We present a new approach for learning to solve SMT formulas. We phrase the challenge of solving SMT formulas as a tree search problem where at each step a transformation is applied to the input formula until the formula is solved. Our approach works in two phases: first, given a dataset of unsolved formulas we learn a policy that for each formula selects a suitable transformation to apply at each step in order to solve the formula, and second, we synthesize a strategy in the form of a loop-free program with branches. This strategy is an interpretable representation of the policy decisions and is used to guide the SMT solver to decide formulas more efficiently, without requiring any modification to the solver itself and without needing to evaluate the learned policy at inference time. We show that our approach is effective in practice - it solves 17% more formulas over a range of benchmarks and achieves up to 100x runtime improvement over a state-of-the-art SMT solver.

We describe a neural network-based system for text-to-speech (TTS) synthesis that is able to generate speech audio in the voice of many different speakers, including those unseen during training. Our system consists of three independently trained components: (1) a speaker encoder network, trained on a speaker verification task using an independent dataset of noisy speech from thousands of speakers without transcripts, to generate a fixed-dimensional embedding vector from seconds of reference speech from a target speaker; (2) a sequence-to-sequence synthesis network based on Tacotron 2, which generates a mel spectrogram from text, conditioned on the speaker embedding; (3) an auto-regressive WaveNet-based vocoder that converts the mel spectrogram into a sequence of time domain waveform samples. We demonstrate that the proposed model is able to transfer the knowledge of speaker variability learned by the discriminatively-trained speaker encoder to the new task, and is able to synthesize natural speech from speakers that were not seen during training. We quantify the importance of training the speaker encoder on a large and diverse speaker set in order to obtain the best generalization performance. Finally, we show that randomly sampled speaker embeddings can be used to synthesize speech in the voice of novel speakers dissimilar from those used in training, indicating that the model has learned a high quality speaker representation.

We consider the optimization of cost functionals on manifolds and derive a variational approach to accelerated methods on manifolds. We demonstrate the methodology on the infinite-dimensional manifold of diffeomorphisms, motivated by registration problems in computer vision. We build on the variational approach to accelerated optimization by Wibisono, Wilson and Jordan, which applies in finite dimensions, and generalize that approach to infinite dimensional manifolds. We derive the continuum evolution equations, which are partial differential equations (PDE), and relate them to simple mechanical principles. Our approach can also be viewed as a generalization of the $L^2$ optimal mass transport problem. Our approach evolves an infinite number of particles endowed with mass, represented as a mass density.

As an incremental-gradient algorithm, the hybrid stochastic gradient descent (HSGD) enjoys merits of both stochastic and full gradient methods for finite-sum minimization problem. However, the existing rate-of-convergence analysis for HSGD is made under with-replacement sampling (WRS) and is restricted to convex problems. It is not clear whether HSGD still carries these advantages under the common practice of without-replacement sampling (WoRS) for non-convex problems. In this paper, we affirmatively answer this open question by showing that under WoRS and for both convex and non-convex problems, it is still possible for HSGD (with constant step-size) to match full gradient descent in rate of convergence, while maintaining comparable sample-size-independent incremental first-order oracle complexity to stochastic gradient descent. For a special class of finite-sum problems with linear prediction models, our convergence results can be further improved in some cases. Extensive numerical results confirm our theoretical affirmation and demonstrate the favorable efficiency of WoRS-based HSGD.

Modern Visual Question Answering (VQA) models have been shown to rely heavily on superficial correlations between question and answer words learned during training -- \eg overwhelmingly reporting the type of room as kitchen or the sport being played as tennis, irrespective of the image. Most alarmingly, this shortcoming is often not well reflected during evaluation because the same strong priors exist in test distributions; however, a VQA system that fails to ground questions in image content would likely perform poorly in real-world settings. In this work, we present a novel regularization scheme for VQA that reduces this effect. We introduce a question-only model that takes as input the question encoding from the VQA model and must leverage language biases in order to succeed. We then pose training as an adversarial game between the VQA model and this question-only adversary -- discouraging the VQA model from capturing language biases in its question encoding.Further, we leverage this question-only model to estimate the mutual information between the image and answer given the question, which we maximize explicitly to encourage visual grounding. Our approach is a model agnostic training procedure and simple to implement. We show empirically that it can improve performance significantly on a bias-sensitive split of the VQA dataset for multiple base models -- achieving state-of-the-art on this task. Further, on standard VQA tasks, our approach shows significantly less drop in accuracy compared to existing bias-reducing VQA models.

Synthesizing programs using example input/outputs is a classic problem in artificial intelligence. We present a method for solving Programming By Example (PBE) problems by using a neural model to guide the search of a constraint logic programming system called miniKanren. Crucially, the neural model uses miniKanren's internal representation as input; miniKanren represents a PBE problem as recursive constraints imposed by the provided examples. We explore Recurrent Neural Network and Graph Neural Network models.

We introduce a model that learns to convert simple hand drawings into graphics programs written in a subset of \LaTeX.~The

To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes-Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.

Few-shot learning has become essential for producing models that generalize from few examples. In this work, we identify that metric scaling and metric task conditioning are important to improve the performance of few-shot algorithms. Our analysis reveals that simple metric scaling completely changes the nature of few-shot algorithm parameter updates. Metric scaling provides improvements up to 14% in accuracy for certain metrics on the mini-Imagenet 5-way 5-shot classification task. We further propose a simple and effective way of conditioning a learner on the task sample set, resulting in learning a task-dependent metric space. Moreover, we propose and empirically test a practical end-to-end optimization procedure based on auxiliary task co-training to learn a task-dependent metric space. The resulting few-shot learning model based on the task-dependent scaled metric achieves state of the art on mini-Imagenet. We confirm these results on another few-shot dataset that we introduce in this paper based on CIFAR100.

The question of which global minima are accessible by a stochastic gradient decent (SGD) algorithm with specific learning rate and batch size is studied from the perspective of dynamical stability. The concept of non-uniformity is introduced, which, together with sharpness, characterizes the stability property of a global minimum and hence the accessibility of a particular SGD algorithm to that global minimum. In particular, this analysis shows that learning rate and batch size play different roles in minima selection. Extensive empirical results seem to correlate well with the theoretical findings and provide further support to these claims.