Gradient descent oscillation With gradient descent, you don't decrease the learning rate (for smooth loss functions such as L2). Intuitively, the oscillation can prevent over-greedy convergence which could only leverage the most prominent components of the data, thus allowing for all the useful components to be discovered and learned by gradient descent. The technique seeks to overcome the oscillation problem by adding history to the parameter update equation. In the post, it says if the loss function is flatter in the direction of x (local minima here) compared t The gradient norm along the central flow is much smaller than the gradient norm along the gradient descent trajectory, since most of the latter is dominated by the back-and-forth oscillations "across the valley" that cancel out over the long run. In view of our findings, we refer to such a phenomenon as “benign oscillation". This article covers its iterative process of gradient descent in python for minimizing cost functions, various types like batch, or mini-batch and SGD , and provides insights into implementing it in Python. We incorporate a restarting fast iteration mechanism into the inner loop, which promotes the convergence process of the algorithm. Implementation of the gradient descent method using gradient descent feed forward involves: Gradient descent with momentum ¶ Momentum results in cancellation of gradient changes in opposite directions, and hence damps out oscillations while amplifying consistent changes in the same direction. If certain parameters of the loss function such as smoothness or strong convexity constants are known, theoretical learning rate schedules can be applied. using Newton’s method [Nocedal2006] or Hessian-Free optimization [Martens2010,Martens2011,Sutskever2011]. Jun 25, 2016 · Say we want to minimize this function using gradient descent. Unlike classic gradient descent, they incorporate a "momentum" term that helps the optimizer navigate the loss surface more efficiently. May 25, 2020 · If we use higher learning rate then the frequency of the vertical oscillation would be greater. Learn about the trade-offs between a high and a low learning rate for gradient descent, and how to balance them for your neural network. May 1, 2025 · Stochastic Gradient Descent (SGD) is a highly efficient optimization algorithm, particularly well suited for large datasets due to its incremental par… Stochastic Gradient Descent An essential step in building a deep learning model is solving the underlying optimization problem, as defined by the loss function. May 31, 2023 · Gradient descent is a fundamental algorithm used in machine learning to minimize the cost function and optimize model parameters. 2). Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially Gradient descent ¶ Gradient descent is an optimization algorithm used to minimize some function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. momentum = 0 (default value) implies no acceleration and dampening. Gradient descent algorithms are the optimizers of choice Jun 19, 2025 · In convex settings, such methods can achieve improved convergence rates and reduced oscillations. This chapter covers Stochastic Gradient Descent (SGD), which is the most commonly used algorithm for solving such optimization problems. 3). Jul 11, 2025 · Gradient descent minimizes the Mean Squared Error (MSE) which serves as the loss function to find the best-fit line. org Jan 19, 2016 · This blog post looks at variants of gradient descent and the algorithms that are commonly used to optimize them. To minimise this, instead of summing up the Oct 27, 2023 · Intuitively, the oscillation can prevent over-greedy convergence which could only leverage the most prominent components of the data, thus allowing for all useful components to be discovered and learned via gradient descent. 1 Gradient Descent Method This method is applied to identify the trained neural network between two values. One option is to set the step-size adaptively for every feature. 6 days ago · Abstract In this paper, we propose a fast iterative stochastic gradient method to solve convex optimization problem, referred as the RFISTA-SVRG-TR. Dec 5, 2023 · Data Science DL Notes: Advanced Gradient Descent I researched the main optimization algorithms used for training artificial neural networks, implemented them from scratch in Python and compared them using animated visualizations. The behavior of gradient descent near a local minimum is equivalent to a set of coupled and damped harmonic oscil-lators. Several methods are available to implement gradient descent. Sep 15, 2022 · Oscillations (dotted lines) of Mini-batch Gradient Descent. It includes formulation of learning problems and concepts of representation, over-fitting, and generalization. In this study, we delve deeper into the instability of gradient descent during the training of deep networks. The Gradient Descent Rule Gradient descent is an… Jan 16, 2024 · This paper studies the effects of large learning rate and oscillation in stochastic gradient descent on a specific data generation model. The gradient of the cost function at saddle points ( plateau) is negligible or zero, which in turn leads to small or Gradient Descent with Momentum # We want to create a method with two properties: It should move through bad local minima with high probability. These hyper-parameters include the initial value for parameter , a step-size hyper-parameter , and an accuracy hyper-parameter . Jun 29, 2020 · It dampens the oscillations. Sep 25, 2024 · We present a physiologically inspired speech recognition architecture, compatible and scalable with deep learning frameworks, and demonstrate that end-to-end gradient descent training leads to the emergence of neural oscillations in the central spiking neural network. These optimizers build upon SGD by adding mechanisms like Aug 27, 2023 · Oscillations and Noise The updates in Gradient Descent are influenced solely by the gradient of the current iteration. This is perhaps clearer in the 2D example below. Both are different and if the gradient is too noisy its better to use momentum. Learn about the mathematical principles behind gradient descent, the critical role of the learning rate, and strategies to overcome challenges such as oscillation and slow convergence. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially Apr 7, 2024 · Here is pseudo-code for gradient descent on an arbitrary function f. Aug 5, 2025 · An in-depth explanation of Gradient Descent and how to avoid the problems of local minima and saddle points. , in bilinear settings. This is because the canyon walls are much steeper than the gradual slope of the canyon toward the minimum. (Source) When we update the model parameters in Mini-batch Gradient Descent after iterating through all the data points in the batch, the direction of the update will vary, resulting in oscillations in the model. CMU School of Computer Science Dec 18, 2019 · descent. In machine learning, we use gradient descent to update the parameters of our model. There are various sources online that compare the most famous approaches, such as the blogpost by Sebastian Ruder; this blogpost complements these exisiting overviews with more recent approaches, as well as extensive experiments. CONCLUSION In this paper, we reveal that gradient descent usually suffers from gradient oscillation in training modern deep networks. Adagrad keeps a running average of the squared gradient magnitude and sets a small learning rate for features that have large gradients, and a large learning rate for features with small gradients. 6 days ago · Vaswani 36 combined stochastic gradient descent with a stochastic variant of the classic Armijo line search and this method has to hold the classic Armijo conditions which require function and Dec 18, 2020 · Given the gradient descent optimizer as implemented above, we can now add the adaptive learning rate method to the algorithm by caching the new gradients to determine the new learning rate based on the last two gradients and then performing gradient descent. Gradient descent in that case results in taking large number of steps as we cannot afford to have a large value of the learning rate, which could result in divergence in the steeper dimensions. Image by author It leads to the following problems. 0. Mar 10, 2024 · Traditional gradient descent methods often grapple with challenges like selecting the appropriate learning rate and handling oscillations, hindering their efficiency and convergence speed. It can also alleviate local minima and oscillation phenomena. One way to think about gradient descent is that you start at some arbitrary point on the surface, look to see in which direction the hill goes down most steeply, take a Aug 30, 2019 · This article explains you about the variants of gradient descent algorithm that are used for optimizing the solution of any Deep Learning problem. Oct 25, 2025 · Gradient Descent is an optimization algorithm used to find the local minimum of a function. If you want to understand in depth the gradient Dec 5, 2023 · Photo by Jack Anstey / Unsplash In my previous article about gradient descent, I explained the basic concepts behind it and summarized the main challenges of this kind of optimization. 1 and Section 3. For a neural network on this model, the paper showed that SGD with large learning rates can make correct predictions on test data with only weak features, while SGD with small learning rate could not. Jun 28, 2024 · Selecting the best (or most ideal) learning rate is very important whenever we use gradient descent in ML algorithms. This is then followed by two different low-complexity algorithms to fast track the low-frequency oscillations. There is a better chance we can a bit closer to the minimum than Stochastic Gradient Descent but it may be harder for it to escape from local minima. This helps smooth out the trajectory of the optimization allowing the algorithm to converge faster by reducing oscillations. When confronted with such functions, a possible approach is to use 2 n d order information from the Hessian, e. Ravine is a volume where the gradient is steeper in a particular directions. If we use larger learning rate then the vertical oscillation will have higher magnitude. This up and down oscillations slows down gradient descent and prevents you from using a much larger learning rate. It simply adds a fraction of the direction of the previous step to a current step. Nov 7, 2023 · In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) with \emph {large learning rates}. Recall: When we analyzed gradient descent and SGD for strongly convex objectives, the convergence rate depended on the condition number = L= . Sep 23, 2024 · Introduction Optimization algorithms are very important while training any deep learning models by adjusting the model’s parameters to minimize the loss function. In this tutorial, you will discover the gradient descent with momentum algorithm. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. (2017) and will exploit the chain-rule to compute the hyper-gradient. If we start from some point on the canyon wall, the negative gradient will point in the direction of steepest descent, i. Below, we explicitly give gradient descent algorithms for one- and multidimensional objective functions (Section 3. Gradient Descent minimizes the objective function by iteratively moving in the direction of steepest descent as defined by the negative gradient of the objective function with respect to the parameters . It is a first-order iterative algorithm for minimizing a differentiable multivariate function. And it can choose them stochastically-- meaning randomly, or more systematically-- but we do a batch at a time. name: String. This fraction is usually in the (0, 1 Nov 1, 2024 · Drawing on the physics intuition of momentum, traditional gradient descent uses this extension to improve stability and convergence, helping the model avoid oscillations and escape local minima, thereby reaching global minima more efficiently. It helps navigate the ravines efficiently. Gradient Descent What is Gradient Descent? Gradient Descent is an optimization algorithm used to minimize the loss function, helping the model learn the optimal parameters. weight_decay In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) with large learning rates. Gradient descent is commonly used in machine learning to adjust the parameters of a model in order Apr 22, 2019 · Learn different improvements made to gradient descent and compare their update rule using 2D Contour plots. Under such a training regime, our finding is that, the \emph {oscillation} of the NN weights caused by SGD with large learning rates turns out to be beneficial to the generalization of the NN, potentially improving over 🚀 Day 13: Mastering Gradient Descent - Navigating the Oscillation Challenge! 🔄📉 Hello, LinkedIn community! 👋 On this 13th day of our data science journey, let's unravel a common Gradient Methods Using Momentum The steepest descent method described in Chapter 3 always steps in the negative gradient direction, which is orthogonal to the boundary of the level set for f at the current iterate. Dec 1, 2020 · By invoking the trained CNN model, a preventive control method based on gradient descent is developed to increase the damping of critical modes. This can be accurate but slow. I'm trying to run a basic gradient descent algorithm with a absolute loss function. Poster Benign Oscillation of Stochastic Gradient Descent with Large Learning Rate Miao Lu · Beining Wu · Xiaodong Yang · Difan Zou Halle B #291 Mar 7, 2018 · Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. Whether to apply Nesterov momentum. Aug 7, 2024 · Bibliographic details on Benign Oscillation of Stochastic Gradient Descent with Large Learning Rate. But think of the iterations as stepping through time. See full list on arxiv. Defaults to 0. Mar 18, 2022 · It is not found only in column generation, but in virtually any and all optimization algorithms, whether it's gradient descent, simplex, Benders decomposition, etc. The fundamental intuition behind momentum-based gradient descent is the concept of momentum in physics. Data-Driven Low Frequency Oscillation Mode Identification and Preventive Control Strategy Based on Gradient Descent Accurate mode identification and effective preventive control strategy of low frequency oscillation (LFO) are vital to improve the small signal stability of power system. 2318 Associated training loss: 0. Dec 6, 2022 · Here is pseudo-code for gradient descent on an arbitrary function f. Momentum is a heavy ball rolling down the same hill. With one iteration of batch or mini-batch gradient descent Second iteration of gradient descent Gradient descent will slowly oscillate toward the minimum. The batch size can be a power of 2 like 32,64, etc. Oct 27, 2023 · In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. This direction can change sharply from one iteration to the next. Choosing appropriately is crucial: too small leads to painfully slow learning, while too large can cause divergence or oscillation. 1. Can we do something about it? Understanding optimization in deep learning is a fundamental problem, and recent findings have challenged the previously held belief that gradient descent stably trains deep networks. The optimization dynamics is defined using a covariant force vector and a covariant metric tensor, both computed from the first and second statistical moments of the gradients. Aug 12, 2020 · We observe cyclic oscillations in the training loss, due to the cyclic changes in the learning rate. And that will come after the-- it'll come next week after a marathon, of course, on Monday. The momentum optimizer accelerates gradient descent toward the target point, resulting in faster convergence. Mini-batch Gradient Descent Mini-batch Gradient Descent computes the gradients on small random sets of instances called mini-batches. 2267 Epochs to converge to minimum: 280 Params: Used the settings mentioned The change in learning rate t is the hyper-gradient and (2) therefore corresponds to gradient descent on the hyper-parameter using the hyper-gradient. g. Case study demonstrates that the proposed method can efficiently identify the oscillation modes and the obtained preventive control strategy can effectively prevent the occurrence of LFO. But with SGD, the 'signal' goes to zero but the noise doesn't. Furthermore, in order to shorten the oscillation period and enhance the stability of algorithm, each new iteration In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. [Nes83] showed that a simple variant of gradient de-scent—called accelerated gradient descent and applicable to any -smooth convex function—produces iterates with optimality gap ( ) − of order 1/ 2, ⋆ as opposed to the 1/ rate seen in the previous lecture. OK. The added inertia acts both as a smoother and an accelerator, dampening oscillations and causing us to barrel through narrow valleys, small humps and local minima. Defaults to False. This vertical oscillation therefore slows our gradient descent and prevents us from using a much Jun 11, 2024 · Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e. The idea of gradient descent is then to move in the direction that minimizes the approximation of the objective above, that is, move a certain amount > 0 in the direction −∇ ( ) of steepest descent of the function: Dec 15, 2021 · Momentum improves on gradient descent by reducing oscillatory effects and acting as an accelerator for optimization problem solving. Mathematically, each step updates the model’s parameters (θ) by subtracting a portion of the gradient (∇J (θ)), which indicates the direction of steepest ascent: Oct 25, 2023 · This helps to address some of the problems associated with vanilla gradient descent, such as oscillations, slow convergence, and getting stuck in local minima. 9 - Training Neural Networks [Gradient Descent Oscillations] 0Likes 35Views Feb 232024 In this blog post, we will cover some of the recent advances in optimization for gradient descent algorithms. Because of this oscillation, it is hard to achieve convergence, and the process is slowed down by it. Mar 5, 2020 · I was reading a blog post that talked about the problem of the saddle point in training. However, in practice, such parameters are not known, and the loss function of interest is not convex in Intuitively, the oscillation can prevent over-greedy convergence which could only leverage the most prominent components of the data, thus allowing for all the useful components to be discovered and learned by gradient descent. Gradient descent in the limit of infinitesimal steps is a differential equation # Before we start, let’s revisit gradient descent. Oct 29, 2024 · Jingfeng Wu | Reimaging Gradient Descent: Large Stepsize, Oscillation, and Acceleration on Simons Foundation Oct 31, 2022 · Conceptual view of how different variations of gradient descent step towards the minimum of an objective function; [Source: i2tutorials] Momentum extends on gradient descent, hence we typically refer to it as gradient descent with momentum. Understanding optimization in deep learning is a fundamental problem, and recent findings have challenged the previously held belief that gradient descent stably trains deep networks. These gradients exhibit a high negative correlation between adjacent iterations. It is used in machine learning to minimize a cost or loss function by iteratively updating parameters in the opposite direction of the gradient. Momentum is our tool Here’s a popular story about momentum [1, 2, 3]: gradient descent is a man walking down a hill. The most basic method, Stochastic Gradient Descent (SGD), is widely used, but advanced techniques like Momentum, RMSProp, and Adam improve convergence speed and stability. 0 is vanilla gradient descent. These concepts are exercised in supervised learning and reinforcement learning, with applications to images and to temporal sequences. These bounces occur because gradient descent does not store any history about its previous gradients making gradient steps more undeterministic on each iteration. The May 30, 2024 · We can see the oscillations have reduced in Mini-Batch gradient descent and oscillations are completely contained within the blue curve. With a much larger learning rate you might end up over shooting and end up diverging. In this 1 Abstract Learning Rate Estimation for Stochastic Gradient Descent by Nadia Hyder Master of Science in Electrical Engineering and Computer Science University of California, Berkeley Professor Gerald Friedland, Chair State-of-the-art gradient descent optimizers all attempt to tune learning rate such that we can find the minimum of the loss function without overshooting or approaching it so May 16, 2020 · The accumulation of both the values the history as well as the current gradient of the weight was resulting into larger steps hence larger oscillations. While the first method uses a recursive fast data projection method-based algorithm, the latter runs a gradient-descent based fast recursive algorithm on every PMU to track and monitor low-frequency oscillations. Jul 15, 2019 · Gradient Descent is a better, improvised version of newton raphson (spirit is the same, it depends upon a variable alpha though). Oct 3, 2020 · The problem with gradient descent is that the weight update at a moment (t) is governed by the learning rate and gradient at that moment only. Oct 8, 2025 · Key Idea: The learning rate controls how large a step the gradient descent algorithm takes in each iteration when moving toward the minimum of a cost function. Apr 11, 2022 · Learn how to use the popular gradient descent optimization algorithm to train complex machine learning (ML) and deep learning models. ai and receive clear, expert explanations tailored to your needs. Gradient descent often behaves poorly when the objective function has narrow valleys which cause oscillations. This achieves amplification of speed in the correct direction and softens oscillation in wrong directions. Gradient Descent is used to iteratively update the weights (coefficients) and bias by computing the gradient of the MSE with respect to these parameters. This lack of inertia can cause oscillations, leading to erratic and noisy Apr 7, 2025 · We present a manifestly covariant formulation of the gradient descent method, ensuring consistency across arbitrary coordinate systems and general curved trainable spaces. e. By employing gradient descent to train various modern deep networks, we provide empirical evidence demonstrating that a significant portion of the optimization progress occurs through the utilization of oscillating gradients. Now, our objective is to nd the value at the lowest point on that surface. It is wide Oct 25, 2019 · With each iteration of gradient descent, we move towards the local optima with up and down oscillations. For example, when the contours of f are narrow and elongated, the search directions at successive iterations may Need answers on AI, ML, or LLMs? Ask your questions on Infermatic. Poster in Workshop: Mathematics of Modern Machine Learning (M3L) Benign Oscillation of Stochastic Gradient Descent with Large Learning Rate Miao Lu · Beining Wu · Xiaodong Yang · Difan Zou Red position represents the minimum. [some column generation-specific remarks are below] Here is an example for the simplex algorithm. The intuition behind accelerated gradient descent is notoriously hard to grasp. Each iteration is a Jan 20, 2025 · We propose a novel adaptive step size-based gradient descent algorithm designed to reduce the oscillation near local optima, reach better minima with good generalizable test set accuracy, and improve the guarantee of remaining in the region of local minima without divergence near a zero-gradient region and under the nonconvexity. These discoveries indicate that GO is an inherent characteristic of training different types of neural networks and may serve as a source of inspiration for the development of novel optimizer designs. We also see these oscillations to a lesser extend in the validation loss. A classic and simple example is a ball rolling down a hill that gathers enough momentum to overcome a plateau region and make it to Here is a brief explanation based on my understanding: momentum helps SGD to navigate along the relevant directions and softens the oscillations in the irrelevant. Mar 5, 2024 · CS 201 | Reimagining Gradient Descent: Large Stepsize, Oscillation, and Acceleration, JINGFENG WU, UC Berkeley Mar 5, 2024 Oct 12, 2021 · Momentum is an extension to the gradient descent optimization algorithm that allows the search to build inertia in a direction in the search space and overcome the oscillations of noisy gradients and coast across flat spots of the search space. We also cover a breadth of algorithmic variations published in academic literature which improve On the Generalization of Stochastic Gradient Descent with Momentum Ali Ramezani-Kebrya, Kimon Antonakopoulos, Volkan Cevher, Ashish Khisti, Ben Liang; 25 (22):1−56, 2024. Gradient descent, geometric interpretation, stopping criteria, avoiding oscillations, convergence, deep neural networks May 22, 2024 · How does the gradient descent algorithm update the model parameters to minimize the objective function, and what role does the learning rate play in this process? momentum: float hyperparameter >= 0 that accelerates gradient descent in the relevant direction and dampens oscillations. Optimization refers to the task of minimizing/maximizing an objective function parameterized by . Intuitively, in one or two dimensions, we can easily think of J( ) as dening a surface over ; that same idea extends to higher dimensions. This example can be generalized to a higher number of 1 Introduction While using variants of gradient descent (GD), namely stochastic gradient descent (SGD), has become standard for optimizing neural networks, the reason behind their suc-cess and the effect of various hyperparameters is not yet fully understood. This can So stochastic gradient descent does a mini batch at a time-- a mini batch of training, of samples training data each step. Thus, you want to increase the SNR, which is what smaller step sizes in effect do -- you can think of it as many small steps together make up a normal-sized step with a larger batch size. In practice, we choose the batch size equal to 16, 32 and 64. Along with f and its gradient r f (which, in the case of a scalar , is the same as its derivative f0), we have to specify some hyper- parameters. The name to use for momentum accumulator weights created by the optimizer. momentum hyperparameter - accelerates gradient descent in the relevant direction and dampens oscillations. If Gradient Descent is like carefully stepping downhill, Momentum Gradient Descent is like rolling a ball—it builds speed while staying on track. Within a reasonable parameter range, the momentum term can improve the speed of convergence for most eigen components in the system by bringing them closer to critical damping. The learning rate η (t) adapts the step sizes based on the progress of optimization to ensure efficient convergence. By invoking the trained CNN model, a preventive control method based on gradient descent is developed to increase the damping of critical modes. However, I only covered Stochastic Gradient Descent (SGD) and the "batch" and "mini-batch" implementation of gradient descent. This leads to faster convergence, reduced oscillations and improved performance particularly when training deep neural networks or working with Feb 18, 2025 · First-order optimization methods that leverage gradient information are fundamental for solving problems across diverse domains due to their scalability and computational efficiency. We then illustrate the application of gradient descent to a loss function which is not merely mean squared loss (Section 3. Despite their effectiveness, traditional methods like Gradient Descent (GD) often face challenges related to noise, scalability, and convergence to local optima. Additionally, it finds the global (and not just local) optimum. Nov 27, 2019 · Gradient descent is an optimization technique which is used to optimize parameter and cost function of the CNN. For example, the noise ball size for SGD with a constant step size was determined by Jun 15, 2021 · In this article, we’ll cover Gradient Descent along with its variants (Mini batch Gradient Descent, SGD with Momentum) along with python implementation. At the same time, every state-of-the-art Deep Learning The stochastic gradient descent algorithm is an extension of the gradient descent algorithm which is efficient for high-order tensors [63]. I can get it to converge to a good solution by it requires a much lower step size and more iterations than had I Mar 10, 2024 · Traditional gradient descent methods often grapple with challenges like selecting the appropriate learning rate and handling oscillations, hindering their efficiency and convergence speed. One example is the practical observation that using a large learning rate in the initial phase of training is necessary for obtaining V. Such gradient oscillation follows diverse transition patterns depending on the learning rate, model architecture and different layers. But you are right using momentum or accelerated gradient descent might overcome the problem. The following development mirrors that of Franceschi et al. Here’s some intuition to help understand why a high learning rate (even when not diverging) might converge to a worse local minimum: When the learning rate is too high, each step taken during gradient descent is large. Other algorithms offer advantages in terms of convergence speed, robustness to Dec 17, 2024 · Learn about Stochastic Gradient Descent (SGD), its challenges, enhancements, and applications in Machine Learning for efficient model optimisation. Best CLR training and validation loss Best validation loss: 0. It doesn’t take into account the past steps taken while traversing the cost space. Gradient descent works by iteratively moving in the direction opposite to the gradient of the function, with the step size determined by a hyperparameter called “ learning rate ”. So Conference Paper: Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates Show simple item record Show full item record Export item record Jan 18, 2025 · Why Stochastic Gradient Descent Oscillates Towards Local Minima: An In-Depth Analysis January 18, 2025 Artificial Intelligence Open Source Resources May 18, 2023 · Gradient descent is an optimization search algorithm that is widely used in machine learning to train neural networks and other models. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Despite oscillations, it faster than gradient descent. Setting di erent learning rates for di erent features is particularly important if they are of di erent scale or vary in frequency Nov 2, 2024 · Common optimizers include gradient descent variants like: Batch Gradient Descent: Uses all data points to compute the gradient and update weights. Sep 30, 2025 · Momentum-based gradient optimizers are advanced techniques used to enhance the training of machine learning models. May 8, 2023 · This is because momentum-based gradient descent uses an exponentially weighted moving average of the gradients to update the parameters, which can help to reduce oscillations and improve the convergence rate. Under such a training regime, our finding is that, the oscillation of the NN weights caused by SGD with large learning rates turns out to be beneficial to the generalization of the NN, potentially improving over the same NN Aug 29, 2020 · Gradient descent is one of the most popular algorithms to perform optimization and by far the most common way to optimize neural networks. Afterwards, the new gradients are cached for the next optimization step. It should eventually stop at a local minimum. . nesterov: boolean. Feb 28, 2025 · A practical breakdown of Gradient Descent, the backbone of ML optimization, with step-by-step examples and visualizations. Apr 27, 2024 · The phenomenon you're observing is related to how the learning rate affects the trajectory and stability of gradient descent as it moves through the loss landscape. By employing gradient descent to train various modern deep networks, we provide empirical evidence May 2, 2021 · Gradient descent is an optimization algorithm. From a computational perspective, divergence, curl, gradient, and gradient descent methods can be interpreted as tensor multiplication with time complexity of O (n3). Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially Comments Description Lecture 7. The size of the steps taken in the negative Mar 19, 2018 · ADAM Gradient descent oscillates close to minimum Ask Question Asked 7 years, 8 months ago Modified 6 years, 3 months ago Oct 26, 2023 · In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. He follows the steepest path downwards; his progress is slow, but steady. Simple Analogy Imagine you are lost on a mountain, and you don’t know your […] This course introduces principles, algorithms, and applications of machine learning from the point of view of modeling and prediction. 3. mostly toward the canyon floor. In nonconvex settings, HBF may still outperform basic gradient descent, even though it may exhibit oscillatory behavior in poorly conditioned regions. In a groundbreaking paper in 1983, Nesterov, Y. Gradient descent refinement then optimizes PSO-identified parameters using momentum-based updates, where the momentum term β m t prevents oscillations while accelerating convergence along consistent descent directions. This paper introduces Spawning Gradient Descent Just mentioning- momentum is not accelerated gradient descent. Jan 21, 2023 · Photo by Milad Fakurian on Unsplash G radient descent is an optimization algorithm used to minimize a function. Say instead of waiting for that tangent to cut the X axis, we take Intuitively, the oscillation can prevent over-greedy convergence which could only leverage the most prominent components of the data, thus allowing for all useful components to be discovered and learned via gradient descent. Along with f and its gradient f0, we have to specify the initial value for parameter , a step-size parameter , and an accuracy parame-The parameter is of- ten called learning rate when gradient descent is applied in machine learning. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized Sep 21, 2024 · This is the essence of vanilla gradient descent. Oct 4, 2025 · Momentum is used to accelerate the gradient descent process by incorporating an exponentially weighted moving average of past gradients. These moments are estimated through time Dec 30, 2023 · Using gradient descent to find the local minima will likely make the loss function slowly oscillate towards vertical axes. Observations Takes lots of turns/oscillations before converging. a good learning rate… Abstract: This study explores machine learning gradient-based optimization algorithms, highlighting the critical importance of gradient descent and investigating adaptive strategies to improve its Nov 2, 2024 · Hello, deep learning enthusiasts! In this article, we’ll dive into the optimization technique called Stochastic Gradient Descent with Momentum (SGD with Momentum). ahgbw ssztc emg yjhmjxe iupkn kaznv fmhc vesgyj djrnmvx lbcuiy dkr nokqi ljxaor fggv ijgtpyo