TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Music relies heavily on repetition to build structure and meaning.   Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure.   The Transformer (Vaswani et al., 2017), a sequence model based on self-attention, has achieved compelling results in many generation tasks that require maintaining long-range coherence. This suggests that self-attention might also be well-suited to modeling music. In musical composition and performance, however, relative timing is critically important.   Existing approaches for representing relative positional information in the Transformer modulate attention based on pairwise distance (Shaw et al., 2018).   This is impractical for long sequences such as musical compositions since their memory complexity is quadratic in the sequence length.   We propose an algorithm that reduces the intermediate memory requirements to linear in the sequence length. This enables us to demonstrate that a Transformer with our modified relative attention mechanism can generate minute-long (thousands of steps) compositions with compelling structure, generate continuations that coherently elaborate on a given motif, and in a seq2seq setup generate accompaniments conditioned on melodies.    We evaluate the Transformer with our relative attention mechanism on two datasets, JSB Chorales and Piano-e-competition, and obtain state-of-the-art results on the latter.

SOLUTION: We show the first successful use of Transformer in generating music that exhibits long-term structure. 

PROBLEM: We present a graph neural network assisted Monte Carlo Tree Search approach for the classical traveling salesman problem (TSP). We adopt a greedy algorithm framework to construct the optimal solution to TSP by adding the nodes successively. A graph neural network (GNN) is trained to capture the local and global graph structure and give the prior probability of selecting each vertex every step. The prior probability provides a heuristics for MCTS, and the MCTS output is an improved probability for selecting the successive vertex, as it is the feedback information by fusing the prior with the scouting procedure. Experimental results on TSP up to 100 nodes demonstrate that the proposed method obtains shorter tours than other learning-based methods.

SOLUTION: A Graph Neural Network Assisted Monte Carlo Tree Search Approach to Traveling Salesman Problem

PROBLEM: Distributed optimization is essential for training large models on large datasets. Multiple approaches have been proposed to reduce the communication overhead in distributed training, such as synchronizing only after performing multiple local SGD steps, and decentralized methods (e.g., using gossip algorithms) to decouple communications among workers. Although these methods run faster than AllReduce-based methods, which use blocking communication before every update, the resulting models may be less accurate after the same number of updates. Inspired by the BMUF method of Chen & Huo (2016), we propose a slow momentum (SloMo) framework, where workers periodically synchronize and perform a momentum update, after multiple iterations of a base optimization algorithm. Experiments on image classification and machine translation tasks demonstrate that SloMo consistently yields improvements in optimization and generalization performance relative to the base optimizer, even when the additional overhead is amortized over many updates so that the SloMo runtime is on par with that of the base optimizer. We provide theoretical convergence guarantees showing that SloMo converges to a stationary point of smooth non-convex losses. Since BMUF is a particular instance of the SloMo framework, our results also correspond to the first theoretical convergence guarantees for BMUF.

SOLUTION:
SlowMo improves the optimization and generalization performance of communication-efficient decentralized algorithms without sacrificing speed.