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.
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.
Each year, the treatment decisions for more than 230,000 breast cancer patients in the U.S. hinge on whether the cancer has metastasized away from the breast. Metastasis detection is currently performed by pathologists reviewing large expanses of biological tissues. This process is labor intensive and error-prone. We present a framework to automatically detect and localize tumors as small as 100 x 100 pixels in gigapixel microscopy images sized 100,000 x 100,000 pixels. Our method leverages a convolutional neural network (CNN) architecture and obtains state-of-the-art results on the Camelyon16 dataset in the challenging lesion-level tumor detection task. At 8 false positives per image, we detect 92.4% of the tumors, relative to 82.7% by the previous best automated approach. For comparison, a human pathologist attempting exhaustive search achieved 73.2% sensitivity. We achieve image-level AUC scores above 97% on both the Camelyon16 test set and an independent set of 110 slides. In addition, we discover that two slides in the Camelyon16 training set were erroneously labeled normal. Our approach could considerably reduce false negative rates in metastasis detection.
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items.
A key problem in structured output prediction is direct optimization of the task reward function that matters for test evaluation. This paper presents a simple and computationally efficient approach to incorporate task reward into a maximum likelihood framework. By establishing a link between the log-likelihood and expected reward objectives, we show that an optimal regularized expected reward is achieved when the conditional distribution of the outputs given the inputs is proportional to their exponentiated scaled rewards. Accordingly, we present a framework to smooth the predictive probability of the outputs using their corresponding rewards. We optimize the conditional log-probability of augmented outputs that are sampled proportionally to their exponentiated scaled rewards. Experiments on neural sequence to sequence models for speech recognition and machine translation show notable improvements over a maximum likelihood baseline by using reward augmented maximum likelihood (RAML), where the rewards are defined as the negative edit distance between the outputs and the ground truth labels.
Neural Machine Translation (NMT) is an end-to-end learning approach for automated translation, with the potential to overcome many of the weaknesses of conventional phrase-based translation systems. Unfortunately, NMT systems are known to be computationally expensive both in training and in translation inference. Also, most NMT systems have difficulty with rare words. These issues have hindered NMT's use in practical deployments and services, where both accuracy and speed are essential. In this work, we present GNMT, Google's Neural Machine Translation system, which attempts to address many of these issues. Our model consists of a deep LSTM network with 8 encoder and 8 decoder layers using attention and residual connections. To improve parallelism and therefore decrease training time, our attention mechanism connects the bottom layer of the decoder to the top layer of the encoder. To accelerate the final translation speed, we employ low-precision arithmetic during inference computations. To improve handling of rare words, we divide words into a limited set of common sub-word units ("wordpieces") for both input and output. This method provides a good balance between the flexibility of "character"-delimited models and the efficiency of "word"-delimited models, naturally handles translation of rare words, and ultimately improves the overall accuracy of the system. Our beam search technique employs a length-normalization procedure and uses a coverage penalty, which encourages generation of an output sentence that is most likely to cover all the words in the source sentence. On the WMT'14 English-to-French and English-to-German benchmarks, GNMT achieves competitive results to state-of-the-art. Using a human side-by-side evaluation on a set of isolated simple sentences, it reduces translation errors by an average of 60% compared to Google's phrase-based production system.
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. The run-time of computing the gradient of the proposed surrogate objective with respect to each training exemplar is quadratic in the the tree depth, and thus training deep trees is feasible. The use of stochastic gradient descent for optimization enables effective training with large datasets. Experiments on several classification benchmarks demonstrate that the resulting non-greedy decision trees outperform greedy decision tree baselines.
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.
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.
Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional \nway{} classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing \nway{} image classifier and a semantic word embedding model, which contains the $\n$ class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.