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.
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Question: 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.

Answer: A tailored version of Adam for training DNNs, which bridges the generalization gap between Adam and SGD.


Question: We introduce NAMSG, an adaptive first-order algorithm for training neural networks. The method is efficient in computation and memory, and is straightforward to implement. It computes the gradients at configurable remote observation points, in order to expedite the convergence by adjusting the step size for directions with different curvatures in the stochastic setting. It also scales the updating vector elementwise by a nonincreasing preconditioner to take the advantages of AMSGRAD. We analyze the convergence properties for both convex and nonconvex problems by modeling the training process as a dynamic system, and provide a strategy to select the observation factor without grid search. A data-dependent regret bound is proposed to guarantee the convergence in the convex setting. The method can further achieve a O(log(T)) regret bound for strongly convex functions. Experiments demonstrate that NAMSG works well in practical problems and compares favorably to popular adaptive methods, such as ADAM, NADAM, and AMSGRAD.

Answer: A new algorithm for training neural networks that compares favorably to popular adaptive methods.


Question: As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large integrated systems of deep networks, which may have non-differentiable components and must avoid vanishing and exploding gradients for effective learning. However, since gradient descent is not applicable to hard-threshold functions, it is not clear how to learn them in a principled way. We address this problem by observing that setting targets for hard-threshold hidden units in order to minimize loss is a discrete optimization problem, and can be solved as such. The discrete optimization goal is to find a set of targets such that each unit, including the output, has a linearly separable problem to solve. Given these targets, the network decomposes into individual perceptrons, which can then be learned with standard convex approaches. Based on this, we develop a recursive mini-batch algorithm for learning deep hard-threshold networks that includes the popular but poorly justified straight-through estimator as a special case. Empirically, we show that our algorithm improves classification accuracy in a number of settings, including for AlexNet and ResNet-18 on ImageNet, when compared to the straight-through estimator.

Answer:
We learn deep networks of hard-threshold units by setting hidden-unit targets using combinatorial optimization and weights by convex optimization, resulting in improved performance on ImageNet.