arXiv:2605.16157v1 Announce Type: new
Abstract: This paper explores epistemic realizability, a form of realizability in which the property that a piece of data constitutes evidence for a logical proposition is semi-decidable. In this framework, each proposition A is assigned a verifier} program that checks whether a datum X is a realizer for A, and a dual generator program that behaves as a generic realizer for X. We propose epistemic realizability interpretations for minimal logic, second-order intuitionistic logic, and higher-order intuitionistic logic, proving that each system is sound and complete under the proposed semantics.
Science Journals
arXiv:2605.16129v1 Announce Type: new
Abstract: The IoT's explosive growth has led to a massive number of connected devices, which demand high-speed and pervasive connectivity, posing significant challenges for current-generation wireless communication infrastructures. Considering our evolution toward 5G and beyond 5G (B5G) and 6G networks, providing scalable, reliable, and low-latency communication for billions of devices is therefore essential. Massive Multi-Input Multi-Output (Massive MIMO) is a promising technology for fulfilling the requirements of 5G, as it can spatially multiplex a large number of users and increase the spectral efficiency per user. In this paper, we focus on optimizing the performance of Massive MIMO systems in IoT connectivity and low-latency use cases for 5G and B5G. It studies key issues, including pilot contamination, energy efficiency, and user scheduling, among dense IoT deployments. In addition, it surveys all recent progress in channel estimation, hybrid beamforming, and machine learning-based resource allocation technologies for enhancing IoT scenarios related to Massive MIMO. Simulation-based results reveal the trade-offs between capacity, latency, and energy utilization, indicating an optimal operating point that ensures optimal performance for diverse IoT applications. The work concludes with a discussion of future research avenues, such as integration with cell-free designs, intelligent reflecting surfaces, or AI-based network orchestration for enhanced IoT capabilities.
arXiv:2605.16133v1 Announce Type: new
Abstract: Technical Debt (TD) refers to the long-term costs incurred when developers prioritize short-term delivery over quality-improving work. Architectural Technical Debt (ATD) arises when architectural decisions (e.g., technology choices, patterns, or decomposition) prioritize near-term progress over future maintainability and evolvability. Because ATD affects a system's core structure and propagates through architectural dependencies, it is often more expensive and disruptive to remediate than localized code-level debt. Although ATD has been widely studied, an important but underexplored aspect of repayment is who performs it. Prior work provides limited empirical evidence on repayment responsibility in ATD and its relationship to time-to-fix.
We empirically study self-fixed ATD, where the introducer also repays the debt, and contrast it with non-self-fixed ATD in large Apache open-source projects. We reconstruct ATD lifecycles by tracing Jira artifacts to version-control history to identify introduction and repayment points and attribute developer roles. We address three research questions on the prevalence of self-fixed ATD, time-to-fix differences between self-fixed and non--self-fixed items, and how factors related to code change and collaboration metrics relate to repayment speed. Using descriptive statistics, non-parametric tests, and survival analysis, we show that self-fixed and non--self-fixed ATD exhibit distinct repayment dynamics and differences in how changes are shared on ATD-affected files. In particular, non--self-fixed ATD is more likely to remain unresolved longer when changes are spread across many developers. These results provide actionable guidance for maintainers to identify high-risk ATD items and to reduce handoff costs by increasing introducer involvement when possible and documenting the design rationale during repayment.
arXiv:2605.16120v1 Announce Type: new
Abstract: The growth of online video platforms drives the need for effective, semantically grounded event retrieval. We present MERVIN, a unified multimodal framework for Vietnamese news videos that integrates keyframes, transcripts, and video summaries. Transcript quality is enhanced via Gemini 1.5 Flash, reducing noise from accents, background sounds, and recognition errors. Visual features are extracted with Perception Encoder, while a Vietnamese language model produces textual embeddings; both are indexed in Milvus for efficient similarity-based retrieval. In addition, a React-based interface enables iterative query refinement across modalities, improving semantic alignment. Experimental results on Vietnamese news videos demonstrate the effectiveness of the proposed system, with MERVIN achieving 79 out of 88 points in AI Challenge HCMC 2025 qualification phase and successfully retrieved all results for every query in the final round.
arXiv:2605.04336v2 Announce Type: replace-cross
Abstract: We study a contest-theoretic model of adversarial investment in which an attacker and a defender allocate resources to AI-augmented capabilities across multiple attack surfaces. The attacker's investment operates through two channels: it amplifies offensive potency unconditionally and erodes defensive effectiveness conditionally, generating an adversarial discount that deepens endogenously with the defender's own investment. We derive a closed-form arms race ratio decomposing the relative marginal effectiveness of offensive and defensive investment into six structural primitives and establish equilibrium uniqueness and global convergence under a continuous best-response dynamic. The central result concerns signal cross-correlation, the degree to which threat intelligence on one surface informs detection on another. With full cross-correlation, the arms race ratio is independent of the number of attack surfaces: the attacker's structural advantage from surface proliferation is completely neutralized. Under the benchmark full-dilution case, without cross-correlation, per-surface defense effectiveness vanishes as the attack surface grows. Extending the analysis to heterogeneous defenders facing an attacker who targets by expected value, we argue that the model points to a dual inefficiency: overinvestment in private defense (a zero-sum redirective externality) and underinvestment in shared signal correlation (a public good). These formal results, together with public-good reasoning outside the base model, characterize when collective information aggregation can dominate private capability investment as the decisive margin in adversarial contests.
arXiv:2604.10785v2 Announce Type: replace-cross
Abstract: For a connected simple graph $G$ on $n$ vertices with chromatic number $\chi$, the distance Laplacian matrix is $\DL(G)=\operatorname{diag}(\Tr_G(v_1),\dots,\Tr_G(v_n))-D(G)$, where $D(G)$ is the distance matrix and $\Tr_G(v)=\sum_{u\in V(G)} d_G(u,v)$ is the transmission. The eigenvalues of $\DL(G)$ are ordered as $\partial^{L}_1(G)\ge \partial^{L}_2(G)\ge \cdots \ge \partial^{L}_n(G)=0$. Building on the chromatic lower bound $\partial^{L}_1(G)\ge n+\ceil{n/\chi}$ and subsequent developments, we prove a \emph{color-class majorization principle}: if $(\ell_1,\dots,\ell_\chi)$ are the color-class sizes in an optimal $\chi$-coloring with $\ell_1\ge\cdots\ge\ell_\chi$, then the first $\ell_1-1$ distance Laplacian eigenvalues satisfy $\partial^{L}_i(G)\ge n+\ell_1$, for $1\le i\le \ell_1-1$. This gives sharp lower bounds on the number of eigenvalues above the chromatic threshold $b_\chi=n+\ceil{n/\chi}$, thereby refining distribution theorems of [Aouchiche and Hansen, Filomat, 2017] and [Pirzada and Khan LAA, 2021]. We further refine clique/independent-set based multiplicity results by deriving explicit chromatic criteria in terms of neighborhood compression, and we generalize the extremal problem for minimum $\partial^{L}_1$ at fixed chromatic number by characterizing the balanced complete multipartite minimizers. Finally, we present a Ky Fan type result, and complement-component consequences of the majorization principle.
arXiv:2602.14342v2 Announce Type: replace-cross
Abstract: We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic gradients with subexponential tails. Notably, this exhibits a separation with the problem of convex optimization, where stochasticity (even additive Gaussian noise) in the gradient oracle incurs $\mathrm{poly}(1/\delta)$ queries. We also give an information-theoretic argument that light-tailed stochastic gradients are necessary for high accuracy: for example, in the bounded variance case, we show that the minimax-optimal query complexity scales as $\Theta(1/\delta)$. Our framework also provides similar high accuracy guarantees under stochastic zeroth order (value) queries, and an improved complexity result for sampling from finite-sum potentials.
arXiv:2605.16118v1 Announce Type: new
Abstract: The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low-to-high-fidelity residual scale with local Gaussian-blur correlation, and the velocity network is conditioned on the low-fidelity solution. Conditioning makes the residual refinement problem substantially easier than unconditional field generation, while residual-calibrated source noise improves the flow-matching training geometry. A multi-resolution cascade applies the same construction independently between adjacent fidelities. After level-wise flow-matching pretraining, we fine-tune the composed cascade end-to-end with a deterministic one-step rollout, which makes one velocity evaluation per cascade level the optimized operating point at inference. The result is a learned analog of multigrid refinement that reaches the finest grid in $L$ deterministic network evaluations per query. We validate MFFM on eight benchmarks: two super-resolution problems and six spatiotemporal forecasting tasks from PDEBench, The Well, and the FNO Navier--Stokes dataset.
arXiv:2604.04310v2 Announce Type: replace
Abstract: In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU execution or high-throughput GPU workloads, few provide a unified framework that targets multiple architectures without compromising performance or ease-of-use. To address this, we introduce frax, a JAX-based library for robot kinematics and dynamics, providing a high-performance, pure-Python interface across CPU, GPU, and TPU. Via a fully-vectorized approach to robot dynamics, frax enables efficient real-time control and parallelization, while supporting automatic differentiation for optimization-based methods. On CPU, frax achieves low-microsecond computation times suitable for kilohertz control rates, outperforming common libraries in Python and approaching optimized C++ implementations. On GPU, the same code scales to thousands of instances, reaching upwards of 100 million dynamics evaluations per second. We validate performance on a Franka Panda manipulator and a Unitree G1 humanoid, and release frax as an open-source library.
arXiv:2605.15879v1 Announce Type: new
Abstract: The available potential energy (APE) of a fluid can be defined locally in space, providing useful insights into both the energetics and dynamics of stratified flows ranging from three-dimensional turbulence to planetary scale circulations. Here we develop a framework for considering the multi-scale evolution of the local APE using a spatial filtering, or coarse-graining, approach. Evolution equations for the APE at scales larger, and smaller, than the filtering scale are derived -- including the cross-scale APE flux term. These results can be paired with existing frameworks for coarse-grained kinetic energy, offering the potential for examining a complete energy cycle that accounts for conversions between both spatial scales and energy reservoirs. An illustrative example of the application of this approach to a simulation of two-dimensional Kelvin-Helmholtz instability is provided.
arXiv:2604.26139v2 Announce Type: replace
Abstract: Diffusion large language models generate text through multi-step denoising, where hallucination signals may emerge throughout the trajectory rather than only in the final output. Existing detectors mainly rely on output uncertainty or coarse trace statistics, which often fail to capture the richer hidden dynamics of D-LLMs. We propose HIVE, a hidden-evidence verification framework that extracts compressed hidden evidence from denoising trajectories, selects informative step-layer evidence, and conditions a verifier language model on the selected evidence through prefix embeddings. HIVE produces both a continuous hallucination score from verifier decision logits and structured verification outputs, including hallucination types, evidence pairs, and short rationales. Across two D-LLMs and three QA benchmarks, HIVE consistently outperforms eight strong baselines and achieves up to 0.9236 AUROC and 0.9537 AUPRC. Ablation studies further confirm the importance of hidden-evidence conditioning, learned evidence selection, two-stream evidence representation, and step-layer embeddings. These results suggest that selected hidden evidence from denoising trajectories provides a stronger and more usable hallucination signal than output-only uncertainty or coarse trace statistics.
arXiv:2605.15851v1 Announce Type: new
Abstract: This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.
arXiv:2603.18527v4 Announce Type: replace
Abstract: High-frequency Helmholtz problems in heterogeneous media remain challenging for both classical iterative methods and end-to-end neural PDE solvers. We propose Neural Preconditioned Born Series (NPBS), a learned iterative preconditioning framework that operates in preconditioned residual coordinates induced by the Convergent Born Series (CBS). Existing learned Born-series methods primarily use Born-style unrolling for forward wavefield prediction, while learned Helmholtz preconditioners are usually formulated in physical residual coordinates. NPBS fills this gap by recasting Born-series iteration as shifted-Laplacian left preconditioning, and replacing the CBS preconditioner with a learned residual-to-correction map in the Born-preconditioned coordinates. The left preconditioner further induces a residual metric, which yields a metric-matched training objective that aligns optimization with the preconditioned geometry used at inference. On heterogeneous Helmholtz benchmarks, metric-matched NPBS reduces iteration counts by up to $1.9\times$ over direct residual learning, with gains increasing from $1.2\times$ to $1.9\times$ as the wavenumber rises. Compared to classical CBS, learned NPBS reduces stationary iteration counts by over $20\times$; when used as a preconditioner for FGMRES, it further achieves the lowest wall-clock time among all evaluated methods. The same metric-matched formulation also improves convergence on convection--diffusion--reaction systems and Newton linear systems for nonlinear PDEs, indicating that residual-metric matching is a general design principle for neural preconditioners.
arXiv:2605.15465v1 Announce Type: new
Abstract: Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.
arXiv:2605.16114v1 Announce Type: new
Abstract: We propose a scalable neuromorphic architecture based on spiking dynamics emerging from the autonomous time-continuous evolution of clockless (asynchronous) digital circuits. Implemented on commercially available field-programmable gate arrays (FPGAs), our system implements networks of interacting Boolean spiking neurons with configurable excitatory and inhibitory synaptic weights. A complete processing pipeline enables efficient handling of spike-encoded data for solving machine-learning tasks. We demonstrate competitive performance for an audio classification task with spike-based encoding and high-speed processing. Power consumption is significantly lower than traditional digital implementations; this makes our approach an efficient alternative that bridges the gap to dedicated analog neuromorphic systems without the need for specialized hardware design. More generally, our approach establishes clockless digital hardware as a viable platform for neuromorphic computing. It paves the way for reconfigurable chips to be turned into energy-efficient quasi-analog neuromorphic processors.
arXiv:2605.16112v1 Announce Type: new
Abstract: Transformer-based architectures have become the dominant paradigm for Continuous-Time Dynamic Graph (CTDG) learning, yet their performance remains limited on temporally shifted datasets. In this work, we identify attention dispersion as a shared failure mode of dynamic graph Transformers under temporal distribution shift. Through controlled ablation contrasting structurally and temporally distinguished historical neighbors against random ones, we show that prediction depends on a class of critical nodes that carry consistently more predictive signal than arbitrary neighbors. However, existing Transformers fail to focus on these nodes even when they are present in the input, as temporal shift weakens attention contrast and produces overly dispersed attention distributions. This diagnosis suggests a simple and transferable fix: replace standard attention with differential attention, which suppresses common-mode attention and amplifies distinctive token-level signals. When added to three representative CTDG Transformer baselines, differential attention consistently improves performance, with gains concentrated on high-shift datasets. Attention-level measurements further confirm the mechanism, showing reduced attention entropy and increased attention mass on critical nodes. Building on these findings, we introduce DiffDyG, a reference implementation combining differential attention with standard input encodings. Across 9 benchmarks and three negative sampling protocols, DiffDyG achieves SOTA performance, with especially large gains on the most shifted datasets.
arXiv:2509.01685v2 Announce Type: replace-cross
Abstract: We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically tractable score of a regularized Wasserstein proximal operator. This is derived by a Cole--Hopf transformation on coupled anisotropic heat equations, yielding a kernel formulation for the preconditioned regularized Wasserstein proximal. The diffusion component of the proposed method is also interpreted as a modified self-attention block, as in transformer architectures. For quadratic potentials, we provide a discrete-time non-asymptotic convergence analysis and explicitly characterize the bias, which is dependent on regularization and independent of step-size. Experiments demonstrate acceleration and particle-level stability on various log-concave and non-log-concave toy examples to Bayesian total-variation regularized image deconvolution, and competitive/better performance on non-convex Bayesian neural network training when utilizing variable preconditioning matrices.
arXiv:2605.16109v1 Announce Type: new
Abstract: The increasing environmental impact of the telecom industry has heightened the need for sustainable telecommunications networks. With skyrocketing data traffic and 5G gaining a foothold, telecom operators are under pressure to sustain digital growth while meeting their environmental responsibilities. In this paper, we discuss two fundamental drivers of sustainability in the telecom sector, namely, the design of environmentally friendly networks and the implementation of circular economy (CE) principles. Energy efficiency is pursued through dynamic network sleep modes, AI-based traffic management, and the utilization of renewable energy sources in base stations and data centers. Concurrently, circular economy practices, including device second-hand sales, e-waste treatment, and equipment lifespan extension, are becoming increasingly popular to address resource demand and mitigate carbon footprint. Case histories from the world's largest operators demonstrate some of the reductions in power consumption and operational emissions, as well as the associated savings and public image benefits. Although these solutions are promising, the paper also highlights several limitations, including technology constraints, policy shortcomings, and the need for cross-sector partnerships. We conclude with research implications in the form of a sustainable perspective that integrates the green adoption of technology, circular supply chains, and the role of regulation in driving long-term environmental and economic sustainability in the telecom industry.
arXiv:2407.08094v3 Announce Type: replace-cross
Abstract: We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences between neighbouring data points. Subsequently, such differences are integrated, weighted by their associated uncertainties, using a maximum-likelihood formulation. This procedure can be seen as an extension to a multidimensional setting of the thermodynamic integration, a technique developed in statistical physics. The method leverages the manifold hypothesis, estimating quantities within the intrinsic data manifold without defining an explicit coordinate map. It does not rely on any binning or space partitioning, but rather on the construction of a neighbourhood graph based on an adaptive bandwidth selection procedure. BMTI mitigates the limitations commonly associated with traditional nonparametric density estimators, effectively reconstructing smooth profiles even in high-dimensional embedding spaces. The method is tested on a variety of complex synthetic high-dimensional datasets, where it is shown to outperform traditional estimators, and is benchmarked on realistic datasets from the chemical physics literature.
arXiv:2605.15848v1 Announce Type: new
Abstract: Conversational interfaces powered by large language models (LLMs) are widely used for ideation and analysis, yet their linear structure limits exploration of alternatives and management of long-running interactions. We present CanvasConvo, a conversational interface concept that transforms linear chat into a branching conversation tree embedded in a spatial canvas. CanvasConvo enables users to explore what-if scenarios by branching directly from conversational content, supporting parallel development of alternative directions. These branches are visualized on a canvas while remaining integrated with a familiar chat interface, allowing users to switch between linear and non-linear interaction. Features such as timeline-based navigation, automatic tagging and summarization, and context-aware controls (e.g., goals, reusable prompts) support structured interaction and continuity. We evaluated CanvasConvo in a 5-7 day field study with 24 participants. Our findings highlight how non-linear conversational structures support exploratory workflows and different interactions in LLM-based work.
arXiv:2605.15845v1 Announce Type: new
Abstract: This paper presents a novel framework for Jacobian computation in motion optimization problems involving multi-link systems, where physical quantities are represented using higher-order time derivatives. In motion optimization of robots and humans, cost functions may incorporate higher-order time derivatives, such as jerk or the time variation of forces, to capture smoothness and perceptual characteristics, particularly in motion skill analysis and expressive behaviors, thereby necessitating Jacobian computations involving these quantities. However, such Jacobians are typically computed using numerical or automatic differentiation without explicitly exploiting the underlying multi-link structure, which can lead to increased computational cost and numerical instability. To address this limitation, we propose a structured Jacobian formulation for motion optimization, based on the comprehensive motion computation framework, in which physical quantities and their higher-order time derivatives are systematically represented along the multi-link structure. The proposed method systematically derives analytical expressions for Jacobians of kinematic and dynamic quantities, including momentum, forces, and joint torques, with respect to generalized coordinates and their higher-order derivatives. The resulting framework is applicable to both direct and inverse optimization. Through numerical experiments, we demonstrate that the proposed method improves computational efficiency compared to numerical and automatic differentiation, while achieving comparable accuracy. Furthermore, we demonstrate its effectiveness in inverse optimization by recovering cost function weights from motion data. Together, these results indicate that the proposed formulation provides a scalable and structured computational foundation for motion optimization involving higher-order time derivatives in multi-link systems.
arXiv:2605.16107v1 Announce Type: new
Abstract: Machine-generated texts (MGTs) pose risks such as disinformation and phishing, underscoring the need for reliable detection. Metric-based methods, which extract statistically distinguishable features of MGTs, are often more practical than complex model-based methods that are prone to overfitting. Given their diverse designs, we first place representative metric-based methods within a unified framework, enabling a clear assessment of their advantages and limitations. Our analysis identifies a core challenge across these methods: the token-level detection score is easily biased by the inherent randomness of the MGTs generation process. Then, we theoretically derive the multi-hop transitions of the token-level detection score and explore their local and global relations. Based on these findings, we propose a multi-level contextual token relation modeling framework for MGT detection. Specifically, for local relations, we model them through a lightweight Markov-informed calibration module that refines token-level evidence before aggregation. For global relations, we introduce a rule-support reasoning module that uses explicit logical rules derived from contextual score statistics. Finally, we combine the local calibrated score and the global rule-support reasoning signal in a joint multi-level inference framework. Extensive experiments show broad and substantial improvements across various real-world scenarios, including cross-LLM and cross-domain settings, with low computational overhead.
arXiv:2601.23030v2 Announce Type: replace-cross
Abstract: Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general nonlinear dynamics. We propose Neural Backward Filtering Forward Guiding (NBFFG), a unified framework for both discrete transitions and continuous diffusions. Our method constructs a variational posterior by leveraging a proxy linear-Gaussian process. This proxy process yields a closed-form backward filter that serves as a guide, steering the generative path toward high-likelihood regions. We then learn a neural residual to capture the non-linear discrepancies. This formulation allows for an unbiased pathwise subsampling scheme, reducing the training complexity from tree-size dependent to path-length dependent. Empirical results show that NBFFG outperforms baselines on synthetic benchmarks, and we demonstrate the method on a high-dimensional inference task in phylogenetic analysis with reconstruction of ancestral butterfly wing shapes.
arXiv:2605.16102v1 Announce Type: new
Abstract: Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo operator, which is particularly suited for modeling physical phenomena exhibiting symmetric diffusive effects. We provide an integral representation of the solution to prove existence and uniqueness of the fractional differential problem. We introduce a B-spline collocation method to approximate the solution of the problem and provide a convergence analysis, with both theoretical insights and numerical experiments.
arXiv:2605.16099v1 Announce Type: new
Abstract: Federated Learning (FL) enables collaborative training across decentralized clients, but most methods assume aligned feature schemas, an assumption that rarely holds in tabular settings where clients observe only partially overlapping feature subsets. In these heterogeneous feature spaces, parameter-averaging methods (e.g., FedAvg) transfer little information across weakly overlapping or disjoint feature groups, limiting their effectiveness for federated imputation. To overcome this, we propose \textbf{FedHF-Impute}, a federated imputation framework that separates structural feature unavailability from conventional missingness and uses a shared global feature graph to propagate information across statistically related features through message passing. This enables indirect cross-client knowledge transfer, even when features are never jointly observed locally, while preserving standard federated communication. Under simulated partial schema overlap on the SECOM and AirQuality datasets, FedHF-Impute improves imputation accuracy (RMSE) over FL baselines by 26.9\%, and 8.4\% respectively, while achieving comparable performance on PhysioNET, with only a 0.3\% difference relative to the best baseline.