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What do β₁ and β₂ mean in Adam?
Adam keeps two exponentially weighted running estimates. At training step t, they are:
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mₜ = β₁mₜ₋₁ + (1 − β₁)gₜ
vₜ = β₂vₜ₋₁ + (1 − β₂)gₜ²
Here, gₜ is the current gradient. The first estimate, mₜ, smooths the gradient and tracks its direction. The second, vₜ, smooths squared gradients and tracks their scale. Adam uses bias-corrected versions of both to scale parameter updates.
β₁ smooths the gradient
β₁ sets the decay rate for the first-moment estimate. It determines how quickly the running average of gradients forgets earlier values.
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β₂ smooths squared gradients
β₂ sets the decay rate for the second-moment estimate. Because this estimate uses squared gradients, it tracks their recent scale rather than their signed direction.
Why are Adam’s betas close to 1?
A beta closer to 1 makes its running estimate decay more slowly and retain more history. A smaller beta gives recent gradients more influence and makes the estimate respond more quickly to them. This follows from the moving-average equations; it does not guarantee that either a higher or lower value will improve a particular model.
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The two parameters apply to different statistics, so they need not be equal. In the conventional setup, β₂ is higher than β₁, meaning the squared-gradient estimate retains history longer than the gradient average.
Why does Adam use bias correction?
Adam initializes both running estimates at zero. Early in training, that initialization pulls the averages toward zero, especially when a beta is close to 1. Adam corrects for this by dividing the estimates by 1 − β₁ᵗ and 1 − β₂ᵗ, respectively.
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What should you set β₁ and β₂ to?
- Start with β₁ = 0.9 and β₂ = 0.999 if you do not have a more specific recipe. Kingma and Ba described these as good defaults for the machine-learning problems they tested; official framework documentation also lists them as conventional values. Read the Adam paper, check PyTorch’s Adam API, and check TensorFlow’s Adam API.
- For reproduction, use the model’s stated recipe. Match the settings in the paper or reference implementation rather than assuming the conventional values were used.
- If tuning, compare controlled runs. Change one factor at a time where practical, keep the learning-rate schedule and other training conditions consistent, and compare the metric that matters for your task. The available sources do not establish one alternative beta pair as generally superior.
- Check the rest of the setup. Betas are not a substitute for checking the learning rate, epsilon convention, data pipeline, or model-specific training recipe.
TensorFlow cautions that a prebuilt optimizer may not be best for every model or dataset. Its training guide is a reminder to validate the full setup against the task rather than treating defaults as a guarantee.
Why can framework settings differ?
The same beta values do not guarantee that every optimizer configuration is identical: epsilon conventions and API versions matter too. For example, the current PyTorch main documentation lists betas of (0.9, 0.999) and epsilon of 1e-8, while the Keras 2 API lists beta_1 = 0.9, beta_2 = 0.999, and epsilon = 1e-7. Keras 2 describes its epsilon as “epsilon hat” under its default convention and warns that the default may not suit every case. PyTorch Adam documentation and Keras 2 Adam documentation are version-specific references; check the API for the framework version you are actually using.
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How are betas different from the learning rate?
The learning rate scales the resulting parameter update. Betas control how much history the two gradient estimates retain. They affect different parts of Adam’s update, so changing a beta is not the same as increasing or decreasing the learning rate.
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