arXiv:2510.01663v2 Announce Type: replace Abstract: For many real-world applications, understanding feature-outcome relationships is as crucial as achieving high predictive accuracy. While traditional neural networks excel at prediction, their black-box nature obscures underlying functional relationships. Kolmogorov--Arnold Networks (KANs) address this by employing learnable spline-based activation functions on edges, enabling recovery of symbolic representations while maintaining competitive performance. However, KAN's architecture presents unique challenges for network pruning. Conventional magnitude-based methods become unreliable due to sensitivity to input coordinate shifts. We propose \textbf{ShapKAN}, a pruning framework using Shapley value attribution to assess node importance in a shift-invariant manner. Unlike magnitude-based approaches, ShapKAN quantifies each node's actual contribution, ensuring consistent importance rankings regardless of input parameterization. Extensive experiments on synthetic and real-world datasets demonstrate that ShapKAN preserves true node importance while enabling effective network compression. Our approach improves KAN's interpretability advantages, facilitating deployment in resource-constrained environments.
Science Journals
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.
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:2511.05017v3 Announce Type: replace Abstract: Hallucinations in Large Vision-Language Models (LVLMs) remain a persistent challenge, often stemming from inadequate integration of visual information during multimodal reasoning. A key cause is the model's over-reliance on textual priors and underutilization of visual cues, leading to outputs that are linguistically fluent but visually inaccurate. For example, given an image of an empty kitchen countertop, an LVLM might hallucinate a "bowl of fruit" or "cup of coffee", relying on language associations rather than visual evidence. Most LVLMs incorporate visual features by appending them to the input stream of a pre-trained LLM and training on large-scale vision-language datasets. Our systematic analysis reveals that this strategy often leads to over-dependence on textual information due to the inherent bias of LLMs towards language-dominant representations. This imbalance skews attention towards the text over visual content, weakening the model's ability to ground outputs in visual inputs. To address this, we propose a simple yet effective visual feature incorporation method that encourages the model to learn visually-informed textual embeddings distinct from those of the base LLM and promotes a more balanced attention distribution. Experimental results across multiple hallucination benchmarks demonstrate that our method significantly reduces hallucinations and fosters more balanced multimodal reasoning. Notably, our approach achieves substantial gains, including +9.33% on MMVP-MLLM, +2.99% on POPE-AOKVQA, up to +3.4% on Merlin, and +3% on the hard-data split of HallusionBench.
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:2511.19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex setting and develop new hard instances that yield nontrivial lower bounds under deterministic and stochastic first-order oracle models. In the deterministic case, we prove that any first-order zero-respecting algorithm requires at least $\Omega(\kappa^{3/2}\epsilon^{-2})$ oracle calls to find an $\epsilon$-accurate stationary point, improving the optimal lower bounds known for single-level nonconvex optimization and for nonconvex-strongly-convex min-max problems. In the stochastic case, we show that at least $\Omega(\kappa^{5/2}\epsilon^{-4})$ stochastic oracle calls are necessary, again strengthening the best known bounds in related settings. Our results expose substantial gaps between current upper and lower bounds for bilevel optimization and suggest that even simplified regimes, such as those with quadratic lower-level objectives, warrant further investigation toward understanding the optimal complexity of bilevel optimization under standard first-order oracles.
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:2504.16288v3 Announce Type: replace Abstract: It is well-known that checking whether a given string $w$ matches a given regular expression $r$ can be done in quadratic time $O(|w|\cdot |r|)$ and that this cannot be improved to a truly subquadratic running time of $O((|w|\cdot |r|)^{1-\epsilon})$ assuming the strong exponential time hypothesis (SETH). We study the related problem that asks whether $w$ has a \emph{subsequence} that matches $r$, and we show that surprisingly this task admits an algorithm that runs in linear time, i.e., in $O(|w| + |r|)$. We further show that the same holds if we ask for a supersequence instead of a subsequence. Moreover, we show that the \emph{quantitative} problems of computing a longest subsequence or shortest supersequence of $w$ that matches $r$ can be solved with the same complexity as the classical longest common subsequence or shortest common supersequence problems, i.e., in $O(|w|\cdot |r|)$, and conditionally not in $O((|w|\cdot|r|)^{1 - \epsilon})$. By contrast, if instead of subsequences or supersequences we consider other string relations like the infix, prefix, left-extension, or extension relations, then all the corresponding problems (both quantitative and non-quantitative) have the same complexity as classical regex matching, i.e., they can also be solved in $O(|w|\cdot |r|)$, but not in $O((|w|\cdot|r|)^{1 - \epsilon})$ assuming SETH. We last study the complexity of the \emph{universal} problem that asks if \emph{all} subsequences (or supersequences, infixes, prefixes, left-extensions or extensions) of an input string satisfy a given regular expression. For these problems, we show polynomial upper bounds (along with matching conditional lower bounds) for the infix and prefix relations, but PSPACE-completeness for the extension, left-extension and supersequence relations, and coNP-completeness for the subsequence relation.
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:2512.14967v2 Announce Type: replace Abstract: We present a novel numerical method for solving McKean--Vlasov forward--backward stochastic differential equations (MV--FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a pathwise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise, without requiring computationally expensive nested Monte Carlo simulations. The mean-field interaction term is parameterized via a recurrent neural network trained to minimize an elicitable score, while the backward process is approximated through a hybrid feedforward and recurrent network representing the decoupling field. We validate the algorithm on a systemic-risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution. We further extend the model to quantile-mediated interactions, showcasing the flexibility of the elicitability framework beyond conditional means or moments. Finally, we apply the method to a non-stationary Aiyagari--Bewley--Huggett economic growth model with endogenous interest rates, illustrating its applicability to complex mean-field games without closed-form solutions.
arXiv:2512.19945v2 Announce Type: replace Abstract: Securing Internet of Things (IoT) firmware remains difficult due to proprietary binaries, stripped symbols, heterogeneous architectures, and limited access to executable code. Existing analysis methods, such as static analysis, symbolic execution, and fuzzing, depend on binary visibility and functional emulation, making them unreliable when firmware is encrypted or inaccessible. To address this limitation, we propose a binary-free, architecture-agnostic solution that estimates the likelihood of conceptual zero-day vulnerabilities using only high-level descriptors. The approach integrates a tri-LLM reasoning architecture combining a LLaMA-based configuration interpreter, a DeepSeek-based structural abstraction analyzer, and a GPT-4o semantic fusion model. The solution also incorporates LLM computational signatures, including latency patterns, uncertainty markers, and reasoning depth indicators, as well as an energy-aware symbolic load model, to enhance interpretability and operational feasibility. In addition, we formally derive the mathematical foundations of the reasoning pipeline, establishing monotonicity, divergence, and energy-risk coupling properties that theoretically justify the model's behavior. Simulation-based evaluation reveals that high exposure conditions increase the predicted zero-day likelihood by 20 to 35 percent across models, with GPT-4o demonstrating the strongest cross-layer correlations and the highest sensitivity. Energy and divergence metrics significantly predict elevated risk (p < 0.01), reinforcing the effectiveness of the proposed reasoning framework.
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:2507.00481v2 Announce Type: replace Abstract: Although software engineering research has focused on optimizing processes and technology, there is a growing recognition that human factors, particularly teamwork, also significantly impact optimization. Recent research suggests that developer personality has a strong influence on teamwork. In fact, personality considerations may have a greater impact on software development than processes and tools. This paper aims to design a study that measures the impact of HEXACO personality traits on the Teamwork Quality (TWQ) of software teams. A preliminary data collection (n=54) was conducted for this purpose. The analysis showed that several personality traits, as well as their composition, had a significant impact on TWQ. Additionally, other variables, such as the proportion of women and age distribution, also affected TWQ. The study's initial results demonstrate the usefulness and validity of the study design. The results also suggest several opportunities to improve teamwork in IT organizations and avenues for further research.
arXiv:2507.05919v2 Announce Type: replace Abstract: We axiomatically characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S{\o}rensen-Dice and Overlap. We also axiomatically characterize these distances. Our axioms are properties describing how a distance changes when we perform elementary modifications of the sets, like adding one element to one of the sets, to both sets, swapping both sets, permuting some elements, etc.
arXiv:2507.10834v4 Announce Type: replace Abstract: Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such as e-commerce, where platforms must solve thousands of such problems each minute. We propose a graph convolutional network (GCN) framework to efficiently solve constrained assortment optimization problems. Our approach constructs a graph representation of the problem, trains a GCN to learn the mapping from problem parameters to optimal assortments, and develops three inference policies based on the GCN's output. Owing to the GCN's ability to generalize across instance sizes, patterns learned from small-scale samples can be transferred to large-scale problems. Theoretical results are established to show the expressive power of the proposed GCN, and explain the underlying mechanism of the size generalization ability. Numerical experiments show that a GCN trained on instances with 20 products achieves over 85% of the optimal revenue on problems with up to 2,000 products within seconds, outperforming existing heuristics in both accuracy and efficiency. We further extend the framework to settings with an unknown choice model using transaction data and demonstrate similar performance and scalability.
arXiv:2507.13263v4 Announce Type: replace Abstract: Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations. The current state-of-the-art BO approach for permutation spaces relies on an exhaustive $\Omega(n^2)$ pairwise comparison, inducing a dense representation that is impractical for large-scale permutations. To break this barrier, we introduce a novel framework for generating efficient permutation representations via kernel functions derived from sorting algorithms. Within this framework, the Mallows kernel can be viewed as a special instance derived from enumeration sort. Further, we introduce the \textbf{Merge Kernel} , which leverages the divide-and-conquer structure of merge sort to produce a compact, $\Theta(n\log n)$ to achieve the lowest possible complexity with no information loss and effectively capture permutation structure. Our central thesis is that the Merge Kernel performs competitively with the Mallows kernel in low-dimensional settings, but significantly outperforms it in both optimization performance and computational efficiency as the dimension $n$ grows. Extensive evaluations on various permutation optimization benchmarks confirm our hypothesis, demonstrating that the Merge Kernel provides a scalable and more effective solution for Bayesian optimization in high-dimensional permutation spaces, thereby unlocking the potential for tackling previously intractable problems such as large-scale feature ordering and combinatorial neural architecture search.
arXiv:2509.02426v3 Announce Type: replace Abstract: Electrified roadways (ER) equipped with dynamic wireless power transfer (DWPT) capabilities can patently extend the driving range and reduce the battery size of electric vehicles (EVs). However, due to the spatial arrangement of the transmitter coils in the ER, the DWPT load exhibits frequency content that could excite power system frequency dynamics. In this context, this work aims to study the spectrum of DWPT loads under different traffic conditions. Under simplifying assumptions, we develop statistical models to identify the location and relative magnitude of DWPT load harmonics. Our analysis reveals that the fundamental frequency depends on ER coil spacing and average EV speed. In the worst-case yet unlikely scenario that EVs move in a synchronized fashion, the amplitude of harmonics scales with the EV count. On the contrary, when EVs move freely, harmonics scale with the square root of the EV count. Platoon formations can accentuate harmonics. The spectral content around harmonics decreases in magnitude and increases in bandwidth with the harmonic index. The load of a single EV moving at a time-varying speed can be modeled as a frequency-modulated (FM) signal. Despite the simplifying assumptions, the derived models offer valuable insights for ER planners and grid operators. Dynamic simulations of a modified WECC model with DWPT loads synthesized from realistic EV trajectories and ER specifications corroborate some of these insights.