The steps for gradient descent with respect to some variable is:
1. Compute gradient of loss with respect to the variable
2. Update the variable with step in direction of the negative gradient.

The statement claims that the following are different:
1. Gradient descent on the data with frozen weights
2. Computing the gradient of the loss with respect to the input data using the frozen weights, and then update the data by taking a small step in the direction of the negative gradient

However, (1), expands to:
1. Compute the gradient of the loss with respect to [the input data with frozen weights]
2. Update the input data with a small step in the direction of the negative gradient.

Therefore, (1) is equivalent to (2).

Is this argument airtight? If not, explain exactly why it's wrong using clear logic.
user
Thanks for the clarification. From what I understand, the key question you have is whether the two methods for gradient descent are equivalent, specifically:

1. Gradient descent on the data with frozen weights
2. Computing the gradient of the loss with respect to the input data using the frozen weights, and then update the data by taking a small step in the direction of the negative gradient

While these two methods may look similar in the steps involved, they are not necessarily equivalent. The key difference is that in method (1), the weights of the model are frozen, meaning they remain constant during gradient descent. In method (2), the weights are only used to compute the gradient with respect to the input data, but the weights themselves are not updated. As a result, method (2) is only looking at gradient information with respect to the input data, whereas method (1) is performing full gradient descent but holding the weights fixed.

Overall, whether these methods are equivalent depends on the goal and system in question. If the goal is only to update the input data and not the weights, then the methods may be equivalent. However, if the goal is full gradient descent for optimization, then method (1) would be required to also update the weights, in which case the methods are not equivalent.

Does this help clarify the difference between the two methods and answer your question about equivalence? Let me know if you would like me to elaborate on any part of the response or explain other concepts related to gradient descent.
assistant
Can you predict what could be the price of polkadot in May 2023?
user
I’m sorry but I’m not able to predict future prices of cryptocurrencies or any other financial assets. However, I can provide you with information about Polkadot and its current market trends if you would like.
assistant
Could trends be used to identify potential prices of stocks, real estate, and currencies? If so, what types of information should be focused on and why?
user