Graph Neural Networks (GNNs) have emerged as one of the leading approaches for machine learning on graph-structured data. Despite their great success, critical computational challenges such as over-smoothing, over-squashing, and limited expressive power continue to impact the performance of GNNs. In this study, inspired from the time-reversal principle commonly utilized in classical and quantum physics, we reverse the time direction of the graph heat equation. The resulted reversing process yields a class of high pass filtering functions that enhance the sharpness of graph node features. Leveraging this concept, we introduce the Multi-Scaled Heat Kernel based GNN (MHKG) by amalgamating diverse filtering functions' effects on node features. To explore more flexible filtering conditions, we further generalize MHKG into a model termed G-MHKG and thoroughly show the roles of each element in controlling over-smoothing, over-squashing and expressive power. Notably, we illustrate that all aforementioned issues can be characterized and analyzed via the properties of the filtering functions, and uncover a trade-off between over-smoothing and over-squashing: enhancing node feature sharpness will make model suffer more from over-squashing, and vice versa. Furthermore, we manipulate the time again to show how G-MHKG can handle both two issues under mild conditions. Our conclusive experiments highlight the effectiveness of proposed models. It surpasses several GNN baseline models in performance across graph datasets characterized by both homophily and heterophily.
相關內容
Reinforcement learning (RL) has helped improve decision-making in several applications. However, applying traditional RL is challenging in some applications, such as rehabilitation of people with a spinal cord injury (SCI). Among other factors, using RL in this domain is difficult because there are many possible treatments (i.e., large action space) and few patients (i.e., limited training data). Treatments for SCIs have natural groupings, so we propose two approaches to grouping treatments so that an RL agent can learn effectively from limited data. One relies on domain knowledge of SCI rehabilitation and the other learns similarities among treatments using an embedding technique. We then use Fitted Q Iteration to train an agent that learns optimal treatments. Through a simulation study designed to reflect the properties of SCI rehabilitation, we find that both methods can help improve the treatment decisions of physiotherapists, but the approach based on domain knowledge offers better performance. Our findings provide a "proof of concept" that RL can be used to help improve the treatment of those with an SCI and indicates that continued efforts to gather data and apply RL to this domain are worthwhile.
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours. Previous work on NCA focuses on learning rules that give stationary emergent structures. We extend NCA to capture both transient and stable structures within the same system, as well as learning rules that capture the dynamics of Turing pattern formation in nonlinear Partial Differential Equations (PDEs). We demonstrate that NCA can generalise very well beyond their PDE training data, we show how to constrain NCA to respect given symmetries, and we explore the effects of associated hyperparameters on model performance and stability. Being able to learn arbitrary dynamics gives NCA great potential as a data driven modelling framework, especially for modelling biological pattern formation.
Sparse Bayesian learning (SBL) has been extensively utilized in data-driven modeling to combat the issue of overfitting. While SBL excels in linear-in-parameter models, its direct applicability is limited in models where observations possess nonlinear relationships with unknown parameters. Recently, a semi-analytical Bayesian framework known as nonlinear sparse Bayesian learning (NSBL) was introduced by the authors to induce sparsity among model parameters during the Bayesian inversion of nonlinear-in-parameter models. NSBL relies on optimally selecting the hyperparameters of sparsity-inducing Gaussian priors. It is inherently an approximate method since the uncertainty in the hyperparameter posterior is disregarded as we instead seek the maximum a posteriori (MAP) estimate of the hyperparameters (type-II MAP estimate). This paper aims to investigate the hierarchical structure that forms the basis of NSBL and validate its accuracy through a comparison with a one-level hierarchical Bayesian inference as a benchmark in the context of three numerical experiments: (i) a benchmark linear regression example with Gaussian prior and Gaussian likelihood, (ii) the same regression problem with a highly non-Gaussian prior, and (iii) an example of a dynamical system with a non-Gaussian prior and a highly non-Gaussian likelihood function, to explore the performance of the algorithm in these new settings. Through these numerical examples, it can be shown that NSBL is well-suited for physics-based models as it can be readily applied to models with non-Gaussian prior distributions and non-Gaussian likelihood functions. Moreover, we illustrate the accuracy of the NSBL algorithm as an approximation to the one-level hierarchical Bayesian inference and its ability to reduce the computational cost while adequately exploring the parameter posteriors.
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article, the Modulated Fourier Expansion is analytically derived for a linear partial differential equation with a multifrequency highly oscillatory potential. The solution of the equation is expressed as a convergent Neumann series within the appropriate Sobolev space. The proposed approach enables, firstly, to derive a general formula for the error associated with the approximation of the solution by MFE, and secondly, to determine the coefficients for this expansion -- without the need to solve numerically the system of differential equations to find the coefficients of MFE. Numerical experiments illustrate the theoretical investigations.
Large Language Models (LLMs) have been observed to encode and perpetuate harmful associations present in the training data. We propose a theoretically grounded framework called StereoMap to gain insights into their perceptions of how demographic groups have been viewed by society. The framework is grounded in the Stereotype Content Model (SCM); a well-established theory from psychology. According to SCM, stereotypes are not all alike. Instead, the dimensions of Warmth and Competence serve as the factors that delineate the nature of stereotypes. Based on the SCM theory, StereoMap maps LLMs' perceptions of social groups (defined by socio-demographic features) using the dimensions of Warmth and Competence. Furthermore, the framework enables the investigation of keywords and verbalizations of reasoning of LLMs' judgments to uncover underlying factors influencing their perceptions. Our results show that LLMs exhibit a diverse range of perceptions towards these groups, characterized by mixed evaluations along the dimensions of Warmth and Competence. Furthermore, analyzing the reasonings of LLMs, our findings indicate that LLMs demonstrate an awareness of social disparities, often stating statistical data and research findings to support their reasoning. This study contributes to the understanding of how LLMs perceive and represent social groups, shedding light on their potential biases and the perpetuation of harmful associations.
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method interwoven with a simple conventional linear system solver (Jacobi, Gauss-Seidel, conjugate gradients), always taking only one step of the linear system solver for each step of the optimization method. The control parameter is updated on each iteration as determined by the optimization method. We prove linear convergence under a second-order growth condition, and numerically demonstrate the performance on a variety of PDEs related to inverse problems involving boundary measurements.
We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the results of our work on tree models, complex objects, with the reconstruction of which most existing methods cannot handle. The second option allows us to significantly improve the precision by using gradients within memetic algorithm, differentiable rendering and also differentiable procedural generators. In our work we see 2 main contributions. First, we propose a method to join differentiable rendering and inverse procedural modeling. This gives us an opportunity to reconstruct 3D model more accurately than existing approaches when a small number of input images are available (even for single image). Second, we join both differentiable and non-differentiable procedural generators in a single framework which allow us to apply inverse procedural modeling to fairly complex generators: when gradient is available, reconstructions is precise, when gradient is not available, reconstruction is approximate, but always high quality without visual artifacts.
Insurers usually turn to generalized linear models for modelling claim frequency and severity data. Due to their success in other fields, machine learning techniques are gaining popularity within the actuarial toolbox. Our paper contributes to the literature on frequency-severity insurance pricing with machine learning via deep learning structures. We present a benchmark study on four insurance data sets with frequency and severity targets in the presence of multiple types of input features. We compare in detail the performance of: a generalized linear model on binned input data, a gradient-boosted tree model, a feed-forward neural network (FFNN), and the combined actuarial neural network (CANN). Our CANNs combine a baseline prediction established with a GLM and GBM, respectively, with a neural network correction. We explain the data preprocessing steps with specific focus on the multiple types of input features typically present in tabular insurance data sets, such as postal codes, numeric and categorical covariates. Autoencoders are used to embed the categorical variables into the neural network and we explore their potential advantages in a frequency-severity setting. Finally, we construct global surrogate models for the neural nets' frequency and severity models. These surrogates enable the translation of the essential insights captured by the FFNNs or CANNs to GLMs. As such, a technical tariff table results that can easily be deployed in practice.
Deep Learning (DL) is the most widely used tool in the contemporary field of computer vision. Its ability to accurately solve complex problems is employed in vision research to learn deep neural models for a variety of tasks, including security critical applications. However, it is now known that DL is vulnerable to adversarial attacks that can manipulate its predictions by introducing visually imperceptible perturbations in images and videos. Since the discovery of this phenomenon in 2013~[1], it has attracted significant attention of researchers from multiple sub-fields of machine intelligence. In [2], we reviewed the contributions made by the computer vision community in adversarial attacks on deep learning (and their defenses) until the advent of year 2018. Many of those contributions have inspired new directions in this area, which has matured significantly since witnessing the first generation methods. Hence, as a legacy sequel of [2], this literature review focuses on the advances in this area since 2018. To ensure authenticity, we mainly consider peer-reviewed contributions published in the prestigious sources of computer vision and machine learning research. Besides a comprehensive literature review, the article also provides concise definitions of technical terminologies for non-experts in this domain. Finally, this article discusses challenges and future outlook of this direction based on the literature reviewed herein and [2].
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191