pwc-archive/papers-with-abstracts huggingface dataset:
Conservation-preserved Fourier Neural Operator through Adaptive Correction
Authors: Chaoyu Liu, Yangming Li, Zhongying Deng, Chris Budd, Carola-Bibiane Schönlieb
Date: 2025-05-30 00:00:00

Fourier Neural Operators (FNOs) have recently emerged as a promising and efficient approach for learning the numerical solutions to partial differential equations (PDEs) from data. However, standard FNO often fails to preserve key conservation laws, such as mass conservation, momentum conservation, norm conservation, etc., which are crucial for accurately modeling physical systems. Existing methods for incorporating these conservation laws into Fourier neural operators are achieved by designing related loss function or incorporating post-processing method at the training time. None of them can both exactly and adaptively correct the outputs to satisfy conservation laws, and our experiments show that these methods can lead to inferior performance while preserving conservation laws. In this work, we propose a novel adaptive correction approach to ensure the conservation of fundamental quantities. Our method introduces a learnable matrix to adaptively adjust the solution to satisfy the conservation law during training. It ensures that the outputs exactly satisfy the goal conservation law and allow for more flexibility and adaptivity for the model to correct the outputs. We theoretically show that applying our adaptive correction to an unconstrained FNO yields a solution with data loss no worse than that of the best conservation-satisfying FNO. We compare our approach with existing methods on a range of representative PDEs. Experiment results show that our method consistently outperform other methods.
The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches
Authors: Omri Lev, Vishwak Srinivasan, Moshe Shenfeld, Katrina Ligett, Ayush Sekhari, Ashia C. Wilson
Date: 2025-05-30 00:00:00
Tasks: Federated Learning

Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient optimization, coded computing, and federated learning. This operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Renyi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.
Multi-criteria Rank-based Aggregation for Explainable AI
Authors: Sujoy Chatterjee, Everton Romanzini Colombo, Marcos Medeiros Raimundo
Date: 2025-05-30 00:00:00
Tasks: Decision Making, Feature Importance

Explainability is crucial for improving the transparency of black-box machine learning models. With the advancement of explanation methods such as LIME and SHAP, various XAI performance metrics have been developed to evaluate the quality of explanations. However, different explainers can provide contrasting explanations for the same prediction, introducing trade-offs across conflicting quality metrics. Although available aggregation approaches improve robustness, reducing explanations' variability, very limited research employed a multi-criteria decision-making approach. To address this gap, this paper introduces a multi-criteria rank-based weighted aggregation method that balances multiple quality metrics simultaneously to produce an ensemble of explanation models. Furthermore, we propose rank-based versions of existing XAI metrics (complexity, faithfulness and stability) to better evaluate ranked feature importance explanations. Extensive experiments on publicly available datasets demonstrate the robustness of the proposed model across these metrics. Comparative analyses of various multi-criteria decision-making and rank aggregation algorithms showed that TOPSIS and WSUM are the best candidates for this use case.
Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees
Authors: Fu Luo, Yaoxin Wu, Zhi Zheng, Zhenkun Wang
Date: 2025-05-30 00:00:00
Tasks: Combinatorial Optimization

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack research on the effect of constraint tightness on the performance of NCO methods. This paper takes the capacity-constrained vehicle routing problem (CVRP) as an example to empirically analyze the NCO performance under different tightness degrees of the capacity constraint. Our analysis reveals that existing NCO methods overfit the capacity constraint, and they can only perform satisfactorily on a small range of the constraint values but poorly on other values. To tackle this drawback of existing NCO methods, we develop an efficient training scheme that explicitly considers varying degrees of constraint tightness and proposes a multi-expert module to learn a generally adaptable solving strategy. Experimental results show that the proposed method can effectively overcome the overfitting issue, demonstrating superior performances on the CVRP and CVRP with time windows (CVRPTW) with various constraint tightness degrees.
WILTing Trees: Interpreting the Distance Between MPNN Embeddings
Authors: Masahiro Negishi, Thomas Gärtner, Pascal Welke
Date: 2025-05-30 00:00:00

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to structural distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.
Learning Distributions over Permutations and Rankings with Factorized Representations
Authors: Daniel Severo, Brian Karrer, Niklas Nolte
Date: 2025-05-30 00:00:00
Tasks: Combinatorial Optimization, Re-Ranking, Structured Prediction, Variational Inference

Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric families or neural networks with expensive variational inference procedures. In this work, we propose a novel approach that leverages alternative representations for permutations, including Lehmer codes, Fisher-Yates draws, and Insertion-Vectors. These representations form a bijection with the symmetric group, allowing for unconstrained learning using conventional deep learning techniques, and can represent any probability distribution over permutations. Our approach enables a trade-off between expressivity of the model family and computational requirements. In the least expressive and most computationally efficient case, our method subsumes previous families of well established probabilistic models over permutations, including Mallow's and the Repeated Insertion Model. Experiments indicate our method significantly outperforms current approaches on the jigsaw puzzle benchmark, a common task for permutation learning. However, we argue this benchmark is limited in its ability to assess learning probability distributions, as the target is a delta distribution (i.e., a single correct solution exists). We therefore propose two additional benchmarks: learning cyclic permutations and re-ranking movies based on user preference. We show that our method learns non-trivial distributions even in the least expressive mode, while traditional models fail to even generate valid permutations in this setting.
Learning geometry and topology via multi-chart flows
Authors: Hanlin Yu, Søren Hauberg, Marcelo Hartmann, Arto Klami, Georgios Arvanitidis
Date: 2025-05-30 00:00:00

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if the manifold has a non-trivial topology, it can never be correctly learned using a single flow. Instead multiple flows must be `glued together'. In this paper, we first propose the general training scheme for learning such a collection of flows, and secondly we develop the first numerical algorithms for computing geodesics on such manifolds. Empirically, we demonstrate that this leads to highly significant improvements in topology estimation.
Predicting the Past: Estimating Historical Appraisals with OCR and Machine Learning
Authors: Mihir Bhaskar, Jun Tao Luo, Zihan Geng, Asmita Hajra, Junia Howell, Matthew R. Gormley
Date: 2025-05-30 00:00:00
Tasks: Optical Character Recognition (OCR)

Despite well-documented consequences of the U.S. government's 1930s housing policies on racial wealth disparities, scholars have struggled to quantify its precise financial effects due to the inaccessibility of historical property appraisal records. Many counties still store these records in physical formats, making large-scale quantitative analysis difficult. We present an approach scholars can use to digitize historical housing assessment data, applying it to build and release a dataset for one county. Starting from publicly available scanned documents, we manually annotated property cards for over 12,000 properties to train and validate our methods. We use OCR to label data for an additional 50,000 properties, based on our two-stage approach combining classical computer vision techniques with deep learning-based OCR. For cases where OCR cannot be applied, such as when scanned documents are not available, we show how a regression model based on building feature data can estimate the historical values, and test the generalizability of this model to other counties. With these cost-effective tools, scholars, community activists, and policy makers can better analyze and understand the historical impacts of redlining.
Quick-Draw Bandits: Quickly Optimizing in Nonstationary Environments with Extremely Many Arms
Authors: Derek Everett, Fred Lu, Edward Raff, Fernando Camacho, James Holt
Date: 2025-05-30 00:00:00
Tasks: Multi-Armed Bandits

Canonical algorithms for multi-armed bandits typically assume a stationary reward environment where the size of the action space (number of arms) is small. More recently developed methods typically relax only one of these assumptions: existing non-stationary bandit policies are designed for a small number of arms, while Lipschitz, linear, and Gaussian process bandit policies are designed to handle a large (or infinite) number of arms in stationary reward environments under constraints on the reward function. In this manuscript, we propose a novel policy to learn reward environments over a continuous space using Gaussian interpolation. We show that our method efficiently learns continuous Lipschitz reward functions with $\mathcal{O}^*(\sqrt{T})$ cumulative regret. Furthermore, our method naturally extends to non-stationary problems with a simple modification. We finally demonstrate that our method is computationally favorable (100-10000x faster) and experimentally outperforms sliding Gaussian process policies on datasets with non-stationarity and an extremely large number of arms.
PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations
Authors: Benjamin Holzschuh, Qiang Liu, Georg Kohl, Nils Thuerey
Date: 2025-05-30 00:00:00

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations.
Feature Attribution from First Principles
Authors: Magamed Taimeskhanov, Damien Garreau
Date: 2025-05-30 00:00:00

Feature attribution methods are a popular approach to explain the behavior of machine learning models. They assign importance scores to each input feature, quantifying their influence on the model's prediction. However, evaluating these methods empirically remains a significant challenge. To bypass this shortcoming, several prior works have proposed axiomatic frameworks that any feature attribution method should satisfy. In this work, we argue that such axioms are often too restrictive, and propose in response a new feature attribution framework, built from the ground up. Rather than imposing axioms, we start by defining attributions for the simplest possible models, i.e., indicator functions, and use these as building blocks for more complex models. We then show that one recovers several existing attribution methods, depending on the choice of atomic attribution. Subsequently, we derive closed-form expressions for attribution of deep ReLU networks, and take a step toward the optimization of evaluation metrics with respect to feature attributions.
Adapting to Linear Separable Subsets with Large-Margin in Differentially Private Learning
Authors: Erchi Wang, Yuqing Zhu, Yu-Xiang Wang
Date: 2025-05-30 00:00:00

This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of $\tilde{O}\left(\frac{1}{\gamma^2\varepsilon n} + \frac{|S_{\mathrm{out}}|}{\gamma n}\right)$ where $n$ is the number of data points, $S_{\mathrm{out}}$ is an arbitrary subset of data one can remove and $\gamma$ is the margin of linear separation of the remaining data points (after $S_{\mathrm{out}}$ is removed). Here, $\tilde{O}(\cdot)$ hides only logarithmic terms. In the agnostic case, we improve the existing results when the number of outliers is small. Our algorithm is highly adaptive because it does not require knowing the margin parameter $\gamma$ or outlier subset $S_{\mathrm{out}}$. We also derive a utility bound for the advanced private hyperparameter tuning algorithm.
SUMO: Subspace-Aware Moment-Orthogonalization for Accelerating Memory-Efficient LLM Training
Authors: Yehonathan Refael, Guy Smorodinsky, Tom Tirer, Ofir Lindenbaum
Date: 2025-05-30 00:00:00

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these methods primarily emphasize memory savings, often overlooking potential acceleration in convergence due to their reliance on standard isotropic steepest descent techniques, which can perform suboptimally in the highly anisotropic landscapes typical of deep networks, particularly LLMs. In this paper, we propose SUMO (Subspace-Aware Moment-Orthogonalization), an optimizer that employs exact singular value decomposition (SVD) for moment orthogonalization within a dynamically adapted low-dimensional subspace, enabling norm-inducing steepest descent optimization steps. By explicitly aligning optimization steps with the spectral characteristics of the loss landscape, SUMO effectively mitigates approximation errors associated with commonly used methods like Newton-Schulz orthogonalization approximation. We theoretically establish an upper bound on these approximation errors, proving their dependence on the condition numbers of moments, conditions we analytically demonstrate are encountered during LLM training. Furthermore, we both theoretically and empirically illustrate that exact orthogonalization via SVD substantially improves convergence rates while reducing overall complexity. Empirical evaluations confirm that SUMO accelerates convergence, enhances stability, improves performance, and reduces memory requirements by up to 20% compared to state-of-the-art methods.
AFLoRA: Adaptive Federated Fine-Tuning of Large Language Models with Resource-Aware Low-Rank Adaption
Authors: Yajie Zhou, Xiaoyi Pang, Zhibo Wang
Date: 2025-05-30 00:00:00

Federated fine-tuning has emerged as a promising approach to adapt foundation models to downstream tasks using decentralized data. However, real-world deployment remains challenging due to the high computational and communication demands of fine-tuning Large Language Models (LLMs) on clients with data and system resources that are heterogeneous and constrained. In such settings, the global model's performance is often bottlenecked by the weakest clients and further degraded by the non-IID nature of local data. Although existing methods leverage parameter-efficient techniques such as Low-Rank Adaptation (LoRA) to reduce communication and computation overhead, they often fail to simultaneously ensure accurate aggregation of low-rank updates and maintain low system costs, thereby hindering overall performance. To address these challenges, we propose AFLoRA, an adaptive and lightweight federated fine-tuning framework for LLMs. AFLoRA decouples shared and client-specific updates to reduce overhead and improve aggregation accuracy, incorporates diagonal matrix-based rank pruning to better utilize local resources, and employs rank-aware aggregation with public data refinement to strengthen generalization under data heterogeneity. Extensive experiments demonstrate that AFLoRA outperforms state-of-the-art methods in both accuracy and efficiency, providing a practical solution for efficient LLM adaptation in heterogeneous environments in the real world.
Diffusion-Based Symbolic Regression
Authors: Zachary Bastiani, Robert M. Kirby, Jacob Hochhalter, Shandian Zhe
Date: 2025-05-30 00:00:00
Tasks: Audio Synthesis, Denoising, regression, Symbolic Regression

Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic regression. We construct a random mask-based diffusion and denoising process to generate diverse and high-quality equations. We integrate this generative processes with a token-wise Group Relative Policy Optimization (GRPO) method to conduct efficient reinforcement learning on the given measurement dataset. In addition, we introduce a long short-term risk-seeking policy to expand the pool of top-performing candidates, further enhancing performance. Extensive experiments and ablation studies have demonstrated the effectiveness of our approach.
EVA-MILP: Towards Standardized Evaluation of MILP Instance Generation
Authors: Yidong Luo, Chenguang Wang, Jiahao Yang, Fanzeng Xia, Tianshu Yu
Date: 2025-05-30 00:00:00

Mixed-Integer Linear Programming (MILP) is fundamental to solving complex decision-making problems. The proliferation of MILP instance generation methods, driven by machine learning's demand for diverse optimization datasets and the limitations of static benchmarks, has significantly outpaced standardized evaluation techniques. Consequently, assessing the fidelity and utility of synthetic MILP instances remains a critical, multifaceted challenge. This paper introduces a comprehensive benchmark framework designed for the systematic and objective evaluation of MILP instance generation methods. Our framework provides a unified and extensible methodology, assessing instance quality across crucial dimensions: mathematical validity, structural similarity, computational hardness, and utility in downstream machine learning tasks. A key innovation is its in-depth analysis of solver-internal features -- particularly by comparing distributions of key solver outputs including root node gap, heuristic success rates, and cut plane usage -- leveraging the solver's dynamic solution behavior as an `expert assessment' to reveal nuanced computational resemblances. By offering a structured approach with clearly defined solver-independent and solver-dependent metrics, our benchmark aims to facilitate robust comparisons among diverse generation techniques, spur the development of higher-quality instance generators, and ultimately enhance the reliability of research reliant on synthetic MILP data. The framework's effectiveness in systematically comparing the fidelity of instance sets is demonstrated using contemporary generative models.
QGAN-based data augmentation for hybrid quantum-classical neural networks
Authors: Run-Ze He, Jun-Jian Su, Su-Juan Qin, Zheng-Ping Jin, Fei Gao
Date: 2025-05-30 00:00:00
Tasks: Data Augmentation, Quantum Machine Learning

Quantum neural networks converge faster and achieve higher accuracy than classical models. However, data augmentation in quantum machine learning remains underexplored. To tackle data scarcity, we integrate quantum generative adversarial networks (QGANs) with hybrid quantum-classical neural networks (HQCNNs) to develop an augmentation framework. We propose two strategies: a general approach to enhance data processing and classification across HQCNNs, and a customized strategy that dynamically generates samples tailored to the HQCNN's performance on specific data categories, improving its ability to learn from complex datasets. Simulation experiments on the MNIST dataset demonstrate that QGAN outperforms traditional data augmentation methods and classical GANs. Compared to baseline DCGAN, QGAN achieves comparable performance with half the parameters, balancing efficiency and effectiveness. This suggests that QGANs can simplify models and generate high-quality data, enhancing HQCNN accuracy and performance. These findings pave the way for applying quantum data augmentation techniques in machine learning.