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Gradient Descent

A project of upgrading a simple chatbot


I initially wanted to learn how chatbot works and created a simple one on my own. However, there's a surprising amount of available codes that create chatbots of all levels. My task was to learn from this very simple chatbot model that uses straightforward NN of x and y, using stochastic gradient descent to predict the intention of the writer and generate an answer accordingly. As x is the input text, and y is the intention, the author marks 0 or 1 to the input texts. 1 is close to the intention, and 0 is the opposite. My idea of improvement is instead of marking 0 or 1 to the texts, I would implement words to vectors to create one hot encoded (X, Y) matrices, then feed the encoded words into the model.

Gradient descent Method in Machine Learning


Many deep learning models pick up objectives using the gradient-descent method. Gradient-descent optimization needs a big number of training samples for a model to converge. That creates it out of shape for few-shot learning. We train our models to learn to achieve a sure objective in generic deep learning models. However, humans train to learn any objective. There are different optimization methods that emphasize learn-to-learn mechanisms.

Congratulations to the NeurIPS 2021 award winners!


The thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2021) will be held from Monday 6 December to Tuesday 14 December. This week, the awards committees announced the winners of the outstanding paper award, the test of time award and – for the first time – the best paper award in the new datasets and benchmarks track. Six articles received outstanding paper awards this year. A Universal Law of Robustness via Isoperimetry Sébastien Bubeck and Mark Sellke The authors propose a theoretical model to explain why many state-of-the-art deep networks require many more parameters than are necessary to smoothly fit the training data. On the Expressivity of Markov Reward David Abel, Will Dabney, Anna Harutyunyan, Mark K. Ho, Michael Littman, Doina Precup and Satinder Singh This paper provides a clear exposition of when Markov rewards are, or are not, sufficient to enable a system designer to specify a task, in terms of their preference for a particular behaviour, preferences over behaviours, or preferences over state and action sequences.

Optimizers -- Momentum and Nesterov momentum algorithms (Part 2)


Welcome to the second part on optimisers where we will be discussing momentum and Nesterov accelerated gradient. If you want a quick review of vanilla gradient descent algorithms and its variants, please read about it in part1. In part3 of this series, I will be explaining RMSprop and Adam in detail. Gradient descent uses the gradients to update the weights and these can be sometimes noisy. In mini-batch gradient descent while we are updating the weights based on the data in a given batch, there will be some variance in the direction of the update.

How Parallelization and Large Batch Size Improve the Performance of Deep Neural Networks.


Large Batch Size had till recently been viewed as a deterrent for good accuracy. However recent studies show that increasing the batch size can significantly reduce the training time while maintaining a considerable level of accuracy. In this blog, we draw on our inferences from four such technical papers. The RMSprop Warm-up phase is used to address the optimization difficulty at the start of the training. The update rule demonstrated below utilizes both the Stochastic Gradient Descent (SGD) along the RMSprop optimization algorithm.

Vector Calculus for Machine Learning


To keep this post as engaging and entertaining as possible I will first introduce a brief history of Calculus and why I think it is so cool. Then, we will move on to reviewing fundamental concepts of your high school calculus such as derivative rules. Next, we will get our feet wet with vectors and matrices to make sure you are comfortable with these mathematical objects before covering partial and vector derivatives. Finally, I will conclude this post with the concept of a gradient, the intuition behind optimization with Gradient Descent and a cool implementation of calculus with Python leveraging the library SimPy. Feel free to skip any sections you like if you are comfortable with such topics. At the core, Calculus is just a very special way of thinking about large problems by splitting them into several, smaller, problems.

Deep learning via message passing algorithms based on belief propagation Machine Learning

Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on graphs with loops (from inference to optimization, from signal processing to clustering). The BP-based scheme is fundamentally different from stochastic gradient descent (SGD), on which the current success of deep networks is based. In this paper, we present and adapt to mini-batch training on GPUs a family of BP-based message-passing algorithms with a reinforcement field that biases distributions towards locally entropic solutions. These algorithms are capable of training multi-layer neural networks with discrete weights and activations with performance comparable to SGD-inspired heuristics (BinaryNet) and are naturally well-adapted to continual learning. Furthermore, using these algorithms to estimate the marginals of the weights allows us to make approximate Bayesian predictions that have higher accuracy than point-wise solutions.

Gradient Descent with 'Math'


In the last blog we saw about basics of Gradient Descent and how it works.This time we will see math behind it. We are actually subtracting some part from value of parameter and updating it.We keep doing this until we get optimized value of parameter so the cost is minimum. You may be thinking that why '-' sign is used in above equation. If you look at image below, in the right side of curve slope is positive so by subtracting value from theta, we are actually getting closer to the optimal value, while on the left side the slope is negative so we are actually adding some part in value of theta and so getting closer to the optimal value. We keep updating value of theta until the change in value 0.001 (values may vary according to case).Usually we take value of learning rate as 0.01

An overview on gradient descent and its variants


The term "optimization" refers to the process of iteratively training a model to produce a maximum and minimum function evaluation to get a minimum cost function. It is crucial since it will assist us in obtaining a model with the least amount of error (as there will be discrepancies between the actual and predicted values). There are various optimization methods; in this article, we'll look at gradient descent and its three forms: batch, stochastic, and mini-batch. Note: Hyperparameter optimization is required to fine-tune the model. Before you begin training the model, you must first specify hyperparameters.

On the Optimization Landscape of Maximum Mean Discrepancy Machine Learning

Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood calculation. However, it is hard to obtain theoretical guarantees for such models. In particular, it is not understood when they can globally optimize their non-convex objectives. Here we provide such an analysis for the case of Maximum Mean Discrepancy (MMD) learning of generative models. We prove several optimality results, including for a Gaussian distribution with low rank covariance (where likelihood is inapplicable) and a mixture of Gaussians. Our analysis shows that that the MMD optimization landscape is benign in these cases, and therefore gradient based methods will globally minimize the MMD objective.