pwc-archive/papers-with-abstracts huggingface dataset:
Neural Symbolic Regression of Complex Network Dynamics
Authors: Haiquan Qiu, ShuZhi Liu, Quanming Yao
Date: 2024-10-15 00:00:00
Tasks: regression, Symbolic Regression

Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert knowledge to derive. However, because the complex network involves noisy observations from multiple trajectories of nodes, existing symbolic regression methods are either not applicable or ineffective on its dynamics. In this paper, we propose Physically Inspired Neural Dynamics Symbolic Regression (PI-NDSR), a method based on neural networks and genetic programming to automatically learn the symbolic expression of dynamics. Our method consists of two key components: a Physically Inspired Neural Dynamics (PIND) to augment and denoise trajectories through observed trajectory interpolation; and a coordinated genetic search algorithm to derive symbolic expressions. This algorithm leverages references of node dynamics and edge dynamics from neural dynamics to avoid overfitted expressions in symbolic space. We evaluate our method on synthetic datasets generated by various dynamics and real datasets on disease spreading. The results demonstrate that PI-NDSR outperforms the existing method in terms of both recovery probability and error.
Reinforcement Learning Based Bidding Framework with High-dimensional Bids in Power Markets
Authors: Jinyu Liu, Hongye Guo, Yun Li, Qinghu Tang, Fuquan Huang, Tunan Chen, Haiwang Zhong, Qixin Chen
Date: 2024-10-15 00:00:00
Tasks: Reinforcement Learning (RL)

Over the past decade, bidding in power markets has attracted widespread attention. Reinforcement Learning (RL) has been widely used for power market bidding as a powerful AI tool to make decisions under real-world uncertainties. However, current RL methods mostly employ low dimensional bids, which significantly diverge from the N price-power pairs commonly used in the current power markets. The N-pair bidding format is denoted as High Dimensional Bids (HDBs), which has not been fully integrated into the existing RL-based bidding methods. The loss of flexibility in current RL bidding methods could greatly limit the bidding profits and make it difficult to tackle the rising uncertainties brought by renewable energy generations. In this paper, we intend to propose a framework to fully utilize HDBs for RL-based bidding methods. First, we employ a special type of neural network called Neural Network Supply Functions (NNSFs) to generate HDBs in the form of N price-power pairs. Second, we embed the NNSF into a Markov Decision Process (MDP) to make it compatible with most existing RL methods. Finally, experiments on Energy Storage Systems (ESSs) in the PJM Real-Time (RT) power market show that the proposed bidding method with HDBs can significantly improve bidding flexibility, thereby improving the profit of the state-of-the-art RL bidding methods.
A Bilevel Optimization Framework for Imbalanced Data Classification
Authors: Karen Medlin, Sven Leyffer, Krishnan Raghavan
Date: 2024-10-15 00:00:00
Tasks: Bilevel Optimization, Classification

Data rebalancing techniques, including oversampling and undersampling, are a common approach to addressing the challenges of imbalanced data. To tackle unresolved problems related to both oversampling and undersampling, we propose a new undersampling approach that: (i) avoids the pitfalls of noise and overlap caused by synthetic data and (ii) avoids the pitfall of under-fitting caused by random undersampling. Instead of undersampling majority data randomly, our method undersamples datapoints based on their ability to improve model loss. Using improved model loss as a proxy measurement for classification performance, our technique assesses a datapoint's impact on loss and rejects those unable to improve it. In so doing, our approach rejects majority datapoints redundant to datapoints already accepted and, thereby, finds an optimal subset of majority training data for classification. The accept/reject component of our algorithm is motivated by a bilevel optimization problem uniquely formulated to identify the optimal training set we seek. Experimental results show our proposed technique with F1 scores up to 10% higher than state-of-the-art methods.
Toward Efficient Kernel-Based Solvers for Nonlinear PDEs
Authors: Zhitong Xu, Da Long, Yiming Xu, Guang Yang, Shandian Zhe, Houman Owhadi
Date: 2024-10-15 00:00:00

This paper introduces a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing challenges with a large number of collocation points, our approach eliminates these operators from the kernel. We model the solution using a standard kernel interpolation form and differentiate the interpolant to compute the derivatives. Our framework obviates the need for complex Gram matrix construction between solutions and their derivatives, allowing for a straightforward implementation and scalable computation. As an instance, we allocate the collocation points on a grid and adopt a product kernel, which yields a Kronecker product structure in the interpolation. This structure enables us to avoid computing the full Gram matrix, reducing costs and scaling efficiently to a large number of collocation points. We provide a proof of the convergence and rate analysis of our method under appropriate regularity assumptions. In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.
Differentiable Programming for Computational Plasma Physics
Authors: Nick McGreivy
Date: 2024-10-15 00:00:00

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of differentiable programming to computational plasma physics. First, we consider how differentiable programming can be used to simplify and improve stellarator optimization. We introduce a stellarator coil design code (FOCUSADD) that uses gradient-based optimization to produce stellarator coils with finite build. Because we use reverse mode AD, which can compute gradients of scalar functions with the same computational complexity as the function, FOCUSADD is simple, flexible, and efficient. We then discuss two additional applications of AD in stellarator optimization. Second, we explore how machine learning (ML) can be used to improve or replace the numerical methods used to solve partial differential equations (PDEs), focusing on time-dependent PDEs in fluid mechanics relevant to plasma physics. Differentiable programming allows neural networks and other techniques from ML to be embedded within numerical methods. This is a promising, but relatively new, research area. We focus on two basic questions. First, can we design ML-based PDE solvers that have the same guarantees of conservation, stability, and positivity that standard numerical methods do? The answer is yes; we introduce error-correcting algorithms that preserve invariants of time-dependent PDEs. Second, which types of ML-based solvers work best at solving PDEs? We perform a systematic review of the scientific literature on solving PDEs with ML. Unfortunately we discover two issues, weak baselines and reporting biases, that affect the interpretation reproducibility of a significant majority of published research. We conclude that using ML to solve PDEs is not as promising as we initially believed.
Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs
Authors: Severi Rissanen, Markus Heinonen, Arno Solin
Date: 2024-10-15 00:00:00

The covariance for clean data given a noisy observation is an important quantity in many conditional generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using {\em (i)} a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.
Mimetic Initialization Helps State Space Models Learn to Recall
Authors: Asher Trockman, Hrayr Harutyunyan, J. Zico Kolter, Sanjiv Kumar, Srinadh Bhojanapalli
Date: 2024-10-14 00:00:00
Tasks: Mamba, State Space Models

Recent work has shown that state space models such as Mamba are significantly worse than Transformers on recall-based tasks due to the fact that their state size is constant with respect to their input sequence length. But in practice, state space models have fairly large state sizes, and we conjecture that they should be able to perform much better at these tasks than previously reported. We investigate whether their poor copying and recall performance could be due in part to training difficulties rather than fundamental capacity constraints. Based on observations of their "attention" maps, we propose a structured initialization technique that allows state space layers to more readily mimic attention. Across a variety of architecture settings, our initialization makes it substantially easier for Mamba to learn to copy and do associative recall from scratch.
Which Spaces can be Embedded in $L_p$-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
Authors: Yiping Lu, Daozhe Lin, Qiang Du
Date: 2024-10-14 00:00:00

In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function spaces and has implications for their approximability and learnability. Classical results show that embedding a function space into a reproducing kernel Hilbert space (RKHS) implies a bound on its metric entropy growth. Surprisingly, we prove a \textbf{converse}: a bound on the metric entropy growth of a function space allows its embedding to a $L_p-$type Reproducing Kernel Banach Space (RKBS). This shows that the ${L}_p-$type RKBS provides a broad modeling framework for learnable function classes with controlled metric entropies. Our results shed new light on the power and limitations of kernel methods for learning complex function spaces.
Statistical Properties of Deep Neural Networks with Dependent Data
Authors: Chad Brown
Date: 2024-10-14 00:00:00
Tasks: regression, Time Series

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates for convergence in probability under nonstationary data. The second provides non-asymptotic probability bounds on $\mathcal{L}^{2}$-errors under stationary $\beta$-mixing data. I apply these results to DNN estimators in both regression and classification contexts imposing only a standard H\"older smoothness assumption. The DNN architectures considered are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and a width and depth that grows with sample size. The framework provided also offers potential for research into other DNN architectures and time-series applications.
Emulators for stellar profiles in binary population modeling
Authors: Elizabeth Teng, Ugur Demir, Zoheyr Doctor, Philipp M. Srivastava, Shamal Lalvani, Vicky Kalogera, Aggelos Katsaggelos, Jeff J. Andrews, Simone S. Bavera, Max M. Briel, Seth Gossage, Konstantinos Kovlakas, Matthias U. Kruckow, Kyle Akira Rocha, Meng Sun, Zepei Xing, Emmanouil Zapartas
Date: 2024-10-14 00:00:00
Tasks: Dimensionality Reduction

Knowledge about the internal physical structure of stars is crucial to understanding their evolution. The novel binary population synthesis code POSYDON includes a module for interpolating the stellar and binary properties of any system at the end of binary MESA evolution based on a pre-computed set of models. In this work, we present a new emulation method for predicting stellar profiles, i.e., the internal stellar structure along the radial axis, using machine learning techniques. We use principal component analysis for dimensionality reduction and fully-connected feed-forward neural networks for making predictions. We find accuracy to be comparable to that of nearest neighbor approximation, with a strong advantage in terms of memory and storage efficiency. By providing a versatile framework for modeling stellar internal structure, the emulation method presented here will enable faster simulations of higher physical fidelity, offering a foundation for a wide range of large-scale population studies of stellar and binary evolution.
A Two-Stage Federated Learning Approach for Industrial Prognostics Using Large-Scale High-Dimensional Signals
Authors: Yuqi Su, Xiaolei Fang
Date: 2024-10-14 00:00:00
Tasks: Dimensionality Reduction, Federated Learning, parameter estimation, regression

Industrial prognostics aims to develop data-driven methods that leverage high-dimensional degradation signals from assets to predict their failure times. The success of these models largely depends on the availability of substantial historical data for training. However, in practice, individual organizations often lack sufficient data to independently train reliable prognostic models, and privacy concerns prevent data sharing between organizations for collaborative model training. To overcome these challenges, this article proposes a statistical learning-based federated model that enables multiple organizations to jointly train a prognostic model while keeping their data local and secure. The proposed approach involves two key stages: federated dimension reduction and federated (log)-location-scale regression. In the first stage, we develop a federated randomized singular value decomposition algorithm for multivariate functional principal component analysis, which efficiently reduces the dimensionality of degradation signals while maintaining data privacy. The second stage proposes a federated parameter estimation algorithm for (log)-location-scale regression, allowing organizations to collaboratively estimate failure time distributions without sharing raw data. The proposed approach addresses the limitations of existing federated prognostic methods by using statistical learning techniques that perform well with smaller datasets and provide comprehensive failure time distributions. The effectiveness and practicality of the proposed model are validated using simulated data and a dataset from the NASA repository.
Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models
Authors: Cheng Lu, Yang song
Date: 2024-10-14 00:00:00

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.
Predicting Chess Puzzle Difficulty with Transformers
Authors: Szymon Miłosz, Paweł Kapusta
Date: 2024-10-14 00:00:00

This study addresses the challenge of quantifying chess puzzle difficulty - a complex task that combines elements of game theory and human cognition and underscores its critical role in effective chess training. We present GlickFormer, a novel transformer-based architecture that predicts chess puzzle difficulty by approximating the Glicko-2 rating system. Unlike conventional chess engines that optimize for game outcomes, GlickFormer models human perception of tactical patterns and problem-solving complexity. The proposed model utilizes a modified ChessFormer backbone for spatial feature extraction and incorporates temporal information via factorized transformer techniques. This approach enables the capture of both spatial chess piece arrangements and move sequences, effectively modeling spatio-temporal relationships relevant to difficulty assessment. Experimental evaluation was conducted on a dataset of over 4 million chess puzzles. Results demonstrate GlickFormer's superior performance compared to the state-of-the-art ChessFormer baseline across multiple metrics. The algorithm's performance has also been recognized through its competitive results in the IEEE BigData 2024 Cup: Predicting Chess Puzzle Difficulty competition, where it placed 11th. The insights gained from this study have implications for personalized chess training and broader applications in educational technology and cognitive modeling.
Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrix
Authors: Charles C. Margossian, Lawrence K. Saul
Date: 2024-10-14 00:00:00
Tasks: Bayesian Inference, Variational Inference

Given an intractable target density $p$, variational inference (VI) attempts to find the best approximation $q$ from a tractable family $Q$. This is typically done by minimizing the exclusive Kullback-Leibler divergence, $\text{KL}(q||p)$. In practice, $Q$ is not rich enough to contain $p$, and the approximation is misspecified even when it is a unique global minimizer of $\text{KL}(q||p)$. In this paper, we analyze the robustness of VI to these misspecifications when $p$ exhibits certain symmetries and $Q$ is a location-scale family that shares these symmetries. We prove strong guarantees for VI not only under mild regularity conditions but also in the face of severe misspecifications. Namely, we show that (i) VI recovers the mean of $p$ when $p$ exhibits an \textit{even} symmetry, and (ii) it recovers the correlation matrix of $p$ when in addition~$p$ exhibits an \textit{elliptical} symmetry. These guarantees hold for the mean even when $q$ is factorized and $p$ is not, and for the correlation matrix even when~$q$ and~$p$ behave differently in their tails. We analyze various regimes of Bayesian inference where these symmetries are useful idealizations, and we also investigate experimentally how VI behaves in their absence.
Time Series Viewmakers for Robust Disruption Prediction
Authors: Dhruva Chayapathy, Tavis Siebert, Lucas Spangher, Akshata Kishore Moharir, Om Manoj Patil, Cristina Rea
Date: 2024-10-14 00:00:00
Tasks: Data Augmentation, Prediction, Time Series

Machine Learning guided data augmentation may support the development of technologies in the physical sciences, such as nuclear fusion tokamaks. Here we endeavor to study the problem of detecting disruptions i.e. plasma instabilities that can cause significant damages, impairing the reliability and efficiency required for their real world viability. Machine learning (ML) prediction models have shown promise in detecting disruptions for specific tokamaks, but they often struggle in generalizing to the diverse characteristics and dynamics of different machines. This limits the effectiveness of ML models across different tokamak designs and operating conditions, which is a critical barrier to scaling fusion technology. Given the success of data augmentation in improving model robustness and generalizability in other fields, this study explores the use of a novel time series viewmaker network to generate diverse augmentations or "views" of training data. Our results show that incorporating views during training improves AUC and F2 scores on DisruptionBench tasks compared to standard or no augmentations. This approach represents a promising step towards developing more broadly applicable ML models for disruption avoidance, which is essential for advancing fusion technology and, ultimately, addressing climate change through reliable and sustainable energy production.
Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees
Authors: Bo Tang, Elias B. Khalil, Ján Drgoňa
Date: 2024-10-14 00:00:00

Mixed-integer nonlinear programs (MINLPs) arise in domains as diverse as energy systems and transportation, but are notoriously difficult to solve, particularly at scale. While learning-to-optimize (L2O) methods have been successful at continuous optimization, extending them to MINLPs is challenging due to integer constraints. To overcome this, we propose a novel L2O approach with two integer correction layers to ensure the integrality of the solution and a projection step to ensure the feasibility of the solution. We prove that the projection step converges, providing a theoretical guarantee for our method. Our experiments show that our methods efficiently solve MINLPs with up to tens of thousands of variables, providing high-quality solutions within milliseconds, even for problems where traditional solvers and heuristics fail. This is the first general L2O method for parametric MINLPs, finding solutions to some of the largest instances reported to date.
SGUQ: Staged Graph Convolution Neural Network for Alzheimer's Disease Diagnosis using Multi-Omics Data
Authors: Liang Tao, Yixin Xie, Jeffrey D Deng, Hui Shen, Hong-Wen Deng, Weihua Zhou, Chen Zhao
Date: 2024-10-14 00:00:00
Tasks: Uncertainty Quantification

Alzheimer's disease (AD) is a chronic neurodegenerative disorder and the leading cause of dementia, significantly impacting cost, mortality, and burden worldwide. The advent of high-throughput omics technologies, such as genomics, transcriptomics, proteomics, and epigenomics, has revolutionized the molecular understanding of AD. Conventional AI approaches typically require the completion of all omics data at the outset to achieve optimal AD diagnosis, which are inefficient and may be unnecessary. To reduce the clinical cost and improve the accuracy of AD diagnosis using multi-omics data, we propose a novel staged graph convolutional network with uncertainty quantification (SGUQ). SGUQ begins with mRNA and progressively incorporates DNA methylation and miRNA data only when necessary, reducing overall costs and exposure to harmful tests. Experimental results indicate that 46.23% of the samples can be reliably predicted using only single-modal omics data (mRNA), while an additional 16.04% of the samples can achieve reliable predictions when combining two omics data types (mRNA + DNA methylation). In addition, the proposed staged SGUQ achieved an accuracy of 0.858 on ROSMAP dataset, which outperformed existing methods significantly. The proposed SGUQ can not only be applied to AD diagnosis using multi-omics data but also has the potential for clinical decision-making using multi-viewed data. Our implementation is publicly available at https://github.com/chenzhao2023/multiomicsuncertainty.