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.

We give a new algorithm for learning a two-layer neural network under a very general class of input distributions. Assuming there is a ground-truth two-layer network
y = A \sigma(Wx) + \xi,
where A, W are weight matrices, \xi represents noise, and the number of neurons in the hidden layer is no larger than the input or output, our algorithm is guaranteed to recover the parameters A, W of the ground-truth network. The only requirement on the input x is that it is symmetric, which still allows highly complicated and structured input.

Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions.
We give an algorithm for learning a two-layer neural network with symmetric input distribution.

Combining domain knowledge models with neural models has been challenging. End-to-end trained neural models often perform better (lower Mean Square Error) than domain knowledge models or domain/neural combinations, and the combination is inefficient to train. In this paper, we demonstrate that by composing domain models with machine learning models, by using extrapolative testing sets, and invoking decorrelation objective functions, we create models which can predict more complex systems. The models are interpretable, extrapolative, data-efficient, and capture predictable but complex non-stochastic behavior such as unmodeled degrees of freedom and systemic measurement noise. We apply this improved modeling paradigm to several simulated systems and an actual physical system in the context of system identification. Several ways of composing domain models with neural models are examined for time series, boosting, bagging, and auto-encoding on various systems of varying complexity and non-linearity. Although this work is preliminary, we show that the ability to combine models is a very promising direction for neural modeling.
Improved modeling of complex systems uses hybrid neural/domain model composition, new decorrelation loss functions and extrapolative test sets

Optimistic initialisation is an effective strategy for efficient exploration in reinforcement learning (RL). In the tabular case, all provably efficient model-free algorithms rely on it. However, model-free deep RL algorithms do not use optimistic initialisation despite taking inspiration from these provably efficient tabular algorithms. In particular, in scenarios with only positive rewards, Q-values are initialised at their lowest possible values due to commonly used network initialisation schemes, a pessimistic initialisation. Merely initialising the network to output optimistic Q-values is not enough, since we cannot ensure that they remain optimistic for novel state-action pairs, which is crucial for exploration. We propose a simple count-based augmentation to pessimistically initialised Q-values that separates the source of optimism from the neural network. We show that this scheme is provably efficient in the tabular setting and extend it to the deep RL setting. Our algorithm, Optimistic Pessimistically Initialised Q-Learning (OPIQ), augments the Q-value estimates of a DQN-based agent with count-derived bonuses to ensure optimism during both action selection and bootstrapping. We show that OPIQ outperforms non-optimistic DQN variants that utilise a pseudocount-based intrinsic motivation in hard exploration tasks, and that it predicts optimistic estimates for novel state-action pairs.
We augment the Q-value estimates with a count-based bonus that ensures optimism during action selection and bootstrapping, even if the Q-value estimates are pessimistic.