bias-correcting power in nonparametric regression with repeated measurements. A new high-order bias-corrected differencing scheme, adapted to repeated measurements, is proposed by interlacing inter-group and intra-group differencing. The theoretical properties of the new sequences and estimators are studied. Our proposals are particularly efficient in finite samples and under high signal-to-noise ratio scenarios, where asymptotic convergence has not yet fully taken effect, due to their strong bias-correcting power.

In this paper we completely classify the minimizers of a measure constraint global vectorial free boundary problem with a linear datum. More precisely, we show that there exists a unique minimizer whose coincidence set is an ellipsoid. We are motivated by the connection of the problem with the blow-ups of the vectorial Bernoulli free boundary problem and the obstacle problem.