Analyze the memory requirements of the two algorithms described in the case study as the number of processed data points becomes very large. Based on your analysis, which algorithm is superior for a system with strict memory limitations, and why?

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A significant advantage of computing the cumulative average for the memory component with a recursive formula is its memory efficiency. During inference, this method only requires storing the single key-value pair representing the previous state's average, rather than retaining the entire history of all key-value pairs.

Memory Efficiency of Recursive Cumulative Average

Analysis of Memory Efficiency in Running Average Algorithms

A language model processes a very long document (10,000 tokens) and maintains a memory state by computing the cumulative average of all key-value pairs from the beginning of the sequence. If this average is updated at each step using a recursive formula, what information from the past must be stored in memory to compute the state for the 10,000th token?

Consider two methods for calculating the cumulative average of key-value pairs for a memory component in a sequence of length 'N'.

*   **Method A:** Uses a recursive formula, updating the average at each step based only on the previous step's average and the current key-value pair.
*   **Method B:** Re-calculates the average at each step by summing all key-value pairs from the beginning of the sequence up to the current step.

Analyze and compare the memory storage requirements for both methods as 'N' becomes very large. Which method is more memory-efficient and why?

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