DeepNLP/NIPS-2020-Accepted-Papers huggingface dataset:
Monotone operator equilibrium networks
Authors: Ezra Winston, J. Zico Kolter

Abstract: Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence to a solution and lack guarantees that a solution exists. On the other hand, Neural ODEs, another class of implicit-depth models, do guarantee existence of a unique solution but perform poorly compared with traditional networks. In this paper, we develop a new class of implicit-depth model based on the theory of monotone operators, the Monotone Operator Equilibrium Network (monDEQ). We show the close connection between finding the equilibrium point of an implicit network and solving a form of monotone operator splitting problem, which admits efficient solvers with guaranteed, stable convergence. We then develop a parameterization of the network which ensures that all operators remain monotone, which guarantees the existence of a unique equilibrium point. Finally, we show how to instantiate several versions of these models, and implement the resulting iterative solvers, for structured linear operators such as multi-scale convolutions. The resulting models vastly outperform the Neural ODE-based models while also being more computationally efficient. Code is available at http://github.com/locuslab/monotoneopnet.
When and How to Lift the Lockdown? Global COVID-19 Scenario Analysis and Policy Assessment using Compartmental Gaussian Processes
Authors: Zhaozhi Qian, Ahmed M. Alaa, Mihaela van der Schaar

Abstract: The coronavirus disease 2019 (COVID-19) global pandemic has led many countries to impose unprecedented lockdown measures in order to slow down the outbreak. Questions on whether governments have acted promptly enough, and whether lockdown measures can be lifted soon have since been central in public discourse. Data-driven models that predict COVID-19 fatalities under different lockdown policy scenarios are essential for addressing these questions, and for informing governments on future policy directions. To this end, this paper develops a Bayesian model for predicting the effects of COVID-19 containment policies in a global context — we treat each country as a distinct data point, and exploit variations of policies across countries to learn country-specific policy effects. Our model utilizes a two-layer Gaussian process (GP) prior — the lower layer uses a compartmental SEIR (Susceptible, Exposed, Infected, Recovered) model as a prior mean function with “country-and-policy-specific” parameters that capture fatality curves under different “counterfactual” policies within each country, whereas the upper layer is shared across all countries, and learns lower-layer SEIR parameters as a function of country features and policy indicators. Our model combines the solid mechanistic foundations of SEIR models (Bayesian priors) with the flexible data-driven modeling and gradient-based optimization routines of machine learning (Bayesian posteriors) — i.e., the entire model is trained end-to-end via stochastic variational inference. We compare the projections of our model with other models listed by the Center for Disease Control (CDC), and provide scenario analyses for various lockdown and reopening strategies highlighting their impact on COVID-19 fatalities.
Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control
Authors: Yaofeng Desmond Zhong, Naomi Leonard

Abstract: Recent approaches for modelling dynamics of physical systems with neural networks enforce Lagrangian or Hamiltonian structure to improve prediction and generalization. However, when coordinates are embedded in high-dimensional data such as images, these approaches either lose interpretability or can only be applied to one particular example. We introduce a new unsupervised neural network model that learns Lagrangian dynamics from images, with interpretability that benefits prediction and control. The model infers Lagrangian dynamics on generalized coordinates that are simultaneously learned with a coordinate-aware variational autoencoder (VAE). The VAE is designed to account for the geometry of physical systems composed of multiple rigid bodies in the plane. By inferring interpretable Lagrangian dynamics, the model learns physical system properties, such as kinetic and potential energy, which enables long-term prediction of dynamics in the image space and synthesis of energy-based controllers.
High-Dimensional Sparse Linear Bandits
Authors: Botao Hao, Tor Lattimore, Mengdi Wang

Abstract: Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, such as personalized medicine and online advertising. We derive a novel O(n^{2/3}) dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is larger than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that O(n^{2/3}) is the optimal rate in the data-poor regime. The results complement existing bounds for the data-rich regime and also provide another example where carefully balancing the trade-off between information and regret is necessary. Finally, we prove a dimension-free O(\sqrt{n}) regret upper bound under an additional assumption on the magnitude of the signal for relevant features.
Non-Stochastic Control with Bandit Feedback
Authors: Paula Gradu, John Hallman, Elad Hazan

Abstract: We study the problem of controlling a linear dynamical system with adversarial perturbations where the only feedback available to the controller is the scalar loss, and the loss function itself is unknown. For this problem, with either a known or unknown system, we give an efficient sublinear regret algorithm. The main algorithmic difficulty is the dependence of the loss on past controls. To overcome this issue, we propose an efficient algorithm for the general setting of bandit convex optimization for loss functions with memory, which may be of independent interest.
Generalized Leverage Score Sampling for Neural Networks
Authors: Jason D. Lee, Ruoqi Shen, Zhao Song, Mengdi Wang, zheng Yu

Abstract: Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e.g. linear regression, linear programming, semi-definite programming, cutting plane method, graph sparsification, maximum matching and max-flow. Recently, it has been shown that leverage score sampling helps to accelerate kernel methods [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17]. In this work, we generalize the results in [Avron, Kapralov, Musco, Musco, Velingker and Zandieh 17] to a broader class of kernels. We further bring the leverage score sampling into the field of deep learning theory. 
1. We show the connection between the initialization for neural network training and approximating the neural tangent kernel with random features.
2. We prove the equivalence between regularized neural network and neural tangent kernel ridge regression under the initialization of both classical random Gaussian and leverage score sampling.
An Optimal Elimination Algorithm for Learning a Best Arm
Authors: Avinatan Hassidim, Ron Kupfer, Yaron Singer

Abstract: We consider the classic problem of $(\epsilon,\delta)$-\texttt{PAC} learning a best arm where the goal is to identify with confidence $1-\delta$ an arm whose mean is an $\epsilon$-approximation to that of the highest mean arm in a multi-armed bandit setting.  
This problem is one of the most fundamental problems in statistics and learning theory, yet somewhat surprisingly its worst case sample complexity is not well  understood.  In this paper we propose a new approach for $(\epsilon,\delta)$-\texttt{PAC} learning a best arm.  This approach leads to an algorithm whose sample complexity converges to \emph{exactly} the optimal sample complexity of $(\epsilon,\delta)$-learning the mean of $n$ arms separately and we complement this result with a conditional matching lower bound.  More specifically:

\begin{itemize}
\item The algorithm's sample complexity converges to \emph{exactly} $\frac{n}{2\epsilon^2}\log \frac{1}{\delta}$ as $n$ grows and $\delta \geq \frac{1}{n}$;  
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\item We prove that no elimination algorithm obtains sample complexity arbitrarily lower than $\frac{n}{2\epsilon^2}\log \frac{1}{\delta}$.  Elimination algorithms is a broad class of $(\epsilon,\delta)$-\texttt{PAC} best arm learning algorithms that includes many algorithms in the literature.   
\end{itemize}
When $n$ is independent of $\delta$ our approach yields an algorithm whose sample complexity converges to $\frac{2n}{\epsilon^2} \log \frac{1}{\delta}$ as $n$ grows.  In comparison with the best known algorithm for this problem our approach improves the sample complexity by a factor of over 1500 and over 6000 when $\delta\geq \frac{1}{n}$.
Efficient Projection-free Algorithms for Saddle Point Problems
Authors: Cheng Chen, Luo Luo, Weinan Zhang, Yong Yu

Abstract: The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper, we study projection-free algorithms for   convex-strongly-concave saddle point problems with complicated constraints. Our method combines Conditional Gradient Sliding  with Mirror-Prox and show that it only requires $\tilde{\cO}(1/\sqrt{\epsilon})$ gradient evaluations and $\tilde{\cO}(1/\epsilon^2)$ linear optimizations in the batch setting. We also extend our method to the stochastic setting and propose first stochastic projection-free algorithms for saddle point problems. Experimental results demonstrate the effectiveness of our algorithms and verify our theoretical guarantees.
A mathematical model for automatic differentiation in machine learning
Authors: Jérôme Bolte, Edouard Pauwels

Abstract: Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in practice, and differentiation of nonsmooth functions. To this end we provide a simple class of functions, a nonsmooth calculus, and show how they apply to stochastic approximation methods. We also evidence the issue of artificial critical points created by algorithmic differentiation and show how usual methods avoid these points with probability one.
Unsupervised Text Generation by Learning from Search
Authors: Jingjing Li, Zichao Li, Lili Mou, Xin Jiang, Michael Lyu, Irwin King

Abstract: In this work, we propose TGLS, a novel framework for unsupervised Text Generation by Learning from Search. We start by applying a strong search algorithm (in particular, simulated annealing) towards a heuristically defined objective that (roughly) estimates the quality of sentences. Then, a conditional generative model learns from the search results, and meanwhile smooth out the noise of search. The alternation between search and learning can be repeated for performance bootstrapping. We demonstrate the effectiveness of TGLS on two real-world natural language generation tasks, unsupervised paraphrasing and text formalization. Our model significantly outperforms unsupervised baseline methods in both tasks. Especially, it achieves comparable performance to strong supervised methods for paraphrase generation.
Learning Compositional Rules via Neural Program Synthesis
Authors: Maxwell Nye, Armando Solar-Lezama, Josh Tenenbaum, Brenden M. Lake

Abstract: Many aspects of human reasoning, including language, require learning rules from very little data. Humans can do this, often learning systematic rules from very few examples, and combining these rules to form compositional rule-based systems. Current neural architectures, on the other hand, often fail to generalize in a compositional manner, especially when evaluated in ways that vary systematically from training. In this work, we present a neuro-symbolic model which learns entire rule systems from a small set of examples. Instead of directly predicting outputs from inputs, we train our model to induce the explicit system of rules governing a set of previously seen examples, drawing upon techniques from the neural program synthesis literature. Our rule-synthesis approach outperforms neural meta-learning techniques in three domains: an artificial instruction-learning domain used to evaluate human learning, the SCAN challenge datasets, and learning rule-based translations of number words into integers for a wide range of human languages.
Incorporating BERT into Parallel Sequence Decoding with Adapters
Authors: Junliang Guo, Zhirui Zhang, Linli Xu, Hao-Ran Wei, Boxing Chen, Enhong Chen

Abstract: While large scale pre-trained language models such as BERT have achieved great success on various natural language understanding tasks, how to efficiently and effectively incorporate them into sequence-to-sequence models and the corresponding text generation tasks remains a non-trivial problem. In this paper, we propose to address this problem by taking two different BERT models as the encoder and decoder respectively, and fine-tuning them by introducing simple and lightweight adapter modules, which are inserted between BERT layers and tuned on the task-specific dataset. In this way, we obtain a flexible and efficient model which is able to jointly leverage the information contained in the source-side and target-side BERT models, while bypassing the catastrophic forgetting problem. Each component in the framework can be considered as a plug-in unit, making the framework flexible and task agnostic.
Our framework is based on a parallel sequence decoding algorithm named Mask-Predict considering the bi-directional and conditional independent nature of BERT, and can be adapted to traditional autoregressive decoding easily.
We conduct extensive experiments on neural machine translation tasks where
the proposed method consistently outperforms autoregressive baselines while reducing the inference latency by half,
and achieves $36.49$/$33.57$ BLEU scores on IWSLT14 German-English/WMT14 German-English translation. 
When adapted to autoregressive decoding, the proposed method achieves $30.60$/$43.56$ BLEU scores on WMT14 English-German/English-French translation,
on par with the state-of-the-art baseline models.
Estimating Fluctuations in Neural Representations of Uncertain Environments
Authors: Sahand Farhoodi, Mark Plitt, Lisa Giocomo, Uri Eden

Abstract: Neural Coding analyses often reflect an assumption that neural populations respond uniquely and consistently to particular stimuli. For example, analyses of spatial remapping in hippocampal populations often assume that each environment has one unique representation and that remapping occurs over long time scales as an animal traverses between distinct environments. However, as neuroscience experiments begin to explore more naturalistic tasks and stimuli, and reflect more ambiguity in neural representations, methods for analyzing population neural codes must adapt to reflect these features. In this paper, we develop a new state-space modeling framework to address two important issues related to remapping. First, neurons may exhibit significant trial-to-trial or moment-to-moment variability in the firing patterns used to represent a particular environment or stimulus. Second, in ambiguous environments and tasks that involve cognitive uncertainty, neural populations may rapidly fluctuate between multiple representations. The state-space model addresses these two issues by integrating an observation model, which allows for multiple representations of the same stimulus or environment, with a state model, which characterizes the moment-by-moment probability of a shift in the neural representation. These models allow us to compute instantaneous estimates of the stimulus or environment currently represented by the population. We demonstrate the application of this approach to the analysis of population activity in the CA1 region of hippocampus of a mouse moving through ambiguous virtual environments. Our analyses demonstrate that many hippocampal cells express significant trial-to-trial variability in their representations and that the population representation can fluctuate rapidly between environments within a single trial when spatial cues are most ambiguous.
Discover, Hallucinate, and Adapt: Open Compound Domain Adaptation for Semantic Segmentation
Authors: KwanYong Park, Sanghyun Woo, Inkyu Shin, In So Kweon

Abstract: Unsupervised domain adaptation (UDA) for semantic segmentation has been attracting attention recently, as it could be beneficial for various label-scarce real-world scenarios (e.g., robot control, autonomous driving, medical imaging, etc.). Despite the significant progress in this field, current works mainly focus on a single-source single-target setting, which cannot handle more practical settings of multiple targets or even unseen targets. 
In this paper, we investigate open compound domain adaptation (OCDA), which deals with mixed and novel situations at the same time, for semantic segmentation.
We present a novel framework based on three main design principles: discover, hallucinate, and adapt. The scheme first clusters compound target data based on style, discovering multiple latent domains (discover). Then, it hallucinates multiple latent target domains in source by using image-translation (hallucinate). This step ensures the latent domains in the source and the target to be paired. Finally, target-to-source alignment is learned separately between domains (adapt). In high-level, our solution replaces a hard OCDA problem with much easier multiple UDA problems.
We evaluate our solution on standard benchmark GTA to C-driving, and achieved new state-of-the-art results.
SURF: A Simple, Universal, Robust, Fast Distribution Learning Algorithm
Authors: Yi Hao, Ayush Jain, Alon Orlitsky, Vaishakh Ravindrakumar

Abstract: Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present $\SURF$, an algorithm for approximating distributions by piecewise polynomials. $\SURF$ is:
simple, replacing prior complex optimization techniques by straight-forward empirical probability approximation of each potential polynomial piece through simple empirical-probability interpolation, and using plain divide-and-conquer to merge the pieces; universal, as well-known  polynomial-approximation results imply that it accurately approximates a large class of common distributions; 
robust to distribution mis-specification as for any degree $d \le 8$, it estimates any distribution to an $\ell_1$ distance $< 3$ times that of the nearest degree-$d$ piecewise polynomial, improving known factor upper bounds of 3 for single polynomials and 15 for polynomials with arbitrarily many pieces;
fast, using optimal sample complexity, running in near sample-linear time, and if given sorted samples it may be parallelized to run in sub-linear time.
In experiments, $\SURF$ outperforms state-of-the art algorithms.
Understanding Approximate Fisher Information for Fast Convergence of Natural Gradient Descent in Wide Neural Networks
Authors: Ryo Karakida, Kazuki Osawa

Abstract: Natural Gradient Descent (NGD) helps to accelerate the convergence of gradient descent dynamics, but it requires approximations in large-scale deep neural networks because of its high computational cost. Empirical studies have confirmed that some NGD methods with approximate Fisher information converge sufficiently fast in practice. Nevertheless, it remains unclear from the theoretical perspective why and under what conditions such heuristic approximations work well. In this work, we reveal that, under specific conditions, NGD with approximate Fisher information achieves the same fast convergence to global minima as exact NGD. We consider deep neural networks in the infinite-width limit, and analyze the asymptotic training dynamics of NGD in function space via the neural tangent kernel. In the function space, the training dynamics with the approximate Fisher information are identical to those with the exact Fisher information, and they converge quickly. The fast convergence holds in layer-wise approximations; for instance, in block diagonal approximation where each block corresponds to a layer as well as in block tri-diagonal and K-FAC approximations. We also find that a unit-wise approximation achieves the same fast convergence under some assumptions. All of these different approximations have an isotropic gradient in the function space, and this plays a fundamental role in achieving the same convergence properties in training. Thus, the current study gives a novel and unified theoretical foundation with which to understand NGD methods in deep learning.
General Transportability of Soft Interventions: Completeness Results
Authors: Juan Correa, Elias Bareinboim

Abstract: The challenge of generalizing causal knowledge across different environments is pervasive in scientific explorations, including in AI, ML, and Data Science. Experiments are usually performed in one environment (e.g., in a lab, on Earth) with the intent, almost invariably, of being used elsewhere (e.g., outside the lab, on Mars), where the conditions are likely to be different.  In the causal inference literature, this generalization task has been formalized under the rubric of transportability (Pearl and Bareinboim, 2011), where a number of criteria and algorithms have been developed for various settings. Despite the generality of such results, transportability theory has been confined to atomic, do()-interventions. In practice, many real-world applications require more complex, stochastic interventions; for instance, in reinforcement learning, agents need to continuously adapt to the changing conditions of an uncertain and unknown environment.  
In this paper, we extend transportability theory to encompass these more complex types of interventions, which are known as "soft," both relative to the input as well as the target distribution of the analysis. Specifically, we develop a graphical condition that is both necessary and sufficient for deciding soft-transportability. Second, we develop an algorithm to determine whether a non-atomic intervention is computable from a combination of the distributions available across domains. As a corollary, we show that the $\sigma$-calculus is complete for the task of soft-transportability.
GAIT-prop: A biologically plausible learning rule derived from backpropagation of error
Authors: Nasir Ahmad, Marcel A. J. van Gerven, Luca Ambrogioni

Abstract: Traditional backpropagation of error, though a highly successful algorithm for learning in artificial neural network models, includes features which are biologically implausible for learning in real neural circuits. An alternative called target propagation proposes to solve this implausibility by using a top-down model of neural activity to convert an error at the output of a neural network into layer-wise and plausible ‘targets’ for every unit. These targets can then be used to produce weight updates for network training. However, thus far, target propagation has been heuristically proposed without demonstrable equivalence to backpropagation. Here, we derive an exact correspondence between backpropagation and a modified form of target propagation (GAIT-prop) where the target is a small perturbation of the forward pass. Specifically, backpropagation and GAIT-prop give identical updates when synaptic weight matrices are orthogonal. In a series of simple computer vision experiments, we show near-identical performance between backpropagation and GAIT-prop with a soft orthogonality-inducing regularizer.