Complexity dichotomy on partial grid recognition

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even trivial. A natural step, outstanding thus far, was to provide a broad classification of graphs that make for polynomial or NP-complete instances. We provide such a classification based on the set of allowed vertex degrees in the input graphs, yielding a full dichotomy on the complexity of the problem. As byproducts, the previous NP-completeness result for binary trees was strengthened to strictly binary trees, and the three-dimensional version of the problem was for the first time proven to be NP-complete. Our results were made possible by introducing the concepts of consistent orientations and robust gadgets, and by showing how the former allows NP-completeness proofs by local replacement even in the absence of the latter

On Tree-Based Neural Sentence Modeling

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of different tree structures, we replace the parsing trees with trivial trees (i.e., binary balanced tree, left-branching tree and right-branching tree) in the encoders. Though trivial trees contain no syntactic information, those encoders get competitive or even better results on all of the ten downstream tasks we investigated. This surprising result indicates that explicit syntax guidance may not be the main contributor to the superior performances of tree-based neural sentence modeling. Further analysis show that tree modeling gives better results when crucial words are closer to the final representation. Additional experiments give more clues on how to design an effective tree-based encoder. Our code is open-source and available at https://github.com/ExplorerFreda/TreeEnc.Comment: To Appear at EMNLP 201

Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages

We propose an efficient nonparametric strategy for learning a message operator in expectation propagation (EP), which takes as input the set of incoming messages to a factor node, and produces an outgoing message as output. This learned operator replaces the multivariate integral required in classical EP, which may not have an analytic expression. We use kernel-based regression, which is trained on a set of probability distributions representing the incoming messages, and the associated outgoing messages. The kernel approach has two main advantages: first, it is fast, as it is implemented using a novel two-layer random feature representation of the input message distributions; second, it has principled uncertainty estimates, and can be cheaply updated online, meaning it can request and incorporate new training data when it encounters inputs on which it is uncertain. In experiments, our approach is able to solve learning problems where a single message operator is required for multiple, substantially different data sets (logistic regression for a variety of classification problems), where it is essential to accurately assess uncertainty and to efficiently and robustly update the message operator.Comment: accepted to UAI 2015. Correct typos. Add more content to the appendix. Main results unchange

In search of isoglosses: continuous and discrete language embeddings in Slavic historical phonology

This paper investigates the ability of neural network architectures to effectively learn diachronic phonological generalizations in a multilingual setting. We employ models using three different types of language embedding (dense, sigmoid, and straight-through). We find that the Straight-Through model outperforms the other two in terms of accuracy, but the Sigmoid model's language embeddings show the strongest agreement with the traditional subgrouping of the Slavic languages. We find that the Straight-Through model has learned coherent, semi-interpretable information about sound change, and outline directions for future research