Do these 3 things before closing this tab:
1Repair Windows errors before they cause bigger problems2Fix the driver behind crashes, sound loss and screen glitches3Clear out junk files and repair common Windows errorsSGD and Adam both use gradients to update a model’s parameters, but they turn those gradients into steps differently. Basic stochastic gradient descent applies a learning-rate-scaled step opposite the current minibatch gradient. Adam also tracks recent gradients and squared gradients, then adapts the step size for each parameter. That can make Adam a convenient starting point, but it does not guarantee faster training or better validation results. The fair choice depends on the task and on tuning each optimizer for it.
What an optimizer does
Think of each model parameter as a dial and the loss as a measure of how wrong the model’s predictions are. Backpropagation calculates a gradient: an estimate of how changing each dial would change the loss. During minibatch training, that gradient is based on the current batch, so it is a sample-based estimate of the objective’s gradient.
An optimizer turns that gradient into a parameter update. The learning rate scales the update; it does not change the model or replace the loss. The goal is to move parameters in a direction that reduces the objective, though an individual minibatch step does not guarantee that the loss will fall.
How SGD updates parameters
Basic SGD
For parameters θt, minibatch gradient gt, and learning rate η, basic SGD uses:
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θt+1 = θt − ηgt
In other words, it moves opposite the current gradient, with the learning rate setting the step’s scale. This is a comparatively simple update rule and a useful baseline.
SGD with momentum
Momentum SGD is not the same update as plain SGD: it also carries a running direction derived from previous gradients. That can smooth the effect of batch-to-batch variation and influence how the optimizer moves. When someone says “SGD,” check whether momentum is enabled before comparing results.
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How Adam updates parameters
Adam keeps two running estimates: an exponential average of gradients, often called the first moment, and an exponential average of squared gradients, the second moment. It corrects these estimates for initialization bias, then scales the smoothed gradient using the squared-gradient estimate, with a small epsilon for numerical stability.
This gives Adam coordinate-wise adaptive step sizes: parameters with different gradient histories can receive differently scaled updates. Adam does not know the correct answer or replace gradient descent with a guarantee of better progress; it applies a different rule to gradient history. TensorFlow’s Keras API describes Adam as “a stochastic gradient descent method that is based on adaptive estimation of first-order and second-order moments” in its Adam API documentation. The foundational method is described in Kingma and Ba’s Adam paper.
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How the practical trade-offs compare
| Consideration | SGD | Adam |
|---|---|---|
| Update rule | Basic SGD scales the current minibatch gradient by the learning rate. Momentum SGD additionally uses a running direction. | Uses running estimates of gradients and squared gradients, with bias correction, to adapt update scales by coordinate. |
| Optimizer state | Basic SGD needs less optimizer history than Adam; momentum adds state for its running direction. | Stores first- and second-moment estimates in addition to parameters and gradients. |
| Tuning | Learning rate and schedule need to be selected for the task; momentum status also matters. | Learning rate and schedule still need task-specific tuning. Beta parameters and epsilon conventions can vary by framework and configuration. |
| Speed and memory outcome | Depends on implementation and training setup; no universal speed ranking is established here. | Extra optimizer state can affect memory. PyTorch notes that its foreach implementation may use more peak memory than its for-loop implementation; this does not establish a universal speed ranking. |
| Validation outcome | No universal validation-performance winner is established. | No universal validation-performance winner is established. |
PyTorch documents SGD, Adam, AdamW, and other optimizers; these two are not the entire optimizer ecosystem. Its Adam API documentation describes implementation options and state. Exact memory and speed depend on framework, version, hardware, and configuration, so do not infer a runtime result from the update equations alone.
Adam and AdamW are distinct choices
AdamW is related to Adam but should not be reported as if it were the same optimizer when weight decay matters. PyTorch describes AdamW’s weight decay as decoupled: it does not accumulate in the momentum or variance. Record which optimizer and regularization settings you used, rather than labeling an AdamW run simply “Adam.”
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How to compare them fairly
A meaningful comparison tests the optimizers on the actual task rather than treating one default configuration as neutral. Keep the model, data split, batch size, training budget, and evaluation metric the same where possible, and tune each optimizer’s learning rate and schedule fairly.
- Specify the variant. State plain SGD or momentum SGD, and Adam or AdamW. Include relevant settings such as momentum, beta parameters, epsilon, and weight decay.
- Record the implementation. Name the framework and version, since API defaults and epsilon conventions can differ. TensorFlow Keras documents epsilon as epsilon-hat in the Kingma–Ba formulation and exposes configurable beta parameters and AMSGrad in its Adam API.
- Tune both setups. Compare appropriate learning rates and schedules for each optimizer instead of assigning the same default value and calling the comparison fair.
- Evaluate the outcomes that matter. Track training loss and, where useful, steps or time to a target; judge the task using its validation metric. Report wall-clock time or memory only when measured in the stated environment.
Studies have investigated possible conditions and explanations for differences in generalization between adaptive methods and SGD. Such theoretical analysis is not a ranking that applies to every architecture, dataset, or training setup. The relevant result is the validation or test performance under a clearly described, fairly tuned experiment.
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Further reading
For a broader treatment of optimization methods, Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville includes a chapter titled “Optimization for Training Deep Models.” The book is also available free online, so the print edition is an optional format rather than a prerequisite for using either optimizer.
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