pwc-archive/papers-with-abstracts huggingface dataset:
Point Source Identification Using Singularity Enriched Neural Networks
Authors: Tianhao Hu, Bangti Jin, Zhi Zhou
Date: 2024-08-17 00:00:00

The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point source identification, mainly due to the inherent solution singularity. In this work, we develop a novel algorithm to identify point sources, utilizing a neural network combined with a singularity enrichment technique. We employ the fundamental solution and neural networks to represent the singular and regular parts, respectively, and then minimize an empirical loss involving the intensities and locations of the unknown point sources, as well as the parameters of the neural network. Moreover, by combining the conditional stability argument of the inverse problem with the generalization error of the empirical loss, we conduct a rigorous error analysis of the algorithm. We demonstrate the effectiveness of the method with several challenging experiments.
Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs
Authors: Hao Li, Hao Jiang, Jiajun Fan, Dongsheng Ye, Liang Du
Date: 2024-08-17 00:00:00
Tasks: Graph Classification, Graph Neural Network, Topological Data Analysis

Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.
Time Series Analysis by State Space Learning
Authors: André Ramos, Davi Valladão, Alexandre Street
Date: 2024-08-17 00:00:00
Tasks: State Space Models, Time Series, Time Series Analysis

Time series analysis by state-space models is widely used in forecasting and extracting unobservable components like level, slope, and seasonality, along with explanatory variables. However, their reliance on traditional Kalman filtering frequently hampers their effectiveness, primarily due to Gaussian assumptions and the absence of efficient subset selection methods to accommodate the multitude of potential explanatory variables in today's big-data applications. Our research introduces the State Space Learning (SSL), a novel framework and paradigm that leverages the capabilities of statistical learning to construct a comprehensive framework for time series modeling and forecasting. By utilizing a regularized high-dimensional regression framework, our approach jointly extracts typical time series unobservable components, detects and addresses outliers, and selects the influence of exogenous variables within a high-dimensional space in polynomial time and global optimality guarantees. Through a controlled numerical experiment, we demonstrate the superiority of our approach in terms of subset selection of explanatory variables accuracy compared to relevant benchmarks. We also present an intuitive forecasting scheme and showcase superior performances relative to traditional time series models using a dataset of 48,000 monthly time series from the M4 competition. We extend the applicability of our approach to reformulate any linear state space formulation featuring time-varying coefficients into high-dimensional regularized regressions, expanding the impact of our research to other engineering applications beyond time series analysis. Finally, our proposed methodology is implemented within the Julia open-source package, ``StateSpaceLearning.jl".
Training Verifiably Robust Agents Using Set-Based Reinforcement Learning
Authors: Manuel Wendl, Lukas Koller, Tobias Ladner, Matthias Althoff
Date: 2024-08-17 00:00:00
Tasks: reinforcement-learning, Reinforcement Learning

Reinforcement learning often uses neural networks to solve complex control tasks. However, neural networks are sensitive to input perturbations, which makes their deployment in safety-critical environments challenging. This work lifts recent results from formally verifying neural networks against such disturbances to reinforcement learning in continuous state and action spaces using reachability analysis. While previous work mainly focuses on adversarial attacks for robust reinforcement learning, we train neural networks utilizing entire sets of perturbed inputs and maximize the worst-case reward. The obtained agents are verifiably more robust than agents obtained by related work, making them more applicable in safety-critical environments. This is demonstrated with an extensive empirical evaluation of four different benchmarks.
Improved Q-learning based Multi-hop Routing for UAV-Assisted Communication
Authors: N P Sharvari, Dibakar Das, Jyotsna Bapat, Debabrata Das
Date: 2024-08-17 00:00:00
Tasks: Collision Avoidance, Q-Learning

Designing effective Unmanned Aerial Vehicle(UAV)-assisted routing protocols is challenging due to changing topology, limited battery capacity, and the dynamic nature of communication environments. Current protocols prioritize optimizing individual network parameters, overlooking the necessity for a nuanced approach in scenarios with intermittent connectivity, fluctuating signal strength, and varying network densities, ultimately failing to address aerial network requirements comprehensively. This paper proposes a novel, Improved Q-learning-based Multi-hop Routing (IQMR) algorithm for optimal UAV-assisted communication systems. Using Q(\lambda) learning for routing decisions, IQMR substantially enhances energy efficiency and network data throughput. IQMR improves system resilience by prioritizing reliable connectivity and inter-UAV collision avoidance while integrating real-time network status information, all in the absence of predefined UAV path planning, thus ensuring dynamic adaptability to evolving network conditions. The results validate IQMR's adaptability to changing system conditions and superiority over the current techniques. IQMR showcases 36.35\% and 32.05\% improvements in energy efficiency and data throughput over the existing methods.
Dynamic Graph Representation Learning for Passenger Behavior Prediction
Authors: Mingxuan Xie, Tao Zou, Junchen Ye, Bowen Du, Runhe Huang
Date: 2024-08-17 00:00:00
Tasks: Graph Representation Learning, Prediction, Representation Learning

Passenger behavior prediction aims to track passenger travel patterns through historical boarding and alighting data, enabling the analysis of urban station passenger flow and timely risk management. This is crucial for smart city development and public transportation planning. Existing research primarily relies on statistical methods and sequential models to learn from individual historical interactions, which ignores the correlations between passengers and stations. To address these issues, this paper proposes DyGPP, which leverages dynamic graphs to capture the intricate evolution of passenger behavior. First, we formalize passengers and stations as heterogeneous vertices in a dynamic graph, with connections between vertices representing interactions between passengers and stations. Then, we sample the historical interaction sequences for passengers and stations separately. We capture the temporal patterns from individual sequences and correlate the temporal behavior between the two sequences. Finally, we use an MLP-based encoder to learn the temporal patterns in the interactions and generate real-time representations of passengers and stations. Experiments on real-world datasets confirmed that DyGPP outperformed current models in the behavior prediction task, demonstrating the superiority of our model.
Twin Sorting Dynamic Programming Assisted User Association and Wireless Bandwidth Allocation for Hierarchical Federated Learning
Authors: Rung-Hung Gau, Ting-Yu Wang, Chun-Hung Liu
Date: 2024-08-17 00:00:00
Tasks: Combinatorial Optimization, Federated Learning

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.
Improving Rare Word Translation With Dictionaries and Attention Masking
Authors: Kenneth J. Sible, David Chiang
Date: 2024-08-17 00:00:00
Tasks: Decoder, Machine Translation, Translation, Word Translation

In machine translation, rare words continue to be a problem for the dominant encoder-decoder architecture, especially in low-resource and out-of-domain translation settings. Human translators solve this problem with monolingual or bilingual dictionaries. In this paper, we propose appending definitions from a bilingual dictionary to source sentences and using attention masking to link together rare words with their definitions. We find that including definitions for rare words improves performance by up to 1.0 BLEU and 1.6 MacroF1.
Gradient-Variation Online Learning under Generalized Smoothness
Authors: Yan-Feng Xie, Peng Zhao, Zhi-Hua Zhou
Date: 2024-08-17 00:00:00
Tasks: Stochastic Optimization

Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic optimization, hence receiving increased attention. Existing results often require the smoothness condition by imposing a fixed bound on gradient Lipschitzness, which may be unrealistic in practice. Recent efforts in neural network optimization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. In this paper, we systematically study gradient-variation online learning under generalized smoothness. We extend the classic optimistic mirror descent algorithm to derive gradient-variation regret by analyzing stability over the optimization trajectory and exploiting smoothness locally. Then, we explore universal online learning, designing a single algorithm with the optimal gradient-variation regrets for convex and strongly convex functions simultaneously, without requiring prior knowledge of curvature. This algorithm adopts a two-layer structure with a meta-algorithm running over a group of base-learners. To ensure favorable guarantees, we design a new Lipschitz-adaptive meta-algorithm, capable of handling potentially unbounded gradients while ensuring a second-order bound to effectively ensemble the base-learners. Finally, we provide the applications for fast-rate convergence in games and stochastic extended adversarial optimization.
Enhancing Community Detection in Networks: A Comparative Analysis of Local Metrics and Hierarchical Algorithms
Authors: Julio-Omar Palacio-Niño, Fernando Berzal
Date: 2024-08-17 00:00:00
Tasks: Community Detection

The analysis and detection of communities in network structures are becoming increasingly relevant for understanding social behavior. One of the principal challenges in this field is the complexity of existing algorithms. The Girvan-Newman algorithm, which uses the betweenness metric as a measure of node similarity, is one of the most representative algorithms in this area. This study employs the same method to evaluate the relevance of using local similarity metrics for community detection. A series of local metrics were tested on a set of networks constructed using the Girvan-Newman basic algorithm. The efficacy of these metrics was evaluated by applying the base algorithm to several real networks with varying community sizes, using modularity and NMI. The results indicate that approaches based on local similarity metrics have significant potential for community detection.
Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certification
Authors: Robert Reed, Luca Laurenti, Morteza Lahijanian
Date: 2024-08-16 00:00:00
Tasks: GPR

Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they require rigorous error quantification, and (ii) the noise is often bounded and non-Gaussian due to, e.g., physical constraints. While error bounds for applying GPR in the presence of non-Gaussian noise exist, they tend to be overly restrictive and conservative in practice. In this paper, we provide novel error bounds for GPR under bounded support noise. Specifically, by relying on concentration inequalities and assuming that the latent function has low complexity in the reproducing kernel Hilbert space (RKHS) corresponding to the GP kernel, we derive both probabilistic and deterministic bounds on the error of the GPR. We show that these errors are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels, i.e., Deep Kernel Learning (DKL). Furthermore, motivated by applications in safety-critical domains, we illustrate how these bounds can be combined with stochastic barrier functions to successfully quantify the safety probability of an unknown dynamical system from finite data. We validate the efficacy of our approach through several benchmarks and comparisons against existing bounds. The results show that our bounds are consistently smaller, and that DKLs can produce error bounds tighter than sample noise, significantly improving the safety probability of control systems.
AdaRank: Disagreement Based Module Rank Prediction for Low-rank Adaptation
Authors: Yihe Dong
Date: 2024-08-16 00:00:00
Tasks: Transfer Learning

With the rise of language and multimodal models of ever-increasing size, pretraining a general-purpose foundational model and adapting it to downstream tasks has become common practice. To this end, adaptation efficiency can be a critical bottleneck given the large model sizes, hence efficient finetuning methods such as LoRA have become prevalent. However, LoRA is typically applied with the same rank across all model layers, despite mounting evidence from transfer learning literature that during finetuning, later layers diverge more from pretrained weights. Inspired by the theory and observations around feature learning and module criticality, we develop a simple model disagreement based technique to predict the rank of a given module relative to the other modules. Empirically, AdaRank generalizes notably better on unseen data than using uniform ranks with the same number of parameters. Compared to prior work, AdaRank has the unique advantage of leaving the pretraining and adaptation stages completely intact: no need for any additional objectives or regularizers, which can hinder adaptation accuracy and performance. Our code is publicly available at https://github.com/google-research/google-research/tree/master/adaptive_low_rank.
An optimal pairwise merge algorithm improves the quality and consistency of nonnegative matrix factorization
Authors: Youdong Guo, Timothy E. Holy
Date: 2024-08-16 00:00:00

Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value but differing feature parametrizations. Here we show that some of these weaknesses may be mitigated by performing NMF in a higher-dimensional feature space and then iteratively combining components with an analytically-solvable pairwise merge strategy. Experimental results demonstrate our method helps non-ideal NMF solutions escape to better local optima and achieve greater consistency of the solutions. Despite these extra steps, our approach exhibits similar computational performance to established methods by reducing the occurrence of "plateau phenomenon" near saddle points. Moreover, the results also illustrate that our method is compatible with different NMF algorithms. Thus, this can be recommended as a preferred approach for most applications of NMF.
Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
Authors: Unique Subedi, Ambuj Tewari
Date: 2024-08-16 00:00:00
Tasks: Operator learning

We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main errors that occur during the learning process: statistical error due to finite sample size, truncation error from finite rank approximation of the operator, and discretization error from handling functional data on a finite grid of domain points. Finally, we analyze a Discrete Fourier Transform (DFT) based least squares estimator, establishing both upper and lower bounds on the aforementioned errors.
A Confidence Interval for the $\ell_2$ Expected Calibration Error
Authors: Yan Sun, Pratik Chaudhari, Ian J. Barnett, Edgar Dobriban
Date: 2024-08-16 00:00:00
Tasks: valid

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the $\ell_2$ Expected Calibration Error (ECE). We consider top-1-to-$k$ calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.
Model-based RL as a Minimalist Approach to Horizon-Free and Second-Order Bounds
Authors: Zhiyong Wang, Dongruo Zhou, John C. S. Lui, Wen Sun
Date: 2024-08-16 00:00:00
Tasks: Model-based Reinforcement Learning, Offline RL, Reinforcement Learning (RL)

Learning a transition model via Maximum Likelihood Estimation (MLE) followed by planning inside the learned model is perhaps the most standard and simplest Model-based Reinforcement Learning (RL) framework. In this work, we show that such a simple Model-based RL scheme, when equipped with optimistic and pessimistic planning procedures, achieves strong regret and sample complexity bounds in online and offline RL settings. Particularly, we demonstrate that under the conditions where the trajectory-wise reward is normalized between zero and one and the transition is time-homogenous, it achieves nearly horizon-free and second-order bounds. Nearly horizon-free means that our bounds have no polynomial dependence on the horizon of the Markov Decision Process. A second-order bound is a type of instance-dependent bound that scales with respect to the variances of the returns of the policies which can be small when the system is nearly deterministic and (or) the optimal policy has small values. We highlight that our algorithms are simple, fairly standard, and indeed have been extensively studied in the RL literature: they learn a model via MLE, build a version space around the MLE solution, and perform optimistic or pessimistic planning depending on whether operating in the online or offline mode. These algorithms do not rely on additional specialized algorithmic designs such as learning variances and performing variance-weighted learning and thus can easily leverage non-linear function approximations. The simplicity of the algorithms also implies that our horizon-free and second-order regret analysis is actually standard and mainly follows the general framework of optimism/pessimism in the face of uncertainty.
Electroencephalogram Emotion Recognition via AUC Maximization
Authors: Minheng Xiao
Date: 2024-08-16 00:00:00
Tasks: Emotion Recognition

Imbalanced datasets pose significant challenges in areas including neuroscience, cognitive science, and medical diagnostics, where accurately detecting minority classes is essential for robust model performance. This study addresses the issue of class imbalance, using the `Liking' label in the DEAP dataset as an example. Such imbalances are often overlooked by prior research, which typically focuses on the more balanced arousal and valence labels and predominantly uses accuracy metrics to measure model performance. To tackle this issue, we adopt numerical optimization techniques aimed at maximizing the area under the curve (AUC), thus enhancing the detection of underrepresented classes. Our approach, which begins with a linear classifier, is compared against traditional linear classifiers, including logistic regression and support vector machines (SVM). Our method significantly outperforms these models, increasing recall from 41.6\% to 79.7\% and improving the F1-score from 0.506 to 0.632. These results highlight the efficacy of AUC maximization via numerical optimization in managing imbalanced datasets, providing an effective solution for enhancing predictive accuracy in detecting minority but crucial classes in out-of-sample datasets.
Information-Theoretic Progress Measures reveal Grokking is an Emergent Phase Transition
Authors: Kenzo Clauw, Sebastiano Stramaglia, Daniele Marinazzo
Date: 2024-08-16 00:00:00
Tasks: Attribute, Memorization

This paper studies emergent phenomena in neural networks by focusing on grokking where models suddenly generalize after delayed memorization. To understand this phase transition, we utilize higher-order mutual information to analyze the collective behavior (synergy) and shared properties (redundancy) between neurons during training. We identify distinct phases before grokking allowing us to anticipate when it occurs. We attribute grokking to an emergent phase transition caused by the synergistic interactions between neurons as a whole. We show that weight decay and weight initialization can enhance the emergent phase.