We propose a method for non-projective dependency parsing by incrementally predicting a set of edges. Since the edges do not have a pre-specified order, we propose a set-based learning method. Our method blends graph, transition, and easy-first parsing, including a prior state of the parser as a special case. The proposed transition-based method successfully parses near the state of the art on both projective and non-projective languages, without assuming a certain parsing order.
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. We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification, ranking and sequence generation, there is no known order among items in a target multiset, and each item in the multiset may appear more than once, making this problem extremely challenging. In this paper, we propose a novel multiset loss function by viewing this problem from the perspective of sequential decision making. The proposed multiset loss function is empirically evaluated on two families of datasets, one synthetic and the other real, with varying levels of difficulty, against various baseline loss functions including reinforcement learning, sequence, and aggregated distribution matching loss functions. The experiments reveal the effectiveness of the proposed loss function over the others. Graphs are fundamental data structures required to model many important real-world data, from knowledge graphs, physical and social interactions to molecules and proteins. In this paper, we study the problem of learning generative models of graphs from a dataset of graphs of interest. After learning, these models can be used to generate samples with similar properties as the ones in the dataset. Such models can be useful in a lot of applications, e.g. drug discovery and knowledge graph construction. The task of learning generative models of graphs, however, has its unique challenges. In particular, how to handle symmetries in graphs and ordering of its elements during the generation process are important issues. We propose a generic graph neural net based model that is capable of generating any arbitrary graph. We study its performance on a few graph generation tasks compared to baselines that exploit domain knowledge. We discuss potential issues and open problems for such generative models going forward. Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models. Humans process visual scenes selectively and sequentially using attention. Central to models of human visual attention is the saliency map. We propose a hierarchical visual architecture that operates on a saliency map and uses a novel attention mechanism to sequentially focus on salient regions and take additional glimpses within those regions. The architecture is motivated by human visual attention, and is used for multi-label image classification on a novel multiset task, demonstrating that it achieves high precision and recall while localizing objects with its attention. Unlike conventional multi-label image classification models, the model supports multiset prediction due to a reinforcement-learning based training process that allows for arbitrary label permutation and multiple instances per label. Conventional neural autoregressive decoding commonly assumes a fixed left-to-right generation order, which may be sub-optimal. In this work, we propose a novel decoding algorithm -- InDIGO -- which supports flexible sequence generation in arbitrary orders through insertion operations. We extend Transformer, a state-of-the-art sequence generation model, to efficiently implement the proposed approach, enabling it to be trained with either a pre-defined generation order or adaptive orders obtained from beam-search. Experiments on four real-world tasks, including word order recovery, machine translation, image caption and code generation, demonstrate that our algorithm can generate sequences following arbitrary orders, while achieving competitive or even better performance compared to the conventional left-to-right generation. The generated sequences show that InDIGO adopts adaptive generation orders based on input information. We present the Insertion Transformer, an iterative, partially autoregressive model for sequence generation based on insertion operations. Unlike typical autoregressive models which rely on a fixed, often left-to-right ordering of the output, our approach accommodates arbitrary orderings by allowing for tokens to be inserted anywhere in the sequence during decoding. This flexibility confers a number of advantages: for instance, not only can our model be trained to follow specific orderings such as left-to-right generation or a binary tree traversal, but it can also be trained to maximize entropy over all valid insertions for robustness. In addition, our model seamlessly accommodates both fully autoregressive generation (one insertion at a time) and partially autoregressive generation (simultaneous insertions at multiple locations). We validate our approach by analyzing its performance on the WMT 2014 English-German machine translation task under various settings for training and decoding. We find that the Insertion Transformer outperforms many prior non-autoregressive approaches to translation at comparable or better levels of parallelism, and successfully recovers the performance of the original Transformer while requiring only logarithmically many iterations during decoding. 