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: Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.

Output: A method for learning quantization configuration for low precision networks that achieves state of the art performance for quantized networks.


Input: Consider Input: Unsupervised anomaly detection on multi- or high-dimensional data is of great importance in both fundamental machine learning research and industrial applications, for which density estimation lies at the core. Although previous approaches based on dimensionality reduction followed by density estimation have made fruitful progress, they mainly suffer from decoupled model learning with inconsistent optimization goals and incapability of preserving essential information in the low-dimensional space. In this paper, we present a Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. Our model utilizes a deep autoencoder to generate a low-dimensional representation and reconstruction error for each input data point, which is further fed into a Gaussian Mixture Model (GMM). Instead of using decoupled two-stage training and the standard Expectation-Maximization (EM) algorithm, DAGMM jointly optimizes the parameters of the deep autoencoder and the mixture model simultaneously in an end-to-end fashion, leveraging a separate estimation network to facilitate the parameter learning of the mixture model. The joint optimization, which well balances autoencoding reconstruction, density estimation of latent representation, and regularization, helps the autoencoder escape from less attractive local optima and further reduce reconstruction errors, avoiding the need of pre-training. Experimental results on several public benchmark datasets show that, DAGMM significantly outperforms state-of-the-art anomaly detection techniques, and achieves up to 14% improvement based on the standard F1 score.

Output: An end-to-end trained deep neural network that leverages Gaussian Mixture Modeling to perform density estimation and unsupervised anomaly detection in a low-dimensional space learned by deep autoencoder.


Input: Consider Input: A Synaptic Neural Network (SynaNN) consists of synapses and neurons. Inspired by the synapse research of neuroscience, we built a synapse model with a nonlinear synapse function of excitatory and inhibitory channel probabilities. Introduced the concept of surprisal space and constructed a commutative diagram, we proved that the inhibitory probability function -log(1-exp(-x)) in surprisal space is the topologically conjugate function of the inhibitory complementary probability 1-x in probability space. Furthermore, we found that the derivative of the synapse over the parameter in the surprisal space is equal to the negative Bose-Einstein distribution. In addition, we constructed a fully connected synapse graph (tensor) as a synapse block of a synaptic neural network. Moreover, we proved the gradient formula of a cross-entropy loss function over parameters, so synapse learning can work with the gradient descent and backpropagation algorithms. In the proof-of-concept experiment, we performed an MNIST training and testing on the MLP model with synapse network as hidden layers.


Output: A synaptic neural network with synapse graph and learning that has the feature of topological conjugation and Bose-Einstein distribution in surprisal space.