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Kingma & Ba, "Adam: A Method for Stochastic Optimization" (arXiv)

Diederik P. Kingma, Jimmy Ba · 22 Dec 2014 · arxiv.org

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In plain words

A new algorithm called Adam finds good solutions to huge noisy problems by tracking running averages of gradients and their sizes so steps adjust themselves with almost no tuning. It suits large data or many parameters, noisy or sparse signals, uses little memory and compute, works well in tests against other methods, and comes with a matching best-known convergence guarantee. It proposes the method with links to earlier algorithms it builds on, theoretical analysis, empirical comparisons, and a simple variant.

Our summary of the paper, not the authors' words — written to be readable without the field's vocabulary, from the stored copy of the paper and nothing else. Drafted with xai:grok-4.5 and checked by a person. The authors' own sentences are the quotes below.

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Diederik P. Kingma, Jimmy Ba did not write this page.

Every claim below was made in this piece, quoted word for word and numbered in the order the piece makes them, so you can read it there rather than take our word for it. The sentence above each quote is our reading of the claim, not their wording. Each quote was checked against a stored copy of the page at build time; where the two differ, the quote is the fact.

  1. We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments.
  2. We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments.
  3. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters.
  4. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters.
  5. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients.
  6. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients.
  7. The hyper-parameters have intuitive interpretations and typically require little tuning.
  8. The hyper-parameters have intuitive interpretations and typically require little tuning.