Research papers and code for "Mohammad Norouzi":
Sequence to sequence (SEQ2SEQ) models often lack diversity in their generated translations. This can be attributed to the limitation of SEQ2SEQ models in capturing lexical and syntactic variations in a parallel corpus resulting from different styles, genres, topics, or ambiguity of the translation process. In this paper, we develop a novel sequence to sequence mixture (S2SMIX) model that improves both translation diversity and quality by adopting a committee of specialized translation models rather than a single translation model. Each mixture component selects its own training dataset via optimization of the marginal loglikelihood, which leads to a soft clustering of the parallel corpus. Experiments on four language pairs demonstrate the superiority of our mixture model compared to a SEQ2SEQ baseline with standard or diversity-boosted beam search. Our mixture model uses negligible additional parameters and incurs no extra computation cost during decoding.

* 11 pages, 5 figures, accepted to CoNLL2018
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Reflecting on the advances of off-policy deep reinforcement learning (RL) algorithms since the development of DQN in 2013, it is important to ask: are the complexities of recent off-policy methods really necessary? In an attempt to isolate the contributions of various factors of variation in off-policy deep RL and to help design simpler algorithms, this paper investigates a set of related questions: First, can effective policies be learned given only access to logged offline experience? Second, how much of the benefits of recent distributional RL algorithms is attributed to improvements in exploration versus exploitation behavior? Third, can simpler off-policy RL algorithms outperform distributional RL without learning explicit distributions over returns? This paper uses a batch RL experimental setup on Atari 2600 games to investigate these questions. Unexpectedly, we find that batch RL algorithms trained solely on logged experiences of a DQN agent are able to significantly outperform online DQN. Our experiments suggest that the benefits of distributional RL mainly stem from better exploitation. We present a simple and novel variant of ensemble Q-learning called Random Ensemble Mixture (REM), which enforces optimal Bellman consistency on random convex combinations of the Q-heads of a multi-head Q-network. The batch REM agent trained offline on DQN data outperforms the batch QR-DQN and online C51 algorithms.

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We present Optimal Completion Distillation (OCD), a training procedure for optimizing sequence to sequence models based on edit distance. OCD is efficient, has no hyper-parameters of its own, and does not require pretraining or joint optimization with conditional log-likelihood. Given a partial sequence generated by the model, we first identify the set of optimal suffixes that minimize the total edit distance, using an efficient dynamic programming algorithm. Then, for each position of the generated sequence, we use a target distribution that puts equal probability on the first token of all the optimal suffixes. OCD achieves the state-of-the-art performance on end-to-end speech recognition, on both Wall Street Journal and Librispeech datasets, achieving $9.3\%$ WER and $4.5\%$ WER respectively.

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We approach structured output prediction by optimizing a deep value network (DVN) to precisely estimate the task loss on different output configurations for a given input. Once the model is trained, we perform inference by gradient descent on the continuous relaxations of the output variables to find outputs with promising scores from the value network. When applied to image segmentation, the value network takes an image and a segmentation mask as inputs and predicts a scalar estimating the intersection over union between the input and ground truth masks. For multi-label classification, the DVN's objective is to correctly predict the F1 score for any potential label configuration. The DVN framework achieves the state-of-the-art results on multi-label prediction and image segmentation benchmarks.

* Published at ICML 2017
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We investigate the effective memory depth of RNN models by using them for $n$-gram language model (LM) smoothing. Experiments on a small corpus (UPenn Treebank, one million words of training data and 10k vocabulary) have found the LSTM cell with dropout to be the best model for encoding the $n$-gram state when compared with feed-forward and vanilla RNN models. When preserving the sentence independence assumption the LSTM $n$-gram matches the LSTM LM performance for $n=9$ and slightly outperforms it for $n=13$. When allowing dependencies across sentence boundaries, the LSTM $13$-gram almost matches the perplexity of the unlimited history LSTM LM. LSTM $n$-gram smoothing also has the desirable property of improving with increasing $n$-gram order, unlike the Katz or Kneser-Ney back-off estimators. Using multinomial distributions as targets in training instead of the usual one-hot target is only slightly beneficial for low $n$-gram orders. Experiments on the One Billion Words benchmark show that the results hold at larger scale: while LSTM smoothing for short $n$-gram contexts does not provide significant advantages over classic N-gram models, it becomes effective with long contexts ($n > 5$); depending on the task and amount of data it can match fully recurrent LSTM models at about $n=13$. This may have implications when modeling short-format text, e.g. voice search/query LMs. Building LSTM $n$-gram LMs may be appealing for some practical situations: the state in a $n$-gram LM can be succinctly represented with $(n-1)*4$ bytes storing the identity of the words in the context and batches of $n$-gram contexts can be processed in parallel. On the downside, the $n$-gram context encoding computed by the LSTM is discarded, making the model more expensive than a regular recurrent LSTM LM.

* 10 pages, including references
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We present a pixel recursive super resolution model that synthesizes realistic details into images while enhancing their resolution. A low resolution image may correspond to multiple plausible high resolution images, thus modeling the super resolution process with a pixel independent conditional model often results in averaging different details--hence blurry edges. By contrast, our model is able to represent a multimodal conditional distribution by properly modeling the statistical dependencies among the high resolution image pixels, conditioned on a low resolution input. We employ a PixelCNN architecture to define a strong prior over natural images and jointly optimize this prior with a deep conditioning convolutional network. Human evaluations indicate that samples from our proposed model look more photo realistic than a strong L2 regression baseline.

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This paper presents a novel form of policy gradient for model-free reinforcement learning (RL) with improved exploration properties. Current policy-based methods use entropy regularization to encourage undirected exploration of the reward landscape, which is ineffective in high dimensional spaces with sparse rewards. We propose a more directed exploration strategy that promotes exploration of under-appreciated reward regions. An action sequence is considered under-appreciated if its log-probability under the current policy under-estimates its resulting reward. The proposed exploration strategy is easy to implement, requiring small modifications to an implementation of the REINFORCE algorithm. We evaluate the approach on a set of algorithmic tasks that have long challenged RL methods. Our approach reduces hyper-parameter sensitivity and demonstrates significant improvements over baseline methods. Our algorithm successfully solves a benchmark multi-digit addition task and generalizes to long sequences. This is, to our knowledge, the first time that a pure RL method has solved addition using only reward feedback.

* Published as a conference paper at ICLR 2017
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Aircraft failures alter the aircraft dynamics and cause maneuvering flight envelope to change. Such envelope variations are nonlinear and generally unpredictable by the pilot as they are governed by the aircraft complex dynamics. Hence, in order to prevent in-flight Loss of Control it is crucial to practically predict the impaired aircraft's flight envelope variation due to any a-priori unknown failure degree. This paper investigates the predictability of the number of trim points within the maneuvering flight envelope and its centroid using both linear and nonlinear least-squares estimation methods. To do so, various polynomial models and nonlinear models based on hyperbolic tangent function are developed and compared which incorporate the influencing factors on the envelope variations as the inputs and estimate the centroid and the number of trim points of the maneuvering flight envelope at any intended failure degree. Results indicate that both the polynomial and hyperbolic tangent function-based models are capable of predicting the impaired fight envelope variation with good precision. Furthermore, it is shown that the regression equation of the best polynomial fit enables direct assessment of the impaired aircraft's flight envelope contraction and displacement sensitivity to the specific parameters characterizing aircraft failure and flight condition.

* 47 single-column double-spaced pages, 27 figures, 16 Tables
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There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used as such, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact k-nearest neighbor search in Hamming space. The approach is storage efficient and straightforward to implement. Theoretical analysis shows that the algorithm exhibits sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speedups over a linear scan baseline for datasets of up to one billion codes of 64, 128, or 256 bits.

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Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.

* Accepted to ICML 2019
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We consider the problem of learning from sparse and underspecified rewards, where an agent receives a complex input, such as a natural language instruction, and needs to generate a complex response, such as an action sequence, while only receiving binary success-failure feedback. Such success-failure rewards are often underspecified: they do not distinguish between purposeful and accidental success. Generalization from underspecified rewards hinges on discounting spurious trajectories that attain accidental success, while learning from sparse feedback requires effective exploration. We address exploration by using a mode covering direction of KL divergence to collect a diverse set of successful trajectories, followed by a mode seeking KL divergence to train a robust policy. We propose Meta Reward Learning (MeRL) to construct an auxiliary reward function that provides more refined feedback for learning. The parameters of the auxiliary reward function are optimized with respect to the validation performance of a trained policy. The MeRL approach outperforms our alternative reward learning technique based on Bayesian Optimization, and achieves the state-of-the-art on weakly-supervised semantic parsing. It improves previous work by 1.2% and 2.4% on WikiTableQuestions and WikiSQL datasets respectively.

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State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value. We show that such smoothed Q-values still satisfy a Bellman equation, making them learnable from experience sampled from an environment. Moreover, the gradients of expected reward with respect to the mean and covariance of a parameterized Gaussian policy can be recovered from the gradient and Hessian of the smoothed Q-value function. Based on these relationships, we develop new algorithms for training a Gaussian policy directly from a learned smoothed Q-value approximator. The approach is additionally amenable to proximal optimization by augmenting the objective with a penalty on KL-divergence from a previous policy. We find that the ability to learn both a mean and covariance during training leads to significantly improved results on standard continuous control benchmarks.

* ICML 2018
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This paper presents KeypointNet, an end-to-end geometric reasoning framework to learn an optimal set of category-specific 3D keypoints, along with their detectors. Given a single image, KeypointNet extracts 3D keypoints that are optimized for a downstream task. We demonstrate this framework on 3D pose estimation by proposing a differentiable objective that seeks the optimal set of keypoints for recovering the relative pose between two views of an object. Our model discovers geometrically and semantically consistent keypoints across viewing angles and instances of an object category. Importantly, we find that our end-to-end framework using no ground-truth keypoint annotations outperforms a fully supervised baseline using the same neural network architecture on the task of pose estimation. The discovered 3D keypoints on the car, chair, and plane categories of ShapeNet are visualized at http://keypointnet.github.io/.

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Trust region methods, such as TRPO, are often used to stabilize policy optimization algorithms in reinforcement learning (RL). While current trust region strategies are effective for continuous control, they typically require a prohibitively large amount of on-policy interaction with the environment. To address this problem, we propose an off-policy trust region method, Trust-PCL. The algorithm is the result of observing that the optimal policy and state values of a maximum reward objective with a relative-entropy regularizer satisfy a set of multi-step pathwise consistencies along any path. Thus, Trust-PCL is able to maintain optimization stability while exploiting off-policy data to improve sample efficiency. When evaluated on a number of continuous control tasks, Trust-PCL improves the solution quality and sample efficiency of TRPO.

* ICLR 2018
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We establish a new connection between value and policy based reinforcement learning (RL) based on a relationship between softmax temporal value consistency and policy optimality under entropy regularization. Specifically, we show that softmax consistent action values correspond to optimal entropy regularized policy probabilities along any action sequence, regardless of provenance. From this observation, we develop a new RL algorithm, Path Consistency Learning (PCL), that minimizes a notion of soft consistency error along multi-step action sequences extracted from both on- and off-policy traces. We examine the behavior of PCL in different scenarios and show that PCL can be interpreted as generalizing both actor-critic and Q-learning algorithms. We subsequently deepen the relationship by showing how a single model can be used to represent both a policy and the corresponding softmax state values, eliminating the need for a separate critic. The experimental evaluation demonstrates that PCL significantly outperforms strong actor-critic and Q-learning baselines across several benchmarks.

* NIPS 2017
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Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with exploration by encouraging the selection of more stochastic policies. In this work, we analyze this claim and, through new visualizations of the optimization landscape, we observe that incorporating entropy in policy optimization serves as a regularizer. We show that even with access to the exact gradient, policy optimization is difficult due to the geometry of the objective function. We qualitatively show that, in some environments, entropy regularization can make the optimization landscape smoother, thereby connecting local optima and enabling the use of larger learning rates. This manuscript presents new tools for understanding the underlying optimization landscape and highlights the challenge of designing general-purpose policy optimization algorithms in reinforcement learning.

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Neural language models are a critical component of state-of-the-art systems for machine translation, summarization, audio transcription, and other tasks. These language models are almost universally autoregressive in nature, generating sentences one token at a time from left to right. This paper studies the influence of token generation order on model quality via a novel two-pass language model that produces partially-filled sentence "templates" and then fills in missing tokens. We compare various strategies for structuring these two passes and observe a surprisingly large variation in model quality. We find the most effective strategy generates function words in the first pass followed by content words in the second. We believe these experimental results justify a more extensive investigation of generation order for neural language models.

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We present a simple and powerful algorithm for parallel black box optimization called Successive Halving and Classification (SHAC). The algorithm operates in $K$ stages of parallel function evaluations and trains a cascade of binary classifiers to iteratively cull the undesirable regions of the search space. SHAC is easy to implement, requires no tuning of its own configuration parameters, is invariant to the scale of the objective function and can be built using any choice of binary classifier. We adopt tree-based classifiers within SHAC and achieve competitive performance against several strong baselines for optimizing synthetic functions, hyperparameters and architectures.

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We present Memory Augmented Policy Optimization (MAPO), a simple and novel way to leverage a memory buffer of promising trajectories to reduce the variance of policy gradient estimate. MAPO is applicable to deterministic environments with discrete actions, such as structured prediction and combinatorial optimization tasks. We express the expected return objective as a weighted sum of two terms: an expectation over the high-reward trajectories inside the memory buffer, and a separate expectation over trajectories outside the buffer. To make an efficient algorithm of MAPO, we propose: (1) memory weight clipping to accelerate and stabilize training; (2) systematic exploration to discover high-reward trajectories; (3) distributed sampling from inside and outside of the memory buffer to scale up training. MAPO improves the sample efficiency and robustness of policy gradient, especially on tasks with sparse rewards. We evaluate MAPO on weakly supervised program synthesis from natural language (semantic parsing). On the WikiTableQuestions benchmark, we improve the state-of-the-art by 2.6%, achieving an accuracy of 46.3%. On the WikiSQL benchmark, MAPO achieves an accuracy of 74.9% with only weak supervision, outperforming several strong baselines with full supervision. Our source code is available at https://github.com/crazydonkey200/neural-symbolic-machines

* 16 Pages, 4 figures, 6 tables, accepted as a spotlight paper for NIPS 2018
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We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search to find good univariate split functions. In contrast, our method computes a linear combination of the features at each node, and optimizes the parameters of the linear combination (oblique) split functions by adopting a variant of latent variable SVM formulation. We develop a convex-concave upper bound on the classification loss for a one-level decision tree, and optimize the bound by stochastic gradient descent at each internal node of the tree. Forests of up to 1000 Continuously Optimized Oblique (CO2) decision trees are created, which significantly outperform Random Forest with univariate splits and previous techniques for constructing oblique trees. Experimental results are reported on multi-class classification benchmarks and on Labeled Faces in the Wild (LFW) dataset.

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