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.

Example Input: Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of trained models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization performance than SGD, when used for training deep neural networks (DNNs). In this work, we identify two problems regarding the direction and step size for updating the weight vectors of hidden units, which may degrade the generalization performance of Adam. As a solution, we propose the normalized direction-preserving Adam (ND-Adam) algorithm, which controls the update direction and step size more precisely, and thus bridges the generalization gap between Adam and SGD. Following a similar rationale, we further improve the generalization performance in classification tasks by regularizing the softmax logits. By bridging the gap between SGD and Adam, we also shed some light on why certain optimization algorithms generalize better than others.
Example Output: A tailored version of Adam for training DNNs, which bridges the generalization gap between Adam and SGD.

Example 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.
Example 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.

Example Input: The Convolutional Neural Network (CNN) has been successfully applied in many fields during recent decades; however it lacks the ability to utilize prior domain knowledge when dealing with many realistic problems. We present a framework called Geometric Operator Convolutional Neural Network (GO-CNN) that uses domain knowledge, wherein the kernel of the first convolutional layer is replaced with a kernel generated by a geometric operator function. This framework integrates many conventional geometric operators, which allows it to adapt to a diverse range of problems. Under certain conditions, we theoretically analyze the convergence and the bound of the generalization errors between GO-CNNs and common CNNs. Although the geometric operator convolution kernels have fewer trainable parameters than common convolution kernels, the experimental results indicate that GO-CNN performs more accurately than common CNN on CIFAR-10/100. Furthermore, GO-CNN reduces dependence on the amount of training examples and enhances adversarial stability.
Example Output:
Traditional image processing algorithms are combined with Convolutional Neural Networks，a new neural network.