pwc-archive/papers-with-abstracts huggingface dataset:
Deep Learning of Dynamic Subsurface Flow via Theory-guided Generative Adversarial Network
Authors: Tianhao He, Dongxiao Zhang
Date: 2020-06-02 00:00:00
Tasks: Generative Adversarial Network, Transfer Learning

Generative adversarial network (GAN) has been shown to be useful in various applications, such as image recognition, text processing and scientific computing, due its strong ability to learn complex data distributions. In this study, a theory-guided generative adversarial network (TgGAN) is proposed to solve dynamic partial differential equations (PDEs). Different from standard GANs, the training term is no longer the true data and the generated data, but rather their residuals. In addition, such theories as governing equations, other physical constraints and engineering controls, are encoded into the loss function of the generator to ensure that the prediction does not only honor the training data, but also obey these theories. TgGAN is proposed for dynamic subsurface flow with heterogeneous model parameters, and the data at each time step are treated as a two-dimensional image. In this study, several numerical cases are introduced to test the performance of the TgGAN. Predicting the future response, label-free learning and learning from noisy data can be realized easily by the TgGAN model. The effects of the number of training data and the collocation points are also discussed. In order to improve the efficiency of TgGAN, the transfer learning algorithm is also employed. Numerical results demonstrate that the TgGAN model is robust and reliable for deep learning of dynamic PDEs.
LALR: Theoretical and Experimental validation of Lipschitz Adaptive Learning Rate in Regression and Neural Networks
Authors: Snehanshu Saha, Tejas Prashanth, Suraj Aralihalli, Sumedh Basarkod, T. S. B Sudarshan, Soma S. Dhavala
Date: 2020-05-19 00:00:00
Tasks: regression

We propose a theoretical framework for an adaptive learning rate policy for the Mean Absolute Error loss function and Quantile loss function and evaluate its effectiveness for regression tasks. The framework is based on the theory of Lipschitz continuity, specifically utilizing the relationship between learning rate and Lipschitz constant of the loss function. Based on experimentation, we have found that the adaptive learning rate policy enables up to 20x faster convergence compared to a constant learning rate policy.
Fast Deep Mixtures of Gaussian Process Experts
Authors: Clement Etienam, Kody Law, Sara Wade, Vitaly Zankin
Date: 2020-06-11 00:00:00
Tasks: Gaussian Processes, Mixture-of-Experts, Uncertainty Quantification

Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs. Sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models, and in this article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). Furthermore, a fast one pass algorithm called Cluster-Classify-Regress (CCR) is leveraged to approximate the maximum a posteriori (MAP) estimator extremely quickly. This powerful combination of model and algorithm together delivers a novel method which is flexible, robust, and extremely efficient. In particular, the method is able to outperform competing methods in terms of accuracy and uncertainty quantification. The cost is competitive on low-dimensional and small data sets, but is significantly lower for higher-dimensional and big data sets. Iteratively maximizing the distribution of experts given allocations and allocations given experts does not provide significant improvement, which indicates that the algorithm achieves a good approximation to the local MAP estimator very fast. This insight can be useful also in the context of other mixture of experts models.
Robust Gaussian Covariance Estimation in Nearly-Matrix Multiplication Time
Authors: Jerry Li, Guanghao Ye
Date: 2020-06-23 00:00:00
Proceeding: NeurIPS 2020 12

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples have been arbitrarily corrupted, output $\widehat{\Sigma}$ minimizing the total variation distance between $\mathcal{N}(\boldsymbol{0}, \Sigma)$ and $\mathcal{N}(\boldsymbol{0}, \widehat{\Sigma})$. This corresponds to learning $\Sigma$ in a natural affine-invariant variant of the Frobenius norm known as the \emph{Mahalanobis norm}. Previous work of Cheng et al demonstrated an algorithm that, given $N = \Omega (d^2 / \varepsilon^2)$ samples, achieved a near-optimal error of $O(\varepsilon \log 1 / \varepsilon)$, and moreover, their algorithm ran in time $\widetilde{O}(T(N, d) \log \kappa / \mathrm{poly} (\varepsilon))$, where $T(N, d)$ is the time it takes to multiply a $d \times N$ matrix by its transpose, and $\kappa$ is the condition number of $\Sigma$. When $\varepsilon$ is relatively small, their polynomial dependence on $1/\varepsilon$ in the runtime is prohibitively large. In this paper, we demonstrate a novel algorithm that achieves the same statistical guarantees, but which runs in time $\widetilde{O} (T(N, d) \log \kappa)$. In particular, our runtime has no dependence on $\varepsilon$. When $\Sigma$ is reasonably conditioned, our runtime matches that of the fastest algorithm for covariance estimation without outliers, up to poly-logarithmic factors, showing that we can get robustness essentially "for free."
A Note on Over-Smoothing for Graph Neural Networks
Authors: Chen Cai, Yusu Wang
Date: 2020-06-23 00:00:00
Tasks: Graph Neural Network

Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results \cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure "expressiveness" of embedding is conceptually clean; it leads to simpler proofs than \cite{oono2019graph} and can handle more non-linearities.
Classification Performance Metric for Imbalance Data Based on Recall and Selectivity Normalized in Class Labels
Authors: Robert Burduk
Date: 2020-06-23 00:00:00
Tasks: General Classification, Model Selection

In the classification of a class imbalance dataset, the performance measure used for the model selection and comparison to competing methods is a major issue. In order to overcome this problem several performance measures are defined and analyzed in several perspectives regarding in particular the imbalance ratio. There is still no clear indication which metric is universal and can be used for any skewed data problem. In this paper we introduced a new performance measure based on the harmonic mean of Recall and Selectivity normalized in class labels. This paper shows that the proposed performance measure has the right properties for the imbalanced dataset. In particular, in the space defined by the majority class examples and imbalance ratio it is less sensitive to changes in the majority class and more sensitive to changes in the minority class compared with other existing single-value performance measures. Additionally, the identity of the other performance measures has been proven analytically.
Safe Learning under Uncertain Objectives and Constraints
Authors: Mohammad Fereydounian, Zebang Shen, Aryan Mokhtari, Amin Karbasi, Hamed Hassani
Date: 2020-06-23 00:00:00

In this paper, we consider non-convex optimization problems under \textit{unknown} yet safety-critical constraints. Such problems naturally arise in a variety of domains including robotics, manufacturing, and medical procedures, where it is infeasible to know or identify all the constraints. Therefore, the parameter space should be explored in a conservative way to ensure that none of the constraints are violated during the optimization process once we start from a safe initialization point. To this end, we develop an algorithm called Reliable Frank-Wolfe (Reliable-FW). Given a general non-convex function and an unknown polytope constraint, Reliable-FW simultaneously learns the landscape of the objective function and the boundary of the safety polytope. More precisely, by assuming that Reliable-FW has access to a (stochastic) gradient oracle of the objective function and a noisy feasibility oracle of the safety polytope, it finds an $\epsilon$-approximate first-order stationary point with the optimal ${\mathcal{O}}({1}/{\epsilon^2})$ gradient oracle complexity (resp. $\tilde{\mathcal{O}}({1}/{\epsilon^3})$ (also optimal) in the stochastic gradient setting), while ensuring the safety of all the iterates. Rather surprisingly, Reliable-FW only makes $\tilde{\mathcal{O}}(({d^2}/{\epsilon^2})\log 1/\delta)$ queries to the noisy feasibility oracle (resp. $\tilde{\mathcal{O}}(({d^2}/{\epsilon^4})\log 1/\delta)$ in the stochastic gradient setting) where $d$ is the dimension and $\delta$ is the reliability parameter, tightening the existing bounds even for safe minimization of convex functions. We further specialize our results to the case that the objective function is convex. A crucial component of our analysis is to introduce and apply a technique called geometric shrinkage in the context of safe optimization.
Bach or Mock? A Grading Function for Chorales in the Style of J.S. Bach
Authors: Alexander Fang, Alisa Liu, Prem Seetharaman, Bryan Pardo
Date: 2020-06-23 00:00:00

Deep generative systems that learn probabilistic models from a corpus of existing music do not explicitly encode knowledge of a musical style, compared to traditional rule-based systems. Thus, it can be difficult to determine whether deep models generate stylistically correct output without expert evaluation, but this is expensive and time-consuming. Therefore, there is a need for automatic, interpretable, and musically-motivated evaluation measures of generated music. In this paper, we introduce a grading function that evaluates four-part chorales in the style of J.S. Bach along important musical features. We use the grading function to evaluate the output of a Transformer model, and show that the function is both interpretable and outperforms human experts at discriminating Bach chorales from model-generated ones.
A Mean-Field Theory for Learning the Schönberg Measure of Radial Basis Functions
Authors: Masoud Badiei Khuzani, Yinyu Ye, Sandy Napel, Lei Xing
Date: 2020-06-23 00:00:00
Tasks: Clustering, Image Retrieval, LEMMA, Retrieval, Stochastic Optimization

We develop and analyze a projected particle Langevin optimization method to learn the distribution in the Sch\"{o}nberg integral representation of the radial basis functions from training samples. More specifically, we characterize a distributionally robust optimization method with respect to the Wasserstein distance to optimize the distribution in the Sch\"{o}nberg integral representation. To provide theoretical performance guarantees, we analyze the scaling limits of a projected particle online (stochastic) optimization method in the mean-field regime. In particular, we prove that in the scaling limits, the empirical measure of the Langevin particles converges to the law of a reflected It\^{o} diffusion-drift process. Moreover, the drift is also a function of the law of the underlying process. Using It\^{o} lemma for semi-martingales and Grisanov's change of measure for the Wiener processes, we then derive a Mckean-Vlasov type partial differential equation (PDE) with Robin boundary conditions that describes the evolution of the empirical measure of the projected Langevin particles in the mean-field regime. In addition, we establish the existence and uniqueness of the steady-state solutions of the derived PDE in the weak sense. We apply our learning approach to train radial kernels in the kernel locally sensitive hash (LSH) functions, where the training data-set is generated via a $k$-mean clustering method on a small subset of data-base. We subsequently apply our kernel LSH with a trained kernel for image retrieval task on MNIST data-set, and demonstrate the efficacy of our kernel learning approach. We also apply our kernel learning approach in conjunction with the kernel support vector machines (SVMs) for classification of benchmark data-sets.
Incorporating Music Knowledge in Continual Dataset Augmentation for Music Generation
Authors: Alisa Liu, Alexander Fang, Gaëtan Hadjeres, Prem Seetharaman, Bryan Pardo
Date: 2020-06-23 00:00:00
Tasks: Music Generation

Deep learning has rapidly become the state-of-the-art approach for music generation. However, training a deep model typically requires a large training set, which is often not available for specific musical styles. In this paper, we present augmentative generation (Aug-Gen), a method of dataset augmentation for any music generation system trained on a resource-constrained domain. The key intuition of this method is that the training data for a generative system can be augmented by examples the system produces during the course of training, provided these examples are of sufficiently high quality and variety. We apply Aug-Gen to Transformer-based chorale generation in the style of J.S. Bach, and show that this allows for longer training and results in better generative output.
Thalamocortical motor circuit insights for more robust hierarchical control of complex sequences
Authors: Laureline Logiaco, G. Sean Escola
Date: 2020-06-23 00:00:00
Tasks: Temporal Sequences

We study learning of recurrent neural networks that produce temporal sequences consisting of the concatenation of re-usable "motifs". In the context of neuroscience or robotics, these motifs would be the motor primitives from which complex behavior is generated. Given a known set of motifs, can a new motif be learned without affecting the performance of the known set and then used in new sequences without first explicitly learning every possible transition? Two requirements enable this: (i) parameter updates while learning a new motif do not interfere with the parameters used for the previously acquired ones; and (ii) a new motif can be robustly generated when starting from the network state reached at the end of any of the other motifs, even if that state was not present during training. We meet the first requirement by investigating artificial neural networks (ANNs) with specific architectures, and attempt to meet the second by training them to generate motifs from random initial states. We find that learning of single motifs succeeds but that sequence generation is not robust: transition failures are observed. We then compare these results with a model whose architecture and analytically-tractable dynamics are inspired by the motor thalamocortical circuit, and that includes a specific module used to implement motif transitions. The synaptic weights of this model can be adjusted without requiring stochastic gradient descent (SGD) on the simulated network outputs, and we have asymptotic guarantees that transitions will not fail. Indeed, in simulations, we achieve single-motif accuracy on par with the previously studied ANNs and have improved sequencing robustness with no transition failures. Finally, we show that insights obtained by studying the transition subnetwork of this model can also improve the robustness of transitioning in the traditional ANNs previously studied.
Learning Gradient Boosted Multi-label Classification Rules
Authors: Michael Rapp, Eneldo Loza Mencía, Johannes Fürnkranz, Vu-Linh Nguyen, Eyke Hüllermeier
Date: 2020-06-23 00:00:00
Tasks: Classification, General Classification, Multi-Label Classification, MUlTI-LABEL-ClASSIFICATION

In multi-label classification, where the evaluation of predictions is less straightforward than in single-label classification, various meaningful, though different, loss functions have been proposed. Ideally, the learning algorithm should be customizable towards a specific choice of the performance measure. Modern implementations of boosting, most prominently gradient boosted decision trees, appear to be appealing from this point of view. However, they are mostly limited to single-label classification, and hence not amenable to multi-label losses unless these are label-wise decomposable. In this work, we develop a generalization of the gradient boosting framework to multi-output problems and propose an algorithm for learning multi-label classification rules that is able to minimize decomposable as well as non-decomposable loss functions. Using the well-known Hamming loss and subset 0/1 loss as representatives, we analyze the abilities and limitations of our approach on synthetic data and evaluate its predictive performance on multi-label benchmarks.
Principal Component Networks: Parameter Reduction Early in Training
Authors: Roger Waleffe, Theodoros Rekatsinas
Date: 2020-06-23 00:00:00

Recent works show that overparameterized networks contain small subnetworks that exhibit comparable accuracy to the full model when trained in isolation. These results highlight the potential to reduce training costs of deep neural networks without sacrificing generalization performance. However, existing approaches for finding these small networks rely on expensive multi-round train-and-prune procedures and are non-practical for large data sets and models. In this paper, we show how to find small networks that exhibit the same performance as their overparameterized counterparts after only a few training epochs. We find that hidden layer activations in overparameterized networks exist primarily in subspaces smaller than the actual model width. Building on this observation, we use PCA to find a basis of high variance for layer inputs and represent layer weights using these directions. We eliminate all weights not relevant to the found PCA basis and term these network architectures Principal Component Networks. On CIFAR-10 and ImageNet, we show that PCNs train faster and use less energy than overparameterized models, without accuracy loss. We find that our transformation leads to networks with up to 23.8x fewer parameters, with equal or higher end-model accuracy---in some cases we observe improvements up to 3%. We also show that ResNet-20 PCNs outperform deep ResNet-110 networks while training faster.
Embodied Self-supervised Learning by Coordinated Sampling and Training
Authors: Yifan Sun, Xihong Wu
Date: 2020-06-20 00:00:00
Tasks: Self-Supervised Learning

Self-supervised learning can significantly improve the performance of downstream tasks, however, the dimensions of learned representations normally lack explicit physical meanings. In this work, we propose a novel self-supervised approach to solve inverse problems by employing the corresponding physical forward process so that the learned representations can have explicit physical meanings. The proposed approach works in an analysis-by-synthesis manner to learn an inference network by iteratively sampling and training. At the sampling step, given observed data, the inference network is used to approximate the intractable posterior, from which we sample input parameters and feed them to a physical process to generate data in the observational space; At the training step, the same network is optimized with the sampled paired data. We prove the feasibility of the proposed method by tackling the acoustic-to-articulatory inversion problem to infer articulatory information from speech. Given an articulatory synthesizer, an inference model can be trained completely from scratch with random initialization. Our experiments demonstrate that the proposed method can converge steadily and the network learns to control the articulatory synthesizer to speak like a human. We also demonstrate that trained models can generalize well to unseen speakers or even new languages, and performance can be further improved through self-adaptation.
Bringing Light Into the Dark: A Large-scale Evaluation of Knowledge Graph Embedding Models Under a Unified Framework
Authors: Mehdi Ali, Max Berrendorf, Charles Tapley Hoyt, Laurent Vermue, Mikhail Galkin, Sahand Sharifzadeh, Asja Fischer, Volker Tresp, Jens Lehmann
Date: 2020-06-23 00:00:00
Tasks: Benchmarking, GPU, Graph Embedding, Knowledge Graph Embedding

The heterogeneity in recently published knowledge graph embedding models' implementations, training, and evaluation has made fair and thorough comparisons difficult. In order to assess the reproducibility of previously published results, we re-implemented and evaluated 21 interaction models in the PyKEEN software package. Here, we outline which results could be reproduced with their reported hyper-parameters, which could only be reproduced with alternate hyper-parameters, and which could not be reproduced at all as well as provide insight as to why this might be the case. We then performed a large-scale benchmarking on four datasets with several thousands of experiments and 24,804 GPU hours of computation time. We present insights gained as to best practices, best configurations for each model, and where improvements could be made over previously published best configurations. Our results highlight that the combination of model architecture, training approach, loss function, and the explicit modeling of inverse relations is crucial for a model's performances, and not only determined by the model architecture. We provide evidence that several architectures can obtain results competitive to the state-of-the-art when configured carefully. We have made all code, experimental configurations, results, and analyses that lead to our interpretations available at https://github.com/pykeen/pykeen and https://github.com/pykeen/benchmarking
Spherical Perspective on Learning with Normalization Layers
Authors: Simon Roburin, Yann de Mont-Marin, Andrei Bursuc, Renaud Marlet, Patrick Pérez, Mathieu Aubry
Date: 2020-06-23 00:00:00

Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the optimization of neural networks with NLs from a geometric perspective. Concretely, the radial invariance of groups of parameters, such as filters for convolutional neural networks, allows to translate the optimization steps on the $L_2$ unit hypersphere. This formulation and the associated geometric interpretation shed new light on the training dynamics. Firstly, the first effective learning rate expression of Adam is derived. Then the demonstration that, in the presence of NLs, performing Stochastic Gradient Descent (SGD) alone is actually equivalent to a variant of Adam constrained to the unit hypersphere, stems from the framework. Finally, this analysis outlines phenomena that previous variants of Adam act on and their importance in the optimization process are experimentally validated.