pwc-archive/papers-with-abstracts huggingface dataset:
Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics
Authors: Artur P. Toshev, Jonas A. Erbesdobler, Nikolaus A. Adams, Johannes Brandstetter
Date: 2024-02-09 00:00:00

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving velocity field. Due to the particle-like nature of the simulation, graph neural networks (GNNs) have emerged as appealing and successful surrogates. However, the practical utility of such GNN-based simulators relies on their ability to faithfully model physics, providing accurate and stable predictions over long time horizons - which is a notoriously hard problem. In this work, we identify particle clustering originating from tensile instabilities as one of the primary pitfalls. Based on these insights, we enhance both training and rollout inference of state-of-the-art GNN-based simulators with varying components from standard SPH solvers, including pressure, viscous, and external force components. All Neural SPH-enhanced simulators achieve better performance than the baseline GNNs, often by orders of magnitude in terms of rollout error, allowing for significantly longer rollouts and significantly better physics modeling. Code available at https://github.com/tumaer/neuralsph.
Adaptive proximal gradient methods are universal without approximation
Authors: Konstantinos A. Oikonomidis, Emanuel Laude, Puya Latafat, Andreas Themelis, Panagiotis Patrinos
Date: 2024-02-09 00:00:00

We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere local H\"older gradient continuity, covering in particular continuously differentiable semi-algebraic functions. To mitigate the lack of local Lipschitz continuity, popular approaches revolve around $\varepsilon$-oracles and/or linesearch procedures. In contrast, we exploit plain H\"older inequalities not entailing any approximation, all while retaining the linesearch-free nature of adaptive schemes. Furthermore, we prove full sequence convergence without prior knowledge of local H\"older constants nor of the order of H\"older continuity. Numerical experiments make comparisons with baseline methods on diverse tasks from machine learning covering both the locally and the globally H\"older setting.
YAMLE: Yet Another Machine Learning Environment
Authors: Martin Ferianc, Miguel Rodrigues
Date: 2024-02-09 00:00:00

YAMLE: Yet Another Machine Learning Environment is an open-source framework that facilitates rapid prototyping and experimentation with machine learning (ML) models and methods. The key motivation is to reduce repetitive work when implementing new approaches and improve reproducibility in ML research. YAMLE includes a command-line interface and integrations with popular and well-maintained PyTorch-based libraries to streamline training, hyperparameter optimisation, and logging. The ambition for YAMLE is to grow into a shared ecosystem where researchers and practitioners can quickly build on and compare existing implementations. Find it at: https://github.com/martinferianc/yamle.
Value function interference and greedy action selection in value-based multi-objective reinforcement learning
Authors: Peter Vamplew, Cameron Foale, Richard Dazeley
Date: 2024-02-09 00:00:00
Tasks: Multi-Objective Reinforcement Learning, Q-Learning, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Multi-objective reinforcement learning (MORL) algorithms extend conventional reinforcement learning (RL) to the more general case of problems with multiple, conflicting objectives, represented by vector-valued rewards. Widely-used scalar RL methods such as Q-learning can be modified to handle multiple objectives by (1) learning vector-valued value functions, and (2) performing action selection using a scalarisation or ordering operator which reflects the user's utility with respect to the different objectives. However, as we demonstrate here, if the user's utility function maps widely varying vector-values to similar levels of utility, this can lead to interference in the value-function learned by the agent, leading to convergence to sub-optimal policies. This will be most prevalent in stochastic environments when optimising for the Expected Scalarised Return criterion, but we present a simple example showing that interference can also arise in deterministic environments. We demonstrate empirically that avoiding the use of random tie-breaking when identifying greedy actions can ameliorate, but not fully overcome, the problems caused by value function interference.
N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network
Authors: Thuan Pham, Xingpeng Li
Date: 2024-02-09 00:00:00
Tasks: Graph Neural Network

Optimal power flow (OPF) is used to perform generation redispatch in power system real-time operations. N-1 OPF can ensure safe grid operations under diverse contingency scenarios. For large and intricate power networks with numerous variables and constraints, achieving an optimal solution for real-time N-1 OPF necessitates substantial computational resources. To mitigate this challenge, machine learning (ML) is introduced as an additional tool for predicting congested or heavily loaded lines dynamically. In this paper, an advanced ML model known as the augmented hierarchical graph neural network (AHGNN) was proposed to predict critical congested lines and create N-1 reduced OPF (N-1 ROPF). The proposed AHGNN-enabled N-1 ROPF can result in a remarkable reduction in computing time while retaining the solution quality. Several variations of GNN-based ML models are also implemented as benchmark to demonstrate effectiveness of the proposed AHGNN approach. Case studies prove the proposed AHGNN and the associated N-1 ROPF are highly effective in reducing computation time while preserving solution quality, highlighting the promising potential of ML, particularly GNN in enhancing power system operations.
Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
Authors: Nguyen Anh Minh, Le Dung Muu, Tran Ngoc Thang
Date: 2024-02-09 00:00:00
Tasks: Multi-Task Learning

We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction up until a predetermined condition is met. It can be specifically applied to offer an innovative multi-gradient projection method for unbounded constrained optimization issues. Preliminary findings from a few computational examples confirm the accuracy of the strategy. We apply the proposed technique to some multi-task learning experiments to show its efficacy for large-scale challenges.
The boundary of neural network trainability is fractal
Authors: Jascha Sohl-Dickstein
Date: 2024-02-09 00:00:00

Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains bounded. Neural network training similarly involves iterating an update function (e.g. repeated steps of gradient descent), can result in convergent or divergent behavior, and can be extremely sensitive to small changes in hyperparameters. Motivated by these similarities, we experimentally examine the boundary between neural network hyperparameters that lead to stable and divergent training. We find that this boundary is fractal over more than ten decades of scale in all tested configurations.
SMC Is All You Need: Parallel Strong Scaling
Authors: Xinzhu Liang, Joseph M. Lukens, Sanjaya Lohani, Brian T. Kirby, Thomas A. Searles, Kody J. H. Law
Date: 2024-02-09 00:00:00
Tasks: All, Bayesian Inference

The Bayesian posterior distribution can only be evaluated up-to a constant of proportionality, which makes simulation and consistent estimation challenging. Classical consistent Bayesian methods such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have unbounded time complexity requirements. We develop a fully parallel sequential Monte Carlo (pSMC) method which provably delivers parallel strong scaling, i.e. the time complexity (and per-node memory) remains bounded if the number of asynchronous processes is allowed to grow. More precisely, the pSMC has a theoretical convergence rate of Mean Square Error (MSE)$ = O(1/NP)$, where $N$ denotes the number of communicating samples in each processor and $P$ denotes the number of processors. In particular, for suitably-large problem-dependent $N$, as $P \rightarrow \infty$ the method converges to infinitesimal accuracy MSE$=O(\varepsilon^2)$ with a fixed finite time-complexity Cost$=O(1)$ and with no efficiency leakage, i.e. computational complexity Cost$=O(\varepsilon^{-2})$. A number of Bayesian inference problems are taken into consideration to compare the pSMC and MCMC methods.
Pushing Boundaries: Mixup's Influence on Neural Collapse
Authors: Quinn Fisher, Haoming Meng, Vardan Papyan
Date: 2024-02-09 00:00:00
Tasks: Data Augmentation

Mixup is a data augmentation strategy that employs convex combinations of training instances and their respective labels to augment the robustness and calibration of deep neural networks. Despite its widespread adoption, the nuanced mechanisms that underpin its success are not entirely understood. The observed phenomenon of Neural Collapse, where the last-layer activations and classifier of deep networks converge to a simplex equiangular tight frame (ETF), provides a compelling motivation to explore whether mixup induces alternative geometric configurations and whether those could explain its success. In this study, we delve into the last-layer activations of training data for deep networks subjected to mixup, aiming to uncover insights into its operational efficacy. Our investigation, spanning various architectures and dataset pairs, reveals that mixup's last-layer activations predominantly converge to a distinctive configuration different than one might expect. In this configuration, activations from mixed-up examples of identical classes align with the classifier, while those from different classes delineate channels along the decision boundary. Moreover, activations in earlier layers exhibit patterns, as if trained with manifold mixup. These findings are unexpected, as mixed-up features are not simple convex combinations of feature class means (as one might get, for example, by training mixup with the mean squared error loss). By analyzing this distinctive geometric configuration, we elucidate the mechanisms by which mixup enhances model calibration. To further validate our empirical observations, we conduct a theoretical analysis under the assumption of an unconstrained features model, utilizing the mixup loss. Through this, we characterize and derive the optimal last-layer features under the assumption that the classifier forms a simplex ETF.
Wasserstein proximal operators describe score-based generative models and resolve memorization
Authors: Benjamin J. Zhang, Siting Liu, Wuchen Li, Markos A. Katsoulakis, Stanley J. Osher
Date: 2024-02-09 00:00:00
Tasks: Inductive Bias, Memorization

We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstrate that, via mean-field games (MFGs), the WPO formulation reveals mathematical structure that describes the inductive bias of diffusion and score-based models. In particular, MFGs yield optimality conditions in the form of a pair of coupled partial differential equations: a forward-controlled Fokker-Planck (FP) equation, and a backward Hamilton-Jacobi-Bellman (HJB) equation. Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation. Second, with the mathematical structure at hand, we present an interpretable kernel-based model for the score function which dramatically improves the performance of SGMs in terms of training samples and training time. In addition, the WPO-informed kernel model is explicitly constructed to avoid the recently studied memorization effects of score-based generative models. The mathematical form of the new kernel-based models in combination with the use of the terminal condition of the MFG reveals new explanations for the manifold learning and generalization properties of SGMs, and provides a resolution to their memorization effects. Finally, our mathematically informed, interpretable kernel-based model suggests new scalable bespoke neural network architectures for high-dimensional applications.
Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?
Authors: Maohao Shen, J. Jon Ryu, Soumya Ghosh, Yuheng Bu, Prasanna Sattigeri, Subhro Das, Gregory W. Wornell
Date: 2024-02-09 00:00:00
Tasks: Deep Learning, Out-of-Distribution Detection, Uncertainty Quantification, Variational Inference

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called \emph{evidential deep learning} (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their perceived strong empirical performance on downstream tasks, a line of recent studies by Bengs et al. identify limitations of the existing methods to conclude their learned epistemic uncertainties are unreliable, e.g., in that they are non-vanishing even with infinite data. Building on and sharpening such analysis, we 1) provide a sharper understanding of the asymptotic behavior of a wide class of EDL methods by unifying various objective functions; 2) reveal that the EDL methods can be better interpreted as an out-of-distribution detection algorithm based on energy-based-models; and 3) conduct extensive ablation studies to better assess their empirical effectiveness with real-world datasets. Through all these analyses, we conclude that even when EDL methods are empirically effective on downstream tasks, this occurs despite their poor uncertainty quantification capabilities. Our investigation suggests that incorporating model uncertainty can help EDL methods faithfully quantify uncertainties and further improve performance on representative downstream tasks, albeit at the cost of additional computational complexity.
POTEC: Off-Policy Learning for Large Action Spaces via Two-Stage Policy Decomposition
Authors: Yuta Saito, Jihan Yao, Thorsten Joachims
Date: 2024-02-09 00:00:00
Tasks: regression

We study off-policy learning (OPL) of contextual bandit policies in large discrete action spaces where existing methods -- most of which rely crucially on reward-regression models or importance-weighted policy gradients -- fail due to excessive bias or variance. To overcome these issues in OPL, we propose a novel two-stage algorithm, called Policy Optimization via Two-Stage Policy Decomposition (POTEC). It leverages clustering in the action space and learns two different policies via policy- and regression-based approaches, respectively. In particular, we derive a novel low-variance gradient estimator that enables to learn a first-stage policy for cluster selection efficiently via a policy-based approach. To select a specific action within the cluster sampled by the first-stage policy, POTEC uses a second-stage policy derived from a regression-based approach within each cluster. We show that a local correctness condition, which only requires that the regression model preserves the relative expected reward differences of the actions within each cluster, ensures that our policy-gradient estimator is unbiased and the second-stage policy is optimal. We also show that POTEC provides a strict generalization of policy- and regression-based approaches and their associated assumptions. Comprehensive experiments demonstrate that POTEC provides substantial improvements in OPL effectiveness particularly in large and structured action spaces.
On the Privacy of Selection Mechanisms with Gaussian Noise
Authors: Jonathan Lebensold, Doina Precup, Borja Balle
Date: 2024-02-09 00:00:00

Report Noisy Max and Above Threshold are two classical differentially private (DP) selection mechanisms. Their output is obtained by adding noise to a sequence of low-sensitivity queries and reporting the identity of the query whose (noisy) answer satisfies a certain condition. Pure DP guarantees for these mechanisms are easy to obtain when Laplace noise is added to the queries. On the other hand, when instantiated using Gaussian noise, standard analyses only yield approximate DP guarantees despite the fact that the outputs of these mechanisms lie in a discrete space. In this work, we revisit the analysis of Report Noisy Max and Above Threshold with Gaussian noise and show that, under the additional assumption that the underlying queries are bounded, it is possible to provide pure ex-ante DP bounds for Report Noisy Max and pure ex-post DP bounds for Above Threshold. The resulting bounds are tight and depend on closed-form expressions that can be numerically evaluated using standard methods. Empirically we find these lead to tighter privacy accounting in the high privacy, low data regime. Further, we propose a simple privacy filter for composing pure ex-post DP guarantees, and use it to derive a fully adaptive Gaussian Sparse Vector Technique mechanism. Finally, we provide experiments on mobility and energy consumption datasets demonstrating that our Sparse Vector Technique is practically competitive with previous approaches and requires less hyper-parameter tuning.
Jointly Learning Representations for Map Entities via Heterogeneous Graph Contrastive Learning
Authors: Jiawei Jiang, Yifan Yang, Jingyuan Wang, Junjie Wu
Date: 2024-02-09 00:00:00
Tasks: Contrastive Learning, Representation Learning

The electronic map plays a crucial role in geographic information systems, serving various urban managerial scenarios and daily life services. Developing effective Map Entity Representation Learning (MERL) methods is crucial to extracting embedding information from electronic maps and converting map entities into representation vectors for downstream applications. However, existing MERL methods typically focus on one specific category of map entities, such as POIs, road segments, or land parcels, which is insufficient for real-world diverse map-based applications and might lose latent structural and semantic information interacting between entities of different types. Moreover, using representations generated by separate models for different map entities can introduce inconsistencies. Motivated by this, we propose a novel method named HOME-GCL for learning representations of multiple categories of map entities. Our approach utilizes a heterogeneous map entity graph (HOME graph) that integrates both road segments and land parcels into a unified framework. A HOME encoder with parcel-segment joint feature encoding and heterogeneous graph transformer is then deliberately designed to convert segments and parcels into representation vectors. Moreover, we introduce two types of contrastive learning tasks, namely intra-entity and inter-entity tasks, to train the encoder in a self-supervised manner. Extensive experiments on three large-scale datasets covering road segment-based, land parcel-based, and trajectory-based tasks demonstrate the superiority of our approach. To the best of our knowledge, HOME-GCL is the first attempt to jointly learn representations for road segments and land parcels using a unified model.
CityFlowER: An Efficient and Realistic Traffic Simulator with Embedded Machine Learning Models
Authors: Longchao Da, Chen Chu, Weinan Zhang, Hua Wei
Date: 2024-02-09 00:00:00

Traffic simulation is an essential tool for transportation infrastructure planning, intelligent traffic control policy learning, and traffic flow analysis. Its effectiveness relies heavily on the realism of the simulators used. Traditional traffic simulators, such as SUMO and CityFlow, are often limited by their reliance on rule-based models with hyperparameters that oversimplify driving behaviors, resulting in unrealistic simulations. To enhance realism, some simulators have provided Application Programming Interfaces (APIs) to interact with Machine Learning (ML) models, which learn from observed data and offer more sophisticated driving behavior models. However, this approach faces challenges in scalability and time efficiency as vehicle numbers increase. Addressing these limitations, we introduce CityFlowER, an advancement over the existing CityFlow simulator, designed for efficient and realistic city-wide traffic simulation. CityFlowER innovatively pre-embeds ML models within the simulator, eliminating the need for external API interactions and enabling faster data computation. This approach allows for a blend of rule-based and ML behavior models for individual vehicles, offering unparalleled flexibility and efficiency, particularly in large-scale simulations. We provide detailed comparisons with existing simulators, implementation insights, and comprehensive experiments to demonstrate CityFlowER's superiority in terms of realism, efficiency, and adaptability.
Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams
Authors: Brian Cho, Kyra Gan, Nathan Kallus
Date: 2024-02-09 00:00:00
Tasks: Computational Efficiency

We propose a novel nonparametric sequential test for composite hypotheses for means of multiple data streams. Our proposed method, \emph{peeking with expectation-based averaged capital} (PEAK), builds upon the testing-by-betting framework and provides a non-asymptotic $\alpha$-level test across any stopping time. Our contributions are two-fold: (1) we propose a novel betting scheme and provide theoretical guarantees on type-I error control, power, and asymptotic growth rate/$e$-power in the setting of a single data stream; (2) we introduce PEAK, a generalization of this betting scheme to multiple streams, that (i) avoids using wasteful union bounds via averaging, (ii) is a test of power one under mild regularity conditions on the sampling scheme of the streams, and (iii) reduces computational overhead when applying the testing-as-betting approaches for pure-exploration bandit problems. We illustrate the practical benefits of PEAK using both synthetic and real-world HeartSteps datasets. Our experiments show that PEAK provides up to an 85\% reduction in the number of samples before stopping compared to existing stopping rules for pure-exploration bandit problems, and matches the performance of state-of-the-art sequential tests while improving upon computational complexity.