instruction:
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.
question:
We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, $Q$-functions, and dynamics. We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal $Q$-functions and policies are much more complex than the dynamics. We hypothesize many real-world MDPs also have a similar property. For these MDPs, model-based planning is a favorable algorithm, because the resulting policies can approximate the optimal policy significantly better than a neural network parameterization can, and model-free or model-based policy optimization rely on policy parameterization. Motivated by the theory, we apply a simple multi-step model-based bootstrapping planner (BOOTS) to bootstrap a weak $Q$-function into a stronger policy. Empirical results show that applying BOOTS on top of model-based or model-free policy optimization algorithms at the test time improves the performance on MuJoCo benchmark tasks.
answer:
We compare deep model-based and model-free RL algorithms by studying the approximability of $Q$-functions, policies, and dynamics by neural networks.

question:
We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, they can be a powerful tool for unsupervised representation learning from video or graph-structured data. We cast training Spectral Inference Networks as a bilevel optimization problem, which allows for online learning of multiple eigenfunctions. We show results of training Spectral Inference Networks on problems in quantum mechanics and feature learning for videos on synthetic datasets. Our results demonstrate that Spectral Inference Networks accurately recover eigenfunctions of linear operators and can discover interpretable representations from video in a fully unsupervised manner.
answer:
We show how to learn spectral decompositions of linear operators with deep learning, and use it for unsupervised learning without a generative model.

question:
This paper presents two methods to disentangle and interpret contextual effects that are encoded in a pre-trained deep neural network. Unlike convolutional studies that visualize image appearances corresponding to the network output or a neural activation from a global perspective, our research aims to clarify how a certain input unit (dimension) collaborates with other units (dimensions) to constitute inference patterns of the neural network and thus contribute to the network output. The analysis of local contextual effects w.r.t. certain input units is of special values in real applications. In particular, we used our methods to explain the gaming strategy of the alphaGo Zero model in experiments, and our method successfully disentangled the rationale of each move during the game.
answer:
This paper presents methods to disentangle and interpret contextual effects that are encoded in a deep neural network.