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.

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.
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.

Neural models achieved considerable improvement for many natural language processing tasks, but they offer little transparency, and interpretability comes at a cost. In some domains, automated predictions without justifications have limited applicability. Recently, progress has been made regarding single-aspect sentiment analysis for reviews, where the ambiguity of a justification is minimal. In this context, a justification, or mask, consists of (long) word sequences from the input text, which suffice to make the prediction. Existing models cannot handle more than one aspect in one training and induce binary masks that might be ambiguous. In our work, we propose a neural model for predicting multi-aspect sentiments for reviews and generates a probabilistic multi-dimensional mask (one per aspect) simultaneously, in an unsupervised and multi-task learning manner. Our evaluation shows that on three datasets, in the beer and hotel domain, our model outperforms strong baselines and generates masks that are: strong feature predictors, meaningful, and interpretable.
Neural model predicting multi-aspect sentiments and generating a probabilistic multi-dimensional mask simultaneously. Model outperforms strong baselines and generates masks that are: strong feature predictors, meaningful, and interpretable.

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful properties, like time reversibility and smooth interpolation in time. These properties are important for many machine learning problems - from sequence prediction to reinforcement learning and density modelling - but are not typically provided out of the box by standard tools such as recurrent neural networks. In this paper, we introduce the Hamiltonian Generative Network (HGN), the first approach capable of consistently learning Hamiltonian dynamics from high-dimensional observations (such as images) without restrictive domain assumptions. Once trained, we can use HGN to sample new trajectories, perform rollouts both forward and backward in time, and even speed up or slow down the learned dynamics. We demonstrate how a simple modification of the network architecture turns HGN into a powerful normalising flow model, called Neural Hamiltonian Flow (NHF), that uses Hamiltonian dynamics to model expressive densities. Hence, we hope that our work serves as a first practical demonstration of the value that the Hamiltonian formalism can bring to machine learning. More results and video evaluations are available at: http://tiny.cc/hgn

We introduce a class of generative models that reliably learn Hamiltonian dynamics from high-dimensional observations. The learnt Hamiltonian can be applied to sequence modeling or as a normalising flow.