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.

Input: Consider Input: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.

Output: The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.


Input: Consider Input: Conventional deep reinforcement learning typically determines an appropriate primitive action at each timestep, which requires enormous amount of time and effort for learning an effective policy, especially in large and complex environments. To deal with the issue fundamentally, we incorporate macro actions, defined as sequences of primitive actions, into the primitive action space to form an augmented action space. The problem lies in how to find an appropriate macro action to augment the primitive action space.   The agent using a proper augmented action space is able to jump to a farther state and thus speed up the exploration process as well as facilitate the learning procedure. In previous researches, macro actions are developed by mining the most frequently used action sequences or repeating previous actions. However, the most frequently used action sequences are extracted from a past policy, which may only reinforce the original behavior of that policy. On the other hand, repeating actions may limit the diversity of behaviors of the agent. Instead, we propose to construct macro actions by a genetic algorithm, which eliminates the dependency of the macro action derivation procedure from the past policies of the agent.   Our approach appends a macro action to the primitive action space once at a time and evaluates whether the augmented action space leads to promising performance or not.    We perform extensive experiments and show that the constructed macro actions are able to speed up the learning process for a variety of deep reinforcement learning methods. Our experimental results also demonstrate that the macro actions suggested by our approach are transferable among deep reinforcement learning methods and similar environments. We further provide a comprehensive set of ablation analysis to validate our methodology.

Output: We propose to construct macro actions by a genetic algorithm, which eliminates the dependency of the macro action derivation procedure from the past policies of the agent.


Input: Consider Input: Memorization in over-parameterized neural networks can severely hurt generalization in the presence of mislabeled examples. However, mislabeled examples are to hard avoid in extremely large datasets. We address this problem using the implicit regularization effect of stochastic gradient descent with large learning rates, which we find to be able to separate clean and mislabeled examples with remarkable success using loss statistics. We leverage this to identify and on-the-fly discard mislabeled examples using a threshold on their losses. This leads to On-the-fly Data Denoising (ODD), a simple yet effective algorithm that is robust to mislabeled examples, while introducing almost zero computational overhead. Empirical results demonstrate the effectiveness of ODD on several datasets containing artificial and real-world mislabeled examples.


Output: We introduce a fast and easy-to-implement algorithm that is robust to dataset noise.