pwc-archive/papers-with-abstracts huggingface dataset:
Learned Regularization for Inverse Problems: Insights from a Spectral Model
Authors: Martin Burger, Samira Kabri
Date: 2023-12-15 00:00:00
Tasks: Spectral Reconstruction

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit.
Disentangling Linear Mode-Connectivity
Authors: Gul Sena Altintas, Gregor Bachmann, Lorenzo Noci, Thomas Hofmann
Date: 2023-12-15 00:00:00
Tasks: Linear Mode Connectivity

Linear mode-connectivity (LMC) (or lack thereof) is one of the intriguing characteristics of neural network loss landscapes. While empirically well established, it unfortunately still lacks a proper theoretical understanding. Even worse, although empirical data points are abound, a systematic study of when networks exhibit LMC is largely missing in the literature. In this work we aim to close this gap. We explore how LMC is affected by three factors: (1) architecture (sparsity, weight-sharing), (2) training strategy (optimization setup) as well as (3) the underlying dataset. We place particular emphasis on minimal but non-trivial settings, removing as much unnecessary complexity as possible. We believe that our insights can guide future theoretical works on uncovering the inner workings of LMC.
Data-Driven Socio-Economic Deprivation Prediction via Dimensionality Reduction: The Power of Diffusion Maps
Authors: June Moh Goo
Date: 2023-12-15 00:00:00
Tasks: Dimensionality Reduction

This research proposes a model to predict the location of the most deprived areas in a city using data from the census. Census data is very high-dimensional and needs to be simplified. We use the diffusion map algorithm to reduce dimensionality and find patterns. Features are defined by eigenvectors of the Laplacian matrix that defines the diffusion map. The eigenvectors corresponding to the smallest eigenvalues indicate specific characteristics of the population. Previous work has found qualitatively that the second most important dimension for describing the census data in Bristol, UK is linked to deprivation. In this research, we analyse how good this dimension is as a model for predicting deprivation by comparing it with the recognised measures. The Pearson correlation coefficient was found to be greater than 0.7. The top 10 per cent of deprived areas in the UK, which are also located in Bristol, are extracted to test the accuracy of the model. There are 52 of the most deprived areas, and 38 areas are correctly identified by comparing them to the model. The influence of scores of IMD domains that do not correlate with the models and Eigenvector 2 entries of non-deprived Output Areas cause the model to fail the prediction of 14 deprived areas. The model demonstrates strong performance in predicting future deprivation in the project areas, which is expected to assist in government resource allocation and funding greatly. The codes can be accessed here: https://github.com/junegoo94/diffusion_maps
On the locality of local neural operator in learning fluid dynamics
Authors: Ximeng Ye, Hongyu Li, Jingjie Huang, Guoliang Qin
Date: 2023-12-15 00:00:00

This paper launches a thorough discussion on the locality of local neural operator (LNO), which is the core that enables LNO great flexibility on varied computational domains in solving transient partial differential equations (PDEs). We investigate the locality of LNO by looking into its receptive field and receptive range, carrying a main concern about how the locality acts in LNO training and applications. In a large group of LNO training experiments for learning fluid dynamics, it is found that an initial receptive range compatible with the learning task is crucial for LNO to perform well. On the one hand, an over-small receptive range is fatal and usually leads LNO to numerical oscillation; on the other hand, an over-large receptive range hinders LNO from achieving the best accuracy. We deem rules found in this paper general when applying LNO to learn and solve transient PDEs in diverse fields. Practical examples of applying the pre-trained LNOs in flow prediction are presented to confirm the findings further. Overall, with the architecture properly designed with a compatible receptive range, the pre-trained LNO shows commendable accuracy and efficiency in solving practical cases.
Calibrated One Round Federated Learning with Bayesian Inference in the Predictive Space
Authors: Mohsin Hasan, Guojun Zhang, Kaiyang Guo, Xi Chen, Pascal Poupart
Date: 2023-12-15 00:00:00
Tasks: Bayesian Inference, Federated Learning

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL
PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNs
Authors: Deividas Eringis, John Leth, Zheng-Hua Tan, Rafal Wisniewski, Mihaly Petreczky
Date: 2023-12-15 00:00:00
Tasks: Time Series

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the motivation for this work was its application to RNNs. In order to achieve the results, we impose some stability constraints, on the allowed models. Here, stability is understood in the sense of dynamical systems. For RNNs, these stability conditions can be expressed in terms of conditions on the weights. We assume the processes involved are essentially bounded and the loss functions are Lipschitz. The proposed bound on the generalisation gap depends on the mixing coefficient of the data distribution, and the essential supremum of the data. Furthermore, the bound converges to zero as the dataset size increases. In this paper, we 1) formalize the learning problem, 2) derive a PAC-Bayesian error bound for such systems, 3) discuss various consequences of this error bound, and 4) show an illustrative example, with discussions on computing the proposed bound. Unlike other available bounds the derived bound holds for non i.i.d. data (time-series) and it does not grow with the number of steps of the RNN.
End-to-End Training of Neural Networks for Automotive Radar Interference Mitigation
Authors: Christian Oswald, Mate Toth, Paul Meissner, Franz Pernkopf
Date: 2023-12-15 00:00:00
Tasks: Object, object-detection, Object Detection

In this paper we propose a new method for training neural networks (NNs) for frequency modulated continuous wave (FMCW) radar mutual interference mitigation. Instead of training NNs to regress from interfered to clean radar signals as in previous work, we train NNs directly on object detection maps. We do so by performing a continuous relaxation of the cell-averaging constant false alarm rate (CA-CFAR) peak detector, which is a well-established algorithm for object detection using radar. With this new training objective we are able to increase object detection performance by a large margin. Furthermore, we introduce separable convolution kernels to strongly reduce the number of parameters and computational complexity of convolutional NN architectures for radar applications. We validate our contributions with experiments on real-world measurement data and compare them against signal processing interference mitigation methods.
Optimization meets Machine Learning: An Exact Algorithm for Semi-Supervised Support Vector Machines
Authors: Veronica Piccialli, Jan Schwiddessen, Antonio M. Sudoso
Date: 2023-12-15 00:00:00
Tasks: Binary Classification, valid

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to manually label these instances. Semi-supervised support vector machines (S3VMs) extend the well-known SVM classifiers to the semi-supervised approach, aiming at maximizing the margin between samples in the presence of unlabeled data. By leveraging both labeled and unlabeled data, S3VMs attempt to achieve better accuracy and robustness compared to traditional SVMs. Unfortunately, the resulting optimization problem is non-convex and hence difficult to solve exactly. In this paper, we present a new branch-and-cut approach for S3VMs using semidefinite programming (SDP) relaxations. We apply optimality-based bound tightening to bound the feasible set. Box constraints allow us to include valid inequalities, strengthening the lower bound. The resulting SDP relaxation provides bounds significantly stronger than the ones available in the literature. For the upper bound, instead, we define a local search exploiting the solution of the SDP relaxation. Computational results highlight the efficiency of the algorithm, showing its capability to solve instances with a number of data points 10 times larger than the ones solved in the literature.
Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models
Authors: Federica Caforio, Francesco Regazzoni, Stefano Pagani, Elias Karabelas, Christoph Augustin, Gundolf Haase, Gernot Plank, Alfio Quarteroni
Date: 2023-12-15 00:00:00

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method and its great potential to enable the robust and effective identification of patient-specific, heterogeneous physical properties, s.a. tissue stiffness properties. In particular, we demonstrate the capability of the PINN to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.
Hypergraph-MLP: Learning on Hypergraphs without Message Passing
Authors: Bohan Tang, Siheng Chen, Xiaowen Dong
Date: 2023-12-15 00:00:00
Tasks: Node Classification, Representation Learning

Hypergraphs are vital in modelling data with higher-order relations containing more than two entities, gaining prominence in machine learning and signal processing. Many hypergraph neural networks leverage message passing over hypergraph structures to enhance node representation learning, yielding impressive performances in tasks like hypergraph node classification. However, these message-passing-based models face several challenges, including oversmoothing as well as high latency and sensitivity to structural perturbations at inference time. To tackle those challenges, we propose an alternative approach where we integrate the information about hypergraph structures into training supervision without explicit message passing, thus also removing the reliance on it at inference. Specifically, we introduce Hypergraph-MLP, a novel learning framework for hypergraph-structured data, where the learning model is a straightforward multilayer perceptron (MLP) supervised by a loss function based on a notion of signal smoothness on hypergraphs. Experiments on hypergraph node classification tasks demonstrate that Hypergraph-MLP achieves competitive performance compared to existing baselines, and is considerably faster and more robust against structural perturbations at inference.
A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learning
Authors: Zi-Yu Khoo, Jonathan Sze Choong Low, Stéphane Bressan
Date: 2023-12-15 00:00:00
Tasks: Physics-informed machine learning

Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.
Celestial Machine Learning: From Data to Mars and Beyond with AI Feynman
Authors: Zi-Yu Khoo, Abel Yang, Jonathan Sze Choong Low, Stéphane Bressan
Date: 2023-12-15 00:00:00
Tasks: regression, Symbolic Regression

Can a machine or algorithm discover or learn Kepler's first law from astronomical sightings alone? We emulate Johannes Kepler's discovery of the equation of the orbit of Mars with the Rudolphine tables using AI Feynman, a physics-inspired tool for symbolic regression.
VNN: Verification-Friendly Neural Networks with Hard Robustness Guarantees
Authors: Anahita Baninajjar, Ahmed Rezine, Amir Aminifar
Date: 2023-12-15 00:00:00

Machine learning techniques often lack formal correctness guarantees, evidenced by the widespread adversarial examples that plague most deep-learning applications. This lack of formal guarantees resulted in several research efforts that aim at verifying Deep Neural Networks (DNNs), with a particular focus on safety-critical applications. However, formal verification techniques still face major scalability and precision challenges. The over-approximation introduced during the formal verification process to tackle the scalability challenge often results in inconclusive analysis. To address this challenge, we propose a novel framework to generate Verification-Friendly Neural Networks (VNNs). We present a post-training optimization framework to achieve a balance between preserving prediction performance and verification-friendliness. Our proposed framework results in VNNs that are comparable to the original DNNs in terms of prediction performance, while amenable to formal verification techniques. This essentially enables us to establish robustness for more VNNs than their DNN counterparts, in a time-efficient manner.
Bridging the Semantic-Numerical Gap: A Numerical Reasoning Method of Cross-modal Knowledge Graph for Material Property Prediction
Authors: Guangxuan Song, Dongmei Fu, Zhongwei Qiu, Zijiang Yang, Jiaxin Dai, Lingwei Ma, Dawei Zhang
Date: 2023-12-15 00:00:00
Tasks: Graph Neural Network, Knowledge Graphs, Property Prediction

Using machine learning (ML) techniques to predict material properties is a crucial research topic. These properties depend on numerical data and semantic factors. Due to the limitations of small-sample datasets, existing methods typically adopt ML algorithms to regress numerical properties or transfer other pre-trained knowledge graphs (KGs) to the material. However, these methods cannot simultaneously handle semantic and numerical information. In this paper, we propose a numerical reasoning method for material KGs (NR-KG), which constructs a cross-modal KG using semantic nodes and numerical proxy nodes. It captures both types of information by projecting KG into a canonical KG and utilizes a graph neural network to predict material properties. In this process, a novel projection prediction loss is proposed to extract semantic features from numerical information. NR-KG facilitates end-to-end processing of cross-modal data, mining relationships and cross-modal information in small-sample datasets, and fully utilizes valuable experimental data to enhance material prediction. We further propose two new High-Entropy Alloys (HEA) property datasets with semantic descriptions. NR-KG outperforms state-of-the-art (SOTA) methods, achieving relative improvements of 25.9% and 16.1% on two material datasets. Besides, NR-KG surpasses SOTA methods on two public physical chemistry molecular datasets, showing improvements of 22.2% and 54.3%, highlighting its potential application and generalizability. We hope the proposed datasets, algorithms, and pre-trained models can facilitate the communities of KG and AI for materials.
PELP: Pioneer Event Log Prediction Using Sequence-to-Sequence Neural Networks
Authors: Wenjun Zhou, Artem Polyvyanyy, James Bailey
Date: 2023-12-15 00:00:00
Tasks: Deep Learning, Management, Prediction

Process mining, a data-driven approach for analyzing, visualizing, and improving business processes using event logs, has emerged as a powerful technique in the field of business process management. Process forecasting is a sub-field of process mining that studies how to predict future processes and process models. In this paper, we introduce and motivate the problem of event log prediction and present our approach to solving the event log prediction problem, in particular, using the sequence-to-sequence deep learning approach. We evaluate and analyze the prediction outcomes on a variety of synthetic logs and seven real-life logs and show that our approach can generate perfect predictions on synthetic logs and that deep learning techniques have the potential to be applied in real-world event log prediction tasks. We further provide practical recommendations for event log predictions grounded in the outcomes of the conducted experiments.
Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces
Authors: Torbjørn Smith, Olav Egeland
Date: 2023-12-15 00:00:00

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently Hamiltonian, and where the vector field is required to be odd or even. This is done with a symplectic kernel, and it is shown how this symplectic kernel can be modified to be odd or even. The performance of the method is validated in simulations for two Hamiltonian systems. The simulations show that the learned dynamics reflect the energy-preservation of the Hamiltonian dynamics, and that the restriction to symplectic and odd dynamics gives improved accuracy over a large domain of the phase space.
Optimal Regret Bounds for Collaborative Learning in Bandits
Authors: Amitis Shidani, Sattar Vakili
Date: 2023-12-15 00:00:00

We consider regret minimization in a general collaborative multi-agent multi-armed bandit model, in which each agent faces a finite set of arms and may communicate with other agents through a central controller. The optimal arm for each agent in this model is the arm with the largest expected mixed reward, where the mixed reward of each arm is a weighted average of its rewards across all agents, making communication among agents crucial. While near-optimal sample complexities for best arm identification are known under this collaborative model, the question of optimal regret remains open. In this work, we address this problem and propose the first algorithm with order optimal regret bounds under this collaborative bandit model. Furthermore, we show that only a small constant number of expected communication rounds is needed.
Toward Deep Drum Source Separation
Authors: Alessandro Ilic Mezza, Riccardo Giampiccolo, Alberto Bernardini, Augusto Sarti
Date: 2023-12-15 00:00:00

In the past, the field of drum source separation faced significant challenges due to limited data availability, hindering the adoption of cutting-edge deep learning methods that have found success in other related audio applications. In this manuscript, we introduce StemGMD, a large-scale audio dataset of isolated single-instrument drum stems. Each audio clip is synthesized from MIDI recordings of expressive drums performances using ten real-sounding acoustic drum kits. Totaling 1224 hours, StemGMD is the largest audio dataset of drums to date and the first to comprise isolated audio clips for every instrument in a canonical nine-piece drum kit. We leverage StemGMD to develop LarsNet, a novel deep drum source separation model. Through a bank of dedicated U-Nets, LarsNet can separate five stems from a stereo drum mixture faster than real-time and is shown to significantly outperform state-of-the-art nonnegative spectro-temporal factorization methods.