Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.

Models for predicting the time of a future event are crucial for risk assessment, across a diverse range of applications. Existing time-to-event (survival) models have focused primarily on preserving pairwise ordering of estimated event times, or relative risk. Model calibration is relatively under explored, despite its critical importance in time-to-event applications. We present a survival function estimator for probabilistic predictions in time-to-event models, based on a neural network model for draws from the distribution of event times, without explicit assumptions on the form of the distribution. This is done like in adversarial learning, but we achieve learning without a discriminator or adversarial objective. The proposed estimator can be used in practice as a means of estimating and comparing conditional survival distributions, while accounting for the predictive uncertainty of probabilistic models. Extensive experiments show that the proposed model outperforms existing approaches, trained both with and without adversarial learning, in terms of both calibration and concentration of time-to-event distributions.

Numerous methods for crafting adversarial examples were proposed recently with high success rate. Most existing works normalize images into a continuous, real vector, domain firstly, and then craft adversarial examples in this domain. However, "adversarial" examples may become benign after de-normalizing them back into the discrete integer domain, known as the discretization problem. The discretization problem was mentioned in some work, but was underestimated and has received relatively little attention. In this work, we conduct the first comprehensive study of the discretization problem. We theoretically analyze 34 representative methods and empirically study 20 representative open source tools for crafting adversarial images. Our study reveals that almost all existing works suffer from the discretization problem and it is far more serious than originally thought. For instance, most black-box methods downgrade to white-box ones and methods having higher success rates drop down to lower high success rates, e.g., from 100% to 10%. This suggests that the discretization problem should be taken into account when crafting adversarial examples. As a first step towards addressing this problem, we propose a black-box method which reduces the adversarial example searching problem to a derivative-free optimization problem. Our method is able to craft `real' adversarial images by derivative-free search on the discrete integer domain. Experimental results show that our method achieves significantly higher success rate in terms of adversarial examples in the discrete integer domain than most other methods, no matter white-box or black-box. Moreover, our method is able to handle models that is non-differentiable and we successfully break the winner of NIPS 17 competition on defense with 95% success rate.

Esports have become major international sports with hundreds of millions of spectators. Esports games generate massive amounts of telemetry data. Using these to predict the outcome of esports matches has received considerable attention, but micro-predictions, which seek to predict events inside a match, is as yet unknown territory. Micro-predictions are however of perennial interest across esports commentators and audience, because they provide the ability to observe events that might otherwise be missed: esports games are highly complex with fast-moving action where the balance of a game can change in the span of seconds, and where events can happen in multiple areas of the playing field at the same time. Such events can happen rapidly, and it is easy for commentators and viewers alike to miss an event and only observe the following impact of events. In Dota 2, a player hero being killed by the opposing team is a key event of interest to commentators and audience. We present a deep learning network with shared weights which provides accurate death predictions within a five-second window. The network is trained on a vast selection of Dota 2 gameplay features and professional/semi-professional level match dataset. Even though death events are rare within a game (1\% of the data), the model achieves 0.377 precision with 0.725 recall on test data when prompted to predict which of any of the 10 players of either team will die within 5 seconds. An example of the system applied to a Dota 2 match is presented. This model enables real-time micro-predictions of kills in Dota 2, one of the most played esports titles in the world, giving commentators and viewers time to move their attention to these key events.

Legged locomotion is a challenging task for learning algorithms, especially when the task requires a diverse set of primitive behaviors. To solve these problems, we introduce a hierarchical framework to automatically decompose complex locomotion tasks. A high-level policy issues commands in a latent space and also selects for how long the low-level policy will execute the latent command. Concurrently, the low-level policy uses the latent command and only the robot's on-board sensors to control the robot's actuators. Our approach allows the high-level policy to run at a lower frequency than the low-level one. We test our framework on a path-following task for a dynamic quadruped robot and we show that steering behaviors automatically emerge in the latent command space as low-level skills are needed for this task. We then show efficient adaptation of the trained policy to a different task by transfer of the trained low-level policy. Finally, we validate the policies on a real quadruped robot. To the best of our knowledge, this is the first application of end-to-end hierarchical learning to a real robotic locomotion task.

We present a system for learning full-body neural avatars, i.e. deep networks that produce full-body renderings of a person for varying body pose and camera position. Our system takes the middle path between the classical graphics pipeline and the recent deep learning approaches that generate images of humans using image-to-image translation. In particular, our system estimates an explicit two-dimensional texture map of the model surface. At the same time, it abstains from explicit shape modeling in 3D. Instead, at test time, the system uses a fully-convolutional network to directly map the configuration of body feature points w.r.t. the camera to the 2D texture coordinates of individual pixels in the image frame. We show that such a system is capable of learning to generate realistic renderings while being trained on videos annotated with 3D poses and foreground masks. We also demonstrate that maintaining an explicit texture representation helps our system to achieve better generalization compared to systems that use direct image-to-image translation.

Lake and Baroni (2018) introduced the SCAN dataset probing the ability of seq2seq models to capture compositional generalizations, such as inferring the meaning of "jump around" 0-shot from the component words. Recurrent networks (RNNs) were found to completely fail the most challenging generalization cases. We test here a convolutional network (CNN) on these tasks, reporting hugely improved performance with respect to RNNs. Despite the big improvement, the CNN has however not induced systematic rules, suggesting that the difference between compositional and non-compositional behaviour is not clear-cut.

The performance of a Part-of-speech (POS) tagger is highly dependent on the domain ofthe processed text, and for many domains there is no or only very little training data available. This work addresses the problem of POS tagging noisy user-generated text using a neural network. We propose an architecture that trains an out-of-domain model on a large newswire corpus, and transfers those weights by using them as a prior for a model trained on the target domain (a data-set of German Tweets) for which there is very little an-notations available. The neural network has two standard bidirectional LSTMs at its core. However, we find it crucial to also encode a set of task-specific features, and to obtain reliable (source-domain and target-domain) word representations. Experiments with different regularization techniques such as early stopping, dropout and fine-tuning the domain adaptation prior weights are conducted. Our best model uses external weights from the out-of-domain model, as well as feature embeddings, pre-trained word and sub-word embeddings and achieves a tagging accuracy of slightly over 90%, improving on the previous state of the art for this task.

We present a novel method named Latent Semantic Imputation (LSI) to transfer external knowledge into semantic space for enhancing word embedding. The method integrates graph theory to extract the latent manifold structure of the entities in the affinity space and leverages non-negative least squares with standard simplex constraints and power iteration method to derive spectral embeddings. It provides an effective and efficient approach to combining entity representations defined in different Euclidean spaces. Specifically, our approach generates and imputes reliable embedding vectors for low-frequency words in the semantic space and benefits downstream language tasks that depend on word embedding. We conduct comprehensive experiments on a carefully designed classification problem and language modeling and demonstrate the superiority of the enhanced embedding via LSI over several well-known benchmark embeddings. We also confirm the consistency of the results under different parameter settings of our method.

A new approach for blind channel equalization and decoding, using variational autoencoders (VAEs), is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximated maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equalization methods such as constant modulus, thus enabling faster channel acquisition. The VAE equalizer uses a fully convolutional neural network with a small number of free parameters. These results are extended to blind equalization over a noisy nonlinear ISI channel with unknown parameters. We then consider coded communication using low-density parity-check (LDPC) codes transmitted over a noisy linear or nonlinear ISI channel. The goal is to reconstruct the transmitted message from the channel observations corresponding to a transmitted codeword, without using pilot symbols. We demonstrate substantial improvements compared to expectation maximization (EM) using turbo equalization. Furthermore, in our simulations we demonstrate a relatively small gap between the performance of the new unsupervised equalization method and that of the fully channel informed (non-blind) turbo equalizer.