TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has been thought that to learn the order of n rules one must go through all n! permutations. Thus to learn the order of 27 rules would require 27! steps or 1.08889x10 steps. This number is much greater than the number of seconds since the beginning of the universe! In an insightful analysis the linguist Block ([Block 86], pp. 62-63, p.238) showed that with the assumption of transitivity this vast number of learning steps reduces to a mere 377 steps. We present a mathematical analysis of the complexity of Block’s algorithm. The algorithm has a complexity of order n given n rules. In addition, we improve Block’s results exponentially, by introducing an algorithm that has complexity of order less than n log n.

SOLUTION: On the complexity of learning a language: An improvement of Block’s algorithm

PROBLEM: We introduce a compact graph-theoretic repre­ sentation for multi-party game theory. Our main result is a provably correct and efficient algo­ rithm for computing approximate Nash equilibria in one-stage games represented by trees or sparse graphs.

SOLUTION: Graphical Models for Game Theory

PROBLEM: In this paper, we extend the deep long short-term memory (DLSTM) recurrent neural networks by introducing gated direct connections between memory cells in adjacent layers. These direct links, called highway connections, enable unimpeded information flow across different layers and thus alleviate the gradient vanishing problem when building deeper LSTMs. We further introduce the latency-controlled bidirectional LSTMs (BLSTMs) which can exploit the whole history while keeping the latency under control. Efficient algorithms are proposed to train these novel networks using both frame and sequence discriminative criteria. Experiments on the AMI distant speech recognition (DSR) task indicate that we can train deeper LSTMs and achieve better improvement from sequence training with highway LSTMs (HLSTMs). Our novel model obtains 43.9/47.7% WER on AMI (SDM) dev and eval sets, outperforming all previous works. It beats the strong DNN and DLSTM baselines with 15.7% and 5.3% relative improvement respectively.

SOLUTION:
HIGHWAY LONG SHORT-TERM MEMORY RNNS FOR DISTANT SPEECH RECOGNITION