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: The softmax function is widely used to train deep neural networks for multi-class classification. Despite its outstanding performance in classification tasks, the features derived from the supervision of softmax are usually sub-optimal in some scenarios where Euclidean distances apply in feature spaces. To address this issue, we propose a new loss, dubbed the isotropic loss, in the sense that the overall distribution of data points is regularized to approach the isotropic normal one. Combined with the vanilla softmax, we formalize a novel criterion called the isotropic softmax, or isomax for short, for supervised learning of deep neural networks. By virtue of the isomax, the intra-class features are penalized by the isotropic loss while inter-class distances are well kept by the original softmax loss. Moreover, the isomax loss does not require any additional modifications to the network, mini-batches or the training process. Extensive experiments on classification and clustering are performed to demonstrate the superiority and robustness of the isomax loss.

Answer: The discriminative capability of softmax for learning feature vectors of objects is effectively enhanced by virture of isotropic normalization on global distribution of data points.

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: Operating deep neural networks on devices with limited resources requires the reduction of their memory footprints and computational requirements. In this paper we introduce a training method, called look-up table quantization (LUT-Q), which learns a dictionary and assigns each weight to one of the dictionary's values. We show that this method is very flexible and that many other techniques can be seen as special cases of LUT-Q. For example, we can constrain the dictionary trained with LUT-Q to generate networks with pruned weight matrices or restrict the dictionary to powers-of-two to avoid the need for multiplications. In order to obtain fully multiplier-less networks, we also introduce a multiplier-less version of batch normalization. Extensive experiments on image recognition and object detection tasks show that LUT-Q consistently achieves better performance than other methods with the same quantization bitwidth.

Answer:
In this paper we introduce a training method, called look-up table quantization (LUT-Q), which learns a dictionary and assigns each weight to one of the dictionary's values