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 consider a simple and overarching representation for permutation-invariant functions of sequences (or set functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.

Ex Output:
We propose Janossy pooling, a method for learning deep permutation invariant functions designed to exploit relationships within the input sequence and tractable inference strategies such as a stochastic optimization procedure we call piSGD


Ex Input:
In this paper, a new intrinsic reward generation method for sparse-reward reinforcement learning is proposed based on an ensemble of dynamics models. In the proposed method, the mixture of multiple dynamics models is used to approximate the true unknown transition probability, and the intrinsic reward is designed as the minimum of the surprise seen from each dynamics model to the mixture of the dynamics models. In order to show the effectiveness of the proposed intrinsic reward generation method, a working algorithm is constructed by combining the proposed intrinsic reward generation method with the proximal policy optimization (PPO) algorithm. Numerical results show that for representative locomotion tasks, the proposed model-ensemble-based intrinsic reward generation method outperforms the previous methods based on a single dynamics model.

Ex Output:
For sparse-reward reinforcement learning, the ensemble of multiple dynamics models is used to generate intrinsic reward designed as the minimum of the surprise.


Ex Input:
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain adaptation, dimensionality reduction or generative models. However, its use is still limited by a heavy computational cost. Our goal is to alleviate this problem by providing an approximation mechanism that allows to break its inherent complexity. It relies on the search of an embedding where the Euclidean distance mimics the Wasserstein distance. We show that such an embedding can be found with a siamese architecture associated with a decoder network that allows to move from the embedding space back to the original input space. Once this embedding has been found, computing optimization problems in the Wasserstein space (e.g. barycenters, principal directions or even archetypes) can be conducted extremely fast. Numerical experiments supporting this idea are conducted on image datasets, and show the wide potential benefits of our method.

Ex Output:

We show that it is possible to fastly approximate Wasserstein distances computation by finding an appropriate embedding where Euclidean distance emulates the Wasserstein distance