pwc-archive/papers-with-abstracts huggingface dataset:
DeepONet for Solving Nonlinear Partial Differential Equations with Physics-Informed Training
Authors: Yahong Yang
Date: 2024-10-06 00:00:00
Tasks: Operator learning, Physics-informed machine learning

In this paper, we investigate the use of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural networks for each PDE, operator learning enables generalization across different PDEs without retraining. This study examines the performance of DeepONet in physics-informed training, focusing on two key aspects: (1) the approximation capabilities of deep branch and trunk networks, and (2) the generalization error in Sobolev norms. Our results demonstrate that deep branch networks provide substantial performance improvements, while trunk networks achieve optimal results when kept relatively simple. Furthermore, we derive a bound on the generalization error of DeepONet for solving nonlinear PDEs by analyzing the Rademacher complexity of its derivatives in terms of pseudo-dimension. This work bridges a critical theoretical gap by delivering rigorous error estimates. This paper fills a theoretical gap by providing error estimations for a wide range of physics-informed machine learning models and applications.
Leveraging Hierarchical Taxonomies in Prompt-based Continual Learning
Authors: Quyen Tran, Hoang Phan, Minh Le, Tuan Truong, Dinh Phung, Linh Ngo, Thien Nguyen, Nhat Ho, Trung Le
Date: 2024-10-06 00:00:00
Tasks: Continual Learning

Drawing inspiration from human learning behaviors, this work proposes a novel approach to mitigate catastrophic forgetting in Prompt-based Continual Learning models by exploiting the relationships between continuously emerging class data. We find that applying human habits of organizing and connecting information can serve as an efficient strategy when training deep learning models. Specifically, by building a hierarchical tree structure based on the expanding set of labels, we gain fresh insights into the data, identifying groups of similar classes could easily cause confusion. Additionally, we delve deeper into the hidden connections between classes by exploring the original pretrained model's behavior through an optimal transport-based approach. From these insights, we propose a novel regularization loss function that encourages models to focus more on challenging knowledge areas, thereby enhancing overall performance. Experimentally, our method demonstrated significant superiority over the most robust state-of-the-art models on various benchmarks.
Calibrating Expressions of Certainty
Authors: Peiqi Wang, Barbara D. Lam, Yingcheng Liu, Ameneh Asgari-Targhi, Rameswar Panda, William M. Wells, Tina Kapur, Polina Golland
Date: 2024-10-06 00:00:00

We present a novel approach to calibrating linguistic expressions of certainty, e.g., "Maybe" and "Likely". Unlike prior work that assigns a single score to each certainty phrase, we model uncertainty as distributions over the simplex to capture their semantics more accurately. To accommodate this new representation of certainty, we generalize existing measures of miscalibration and introduce a novel post-hoc calibration method. Leveraging these tools, we analyze the calibration of both humans (e.g., radiologists) and computational models (e.g., language models) and provide interpretable suggestions to improve their calibration.
Comprehensive Monitoring of Air Pollution Hotspots Using Sparse Sensor Networks
Authors: Ankit Bhardwaj, Ananth Balashankar, Shiva Iyer, Nita Soans, Anant Sudarshan, Rohini Pande, Lakshminarayanan Subramanian
Date: 2024-10-05 00:00:00

Urban air pollution hotspots pose significant health risks, yet their detection and analysis remain limited by the sparsity of public sensor networks. This paper addresses this challenge by combining predictive modeling and mechanistic approaches to comprehensively monitor pollution hotspots. We enhanced New Delhi's existing sensor network with 28 low-cost sensors, collecting PM2.5 data over 30 months from May 1, 2018, to Nov 1, 2020. Applying established definitions of hotspots to this data, we found the existence of additional 189 hidden hotspots apart from confirming 660 hotspots detected by the public network. Using predictive techniques like Space-Time Kriging, we identified hidden hotspots with 95% precision and 88% recall with 50% sensor failure rate, and with 98% precision and 95% recall with 50% missing sensors. The projected results of our predictive models were further compiled into policy recommendations for public authorities. Additionally, we developed a Gaussian Plume Dispersion Model to understand the mechanistic underpinnings of hotspot formation, incorporating an emissions inventory derived from local sources. Our mechanistic model is able to explain 65% of observed transient hotspots. Our findings underscore the importance of integrating data-driven predictive models with physics-based mechanistic models for scalable and robust air pollution management in resource-constrained settings.
Integrating Physics-Informed Deep Learning and Numerical Methods for Robust Dynamics Discovery and Parameter Estimation
Authors: Caitlin Ho, Andrea Arnold
Date: 2024-10-05 00:00:00
Tasks: parameter estimation

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to solve two challenging problems in dynamical systems theory: dynamics discovery and parameter estimation. Results demonstrate the effectiveness of the proposed approaches on a suite of test problems exhibiting oscillatory and chaotic dynamics. When comparing the performance of various numerical schemes, such as the Runge-Kutta and linear multistep families of methods, we observe promising results in predicting the system dynamics and estimating physical parameters, given appropriate choices of spatial and temporal discretization schemes and numerical method orders.
Bootstrap Sampling Rate Greater than 1.0 May Improve Random Forest Performance
Authors: Stanisław Kaźmierczak, Jacek Mańdziuk
Date: 2024-10-05 00:00:00

Random forests utilize bootstrap sampling to create an individual training set for each component tree. This involves sampling with replacement, with the number of instances equal to the size of the original training set ($N$). Research literature indicates that drawing fewer than $N$ observations can also yield satisfactory results. The ratio of the number of observations in each bootstrap sample to the total number of training instances is called the bootstrap rate (BR). Sampling more than $N$ observations (BR $>$ 1) has been explored in the literature only to a limited extent and has generally proven ineffective. In this paper, we re-examine this approach using 36 diverse datasets and consider BR values ranging from 1.2 to 5.0. Contrary to previous findings, we show that such parameterization can result in statistically significant improvements in classification accuracy compared to standard settings (BR $\leq$ 1). Furthermore, we investigate what the optimal BR depends on and conclude that it is more a property of the dataset than a dependence on the random forest hyperparameters. Finally, we develop a binary classifier to predict whether the optimal BR is $\leq$ 1 or $>$ 1 for a given dataset, achieving between 81.88\% and 88.81\% accuracy, depending on the experiment configuration.
Spectral Densities, Structured Noise and Ensemble Averaging within Open Quantum Dynamics
Authors: Yannick Marcel Holtkamp, Emiliano Godinez-Ramirez, Ulrich Kleinekathöfer
Date: 2024-10-05 00:00:00
Tasks: Computational Efficiency, Numerical Integration

Although recent advances in simulating open quantum systems have lead to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely the Numerical Integration of Schr\"odinger Equation (NISE). Firstly, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed Thermalized NISE. Secondly, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics.
Enhancing Carbon Emission Reduction Strategies using OCO and ICOS data
Authors: Oskar Åström, Carina Geldhauser, Markus Grillitsch, Ola Hall, Alexandros Sopasakis
Date: 2024-10-05 00:00:00

We propose a methodology to enhance local CO2 monitoring by integrating satellite data from the Orbiting Carbon Observatories (OCO-2 and OCO-3) with ground level observations from the Integrated Carbon Observation System (ICOS) and weather data from the ECMWF Reanalysis v5 (ERA5). Unlike traditional methods that downsample national data, our approach uses multimodal data fusion for high-resolution CO2 estimations. We employ weighted K-nearest neighbor (KNN) interpolation with machine learning models to predict ground level CO2 from satellite measurements, achieving a Root Mean Squared Error of 3.92 ppm. Our results show the effectiveness of integrating diverse data sources in capturing local emission patterns, highlighting the value of high-resolution atmospheric transport models. The developed model improves the granularity of CO2 monitoring, providing precise insights for targeted carbon mitigation strategies, and represents a novel application of neural networks and KNN in environmental monitoring, adaptable to various regions and temporal scales.
Unveiling the Impact of Local Homophily on GNN Fairness: In-Depth Analysis and New Benchmarks
Authors: Donald Loveland, Danai Koutra
Date: 2024-10-05 00:00:00
Tasks: Fairness

Graph Neural Networks (GNNs) often struggle to generalize when graphs exhibit both homophily (same-class connections) and heterophily (different-class connections). Specifically, GNNs tend to underperform for nodes with local homophily levels that differ significantly from the global homophily level. This issue poses a risk in user-centric applications where underrepresented homophily levels are present. Concurrently, fairness within GNNs has received substantial attention due to the potential amplification of biases via message passing. However, the connection between local homophily and fairness in GNNs remains underexplored. In this work, we move beyond global homophily and explore how local homophily levels can lead to unfair predictions. We begin by formalizing the challenge of fair predictions for underrepresented homophily levels as an out-of-distribution (OOD) problem. We then conduct a theoretical analysis that demonstrates how local homophily levels can alter predictions for differing sensitive attributes. We additionally introduce three new GNN fairness benchmarks, as well as a novel semi-synthetic graph generator, to empirically study the OOD problem. Across extensive analysis we find that two factors can promote unfairness: (a) OOD distance, and (b) heterophilous nodes situated in homophilous graphs. In cases where these two conditions are met, fairness drops by up to 24% on real world datasets, and 30% in semi-synthetic datasets. Together, our theoretical insights, empirical analysis, and algorithmic contributions unveil a previously overlooked source of unfairness rooted in the graph's homophily information.
MindFlayer SGD: Efficient Parallel SGD in the Presence of Heterogeneous and Random Worker Compute Times
Authors: Artavazd Maranjyan, Omar Shaikh Omar, Peter Richtárik
Date: 2024-10-05 00:00:00
Tasks: Stochastic Optimization

We investigate the problem of minimizing the expectation of smooth nonconvex functions in a distributed setting with multiple parallel workers that are able to compute stochastic gradients. A significant challenge in this context is the presence of arbitrarily heterogeneous and stochastic compute times among workers, which can severely degrade the performance of existing parallel stochastic gradient descent (SGD) methods. While some parallel SGD algorithms achieve optimal performance under deterministic but heterogeneous delays, their effectiveness diminishes when compute times are random - a scenario not explicitly addressed in their design. To bridge this gap, we introduce MindFlayer SGD, a novel parallel SGD method specifically designed to handle stochastic and heterogeneous compute times. Through theoretical analysis and empirical evaluation, we demonstrate that MindFlayer SGD consistently outperforms existing baselines, particularly in environments with heavy-tailed noise. Our results highlight its robustness and scalability, making it a compelling choice for large-scale distributed learning tasks.
Applying Hybrid Graph Neural Networks to Strengthen Credit Risk Analysis
Authors: Mengfang Sun, Wenying Sun, Ying Sun, Shaobo Liu, Mohan Jiang, Zhen Xu
Date: 2024-10-05 00:00:00
Tasks: Decision Making

This paper presents a novel approach to credit risk prediction by employing Graph Convolutional Neural Networks (GCNNs) to assess the creditworthiness of borrowers. Leveraging the power of big data and artificial intelligence, the proposed method addresses the challenges faced by traditional credit risk assessment models, particularly in handling imbalanced datasets and extracting meaningful features from complex relationships. The paper begins by transforming raw borrower data into graph-structured data, where borrowers and their relationships are represented as nodes and edges, respectively. A classic subgraph convolutional model is then applied to extract local features, followed by the introduction of a hybrid GCNN model that integrates both local and global convolutional operators to capture a comprehensive representation of node features. The hybrid model incorporates an attention mechanism to adaptively select features, mitigating issues of over-smoothing and insufficient feature consideration. The study demonstrates the potential of GCNNs in improving the accuracy of credit risk prediction, offering a robust solution for financial institutions seeking to enhance their lending decision-making processes.
Black Boxes and Looking Glasses: Multilevel Symmetries, Reflection Planes, and Convex Optimization in Deep Networks
Authors: Emi Zeger, Mert Pilanci
Date: 2024-10-05 00:00:00

We show that training deep neural networks (DNNs) with absolute value activation and arbitrary input dimension can be formulated as equivalent convex Lasso problems with novel features expressed using geometric algebra. This formulation reveals geometric structures encoding symmetry in neural networks. Using the equivalent Lasso form of DNNs, we formally prove a fundamental distinction between deep and shallow networks: deep networks inherently favor symmetric structures in their fitted functions, with greater depth enabling multilevel symmetries, i.e., symmetries within symmetries. Moreover, Lasso features represent distances to hyperplanes that are reflected across training points. These reflection hyperplanes are spanned by training data and are orthogonal to optimal weight vectors. Numerical experiments support theory and demonstrate theoretically predicted features when training networks using embeddings generated by Large Language Models.
Language Model-Driven Data Pruning Enables Efficient Active Learning
Authors: Abdul Hameed Azeemi, Ihsan Ayyub Qazi, Agha Ali Raza
Date: 2024-10-05 00:00:00
Tasks: Active Learning, Language Modeling, Language Modelling, Sentiment Analysis, Topic Classification

Active learning (AL) optimizes data labeling efficiency by selecting the most informative instances for annotation. A key component in this procedure is an acquisition function that guides the selection process and identifies the suitable instances for labeling from the unlabeled pool. However, these acquisition methods suffer from high computational costs with large unlabeled data pools, posing a roadblock to their applicability on large datasets. To address this challenge and bridge this gap, we introduce a novel plug-and-play unlabeled data pruning strategy, ActivePrune, which leverages language models to prune the unlabeled pool. ActivePrune implements a two-stage pruning process: an initial fast evaluation using perplexity scores from an n-gram language model, followed by a high-quality selection using metrics for data quality computed through a quantized LLM. Additionally, to enhance the diversity in the unlabeled pool, we propose a novel perplexity reweighting method that systematically brings forward underrepresented instances for selection in subsequent labeling iterations. Experiments on translation, sentiment analysis, topic classification, and summarization tasks on four diverse datasets and four active learning strategies demonstrate that ActivePrune outperforms existing data pruning methods. Finally, we compare the selection quality $\leftrightarrow$ efficiency tradeoff of the data pruning methods and demonstrate that ActivePrune is computationally more efficient than other LLM score-based pruning methods, and provides up to 74% reduction in the end-to-end time required for active learning.
Fundamental Limitations on Subquadratic Alternatives to Transformers
Authors: Josh Alman, Hantao Yu
Date: 2024-10-05 00:00:00
Tasks: Mamba, State Space Models

The Transformer architecture is widely deployed in many popular and impactful Large Language Models. At its core is the attention mechanism for calculating correlations between pairs of tokens. Performing an attention computation takes quadratic time in the input size, and had become the time bottleneck for transformer operations. In order to circumvent this, researchers have used a variety of approaches, including designing heuristic algorithms for performing attention computations faster, and proposing alternatives to the attention mechanism which can be computed more quickly. For instance, state space models such as Mamba were designed to replace attention with an almost linear time alternative. In this paper, we prove that any such approach cannot perform important tasks that Transformer is able to perform (assuming a popular conjecture from fine-grained complexity theory). We focus on document similarity tasks, where one is given as input many documents and would like to find a pair which is (approximately) the most similar. We prove that Transformer is able to perform this task, and we prove that this task cannot be performed in truly subquadratic time by any algorithm. Thus, any model which can be evaluated in subquadratic time - whether because of subquadratic-time heuristics for attention, faster attention replacements like Mamba, or any other reason - cannot perform this task. In other words, in order to perform tasks that (implicitly or explicitly) involve document similarity, one may as well use Transformer and cannot avoid its quadratic running time.
Visualising Feature Learning in Deep Neural Networks by Diagonalizing the Forward Feature Map
Authors: Yoonsoo Nam, Chris Mingard, Seok Hyeong Lee, Soufiane Hayou, Ard Louis
Date: 2024-10-05 00:00:00

Deep neural networks (DNNs) exhibit a remarkable ability to automatically learn data representations, finding appropriate features without human input. Here we present a method for analysing feature learning by decomposing DNNs into 1) a forward feature-map $\Phi$ that maps the input dataspace to the post-activations of the penultimate layer, and 2) a final linear layer that classifies the data. We diagonalize $\Phi$ with respect to the gradient descent operator and track feature learning by measuring how the eigenfunctions and eigenvalues of $\Phi$ change during training. Across many popular architectures and classification datasets, we find that DNNs converge, after just a few epochs, to a minimal feature (MF) regime dominated by a number of eigenfunctions equal to the number of classes. This behaviour resembles the neural collapse phenomenon studied at longer training times. For other DNN-data combinations, such as a fully connected network on CIFAR10, we find an extended feature (EF) regime where significantly more features are used. Optimal generalisation performance upon hyperparameter tuning typically coincides with the MF regime, but we also find examples of poor performance within the MF regime. Finally, we recast the phenomenon of neural collapse into a kernel picture which can be extended to broader tasks such as regression.
DeFoG: Discrete Flow Matching for Graph Generation
Authors: Yiming Qin, Manuel Madeira, Dorina Thanou, Pascal Frossard
Date: 2024-10-05 00:00:00
Tasks: Denoising, Graph Generation, Navigate

Graph generation is fundamental in diverse scientific applications, due to its ability to reveal the underlying distribution of complex data, and eventually generate new, realistic data points. Despite the success of diffusion models in this domain, those face limitations in sampling efficiency and flexibility, stemming from the tight coupling between the training and sampling stages. To address this, we propose DeFoG, a novel framework using discrete flow matching for graph generation. DeFoG employs a flow-based approach that features an efficient linear interpolation noising process and a flexible denoising process based on a continuous-time Markov chain formulation. We leverage an expressive graph transformer and ensure desirable node permutation properties to respect graph symmetry. Crucially, our framework enables a disentangled design of the training and sampling stages, enabling more effective and efficient optimization of model performance. We navigate this design space by introducing several algorithmic improvements that boost the model performance, consistently surpassing existing diffusion models. We also theoretically demonstrate that, for general discrete data, discrete flow models can faithfully replicate the ground truth distribution - a result that naturally extends to graph data and reinforces DeFoG's foundations. Extensive experiments show that DeFoG achieves state-of-the-art results on synthetic and molecular datasets, improving both training and sampling efficiency over diffusion models, and excels in conditional generation on a digital pathology dataset.
Compositional Diffusion Models for Powered Descent Trajectory Generation with Flexible Constraints
Authors: Julia Briden, Yilun Du, Enrico M. Zucchelli, Richard Linares
Date: 2024-10-05 00:00:00

This work introduces TrajDiffuser, a compositional diffusion-based flexible and concurrent trajectory generator for 6 degrees of freedom powered descent guidance. TrajDiffuser is a statistical model that learns the multi-modal distributions of a dataset of simulated optimal trajectories, each subject to only one or few constraints that may vary for different trajectories. During inference, the trajectory is generated simultaneously over time, providing stable long-horizon planning, and constraints can be composed together, increasing the model's generalizability and decreasing the training data required. The generated trajectory is then used to initialize an optimizer, increasing its robustness and speed.