pwc-archive/papers-with-abstracts huggingface dataset:
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks
Authors: Suchuan Dong, Yiran Wang
Date: 2022-10-09 00:00:00

We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs to inverse problems. We develop three algorithms for training the neural network to solve the inverse PDE problem. The first algorithm (NLLSQ) determines the inverse parameters and the trainable network parameters all together by the nonlinear least squares method with perturbations (NLLSQ-perturb). The second algorithm (VarPro-F1) eliminates the inverse parameters from the overall problem by variable projection to attain a reduced problem about the trainable network parameters only. It solves the reduced problem first by the NLLSQ-perturb algorithm for the trainable network parameters, and then computes the inverse parameters by the linear least squares method. The third algorithm (VarPro-F2) eliminates the trainable network parameters from the overall problem by variable projection to attain a reduced problem about the inverse parameters only. It solves the reduced problem for the inverse parameters first, and then computes the trainable network parameters afterwards. VarPro-F1 and VarPro-F2 are reciprocal to each other in a sense. The presented method produces accurate results for inverse PDE problems, as shown by the numerical examples herein. For noise-free data, the errors for the inverse parameters and the solution field decrease exponentially as the number of collocation points or the number of trainable network parameters increases, and can reach a level close to the machine accuracy. For noisy data, the accuracy degrades compared with the case of noise-free data, but the method remains quite accurate. The presented method has been compared with the physics-informed neural network method.
Quantifying Social Biases Using Templates is Unreliable
Authors: Preethi Seshadri, Pouya Pezeshkpour, Sameer Singh
Date: 2022-10-09 00:00:00
Tasks: Attribute, Benchmarking, Diagnostic, Fairness

Recently, there has been an increase in efforts to understand how large language models (LLMs) propagate and amplify social biases. Several works have utilized templates for fairness evaluation, which allow researchers to quantify social biases in the absence of test sets with protected attribute labels. While template evaluation can be a convenient and helpful diagnostic tool to understand model deficiencies, it often uses a simplistic and limited set of templates. In this paper, we study whether bias measurements are sensitive to the choice of templates used for benchmarking. Specifically, we investigate the instability of bias measurements by manually modifying templates proposed in previous works in a semantically-preserving manner and measuring bias across these modifications. We find that bias values and resulting conclusions vary considerably across template modifications on four tasks, ranging from an 81% reduction (NLI) to a 162% increase (MLM) in (task-specific) bias measurements. Our results indicate that quantifying fairness in LLMs, as done in current practice, can be brittle and needs to be approached with more care and caution.
QuTE: decentralized multiple testing on sensor networks with false discovery rate control
Authors: Aaditya Ramdas, Jianbo Chen, Martin J. Wainwright, Michael I. Jordan
Date: 2022-10-09 00:00:00

This paper designs methods for decentralized multiple hypothesis testing on graphs that are equipped with provable guarantees on the false discovery rate (FDR). We consider the setting where distinct agents reside on the nodes of an undirected graph, and each agent possesses p-values corresponding to one or more hypotheses local to its node. Each agent must individually decide whether to reject one or more of its local hypotheses by only communicating with its neighbors, with the joint aim that the global FDR over the entire graph must be controlled at a predefined level. We propose a simple decentralized family of Query-Test-Exchange (QuTE) algorithms and prove that they can control FDR under independence or positive dependence of the p-values. Our algorithm reduces to the Benjamini-Hochberg (BH) algorithm when after graph-diameter rounds of communication, and to the Bonferroni procedure when no communication has occurred or the graph is empty. To avoid communicating real-valued p-values, we develop a quantized BH procedure, and extend it to a quantized QuTE procedure. QuTE works seamlessly in streaming data settings, where anytime-valid p-values may be continually updated at each node. Last, QuTE is robust to arbitrary dropping of packets, or a graph that changes at every step, making it particularly suitable to mobile sensor networks involving drones or other multi-agent systems. We study the power of our procedure using a simulation suite of different levels of connectivity and communication on a variety of graph structures, and also provide an illustrative real-world example.
Deep Learning Inference Frameworks Benchmark
Authors: Pierrick Pochelu
Date: 2022-10-09 00:00:00
Tasks: CPU, Deep Learning, GPU

Deep learning (DL) has been widely adopted those last years but they are computing-intensive method. Therefore, scientists proposed diverse optimization to accelerate their predictions for end-user applications. However, no single inference framework currently dominates in terms of performance. This paper takes a holistic approach to conduct an empirical comparison and analysis of four representative DL inference frameworks. First, given a selection of CPU-GPU configurations, we show that for a specific DL framework, different configurations of its settings may have a significant impact on the prediction speed, memory, and computing power. Second, to the best of our knowledge, this study is the first to identify the opportunities for accelerating the ensemble of co-localized models in the same GPU. This measurement study provides an in-depth empirical comparison and analysis of four representative DL frameworks and offers practical guidance for service providers to deploy and deliver DL predictions.
Dissecting adaptive methods in GANs
Authors: Samy Jelassi, David Dobre, Arthur Mensch, Yuanzhi Li, Gauthier Gidel
Date: 2022-10-09 00:00:00

Adaptive methods are a crucial component widely used for training generative adversarial networks (GANs). While there has been some work to pinpoint the "marginal value of adaptive methods" in standard tasks, it remains unclear why they are still critical for GAN training. In this paper, we formally study how adaptive methods help train GANs; inspired by the grafting method proposed in arXiv:2002.11803 [cs.LG], we separate the magnitude and direction components of the Adam updates, and graft them to the direction and magnitude of SGDA updates respectively. By considering an update rule with the magnitude of the Adam update and the normalized direction of SGD, we empirically show that the adaptive magnitude of Adam is key for GAN training. This motivates us to have a closer look at the class of normalized stochastic gradient descent ascent (nSGDA) methods in the context of GAN training. We propose a synthetic theoretical framework to compare the performance of nSGDA and SGDA for GAN training with neural networks. We prove that in that setting, GANs trained with nSGDA recover all the modes of the true distribution, whereas the same networks trained with SGDA (and any learning rate configuration) suffer from mode collapse. The critical insight in our analysis is that normalizing the gradients forces the discriminator and generator to be updated at the same pace. We also experimentally show that for several datasets, Adam's performance can be recovered with nSGDA methods.
Prediction intervals for neural network models using weighted asymmetric loss functions
Authors: Milo Grillo, Yunpeng Han, Agnieszka Werpachowska
Date: 2022-10-09 00:00:00
Tasks: Prediction Intervals

We propose a simple and efficient approach to generate a prediction intervals (PI) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PI, with the weights determined by its coverage probability. We provide a concise mathematical proof of the method, show how it can be extended to derive PIs for parametrised functions and discuss its effectiveness when training deep neural networks. The presented tests of the method on a real-world forecasting task using a neural network-based model show that it can produce reliable PIs in complex machine learning scenarios.
A Spectral Approach to Item Response Theory
Authors: Duc Nguyen, Anderson Zhang
Date: 2022-10-09 00:00:00
Tasks: Recommendation Systems

The Rasch model is one of the most fundamental models in \emph{item response theory} and has wide-ranging applications from education testing to recommendation systems. In a universe with $n$ users and $m$ items, the Rasch model assumes that the binary response $X_{li} \in \{0,1\}$ of a user $l$ with parameter $\theta^*_l$ to an item $i$ with parameter $\beta^*_i$ (e.g., a user likes a movie, a student correctly solves a problem) is distributed as $\Pr(X_{li}=1) = 1/(1 + \exp{-(\theta^*_l - \beta^*_i)})$. In this paper, we propose a \emph{new item estimation} algorithm for this celebrated model (i.e., to estimate $\beta^*$). The core of our algorithm is the computation of the stationary distribution of a Markov chain defined on an item-item graph. We complement our algorithmic contributions with finite-sample error guarantees, the first of their kind in the literature, showing that our algorithm is consistent and enjoys favorable optimality properties. We discuss practical modifications to accelerate and robustify the algorithm that practitioners can adopt. Experiments on synthetic and real-life datasets, ranging from small education testing datasets to large recommendation systems datasets show that our algorithm is scalable, accurate, and competitive with the most commonly used methods in the literature.
An Instance Selection Algorithm for Big Data in High imbalanced datasets based on LSH
Authors: Germán E. Melo-Acosta, Freddy Duitama-Muñoz, Julián D. Arias-Londoño
Date: 2022-10-09 00:00:00

Training of Machine Learning (ML) models in real contexts often deals with big data sets and high-class imbalance samples where the class of interest is unrepresented (minority class). Practical solutions using classical ML models address the problem of large data sets using parallel/distributed implementations of training algorithms, approximate model-based solutions, or applying instance selection (IS) algorithms to eliminate redundant information. However, the combined problem of big and high imbalanced datasets has been less addressed. This work proposes three new methods for IS to be able to deal with large and imbalanced data sets. The proposed methods use Locality Sensitive Hashing (LSH) as a base clustering technique, and then three different sampling methods are applied on top of the clusters (or buckets) generated by LSH. The algorithms were developed in the Apache Spark framework, guaranteeing their scalability. The experiments carried out in three different datasets suggest that the proposed IS methods can improve the performance of a base ML model between 5% and 19% in terms of the geometric mean.
Data-driven framework for input/output lookup tables reduction: Application to hypersonic flows in chemical non-equilibrium
Authors: Clément Scherding, Georgios Rigas, Denis Sipp, Peter J. Schmid, Taraneh Sayadi
Date: 2022-10-09 00:00:00

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.
Coresets for Wasserstein Distributionally Robust Optimization Problems
Authors: Ruomin Huang, Jiawei Huang, Wenjie Liu, Hu Ding
Date: 2022-10-09 00:00:00

Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \textsf{WDRO} training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \textsf{WDRO}s is still quite limited, to the best of our knowledge. \textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\epsilon$-coreset for the general \textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \textsf{WDRO} problems in the experiments.
A Concentration Bound for Distributed Stochastic Approximation
Authors: Harsh Dolhare, Vivek Borkar
Date: 2022-10-09 00:00:00

We revisit the classical model of Tsitsiklis, Bertsekas and Athans for distributed stochastic approximation with consensus. The main result is an analysis of this scheme using the ODE approach to stochastic approximation, leading to a high probability bound for the tracking error between suitably interpolated iterates and the limiting differential equation. Several future directions will also be highlighted.
Coresets for Relational Data and The Applications
Authors: Jiaxiang Chen, Qingyuan Yang, Ruomin Huang, Hu Ding
Date: 2022-10-09 00:00:00
Tasks: Relational Reasoning

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques assume that the input data set is available to process explicitly. However, this assumption may not hold in real-world scenarios. In this paper, we consider the problem of coresets construction over relational data. Namely, the data is decoupled into several relational tables, and it could be very expensive to directly materialize the data matrix by joining the tables. We propose a novel approach called ``aggregation tree with pseudo-cube'' that can build a coreset from bottom to up. Moreover, our approach can neatly circumvent several troublesome issues of relational learning problems [Khamis et al., PODS 2019]. Under some mild assumptions, we show that our coreset approach can be applied for the machine learning tasks, such as clustering, logistic regression and SVM.
Residual Neural Networks for the Prediction of Planetary Collision Outcomes
Authors: Philip M. Winter, Christoph Burger, Sebastian Lehner, Johannes Kofler, Thomas I. Maindl, Christoph M. Schäfer
Date: 2022-10-09 00:00:00
Tasks: Out-of-Distribution Generalization

Fast and accurate treatment of collisions in the context of modern N-body planet formation simulations remains a challenging task due to inherently complex collision processes. We aim to tackle this problem with machine learning (ML), in particular via residual neural networks. Our model is motivated by the underlying physical processes of the data-generating process and allows for flexible prediction of post-collision states. We demonstrate that our model outperforms commonly used collision handling methods such as perfect inelastic merging and feed-forward neural networks in both prediction accuracy and out-of-distribution generalization. Our model outperforms the current state of the art in 20/24 experiments. We provide a dataset that consists of 10164 Smooth Particle Hydrodynamics (SPH) simulations of pairwise planetary collisions. The dataset is specifically suited for ML research to improve computational aspects for collision treatment and for studying planetary collisions in general. We formulate the ML task as a multi-task regression problem, allowing simple, yet efficient training of ML models for collision treatment in an end-to-end manner. Our models can be easily integrated into existing N-body frameworks and can be used within our chosen parameter space of initial conditions, i.e. where similar-sized collisions during late-stage terrestrial planet formation typically occur.
Fine-Tuning Pre-trained Transformers into Decaying Fast Weights
Authors: Huanru Henry Mao
Date: 2022-10-09 00:00:00
Tasks: GPU

Autoregressive Transformers are strong language models but incur O(T) complexity during per-token generation due to the self-attention mechanism. Recent work proposes kernel-based methods to approximate causal self-attention by replacing it with recurrent formulations with various update rules and feature maps to achieve O(1) time and memory complexity. We explore these approaches and find that they are unnecessarily complex, and propose a simple alternative - decaying fast weights - that runs fast on GPU, outperforms prior methods, and retains 99% of attention's performance for GPT-2. We also show competitive performance on WikiText-103 against more complex attention substitutes.
Learning on the Edge: Online Learning with Stochastic Feedback Graphs
Authors: Emmanuel Esposito, Federico Fusco, Dirk van der Hoeven, Nicolò Cesa-Bianchi
Date: 2022-10-09 00:00:00
Tasks: Decision Making, Sequential Decision Making

The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution similar to the classical Erd\H{o}s-R\'enyi model. Specifically, in each round every edge in the graph is either realized or not with a distinct probability for each edge. We prove nearly optimal regret bounds of order $\min\bigl\{\min_{\varepsilon} \sqrt{(\alpha_\varepsilon/\varepsilon) T},\, \min_{\varepsilon} (\delta_\varepsilon/\varepsilon)^{1/3} T^{2/3}\bigr\}$ (ignoring logarithmic factors), where $\alpha_{\varepsilon}$ and $\delta_{\varepsilon}$ are graph-theoretic quantities measured on the support of the stochastic feedback graph $\mathcal{G}$ with edge probabilities thresholded at $\varepsilon$. Our result, which holds without any preliminary knowledge about $\mathcal{G}$, requires the learner to observe only the realized out-neighborhood of the chosen action. When the learner is allowed to observe the realization of the entire graph (but only the losses in the out-neighborhood of the chosen action), we derive a more efficient algorithm featuring a dependence on weighted versions of the independence and weak domination numbers that exhibits improved bounds for some special cases.
Correlative Information Maximization Based Biologically Plausible Neural Networks for Correlated Source Separation
Authors: Bariscan Bozkurt, Ates Isfendiyaroglu, Cengiz Pehlevan, Alper T. Erdogan
Date: 2022-10-09 00:00:00

The brain effortlessly extracts latent causes of stimuli, but how it does this at the network level remains unknown. Most prior attempts at this problem proposed neural networks that implement independent component analysis which works under the limitation that latent causes are mutually independent. Here, we relax this limitation and propose a biologically plausible neural network that extracts correlated latent sources by exploiting information about their domains. To derive this network, we choose maximum correlative information transfer from inputs to outputs as the separation objective under the constraint that the outputs are restricted to their presumed sets. The online formulation of this optimization problem naturally leads to neural networks with local learning rules. Our framework incorporates infinitely many source domain choices and flexibly models complex latent structures. Choices of simplex or polytopic source domains result in networks with piecewise-linear activation functions. We provide numerical examples to demonstrate the superior correlated source separation capability for both synthetic and natural sources.
Predicting fluid-structure interaction with graph neural networks
Authors: Rui Gao, Rajeev K. Jaiman
Date: 2022-10-09 00:00:00
Tasks: Graph Neural Network

We present a rotation equivariant, quasi-monolithic graph neural network framework for the reduced-order modeling of fluid-structure interaction systems. With the aid of an arbitrary Lagrangian-Eulerian formulation, the system states are evolved temporally with two sub-networks. The movement of the mesh is reduced to the evolution of several coefficients via complex-valued proper orthogonal decomposition, and the prediction of these coefficients over time is handled by a single multi-layer perceptron. A finite element-inspired hypergraph neural network is employed to predict the evolution of the fluid state based on the state of the whole system. The structural state is implicitly modeled by the movement of the mesh on the solid-fluid interface; hence it makes the proposed framework quasi-monolithic. The effectiveness of the proposed framework is assessed on two prototypical fluid-structure systems, namely the flow around an elastically-mounted cylinder, and the flow around a hyperelastic plate attached to a fixed cylinder. The proposed framework tracks the interface description and provides stable and accurate system state predictions during roll-out for at least 2000 time steps, and even demonstrates some capability in self-correcting erroneous predictions. The proposed framework also enables direct calculation of the lift and drag forces using the predicted fluid and mesh states, in contrast to existing convolution-based architectures. The proposed reduced-order model via graph neural network has implications for the development of physics-based digital twins concerning moving boundaries and fluid-structure interactions.