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Gradient Descent


Gentle Introduction to Gradient Descent and Momentum

#artificialintelligence

In this article, we will talk about a fundamental concept in machine learning called the Gradient Descent. The gradient descent is one of the most popular algorithms that tends to reduce the error in prediction i.e minimizing your cost function. This might have been confusing but that's okay, before we jump into more details I'll give a very small gist of where it is mostly used. In deep learning, we have a concept called backpropagation. Wikipedia says " backpropagation computes the gradient of the loss function with respect to the weights of the network for a single input–output example, and does so efficiently, unlike a naïve direct computation of the gradient with respect to each weight individually" I had a brain-freeze when I read this, so let me give you an intuitive example to help you understand better.


A Glance at Optimization algorithms for Deep Learning

#artificialintelligence

Batch Gradient Descent, Mini-batch Gradient Descent and Stochastic Gradient Descent are techniques used for gradient optimization differ in the batch size they use for computing gradients in each iteration. Gradient Descent uses all the data to compute gradients and update weights in each iteration. Minibatch Gradient Descent takes a subset of dataset to update its weights in each iteration. It however takes more iterations to converge to minima, but it is faster as compared to Gradient Descent due to lesser size of batch data used. Stochastic Gradient Descent (SGD) (or also sometimes on-line gradient descent) is the extreme case of this.


Gradient Descent With AdaGrad From Scratch

#artificialintelligence

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. This can be a problem on objective functions that have different amounts of curvature in different dimensions, and in turn, may require a different sized step to a new point. Adaptive Gradients, or AdaGrad for short, is an extension of the gradient descent optimization algorithm that allows the step size in each dimension used by the optimization algorithm to be automatically adapted based on the gradients seen for the variable (partial derivatives) seen over the course of the search. In this tutorial, you will discover how to develop the gradient descent with adaptive gradients optimization algorithm from scratch.


Gradient Descent Optimization With AdaMax From Scratch

#artificialintelligence

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that a single step size (learning rate) is used for all input variables. Extensions to gradient descent, like the Adaptive Movement Estimation (Adam) algorithm, use a separate step size for each input variable but may result in a step size that rapidly decreases to very small values. AdaMax is an extension to the Adam version of gradient descent that generalizes the approach to the infinite norm (max) and may result in a more effective optimization on some problems. In this tutorial, you will discover how to develop gradient descent optimization with AdaMax from scratch.


Let's Develop Artificial Neural Network in 30 lines of code -- II

#artificialintelligence

II Simple yet Complete Guide on how to apply ANN for Regression with K-Fold Validation for accuracy over accuracy OMG! Cheers, Nice to see you again …! Previously we have already learn what is ANN and performed ANN with real life example. If not follow this link. However i will be briefing the definitions of ANN terminologies just in case if i haven't bored you:) I believe you are already aware of how Neural Networks work if not…don't worry,, there are plenty of resource available in web to get started with. However i will too walk you through in brief of what is neuron networks and how it learns?


A 2021 Guide to improving CNNs-Optimizers: Adam vs SGD

#artificialintelligence

This will be my third post on my series A 2021 Guide to improving CNNs. Optimizers can be explained as a mathematical function to modify the weights of the network given the gradients and additional information, depending on the formulation of the optimizer. Optimizers are built upon the idea of gradient descent, the greedy approach of iteratively decreasing the loss function by following the gradient. Such functions can be as simple as subtracting the gradients from the weights, or can also be very complex. Better optimizers are mainly focused on being faster and efficient but are also often known to generalize well(less overfitting) compared to others.


Learning and Generalization in Overparameterized Normalizing Flows

arXiv.org Artificial Intelligence

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with sufficiently small learning rate and suitable initialization. In contrast, the benefit of overparameterization in unsupervised learning is not well understood. Normalizing flows (NFs) constitute an important class of models in unsupervised learning for sampling and density estimation. In this paper, we theoretically and empirically analyze these models when the underlying neural network is one-hidden-layer overparameterized network. Our main contributions are two-fold: (1) On the one hand, we provide theoretical and empirical evidence that for a class of NFs containing most of the existing NF models, overparametrization hurts training. (2) On the other hand, we prove that unconstrained NFs, a recently introduced model, can efficiently learn any reasonable data distribution under minimal assumptions when the underlying network is overparametrized.


Communication Algorithm-Architecture Co-Design for Distributed Deep Learning

#artificialintelligence

Abstract--Large-scale distributed deep learning training has enabled developments of more complex deep neural network models to learn from larger datasets for sophisticated tasks. In particular, distributed stochastic gradient descent intensively invokes all-reduce operations for gradient update, which dominates communication time during iterative training epochs. In this work, we identify the inefficiency in widely used allreduce algorithms, and the opportunity of algorithm-architecture co-design. We propose MULTITREE all-reduce algorithm with topology and resource utilization awareness for efficient and scalable all-reduce operations, which is applicable to different interconnect topologies. Moreover, we co-design the network interface to schedule and coordinate the all-reduce messages for contention-free communications, working in synergy with the algorithm. The flow control is also simplified to exploit the bulk data transfer of big gradient exchange. We evaluate the co-design using different all-reduce data sizes for synthetic study, demonstrating its effectiveness on various interconnection network topologies, in addition to state-of-the-art deep neural networks for real workload experiments. The results show that MULTITREE achieves 2.3 and 1.56 communication speedup, as well as up to 81% and 30% training time reduction compared to ring all-reduce and state-of-the-art approaches, respectively.


Robust Training in High Dimensions via Block Coordinate Geometric Median Descent

arXiv.org Machine Learning

Geometric median (\textsc{Gm}) is a classical method in statistics for achieving a robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 0.5. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent (SGD) for high-dimensional optimization problems. In this paper, we show that by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a time and using a memory mechanism, one can retain the breakdown point of 0.5 for smooth non-convex problems, with non-asymptotic convergence rates comparable to the SGD with \textsc{Gm}.


Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

arXiv.org Machine Learning

Random features are a central technique for scalable learning algorithms based on kernel methods. A recent work has shown that an algorithm for machine learning by quantum computer, quantum machine learning (QML), can exponentially speed up sampling of optimized random features, even without imposing restrictive assumptions on sparsity and low-rankness of matrices that had limited applicability of conventional QML algorithms; this QML algorithm makes it possible to significantly reduce and provably minimize the required number of features for regression tasks. However, a major interest in the field of QML is how widely the advantages of quantum computation can be exploited, not only in the regression tasks. We here construct a QML algorithm for a classification task accelerated by the optimized random features. We prove that the QML algorithm for sampling optimized random features, combined with stochastic gradient descent (SGD), can achieve state-of-the-art exponential convergence speed of reducing classification error in a classification task under a low-noise condition; at the same time, our algorithm with optimized random features can take advantage of the significant reduction of the required number of features so as to accelerate each iteration in the SGD and evaluation of the classifier obtained from our algorithm. These results discover a promising application of QML to significant acceleration of the leading classification algorithm based on kernel methods, without ruining its applicability to a practical class of data sets and the exponential error-convergence speed.