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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchSGD takes a step opposite the current minibatch gradient; Adam uses recent gradient history to adapt the step size for each parameter. Both are ways to update a model during training—not alternatives to the model or its loss—and neither is guaranteed to train faster or produce better validation results. Which one works better depends on the task, implementation, and tuning.
What an optimizer does
Think of each model parameter as a dial and the loss as a measure of how far the model’s predictions are from the desired result. Backpropagation calculates a gradient: an estimate of how changing each dial would affect the loss. An optimizer turns that gradient into a parameter update.
Training usually calculates the gradient from a minibatch rather than the entire dataset. That makes it a sample-based estimate of the objective’s gradient. The optimizer uses it to move parameters in a direction intended to reduce the objective; the learning rate controls the scale of the move.
How SGD updates parameters
Plain stochastic gradient descent
For parameters θt, minibatch gradient gt, and learning rate η, basic SGD applies this update:
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θt+1 = θt − ηgt
The minus sign means the step goes opposite the gradient, which points toward increasing loss locally. Plain SGD uses the current minibatch gradient directly, scaled by the learning rate. Its simplicity makes it a useful baseline, but the step scale must be chosen for the problem.
SGD with momentum
Momentum SGD also uses previous gradients to smooth the update direction. It is not the same update rule as plain SGD, so a comparison that says only “SGD” is incomplete: it should state whether momentum is enabled and how it is configured. PyTorch documents SGD and its options in its optimizer guide.
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How Adam uses gradient history
Adam maintains two exponential moving averages: one for gradients and one for squared gradients. The first provides a smoothed direction; the second estimates the scale of recent gradient magnitudes. Adam corrects for the bias that arises because these averages begin at zero, then uses the estimates to scale the update, with epsilon for numerical stability. The result is an adaptive step scale for each parameter, rather than one learning-rate scale applied identically to all coordinates.
That adaptivity does not mean Adam knows the correct direction or answer. It is a rule for using gradient history to choose updates. Kingma and Ba introduced the method in their 2014 Adam paper. 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”; its Adam documentation also exposes configurable beta parameters, epsilon, and AMSGrad.
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How the practical trade-offs differ
| Question | SGD | Adam |
|---|---|---|
| What shapes the update? | In plain SGD, the current minibatch gradient scaled by the learning rate. Momentum SGD additionally smooths direction using previous gradients. | Running estimates of the gradient and squared gradient, with bias correction and epsilon. |
| Does it adapt step scales by parameter? | Not in the basic rule; momentum smooths direction rather than adding Adam’s second-moment scaling. | Yes. The moment estimates produce coordinate-wise adaptive step scales. |
| What optimizer state is kept? | Plain SGD needs no moment estimates; momentum SGD keeps a running direction. | Running first- and second-moment estimates in addition to model parameters and gradients. |
| Is one faster or more accurate? | No universal ranking is established. Results depend on the task and setup. | No universal ranking is established. Adaptive updates do not guarantee faster training or better validation performance. |
Adam’s additional state can increase memory use, although the exact cost and speed depend on the framework and implementation. PyTorch notes that its foreach Adam implementation may use more peak memory than its for-loop implementation in the Adam API documentation. That is an implementation caveat, not evidence that Adam is always slower or faster than SGD.
Adam is not AdamW
AdamW is a related optimizer, but it should not be reported as Adam when weight decay matters. PyTorch describes AdamW’s weight decay as decoupled: it does not accumulate in the momentum or variance. The framework lists Adam, AdamW, and SGD as separate optimizer choices. State clearly which one an experiment uses, especially when comparing regularization settings.
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How to choose and compare them fairly
There is no optimizer that wins on every model, dataset, or objective. Studies have investigated possible generalization differences between adaptive methods and SGD, but that work does not establish a universal winner. Choose based on the outcome that matters for your use case, and compare actual runs rather than relying on a default setting.
- Keep the training setup comparable. Use the same model, data split, batch size, training budget, and evaluation metric wherever possible.
- Tune each optimizer. Test learning rates and schedules appropriate to each one. A single shared default learning rate is not a neutral comparison.
- Name the exact variants. Specify plain SGD or momentum SGD, and Adam or AdamW. Include relevant settings such as momentum, beta parameters, epsilon, and weight decay.
- Measure both training and the intended outcome. Training loss and steps or time to a target describe optimization behavior; validation performance indicates how well the model performs on the held-out data. Report wall-clock time or memory only when measured in the stated environment.
- Record the implementation. Framework APIs and defaults can differ. For example, Keras documents its epsilon in relation to the epsilon-hat formulation in the Kingma–Ba paper. Record the framework and version, along with optimizer settings, so the comparison is interpretable.
SGD and Adam are common choices, not the only ones; frameworks such as PyTorch support other optimizers too. For broader background on optimization for training deep models, the official Deep Learning textbook site offers a free online edition, while MIT Press describes the book’s coverage of optimization algorithms in its catalog listing. The print edition is an optional reference, not a requirement for using either optimizer.
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