What are the key differences between Adam and Adafactor optimizers, and when might one be preferred over the other?

The key differences between Adam and Adafactor optimizers lie in their memory requirements and update rules, which impact their suitability for different training scenarios. Adam (Adaptive Moment Estimation) is a popular optimizer that maintains a moving average of both the gradients and the squared gradients for each parameter. These moving averages are used to adapt the learning rate for each parameter individually. Adam requires storing these moving averages for every parameter in the model, resulting in a significant memory footprint, especially for large models. Adafactor, on the other hand, is designed to reduce memory consumption by factorizing the adaptive learning rate matrices. Instead of storing a full matrix for each parameter, it stores the row and column sums of the matrix, which significantly reduces the memory requirement, particularly for parameters with large dimensions. Additionally, Adafactor uses a slightly different update rule compared to Adam. Adam uses a biased estimate of the first moment (gradient) and second moment (squared gradient), which are corrected using bias correction terms. Adafactor, in its standard form, does not use bias correction. When to prefer one over the other depends on the available resources and the model size. Adafactor is generally preferred when training very large models with limited memory, as it significantly reduces the memory footprint compared to Adam. This allows training larger models or using larger batch sizes with the same hardware. Adam may be preferred when memory is not a major constraint, as it can sometimes converge faster and achieve slightly better performance than Adafactor in certain scenarios. However, Adafactor often provides a good balance between memory efficiency and performance, making it a strong contender for training large Transformer models.