Deep Learning Optimization Algorithms Marcus D R Klarqvist

Leo Migdal

-Nov 17, 2025, 4:55 AM

deep learning optimization algorithms marcus d r klarqvist

Deep learning optimization algorithms, like Gradient Descent, SGD, and Adam, are essential for training neural networks by minimizing loss functions. Despite their importance, they often feel like black boxes. This guide simplifies these algorithms, offering clear explanations and practical insights Gradient descent is one of the most popular algorithms to perform optimization and the de facto method to optimize neural networks. Every state-of-the-art deep learning library contains implementations of various algorithms to improve on vanilla gradient descent. These algorithms, however, are often used as black-box optimizers, as practical explanations are hard to come by.

This article aims at providing the reader with intuitions with regard to the behaviour of different algorithms for optimizing gradient descent. Taking a step back: Gradient descent is a way to minimize an objective function $J(\theta)$ parameterized by a model's parameters $\theta \in \mathbb{R}^d$ by updating the parameters in the opposite direction of the gradient... to the parameters. The learning rate $\eta$ determines the size of the steps we take to reach a (local) minimum. In other words, we follow the direction of the slope of the surface created by the objective function downhill until we reach a valley. This article discuss various methods to improve on this "blind" stepwise approach to following the slope.

Feel free to review previous articles if you need to brush up on computing partial derivatives, the gradient, gradient descent, regularization, and automatic differentiation (part1 and part 2). CTO, Cambridge Heartwear (AI and medical devices) | PhD Cambridge + Harvard + MIT My overview of optimization functions in deep learning rank between position 2-10 on Google for a variety of queries like "deep learning optimizers" and "otpmizers in deep learning". It covers SGD, Momentum, Nesterov, Adam, RMSprop, Adagrad, Adadelta, Adamax, Nadam, and AdamW. https://lnkd.in/gjMq2zFe Surprisingly, the Beale Function also receives decent search traffic and my "Interesting Functions to Optimize" article also ranks between position 3-10 on Google for many of the described functions. https://lnkd.in/gwFAHZGZ

Machine Learning | Deep Learning | NLP | Data Analysis | Data Science | Microsoft Azure ML cloud user Wrote my first ever Blog but a very detailed blog on the mathematical concepts behind Deep Learning. It contains all the concepts, formulas, proofs, structures, neural networks and all the functionalities that you need to know before diving deep it the world of Deep Learning please read it, save it, use... And give your feedbacks 👇🏻 Mathematical Approach Toward Deep Learning https://lnkd.in/geqeSf_A Ex - Accenture Intern, Final Year Student At Progressive Education Society's Modern College Of Engineering arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Training deep learning models means solving an optimization problem: The model is incrementally adapted to minimize an objective function. The optimizers used for training deep learning models are based on gradient descent, trying to shift the model’s weights towards the objective function’s minimum.

A range of optimization algorithms is used to train deep learning models, each aiming to address a particular shortcoming of the basic gradient descent approach. Optimization algorithms play a crucial role in training deep learning models. They control how a neural network is incrementally changed to model the complex relationships encoded in the training data. With an array of optimization algorithms available, the challenge often lies in selecting the most suitable one for your specific project. Whether you’re working on improving accuracy, reducing training time, or managing computational resources, understanding the strengths and applications of each algorithm is fundamental. In this chapter, we explore common deep learning optimization algorithms in depth.

Almost all optimization problems arising in deep learning are nonconvex. Nonetheless, the design and analysis of algorithms in the context of convex problems have proven to be very instructive. It is for that reason that this chapter includes a primer on convex optimization and the proof for a very simple stochastic gradient descent algorithm on a convex objective function. Although optimization provides a way to minimize the loss function for deep learning, in essence, the goals of optimization and deep learning are fundamentally different. For instance, training error and generalization error generally differ: since the objective function of the optimization algorithm is usually a loss function based on the training dataset, the goal of optimization is to reduce... However, the goal of deep learning (or more broadly, statistical inference) is to reduce the generalization error.

To accomplish the latter we need to pay attention to overfitting in addition to using the optimization algorithm to reduce the training error. To illustrate the aforementioned different goals, let’s consider the empirical risk and the risk. The empirical risk is an average loss on the training dataset while the risk is the expected loss on the entire population of data. Below we define two functions: the risk function $f$ and the empirical risk function $g$. Suppose that we have only a finite amount of training data. As a result, here $g$ is less smooth than $f$.

Figure to show the difference between the empirical loss which is based on the loss function defined by the data and the real risk. Raven Syndrome describes how startups lose momentum by chasing shiny new ideas instead of executing on proven strategies. Learn why technical teams are vulnerable, how to recognize the risk, and how leadership can protect focus and drive real outcomes. When companies prioritize candidates from brand-name schools, elite tech companies, or top-tier startups, it’s not because they believe those people are inherently smarter or more capable. It’s because someone else already absorbed the massive cost of vetting them. A common challenge faced when using LLMs is to generate text depending on the context: Reserved and factual to creative.

Temperature sampling helps fine-tune this balance, ensuring meaningful and engaging responses. Tokenizers are the bridge between human language and computer numbers, enabling AI models like ChatGPT to process and understand text. They break down words into smaller components, or tokens, translating them into numerical codes that computers can work with. Deep learning optimization algorithms, like Gradient Descent, SGD, and Adam, are essential for training neural networks by minimizing loss functions. Despite their importance, they often feel like black boxes. This guide simplifies these algorithms, offering clear explanations and practical insights

If you read the book in sequence up to this point you already used a number of optimization algorithms to train deep learning models. They were the tools that allowed us to continue updating model parameters and to minimize the value of the loss function, as evaluated on the training set. Indeed, anyone content with treating optimization as a black box device to minimize objective functions in a simple setting might well content oneself with the knowledge that there exists an array of incantations of... To do well, however, some deeper knowledge is required. Optimization algorithms are important for deep learning. On the one hand, training a complex deep learning model can take hours, days, or even weeks.

The performance of the optimization algorithm directly affects the model’s training efficiency. On the other hand, understanding the principles of different optimization algorithms and the role of their hyperparameters will enable us to tune the hyperparameters in a targeted manner to improve the performance of deep... In this chapter, we explore common deep learning optimization algorithms in depth. Almost all optimization problems arising in deep learning are nonconvex. Nonetheless, the design and analysis of algorithms in the context of convex problems have proven to be very instructive. It is for that reason that this chapter includes a primer on convex optimization and the proof for a very simple stochastic gradient descent algorithm on a convex objective function.

CTO, Cambridge Heartwear (AI and medical devices) | PhD Cambridge + Harvard + MIT Optimizers in deep learning 📖 New week, new chapter. Want to dive into optimizers in deep learning? Think they are a black box? Learn about the underlying rationale and math with concrete examples and implementations in Python from scratch for most common optimizers. We will cover: * Momentum * Nesterov * Adam * RMSprop * Adagrad * Adadelta * Adamax * Nadam * AdamW

A common challenge faced when using LLMs is to generate text depending on the context: Reserved and factual to creative. Temperature sampling helps fine-tune this balance, ensuring meaningful and engaging responses. Tokenizers are the bridge between human language and computer numbers, enabling AI models like ChatGPT to process and understand text. They break down words into smaller components, or tokens, translating them into numerical codes that computers can work with. Deep learning optimization algorithms, like Gradient Descent, SGD, and Adam, are essential for training neural networks by minimizing loss functions. Despite their importance, they often feel like black boxes.

This guide simplifies these algorithms, offering clear explanations and practical insights Optimization is quintessential to machine learning and deep learning, with objective functions serving to represent the problem's objectives and constraints. These functions vary from straightforward quadratics to intricate landscapes that mirror real-world challenges. Dive deep into model generalizability, bias-variance trade-offs, and the art of regularization. Learn about L2 and L1 penalties and automatic feature selection. Apply these techniques to a real-world use-case!

Deep Learning Optimization Algorithms Marcus D R Klarqvist

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