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Theory Behind 1Cycle Learning Rate Scheduling & Learning Rate Schedules – Day 43

  The 1Cycle Learning Rate Policy: Accelerating Model Training  In our pervious article  (day 42) , we have explained The Power of Learning Rates in Deep Learning and Why Schedules Matter, lets now focus on 1Cycle Learning Rate to explain it  in more detail :  The 1Cycle Learning Rate Policy, first introduced by Leslie Smith in 2018, remains one of the most effective techniques for optimizing model training. By 2025, it continues to prove its efficiency, accelerating convergence by up to 10x compared to traditional learning rate schedules, such as constant or exponentially decaying rates. Today, both researchers and practitioners are pushing the boundaries of deep learning with this method, solidifying its role as a key component in the training of modern AI models. How the 1Cycle Policy Works The 1Cycle policy deviates from conventional learning rate schedules by alternating between two distinct phases: Phase 1: Increasing Learning Rate – The learning rate starts low and steadily rises to a peak value (η_max). This phase promotes rapid exploration of the loss landscape, avoiding sharp local minima. Phase 2: Decreasing Learning Rate – Once the peak is reached, the learning rate gradually decreases to a very low value, enabling the model...

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The Power of Learning Rates in Deep Learning and Why Schedules Matter – Day 42

  The Power of Learning Rates in Deep Learning and Why Schedules Matter In deep learning, one of the most critical yet often overlooked hyperparameters is the learning rate. It dictates how quickly a model updates its parameters during training, and finding the right learning rate can make the difference between a highly effective model and one that never converges. This post delves into the intricacies of learning rates, their sensitivity, and how to fine-tune training using learning rate schedules. Why is Learning Rate Important? The learning rate controls the size of the step the optimizer takes when adjusting model parameters during each iteration of training. If this step is too large, the model may overshoot the optimal values and fail to converge, leading to oscillations in the loss function. On the other hand, a very small learning rate causes training to proceed too slowly, taking many epochs to approach the global minimum. Learning Rate Sensitivity Here’s what happens with different learning rates: Too High: With a high learning rate, the model may diverge entirely, with the loss function increasing rapidly due to overshooting. This can cause the model to fail entirely. Too Low: A low learning rate leads to...

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75

Deep Learning Optimizers: NAdam, AdaMax, AdamW, and NAG Comparison – Day 41

Deep Learning Optimizers: NAdam, AdaMax, AdamW, and NAG A Detailed Comparison of Deep Learning Optimizers: NAdam, AdaMax, AdamW, and NAG Introduction Optimizers are fundamental to training deep learning models effectively. They update the model’s parameters during training to minimize the loss function. In this article, we’ll compare four popular optimizers: NAdam, AdaMax, AdamW, and NAG. We’ll also explore their compatibility across frameworks like TensorFlow, PyTorch, and MLX for Apple Silicon, ensuring you choose the best optimizer for your specific machine learning task. 1. NAdam (Nesterov-accelerated Adam) Overview: NAdam combines the benefits of Adam with Nesterov Accelerated Gradient (NAG). It predicts the future direction of the gradient by adding momentum to Adam’s update rule, resulting in faster and smoother convergence. Key Features: Momentum Component: Utilizes Nesterov momentum to make more informed updates, reducing overshooting and improving convergence speed. Learning Rate Adaptation: Adapts learning rates for each parameter. Convergence: Often faster and more responsive than Adam in practice. Use Cases: Best for RNNs and models that require dynamic momentum adjustment. Particularly effective in recurrent tasks. Framework Support: TensorFlow: Fully supported. PyTorch: Fully supported. MLX (Apple Silicon): Not natively supported. However, users can implement NAdam using TensorFlow or PyTorch, which are compatible with...

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138

Adam Optimizer deeply explained by Understanding Local Minimum – Day 40

Introduction to Optimization Concepts Understanding Local Minimum, Global Minimum, and Gradient Descent in Optimization In optimization problems, especially in machine learning and deep learning, concepts like local minima, global minima, and gradient descent are central to how algorithms find optimal solutions. Let’s break down these concepts: 1. Local Minimum vs. Global Minimum Local Minimum: This is a point in the optimization landscape where the function value is lower than the surrounding points, but it might not be the lowest possible value overall. It’s “locally” the best solution, but there might be a better solution elsewhere in the space. Global Minimum: This is the point where the function attains the lowest possible value across the entire optimization landscape. It’s the “best” solution globally. When using gradient-based methods like gradient descent, the goal is to minimize a loss (or cost) function. If the function has multiple minima, we want to find the global minimum, but sometimes the algorithm might get stuck in a local minimum. 2. Why Are Local Minima Considered “Bad”? Local minima are generally considered problematic because: They might not represent the best (i.e., lowest) solution. If a gradient-based optimization algorithm, like gradient descent, falls into a local minimum, it...

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131

Adam vs SGD vs AdaGrad vs RMSprop vs AdamW – Day 39

Choosing the Best Optimizer for Your Deep Learning Model When training deep learning models, choosing the right optimization algorithm can significantly impact your model’s performance, convergence speed, and generalization ability. Below, we will explore some of the most popular optimization algorithms, their strengths, the reasons they were invented, and the types of problems they are best suited for. 1. Stochastic Gradient Descent (SGD) Why It Was Invented SGD is one of the earliest and most fundamental optimization algorithms used in machine learning and deep learning. It was invented to handle the challenge of minimizing cost functions efficiently, particularly when dealing with large datasets where traditional gradient descent methods would be computationally expensive. Inventor The concept of SGD is rooted in statistical learning, but its application in neural networks is often attributed to Yann LeCun and others in the 1990s. Formula The update rule for SGD is given by: where is the learning rate, is the gradient of the loss function with respect to the model parameters . Strengths and Limitations **Strengths:** SGD is particularly effective in cases where the model is simple, and the dataset is large, making it a robust choice for problems where generalization is important. The simplicity...

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458

AdaGrad vs RMSProp vs Adam: Why Adam is the Most Popular? – Day 38

A Comprehensive Guide to Optimization Algorithms: AdaGrad, RMSProp, and Adam In the realm of machine learning, selecting the right optimization algorithm can significantly impact the performance and efficiency of your models. Among the various options available, AdaGrad, RMSProp, and Adam are some of the most widely used optimization algorithms. Each of these algorithms has its own strengths and weaknesses. In this article, we’ll explore why AdaGrad ( which we explained fully on day 37 ) might not always be the best choice and how RMSProp & Adam could address some of its shortcomings. AdaGrad: Why It’s Not Always the Best Choice What is AdaGrad? AdaGrad (Adaptive Gradient Algorithm) is one of the first adaptive learning rate methods. It adjusts the learning rate for each parameter individually by scaling it inversely with the sum of the squares of all previous gradients. The Core Idea: The idea behind AdaGrad is to use a different learning rate for each parameter that adapts over time based on the historical gradients. Parameters with large gradients will have their learning rates decreased, while parameters with small gradients will have their learning rates increased. The Core Equation: Where: represents the parameters at time step . is the...

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75

A Comprehensive Guide to AdaGrad: Origins, Mechanism, and Mathematical Proof – Day 37

  A Comprehensive Guide to AdaGrad: Origins, Mechanism, and Mathematical Proof Introduction to AdaGrad AdaGrad, short for Adaptive Gradient Algorithm, is a foundational optimization algorithm in machine learning and deep learning. It was introduced in 2011 by John Duchi, Elad Hazan, and Yoram Singer in their paper titled “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization”. AdaGrad revolutionized the field by offering a solution to the limitations of traditional gradient descent, especially in scenarios involving sparse data and high-dimensional optimization problems. The Origins of AdaGrad The motivation behind AdaGrad was to improve the robustness and efficiency of the Stochastic Gradient Descent (SGD) method. In high-dimensional spaces, using a fixed learning rate for all parameters can be inefficient. Some parameters might require a larger step size while others may need smaller adjustments. AdaGrad addresses this by adapting the learning rate individually for each parameter, which allows for better handling of the varying scales in the data. How AdaGrad Works The core idea of AdaGrad is to accumulate the squared gradients for each parameter over time and use this information to scale the learning rate. This means that parameters with large accumulated gradients receive smaller updates, while those with smaller gradients...

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Nag as optimiser in deep learning – day 36

Nesterov Accelerated Gradient (NAG): A Comprehensive Overview Nesterov Accelerated Gradient (NAG): A Comprehensive Overview Introduction to Nesterov Accelerated Gradient Nesterov Accelerated Gradient (NAG), also known as Nesterov Momentum, is an advanced optimization technique introduced by Yurii Nesterov in the early 1980s. It is an enhancement of the traditional momentum-based optimization used in gradient descent, designed to accelerate the convergence rate of the optimization process, particularly in the context of deep learning and complex optimization problems. How NAG Works The core idea behind NAG is the introduction of a “look-ahead” step before calculating the gradient, which allows for a more accurate and responsive update of parameters. In traditional momentum methods, the gradient is computed at the current position of the parameters, which might lead to less efficient convergence if the trajectory is not perfectly aligned with the optimal path. NAG, however, calculates the gradient at a position slightly ahead, based on the accumulated momentum, thus allowing the algorithm to “correct” its course more effectively if it is heading towards a suboptimal direction. The NAG update rule can be summarized as follows: Look-ahead Step: Compute a preliminary update based on the momentum. Gradient Calculation: Evaluate the gradient at this look-ahead position. Momentum...

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Momentum – part 3 – day 35

Understanding Gradient Descent and Momentum in Deep Learning Comprehensive Guide: Understanding Gradient Descent and Momentum in Deep Learning Gradient descent is a cornerstone algorithm in the field of deep learning, serving as the primary method by which neural networks optimize their weights to minimize the loss function. This article will delve into the principles of gradient descent, its importance in deep learning, how momentum enhances its performance, and the role it plays in model training. We will also explore practical examples to illustrate these concepts. What is Gradient Descent? Gradient Descent is an optimization algorithm used to minimize a loss function by iteratively adjusting the model’s parameters (weights and biases). The loss function measures the discrepancy between the model’s predictions and the actual target values. The goal of gradient descent is to find the set of parameters that minimize this loss function, thereby improving the model’s accuracy. The Gradient Descent Formula The basic update rule for gradient descent is expressed as: Where: represents the model parameters at iteration . is the learning rate, a hyperparameter that determines the step size for each iteration. is the gradient of the loss function with respect to the parameters at the previous iteration. How...

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Momentum vs Normalization in Deep learning -Part 2 – Day 34

Comparing Momentum and Normalization in Deep Learning: A Mathematical Perspective Momentum and normalization are two pivotal techniques in deep learning that enhance the efficiency and stability of training. This article explores the mathematics behind these methods, provides examples with and without these techniques, and demonstrates why they are beneficial for deep learning models.  Comparing Momentum and Normalization Momentum: Smoothing and Accelerating Convergence Momentum is an optimization technique that modifies the standard gradient descent by adding a velocity term to the update rule. This velocity term is a running average of past gradients, which helps the optimizer to continue moving in directions where gradients are consistently pointing, thereby accelerating convergence and reducing oscillations. Mathematical Formulation: Without Momentum (Standard Gradient Descent): With Momentum: Here, is the momentum coefficient (typically around 0.9), and accumulates the gradients to provide smoother and more directed updates. Example with and Without Momentum: Consider a simple quadratic loss function , starting with , a learning rate , and for momentum. Without Momentum: Iteration 1: Gradient at : Update: Iteration 2: Gradient at : Update: With Momentum: Iteration 1: Gradient at : Velocity update: Update: Iteration 2: Gradient at : Velocity update: Update: Why Momentum is Better: Faster Convergence:...

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