pwc-archive/papers-with-abstracts huggingface dataset:
Can auto-encoders help with filling missing data?
Authors: Marek Śmieja, Maciej Kołomycki, Łukasz Struski, Mateusz Juda, Mário A. T. Figueiredo
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12
Tasks: Missing Values

This paper introduces an approach to filling in missing data based on deep auto-encoder models, adequate to high-dimensional data exhibiting complex dependencies, such as images. The method exploits the properties of auto-encoders' vector fields, which allows to approximate the gradient of the log-density from its reconstruction error, based on which we propose a projected gradient ascent algorithm to obtain the  conditionally most probable estimate of the missing values. Experiments performed on benchmark datasets show that imputations produced by our model are sharp and realistic.
Fast Convergence for Langevin with Matrix Manifold Structure
Authors: Ankur Moitra, Andrej Risteski
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12
Tasks: Bayesian Inference


In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query. This mode of access to f is natural in the scenarios in which such problems arise, for instance sampling from posteriors in parametric Bayesian models. Classical results show that a natural random walk, Langevin diffusion, mixes rapidly when f is convex. Unfortunately, even in simple examples, the applications listed above will entail working with functions f that are nonconvex -- for which sampling from p may in general require an exponential number of queries.
In this paper, we study one aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability. We give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them. We specialize our arguments to classic matrix factorization-like Bayesian inference problems where we get noisy measurements A(XX^T), X \in R^{d \times k} of a low-rank matrix, i.e. f(X) = \|A(XX^T) - b\|^2_2, X \in R^{d \times k}, and \beta the inverse of the variance of the noise. Such functions f are invariant under orthogonal transformations, and include problems like matrix factorization, sensing, completion. Beyond sampling, Langevin dynamics is a popular toy model for studying stochastic gradient descent. Along these lines, we believe that our work is an important first step towards understanding how SGD behaves when there is a high degree of symmetry in the space of parameters the produce the same output.
Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View.
Authors: Yiping Lu*, Zhuohan Li*, Di He, Zhiqing Sun, Bin Dong, Tao Qin, LiWei Wang, Tie-Yan Liu
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12
Tasks: Sentence

The Transformer architecture is widely used in natural language processing. Despite its success, the design principle of the Transformer remains elusive. In this paper, we provide a novel perspective towards understanding the architecture: we show that the Transformer can be mathematically interpreted as a \emph{numerical Ordinary Differential Equation (ODE) solver for a convection-diffusion equation in a multi-particle dynamic system}. In particular, how words in a sentence are abstracted into contexts by passing through the layers of the Transformer can be interpreted as approximating multiple particles' movement in the space using the Lie-Trotter splitting scheme and the Euler's method. Inspired from such a relationship, we propose to replace the Lie-Trotter splitting scheme by the more accurate Strang-Marchuk splitting scheme and design a new network architecture called Macaron Net. Through extensive experiments, we show that the Macaron Net is superior to the Transformer on both supervised and unsupervised learning tasks.
A Mean-field Analysis of Deep ResNet and Beyond:Towards Provable Optimization Via Overparameterization From Depth
Authors: Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12

Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural networks, this work presents a mean-field analysis of deep residual networks, based on a line of works that interpret the continuum limit of the deep residual network as an ordinary differential equation when the network capacity tends to infinity. Specifically, we propose a \textbf{new continuum limit} of deep residual networks, which enjoys a good landscape in the sense that \textbf{every local minimizer is global}. 
This characterization enables us to derive the first global convergence result for multilayer neural networks in the mean-field regime. Furthermore, without assuming the convexity of the loss landscape, our proof relies on a zero-loss assumption at the global minimizer that can be achieved when the model shares a universal approximation property. Key to our result is the observation that a deep residual network resembles a shallow network ensemble~\cite{veit2016residual}, \emph{i.e.} a two-layer network. We bound the difference between the shallow network and our ResNet model via the adjoint sensitivity method, which enables us to apply existing mean-field analyses of two-layer networks to deep networks. Furthermore, we propose several novel training schemes based on the new continuous model, including one training procedure that switches the order of the residual blocks and results in strong empirical performance on the benchmark datasets.
Encoder-decoder neural network for solving the nonlinear Fokker-Planck-Landau collision operator in XGC
Authors: Marco Andres Miller, Randy Michael Churchill, Choong-Seock Chang, Robert Hager
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12
Tasks: Decoder

An encoder-decoder neural network has been used to accelerate the numerical solving of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code, XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the L2 loss. The run time for the current Picard iterative solver of the operator is $O(n^2)$, where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since the training only scales as $O(n)$. A wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. Eventual work will include expansion of the network to include multiple plasma species.
Solving ODE with Universal Flows: Approximation Theory for Flow-Based Models
Authors: Chin-wei Huang, Laurent Dinh, Aaron Courville
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12
Tasks: Computational Efficiency

Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that allows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.
Urban air pollution forecasts generated from latent space representation
Authors: Cesar Quilodran Casas, Rossella Arcucci, Yike Guo
Date: 2020-02-26 00:00:00
Proceeding: ICLR Workshop DeepDiffEq 2019 12

This paper presents an approach to replicate computational fluid dynamics simulations of air pollution using deep learning. The study area is in London, where a tracer aims to replicate a busy traffic junction. Our method, which integrates Principal Components Analysis (PCA) and autoencoders (AE), is a computationally cheaper way to generate a latent space representation of the original unstructured mesh model. Once the PCA is applied on the original model solution, a Fully-Connected AE is trained on the full-rank PCs. This yields a compression of the original data by $10^{6}$. The number of trainable parameters is also reduced using this method. A LSTM-based approach is used on the latent space to produce faster forecasts of the air pollution tracer.
HyperSpacetime: Complex Algebro-Geometric Analysis of Intelligence Quantum Entanglement Convergent Evolution (Extended Abstract)
Authors: Anonymous
Date: 2020-04-26 00:00:00

Far from the Madding Cloud

When groups of ants in haystack as agents 
Descending gudied by curvatures instead of gradients
No powerful enough in changing their environments 
Being inferior adapters instead of equal gamers 
Exploring and exploiting various actions
Searching and researching origin of intelligence 
Do they  solar system milkyway universe multiverse 

And the same as frogs in well hawks under sky
And dog's year different to human's year 
And elephant in your eyes not the same as mine 
Human in arbifolds just like ants in hay stacks
Hindsight insight foresight aspiration inspiration passion
Hate bacteria virus war all gone with wind 
No hard times only great expectations
Learning to Control PDEs with Differentiable Physics
Authors: Anonymous
Date: 2020-04-26 00:00:00

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations (PDEs) with many degrees of freedom. Existing methods that aim to control the dynamics of such systems are typically limited to relatively short time frames or a small number of interaction parameters. We present a novel hierarchical predictor-corrector scheme which enables neural networks to learn to understand and control complex nonlinear physical systems over long time frames. We propose to split the problem into two distinct tasks: planning and control. To this end, we introduce a predictor network that plans optimal trajectories and a control network that infers the corresponding control parameters. Both stages are trained end-to-end using a differentiable PDE solver. We demonstrate that our method successfully develops an understanding of complex physical systems and learns to control them for tasks involving PDEs such as the incompressible Navier-Stokes equations.
Bayesian Online Meta-Learning
Authors: Pauching Yap, Hippolyt Ritter, David Barber
Date: 2020-09-28 00:00:00
Tasks: Classification, Meta-Learning, Variational Inference

Neural networks are known to suffer from catastrophic forgetting when trained on sequential datasets. While there have been numerous attempts to solve this problem for large-scale supervised classification, little has been done to overcome catastrophic forgetting for few-shot classification problems. Few-shot meta-learning algorithms often require all few-shot tasks to be readily available in a batch for training. The popular gradient-based model-agnostic meta-learning algorithm (MAML) is a typical algorithm that suffers from these limitations. This work introduces a Bayesian online meta-learning framework to tackle the catastrophic forgetting and the sequential few-shot tasks problems. Our framework incorporates MAML into a Bayesian online learning algorithm with Laplace approximation or variational inference.  This framework enables few-shot classification on a range of sequentially arriving datasets with a single meta-learned model and training on sequentially arriving few-shot tasks. The experimental evaluations demonstrate that our framework can effectively prevent catastrophic forgetting and is capable of online meta-learning in various few-shot classification settings.
Expressive yet Tractable Bayesian Deep Learning via Subnetwork Inference
Authors: Erik Daxberger, Eric Nalisnick, James Allingham, Javier Antoran, José Miguel Hernández-Lobato
Date: 2020-09-28 00:00:00
Proceeding: pproximateinference AABI Symposium 2021 1
Tasks: Bayesian Inference, Deep Learning

The Bayesian paradigm has the potential to solve some of the core issues in modern deep learning, such as poor calibration, data inefficiency, and catastrophic forgetting. However, scaling Bayesian inference to the high-dimensional parameter spaces of deep neural networks requires restrictive approximations. In this paper, we propose performing inference over only a small subset of the model parameters while keeping all others as point estimates. This enables us to use expressive posterior approximations that would otherwise be intractable for the full model. In particular, we develop a practical and scalable Bayesian deep learning method that first trains a point estimate, and then infers a full covariance Gaussian posterior approximation over a subnetwork. We propose a subnetwork selection procedure which aims to maximally preserve posterior uncertainty. We empirically demonstrate the effectiveness of our approach compared to point-estimated networks and methods that use less expressive posterior approximations over the full network.
Transfer among Agents: An Efficient Multiagent Transfer Learning Framework
Authors: Tianpei Yang, Jianye Hao, Weixun Wang, Hongyao Tang, Zhaopeng Meng, Hangyu Mao, Dong Li, Wulong Liu, Yujing Hu, Yingfeng Chen, Changjie Fan
Date: 2020-09-28 00:00:00
Tasks: Open-Ended Question Answering, Reinforcement Learning (RL), Transfer Learning

Transfer Learning has shown great potential to enhance the single-agent Reinforcement Learning (RL) efficiency, by sharing learned policies of previous tasks. Similarly, in multiagent settings, the learning performance can also be promoted if agents can share knowledge between each other. However, it remains an open question of how an agent should learn from other agents' knowledge. In this paper, we propose a novel multiagent option-based policy transfer (MAOPT) framework to improve multiagent learning efficiency. Our framework learns what advice to give to each agent and when to terminate it by modeling multiagent policy transfer as the option learning problem. MAOPT provides different kinds of variants which can be classified into two types in terms of the experience used during training. One type is the MAOPT with the Global Option Advisor which has the access to the global information of the environment. However, in many realistic scenarios, we can only obtain each agent's local information due to the partial observation. The other type contains MAOPT with the Local Option Advisor and MAOPT with the Successor Representation Option (SRO) which are suitable for this setting and collect each agent's local experience for the update. In many cases, each agent's experience is inconsistent with each other which causes the option-value estimation to oscillate and to become inaccurate. SRO is used to handle the experience inconsistency by decoupling the dynamics of the environment from the rewards to learn the option-value function under each agent's preference. MAOPT can be easily combined with existing deep RL approaches. Experimental results show it significantly boosts the performance of existing deep RL methods in both discrete and continuous state spaces.
What About Taking Policy as Input of Value Function: Policy-extended Value Function Approximator
Authors: Hongyao Tang, Zhaopeng Meng, Jianye Hao, Chen Chen, Daniel Graves, Dong Li, Wulong Liu, Yaodong Yang
Date: 2020-09-28 00:00:00
Tasks: continuous-control, Continuous Control, Contrastive Learning, MuJoCo, Reinforcement Learning (RL), Representation Learning

The value function lies in the heart of Reinforcement Learning (RL), which defines the long-term evaluation of a policy in a given state. In this paper, we propose Policy-extended Value Function Approximator (PeVFA) which extends the conventional value to be not only a function of state but also an explicit policy representation. Such an extension enables PeVFA to preserve values of multiple policies in contrast to a conventional one with limited capacity for only one policy, inducing the new characteristic of \emph{value generalization among policies}. From both the theoretical and empirical lens, we study value generalization along the policy improvement path (called local generalization), from which we derive a new form of Generalized Policy Iteration with PeVFA to improve the conventional learning process. Besides, we propose a framework to learn the representation of an RL policy,  studying several different approaches to learn an effective policy representation from policy network parameters and state-action pairs through contrastive learning and action prediction. In our experiments, Proximal Policy Optimization (PPO) with PeVFA significantly outperforms its vanilla counterpart in MuJoCo continuous control tasks, demonstrating the effectiveness of value generalization offered by PeVFA and policy representation learning.
Graph Joint Attention Networks
Authors: Tiantian He, Lu Bai, Yew-Soon Ong
Date: 2020-09-28 00:00:00
Tasks: Benchmarking, Graph Attention, Node Classification

Graph attention networks (GATs) have been recognized as powerful tools for learning in graph structured data. However, how to enable the attention mechanisms in GATs to smoothly consider both structural and feature information is still very challenging. In this paper, we propose Graph Joint Attention Networks (JATs) to address the aforementioned challenge. Different from previous attention-based graph neural networks (GNNs), JATs adopt novel joint attention mechanisms which can automatically determine the relative significance between node features and structural coefficients learned from graph subspace, when computing the attention scores. Therefore, representations concerning more structural properties can be inferred by JATs.
Besides, we theoretically analyze the expressive power of JATs and further propose an improved strategy for the joint attention mechanisms that enables JATs to reach the upper bound of expressive power which every message-passing GNN can ultimately achieve, i.e., 1-WL test. JATs can thereby be seen as most powerful message-passing GNNs. The proposed neural architecture has been extensively tested on widely used benchmarking datasets, including Cora, Cite, and Pubmed and has been compared with state-of-the-art GNNs for node classification tasks. Experimental results show that JATs achieve state-of-the-art performance on all the testing datasets.
Neuron Activation Analysis for Multi-Joint Robot Reinforcement Learning
Authors: Benedikt Feldotto, Heiko Lengenfelder, Alois Knoll
Date: 2020-09-28 00:00:00
Tasks: reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

Recent experiments indicate that pre-training of end-to-end Reinforcement Learning neural networks on general tasks can speed up the training process for specific robotic applications. However, it remains open if these networks form general feature extractors and a hierarchical organization that are reused as apparent e.g. in Convolutional Neural Networks. In this paper we analyze the intrinsic neuron activation in networks trained for target reaching of robot manipulators with increasing joint number in a vertical plane. We analyze the individual neuron activity distribution in the network, introduce a pruning algorithm to reduce network size keeping the performance, and with these dense network representations we spot correlations of neuron activity patterns among networks trained for robot manipulators with different joint number. We show that the input and output network layers have more distinct neuron activation in contrast to inner layers. Our pruning algorithm reduces the network size significantly, increases the distance of neuron activation while keeping a high performance in training and evaluation. Our results demonstrate that neuron activity can be mapped among networks trained for robots with different complexity. Hereby, robots with small joint difference show higher layer-wise projection accuracy whereas more different robots mostly show projections to the first layer.
Learning Binary Trees via Sparse Relaxation
Authors: Valentina Zantedeschi, Matt Kusner, Vlad Niculae
Date: 2020-09-28 00:00:00
Tasks: Clustering, regression

One of the most classical problems in machine learning is how to learn binary trees that split data into meaningful partitions. From classification/regression via decision trees to hierarchical clustering, binary trees are useful because they (a) are often easy to visualize; (b) make computationally-efficient predictions; and (c) allow for flexible partitioning. Because of this there has been extensive research on how to learn such trees. Optimization generally falls into one of three categories: 1. greedy node-by-node optimization; 2. probabilistic relaxations for differentiability; 3. mixed-integer programming (MIP). Each of these have downsides: greedy can myopically choose poor splits, probabilistic relaxations do not have principled ways to prune trees, MIP methods can be slow on large problems and may not generalize. In this work we derive a novel sparse relaxation for binary tree learning. By sparsely relaxing a new MIP, our approach is able to learn tree splits and tree pruning using state-of-the-art gradient-based approaches. We demonstrate how our approach is easily visualizable, is efficient, and is competitive with current work in classification/regression and hierarchical clustering.
Revisiting Explicit Regularization in Neural Networks for Reliable Predictive Probability
Authors: Taejong Joo, Uijung Chung
Date: 2020-09-28 00:00:00
Tasks: Memorization

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models, which deters the memorization of intricate patterns existing only in the training data. However, the impressive generalization performance of over-parameterized neural networks with only implicit regularization challenges the importance of explicit regularization. Furthermore, explicit regularization does not prevent neural networks from memorizing unnatural patterns, such as random labels. In this work, we revisit the role and importance of explicit regularization methods for generalization of the predictive probability, not just the generalization of the 0-1 loss. Specifically, we analyze the possible cause of the poor predictive probability and identify that regularization of predictive confidence is required during training. We then empirically show that explicit regularization significantly improves the reliability of the predictive probability, which enables better predictive uncertainty representation and prevents the overconfidence problem. Our findings present a new direction to improve the predictive probability quality of deterministic neural networks, which can be an efficient and scalable alternative to Bayesian neural networks and ensemble methods.