arXiv:2510.09585v4 Announce Type: replace Abstract: Community Notes (formerly known as Birdwatch) is the first large-scale crowdsourced content moderation initiative launched by X (formerly Twitter) in January 2021. As the Community Notes model gains momentum across other social media platforms, there is a growing need to assess its underlying dynamics and effectiveness. This paper provides a descriptive investigation of Community Notes during its first four years, examining its linguistic diversity, sourcing practices, Contributor activity, rating behaviour, and interaction networks. In addition, we release a curated dataset and accompanying source code to support future research, along with a review of prior research on Community Notes. We parsed Notes and ratings data from the first four years of the program and conducted language detection across all Notes. For English-language Notes, we extracted embedded URLs and identified discussion topics in each Note. Additionally, we constructed monthly interaction networks among the Contributors. Together, the descriptive analysis, dataset, code, and literature review provide a foundation for advancing research on Community Notes and community-based content moderation more broadly.
Science Journals
arXiv:2606.13807v1 Announce Type: new Abstract: In this study, we present a novel time-stepping scheme for multiscale differential equations describing oscillatory systems with well-separated scales, where the scale separation is controlled by a small parameter $\epsilon$. The time-stepping method is related to a multi-modal WKB approximation and relies on a transformation of variables derived in this work. The analysis reveals that, in the transformed formulation, the leading-order oscillations are either eliminated or appear only at higher asymptotic order. The method is applied to ordinary differential equations, including the well-known van der Pol oscillator. We investigate the accuracy of the proposed method numerically for different parameter regimes, in particular for decreasing values of $\epsilon$, and study how the parameters of the numerical scheme must be adapted as $\epsilon$ is reduced. In the presented numerical tests, the computational cost remains bounded as $\epsilon$ is decreased.
arXiv:2510.17633v3 Announce Type: replace Abstract: Large Audio-Language Models (LALMs) are becoming essential as a powerful multimodal backbone for real-world applications. However, recent studies show that audio inputs can more easily elicit harmful responses than text, exposing new risks toward deployment. While safety alignment has made initial advances in LLMs and Large Vision-Language Models (LVLMs), we find that vanilla adaptation of these approaches to LALMs faces two key limitations: 1) LLM-based steering fails under audio input due to the large distributional gap between activations, and 2) prompt-based defenses induce over-refusals on benign-speech queries. To address these challenges, we propose Safe-Ablated Refusal Steering (SARSteer), the first inference-time defense framework for LALMs. Specifically, SARSteer leverages text-derived refusal steering to enforce rejection without manipulating audio inputs and introduces decomposed safe-space ablation to mitigate over-refusal. Extensive experiments demonstrate that SARSteer significantly improves harmful-query refusal while preserving benign responses, establishing a principled step toward safety alignment in LALMs. The codes and constructed datasets are released at https://github.com/linweiii/SARSteer.
arXiv:2511.02153v4 Announce Type: replace Abstract: Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from overlapping diffraction patterns, while X-ray fluorescence provides quantitative, element-specific contrast at lower spatial resolution. We formulate a joint variational framework that integrates these two modalities into a single nonlinear least-squares problem with shared spatial variables. This formulation enforces cross-modal consistency between structural and compositional estimates, improving conditioning and promoting stable convergence. The resulting optimization couples complementary contrast mechanisms (i.e., phase and absorption from ptychography, elemental composition from fluorescence) within a unified inverse model. Numerical experiments on simulated data demonstrate that the joint reconstruction achieves faster convergence, sharper and more quantitative reconstructions, and lower relative error compared with separate inversions. The proposed approach illustrates how multimodal variational formulations can enhance stability, resolution, and interpretability in computational X-ray imaging.
arXiv:2511.07075v5 Announce Type: replace Abstract: Spatial semantic segmentation of sound scenes (S5) consists of jointly performing audio source separation and sound event classification from a multichannel audio mixture. Evaluating S5 systems with separation and classification metrics individually makes system comparison difficult, whereas existing joint metrics, such as the class-aware signal-to-distortion ratio (CA-SDR), can conflate separation and labeling errors. In particular, CA-SDR relies on predicted class labels for source matching, which may obscure label swaps or misclassifications when the underlying source estimates remain perceptually correct. In this work, we introduce the class and source-aware signal-to-distortion ratio (CASA-SDR), a new metric that performs permutation-invariant source matching before computing classification errors, thereby shifting from a classification-focused approach to a separation-focused approach. We first analyze CA-SDR in controlled scenarios with oracle separation and synthetic classification errors, as well as under controlled cross-contamination between sources, and compare its behavior to that of the classical SDR and CASA-SDR. We also study the impact of classification errors on the metrics by introducing error-based and source-based aggregation strategies. Finally, we compare CA-SDR and CASA-SDR on systems submitted to Task 4 of the DCASE 2025 challenge, highlighting the cases where CA-SDR over-penalizes label swaps or poorly separated sources, while CASA-SDR provides a more interpretable separation-centric assessment of S5 performance.
arXiv:2511.09789v3 Announce Type: replace Abstract: Short-term energy forecasting plays an important role in real-time operational decision-making, such as electricity market bidding and power system dispatch, where both numerical accuracy and correct directional signals are essential. However, most existing forecasting approaches formulate the problem purely as a regression task, limiting their ability to explicitly capture stepwise directional movements and trend consistency required for operational decisions. To address this limitation, this paper proposes a trend-aware multi-task forecasting framework that decomposes forecasting outputs into directional movements and deviation magnitudes relative to the latest observation, enabling both accurate numerical prediction and interpretable trend-aware outputs. The framework adopts a task-specific dual-stream architecture and explores key design choices for integrating trend and deviation information, including hard versus probabilistic trend representations, symmetric versus asymmetric deviation modelling, and parallel versus sequential conditioning strategies. To stabilize multi-task learning and reduce manual tuning, an uncertainty-aware task weighting scheme is incorporated to automatically balance directional classification, deviation regression, and final output prediction during training. Experimental results on real-world energy datasets demonstrate that the proposed framework achieves competitive numerical accuracy compared with state-of-the-art algorithms, while consistently improving trend prediction performance with moderate computational cost. This capability is particularly beneficial in short-term energy system management, where consistent directional forecasting can provide more reliable decision support for practical operational scenarios such as market bidding, resource scheduling, and risk-aware energy management.
arXiv:2511.14897v2 Announce Type: replace Abstract: We present an unsupervised single image bidirectional Magnetic Resonance Image (MRI) synthesizer that synthesizes an Ultra-Low Field (ULF) like image from a High-Field (HF) magnitude image and vice-versa. Unlike existing MRI synthesis models, our approach is inspired by the physics that drives contrast changes between HF and ULF MRIs. Our forward model simulates a HF to ULF transformation by estimating the tissue-type Signal-to-Noise ratio (SNR) values based on target contrast values. For the Super-Resolution task, we used an Implicit Neural Representation (INR) network to synthesize HF image by simultaneously predicting tissue-type segmentations and image intensity without observed HF data. The proposed method is evaluated using synthetic ULF-like data from generated from standard 3T T$_1$-weighted images for qualitative assessments and paired 3T-64mT T$_1$-weighted images for validation experiments. WM-GM contrast improved by 52% in synthetic ULF-like images and 37% in 64mT images. Sensitivity experiments demonstrated the robustness of our forward model to variations in target contrast, noise and initial seeding.
arXiv:2512.00336v4 Announce Type: replace Abstract: The rapid advancement of AI-generated multimodal video-audio content has raised significant concerns regarding information security and content authenticity. Existing synthetic video datasets predominantly focus on the visual modality alone, while the few incorporating audio are largely confined to facial deepfakes--a limitation that fails to address the expanding landscape of general multimodal AI-generated content and substantially impedes the development of trustworthy detection systems. To bridge this critical gap, we introduce the Multimodal Video-Audio Dataset (MVAD), the first comprehensive dataset specifically designed for detecting AI-generated multimodal video-audio content. Our dataset exhibits three key characteristics: (1) genuine multimodality with samples generated according to three realistic video-audio forgery patterns; (2) high perceptual quality achieved through diverse state-of-the-art generative models; and (3) comprehensive diversity spanning realistic and anime visual styles, four content categories (humans, animals, objects, and scenes), and four video-audio multimodal data types. Our dataset will be available at https://github.com/HuMengXue0104/MVAD.
arXiv:2512.03787v2 Announce Type: replace Abstract: Clinical pathways are specialized healthcare plans that model patient treatment procedures. They are developed to provide criteria-based progression and standardize patient treatment, thereby improving care, reducing resource use, and accelerating patient recovery. However, manual modeling of these pathways based on clinical guidelines and domain expertise is difficult and may not reflect the actual best practices for different variations or combinations of diseases. We propose a two-phase modeling method using process mining, which extends the knowledge base of clinical pathways by leveraging conformance checking diagnostics. In the first phase, historical data of a given disease is collected to capture treatment in the form of a process model. In the second phase, new data is compared against the reference model to verify conformance. Based on the conformance checking results, the knowledge base can be expanded with more specific models tailored to new variants or disease combinations. We demonstrate our approach using Synthea, a benchmark dataset simulating patient treatments for SARS-CoV-2 infections with varying COVID-19 complications. The results show that our method enables expanding the knowledge base of clinical pathways with sufficient precision, peaking to 95.62% AUC while maintaining an arc-degree simplicity of 67.11%.
arXiv:2606.14108v1 Announce Type: new Abstract: We introduce Adelic operation-preserved embeddings (AOE), a training-free representation that captures both a number's real value and its modular (p-adic) signatures. This construction preserves additive and multiplicative structure by design, turning numerical input into embeddings that "speak in the language of mathematics." Unlike prior approaches that rely on task-specific retraining, AOE is plug-and-play and drops seamlessly into existing architectures. On algebraic combinatorics benchmarks, it delivers consistent gains including the first-ever perfect accuracy on the Weaving Pattern task-while suggesting a principled path forward for overcoming the long-standing "number problem" in AI.
arXiv:2512.03883v3 Announce Type: replace Abstract: Increasing evidence supports watch-and-wait (WW) surveillance for patients with rectal cancer who show clinical complete response (cCR) at restaging following total neoadjuvant treatment (TNT). However, accurate methods to early detect local regrowth (LR) from follow-up endoscopy images during WW are essential to manage care and prevent distant metastases. Hence, we developed a Siamese Swin Transformer with Dual Cross-Attention (SSDCA) to combine longitudinal endoscopic images at restaging and follow-up and distinguish cCR from LR. SSDCA leverages pretrained Swin Transformers to extract domain agnostic features and enhance robustness to imaging variations. Dual cross attention is implemented to emphasize features from the paired scans without requiring any spatial alignment to predict response. SSDCA as well as Swin-based baselines were trained using image pairs from 135 patients and evaluated on a held-out set of image pairs from 62 patients. SSDCA produced the best balanced accuracy (81.76% $\pm$ 0.04), sensitivity (90.07% $\pm$ 0.08), and specificity (72.86% $\pm$ 0.05). Robustness analysis showed stable performance irrespective of artifacts including blood, stool, telangiectasia, and poor image quality. UMAP clustering of extracted features showed maximal inter-cluster separation (1.45 $\pm$ 0.18) and minimal intra-cluster dispersion (1.07 $\pm$ 0.19) with SSDCA, confirming discriminative representation learning. Code and weights available at: https://github.com/Jotanator/SSDCA
arXiv:2512.05780v2 Announce Type: replace Abstract: The increasing penetration of converter-interfaced generators in power systems has led to the adoption of impedance-based criteria as an alternative framework for assessing and ensuring stable integration. However, when the impedance criterion is used, identifying the root cause of instabilities is generally more challenging compared to other approaches, such as modal analysis. Moreover, the eigenvalues and characteristic equation used in the impedance criterion are non-linear functions, making it difficult to establish a clear relationship between impedance components and closed-loop stability. To address this issue, this paper proposes the application of the Pauli decomposition to analyse dq impedance matrices and minor-loop equations. By using this decomposition technique, the dq representation can be reformulated into a quaternion-like form, which has explicit algebraic relationships with the determinant, trace, eigenvalues, and characteristic equation. Moreover, this decomposition enables systematic assessment of the influence of each impedance term in the system stability, thus facilitating finding the root-cause of instabilities. The primary objective of this work is to develop the mathematical foundation of the Pauli decomposition and demonstrate its implications for root-cause analysis. The theoretical contributions are validated using a case study consisting of a converter-interfaced generator connected to a weak grid that has been previously analysed in the literature using existing techniques. The proposed Pauli decomposition provides an algebraic tool that enhances interpretability of impedance-based stability analysis and establishes a basis for further investigation of complex converter interactions.
arXiv:2512.10966v3 Announce Type: replace Abstract: Accurate and early diagnosis of Alzheimer's disease (AD) is critical for effective intervention and requires integrating complementary information from multimodal neuroimaging data. However, conventional fusion approaches often rely on simple concatenation of features, which cannot adaptively balance the contributions of biomarkers such as amyloid PET and MRI across brain regions. In this work, we propose MREF-AD, a Multimodal Regional Expert Fusion model for AD diagnosis. It is a Mixture-of-Experts (MoE) framework that models mesoscopic brain regions within each modality as independent experts and employs a gating network to learn subject-specific fusion weights. Utilizing tabular neuroimaging and demographic information from the Alzheimer's Disease Neuroimaging Initiative (ADNI), MREF-AD achieves competitive performance over strong classic and deep baselines while providing interpretable, modality- and region-level insight into how structural and molecular imaging jointly contribute to AD diagnosis. The source code is available at https://github.com/PennShenLab/mref-ad.
arXiv:2512.13069v2 Announce Type: replace Abstract: Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of multi-fidelity strategies that leverage inexpensive low-fidelity information without compromising accuracy. Addressing this challenge, this work presents a multi-fidelity deep learning framework that combines autoencoder-based transfer learning with a newly developed Multi-Split Conformal Prediction (MSCP) strategy to achieve uncertainty-aware aerodynamic data fusion under extreme data scarcity. The methodology leverages abundant Low-Fidelity (LF) data to learn a compact latent physics representation, which acts as a frozen knowledge base for a decoder that is subsequently fine-tuned using scarce HF samples. Tested on surface-pressure distributions for NACA airfoils (2D) and a transonic wing (3D) databases, the model successfully corrects LF deviations and achieves high-accuracy pressure predictions using minimal HF training data. Furthermore, the MSCP framework produces robust, actionable uncertainty bands with pointwise coverage exceeding 95%. By combining extreme data efficiency with uncertainty quantification, this work offers a scalable and reliable solution for aerodynamic regression in data-scarce environments.
arXiv:2512.14366v3 Announce Type: replace Abstract: Implicit Neural Representations (INRs) based on vanilla Multi-Layer Perceptrons (MLPs) are widely believed to be incapable of representing high-frequency content. This has directed research efforts towards architectural interventions, such as coordinate embeddings or specialized activation functions, to represent high-frequency signals. In this paper, we challenge the notion that the low-frequency bias of vanilla MLPs is an intrinsic, architectural limitation to learn high-frequency content, but instead a symptom of stable rank degradation during training. We empirically demonstrate that regulating the network's rank during training substantially improves the fidelity of the learned signal, rendering even simple MLP architectures expressive. Extensive experiments show that using optimizers like Muon, with high-rank, near-orthogonal updates, consistently enhances INR architectures even beyond simple ReLU MLPs. These substantial improvements hold across a diverse range of domains, including natural and medical images and novel view synthesis, with up to +9 dB PSNR over the same architecture. Code is available at (https://rank-inrs.github.io).
arXiv:2512.21201v3 Announce Type: replace Abstract: Zero-shot object navigation (ZSON) requires robots to find target objects in unseen environments without task-specific fine-tuning or pre-built maps, a key capability for general-purpose service robots. Yet methods that perform well in simulation often degrade in cluttered real-world scenes with severe occlusion and latent hazards, where large unseen regions make single-scene inference brittle and unsafe. We propose Schr\"odinger's Navigator, a belief-aware framework that reasons at inference time over multiple trajectory-conditioned imagined 3D futures. Given candidate paths, a trajectory-conditioned 3D world model predicts hypothetical observations and maintains a superposition of plausible scene realizations rather than committing to one map. An adaptive occluder-aware sampler directs imagination to uncertainty-critical regions, while a Future-Aware Value Map (FAVM) aggregates imagined futures for robust, proactive action selection. Experiments in simulation and on a physical Go2 quadruped show that Schr\"odinger's Navigator outperforms strong ZSON baselines, improving hidden-target discovery and risk-aware waypoint selection in occlusion-heavy navigation scenarios. These results highlight imagined 3D futures as a scalable and generalizable strategy for zero-shot navigation in uncertain real-world environments.
arXiv:2512.22484v2 Announce Type: replace Abstract: Geometric mechanics models of locomotion have provided insight into how robots and animals use environmental interactions to convert internal shape changes into displacement through the world, encoding this relationship in a ``motility map''. A key class of such motility maps arises from (possibly anisotropic) linear drag acting on the system's individual body parts, formally described via Riemannian metrics on the motions of the system's individual body parts. The motility map can then be generated by invoking a sub-Riemannian constraint on the aggregate system motion under which the position velocity induced by a given shape velocity is that which minimizes the power dissipated via friction. The locomotion of such systems is ``geometric'' in the sense that the final position reached by the system depends only on the sequence of shapes that the system passes through, but not on the rate with which the shape changes are made. In this paper, we consider a far more general class of systems in which the drag may be not only anisotropic (with different coefficients for forward/backward and left/right motions), but also asymmetric (with different coefficients for forward and backward motions). Formally, including asymmetry in the friction replaces the Riemannian metrics on the body parts with Finsler metrics. We demonstrate that the sub-Riemannian approach to constructing the system motility map extends naturally to a sub-Finslerian approach and identify system properties analogous to the constraint curvature of sub-Riemannian systems that allow for the characterization of the system motion capabilities.
arXiv:2601.03971v2 Announce Type: replace Abstract: In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with linear forward models, Gaussian priors, and Gaussian noise, we use perturbation theory for inverses to bound the error in the approximate posterior mean and posterior covariance resulting from a linear approximate forward model. We then focus on the smoothing problem of inferring the initial condition of linear time-invariant dynamical systems, using finitely many partial state observations. For such problems, and for a specific model order reduction method based on balanced truncation, we show that the impulse response of a certain prior-driven system is closely related to the prior-preconditioned Hessian of the inverse problem. This reveals a novel connection between systems theory and inverse problems. We exploit this connection to prove the first a priori error bounds for system-theoretic model order reduction methods applied to smoothing problems. The bounds control the approximation error of the posterior mean and covariance in terms of the truncated Hankel singular values of the underlying system.
arXiv:2601.04646v4 Announce Type: replace Abstract: Large-scale multi-tenant retrieval systems generate extensive query logs but lack curated relevance labels for effective domain adaptation, resulting in substantial underutilized "dark data." This challenge is compounded by the high cost of model updates, as jointly fine-tuning query and document encoders requires full corpus re-indexing, which is impractical in multi-tenant settings with thousands of isolated indices. We introduce DevRev-Search, a passage retrieval benchmark for technical customer support built via a fully automated pipeline. Candidate generation uses fusion across diverse sparse and dense retrievers, followed by an LLM-as-a-Judge for consistency filtering and relevance labeling. We further study and systematically evaluate index-preserving query-only adaptation strategies that fine-tune only the query-encoder while keeping the document indices fixed. Experiments on DevRev-Search, SciFact, and FiQA-2018 show that parameter-efficient fine-tuning of the query encoder delivers a remarkable quality-efficiency trade-off, enabling scalable and practical enterprise multi-tenant retrieval.
arXiv:2601.04722v3 Announce Type: replace Abstract: Data provenance (the process of determining the origin and derivation of data outputs) has applications across multiple domains including explaining database query results and auditing scientific workflows. Despite decades of research, provenance tracing remains challenging due to its high computational cost and storage requirements. In streaming systems such as Apache Flink, fine-grained provenance graphs can grow super-linearly with data volume, posing significant scalability challenges. We define temporal attribution, a new lightweight form of provenance, appropriate for certain tasks, such as monitoring dependencies between system components over time quantitatively. Temporal attribution enables time-focused analysis that does not require fine-grained, tuple-level dependency meta-data. Inspired by volume-based provenance tracking in Temporal Interaction Networks (TINs), we demonstrate TINs' applicability in succinctly modeling quantified data exchanges between dataflow operators in stream data processing systems and in processing workflows, in general, over time. We classify data into discrete and liquid types, define five temporal provenance query types, and propose a state-based indexing approach. Our vision outlines research directions toward making this new form of temporal attribution a practical tool for large-scale dataflow analytics.
arXiv:2601.04885v3 Announce Type: replace Abstract: As Large Language Models (LLMs) serve a global audience, alignment must transition from enforcing universal consensus to respecting cultural pluralism. We demonstrate that dense models, when forced to fit conflicting value distributions, suffer from \textbf{Mean Collapse}, converging to a generic average that fails to represent diverse groups. We attribute this to \textbf{Cultural Sparsity}, where gradient interference prevents dense parameters from spanning distinct cultural modes. To resolve this, we propose \textbf{\textsc{CuMA}} (\textbf{Cu}ltural \textbf{M}ixture of \textbf{A}dapters), a framework that frames alignment as a \textbf{conditional capacity separation} problem. By incorporating demographic-aware routing, \textsc{CuMA} internalizes a \textit{Latent Cultural Topology} to explicitly disentangle conflicting gradients into specialized expert subspaces. Extensive evaluations on WorldValuesBench, Community Alignment, and PRISM demonstrate that \textsc{CuMA} achieves state-of-the-art performance, significantly outperforming both dense baselines and semantic-only MoEs. Crucially, our analysis confirms that \textsc{CuMA} effectively mitigates mean collapse, preserving cultural diversity. Our code is available at https://github.com/Throll/CuMA.
arXiv:2606.14181v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) are meshless and carry moving geometry and topology change through resampling of collocation points; the finite-element method (FEM) is the workhorse for boundary-fitted discretisations. Coupling the two across a shared interface promises the best of both, yet existing PINN-FEM schemes are validated only empirically. We put the coupling on a domain-decomposition footing: viewing each solver as a Steklov-Poincar\'e (trace-to-flux) operator, we transfer the classical Dirichlet-Neumann (DN) divergence diagnosis and its Robin-Neumann (RN) cure, including a closed-form, sweep-free interface impedance, and prove a PINN-specific contraction theorem: a trained network realises only a perturbed Steklov operator with a per-step training residual, and RN still contracts, with no shared-eigenbasis hypothesis, to a floor set by the achieved training loss. Because a PINN has no stiffness matrix, we introduce a Fourier-mode interface probe that recovers the network's resolvable Steklov eigenvalues to within 0.5% and doubles as a diagnostic of the network's spectral cap. The theory predicts measured PINN-FEM contraction rates to within 7% on 1D and 2D Poisson couplings, and a two-slab analogue of the large-added-mass regime shows RN's per-mode impedance matching winning decisively where tuned scalar relaxation saturates. We demonstrate the framework on a Stokes/rigid-disc problem with Alart-Curnier contact: the meshless PINN fluid absorbs the topology change at contact by collocation exclusion alone, no remeshing and no cut cells, and the static-equilibrium contact reaction matches the submerged weight to 0.4% under mesh refinement. We quantify remaining limitations: the warm-started PINN drifts off the Stokes manifold over long horizons, and matched FEM-FEM benchmarks attribute pre-impact squeeze-film signatures to PINN under-resolution.
arXiv:2601.05106v5 Announce Type: replace Abstract: Large language models (LLMs) exhibit strengths across diverse domains. However, achieving strong performance across these domains with a single general-purpose model typically requires scaling to sizes that are prohibitively expensive to train and deploy. On the other hand, while smaller domain-specialized models are much more efficient, they struggle to generalize beyond their training distributions. To address this dilemma, we propose FusionRoute, a robust and effective token-level multi-LLM collaboration framework in which a lightweight router simultaneously (i) selects the most suitable expert at each decoding step and (ii) contributes a complementary logit that refines or corrects the selected expert's next-token distribution via logit addition. Unlike existing token-level collaboration methods that rely solely on fixed expert outputs, we provide a theoretical analysis showing that pure expert-only routing is fundamentally limited: unless strong global coverage assumptions hold, it cannot in general realize the optimal decoding policy. By augmenting expert selection with a trainable complementary generator, FusionRoute expands the effective policy class and enables recovery of optimal value functions under mild conditions. Empirically, across both Llama-3 and Gemma-2 families and diverse benchmarks spanning mathematical reasoning, code generation, and instruction following, FusionRoute outperforms both sequence- and token-level collaboration, model merging, and direct fine-tuning, while remaining competitive with domain experts on their respective tasks.
arXiv:2601.09337v2 Announce Type: replace Abstract: The Unmapped Tent Pitching (UTP) algorithm is a space--time domain decomposition method for the parallel solution of hyperbolic problems. It was originally introduced for the homogeneous one-dimensional wave equation in [Ciaramella, Gander, Mazzieri, 2024]. UTP is inspired by the Mapped Tent Pitching (MTP) algorithm [Gopalakrishnan, Sch{\"o}berl, Wintersteiger, 2017], which constructs the solution by iteratively building polytopal space--time subdomains, referred to as tents. In MTP, each physical tent is mapped onto a space--time rectangle, where local problems are solved before being mapped back to the original domain. In contrast, UTP avoids the nonlinear and potentially singular mapping step by computing the solution directly on a physical space--time rectangle that contains the tent, at the expense of redundant computations in the region outside the tent. In this work, we investigate several strategies to extend UTP to heterogeneous media, where the wave propagation speed is piecewise constant over two subregions of the domain. Among the considered approaches, the most efficient in terms of computational time is the one employing space--time subdomains with identical spatial and temporal dimensions in both regions, determined by the maximum propagation speed.
arXiv:2606.14421v1 Announce Type: new Abstract: Reliable return navigation remains an important challenge in GPS-denied environments where external positioning infrastructure may be unavailable or unreliable. This paper presents ForestBack, an infrastructure-free pedestrian return navigation framework based on breadcrumb-based pedestrian dead reckoning (PDR). The system records a user's walking route as a sequence of reversible breadcrumb nodes and generates reverse-path guidance without requiring GPS, Wi-Fi, Bluetooth beacons, or pre-installed infrastructure. ForestBack integrates acceleration-based step detection, adaptive step-length estimation, magnetometer-assisted heading estimation, barometric-altitude correction, and bidirectional breadcrumb path reconstruction. The system was evaluated using an indoor obstacle-avoidance route with five checkpoints, where the user navigated around a central obstacle. A dataset of 36 walking trials and 42,474 time-series samples was used for evaluation, including IMU signals, magnetometer readings, barometric variables, turn-event labels, ground-truth trajectories, baseline PDR outputs, proposed ForestBack outputs, and power-related measurements. Experimental results show that ForestBack reduced the mean RMSE from 1.129 m to 0.965 m compared with traditional PDR, corresponding to a 15.76% improvement. The mean final-position error was reduced from 1.781 m to 1.388 m, while turn-event detection consistency reached approximately 99.90%. These results indicate that ForestBack improves trajectory reconstruction and route-preserving return guidance in obstacle-avoidance scenarios. The released dataset and analysis notebook support reproducibility and future benchmarking of infrastructure-free PDR-based return navigation systems.