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: In contrast to the older writing system of the 19th century, modern Hawaiian orthography employs characters for long vowels and glottal stops. These extra characters account for about one-third of the phonemes in Hawaiian, so including them makes a big difference to reading comprehension and pronunciation. However, transliterating between older and newer texts is a laborious task when performed manually. We introduce two related methods to help solve this transliteration problem automatically, given that there were not enough data to train an end-to-end deep learning model. One approach is implemented, end-to-end, using finite state transducers (FSTs). The other is a hybrid deep learning approach which approximately composes an FST with a recurrent neural network (RNN). We find that the hybrid approach outperforms the end-to-end FST by partitioning the original problem into one part that can be modelled by hand, using an FST, and into another part, which is easily solved by an RNN trained on the available data.

SOLUTION: A novel, hybrid deep learning approach provides the best solution to a limited-data problem (which is important to the conservation of the Hawaiian language)

PROBLEM: First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the pro- hibitive computational cost in calculating the second-order information. In this paper, we propose a novel Gram-Gauss-Newton (GGN) algorithm to train deep neural networks for regression problems with square loss. Our method draws inspiration from the connection between neural network optimization and kernel regression of neural tangent kernel (NTK). Different from typical second-order methods that have heavy computational cost in each iteration, GGN only has minor overhead compared to first-order methods such as SGD. We also give theoretical results to show that for sufficiently wide neural networks, the convergence rate of GGN is quadratic. Furthermore, we provide convergence guarantee for mini-batch GGN algorithm, which is, to our knowledge, the first convergence result for the mini-batch version of a second-order method on overparameterized neural net- works. Preliminary experiments on regression tasks demonstrate that for training standard networks, our GGN algorithm converges much faster and achieves better performance than SGD.

SOLUTION: A novel Gram-Gauss-Newton method to train neural networks, inspired by neural tangent kernel and Gauss-Newton method, with fast convergence speed both theoretically and experimentally.

PROBLEM: Wilson et al. (2017) showed that, when the stepsize schedule is properly designed, stochastic gradient generalizes better than ADAM (Kingma & Ba, 2014). In light of recent work on hypergradient methods (Baydin et al., 2018), we revisit these claims to see if such methods close the gap between the most popular optimizers. As a byproduct, we analyze the true benefit of these hypergradient methods compared to more classical schedules, such as the fixed decay of Wilson et al. (2017). In particular, we observe they are of marginal help since their performance varies significantly when tuning their hyperparameters. Finally, as robustness is a critical quality of an optimizer, we provide a sensitivity analysis of these gradient based optimizers to assess how challenging their tuning is.

SOLUTION:
We provide a study trying to see how the recent online learning rate adaptation extends the conclusion made by Wilson et al. 2018 about adaptive gradient methods, along with comparison and sensitivity analysis.