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.

Ex Input:
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.

Ex Output:
We compare deep model-based and model-free RL algorithms by studying the approximability of $Q$-functions, policies, and dynamics by neural networks. 


Ex Input:
We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB.   This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive enough to model multi-hop inferences, and scalable enough to use with realistically large KBs. The sparse-matrix reified KB can be distributed across multiple GPUs, can scale to tens of millions of entities and facts, and is orders of magnitude faster than naive sparse-matrix implementations.   The reified KB enables very simple end-to-end architectures to obtain competitive performance on several benchmarks representing two families of tasks: KB completion, and learning semantic parsers from denotations.

Ex Output:
A scalable differentiable neural module that implements reasoning on symbolic KBs.


Ex Input:
We improve the robustness of deep neural nets  to adversarial attacks by using an interpolating function as the output activation.    This data-dependent activation function remarkably improves both classification accuracy and stability to adversarial perturbations. Together with the total variation minimization of adversarial images and augmented training, under the strongest attack, we achieve up to 20.6%, 50.7%, and 68.7% accuracy improvement w.r.t.   the fast gradient sign method, iterative fast gradient sign method, and Carlini-WagnerL2attacks, respectively.   Our defense strategy is additive to many of the existing methods.   We give an intuitive explanation of our defense strategy via analyzing the geometry of the feature space. For reproducibility, the code will be available on GitHub.

Ex Output:

We proposal strategies for adversarial defense based on data dependent activation function, total variation minimization, and training data augmentation