Evaluating a Sequential Memory Mechanism

Consider a simple memory model that processes a sequence of inputs, input_1, input_2, ..., input_n. It maintains a single memory state, h, which is updated at each step i by calculating the cumulative average of all inputs seen so far: h_i = (1/i) * sum(input_1 to input_i). How does this update mechanism influence the final memory state h_n as the sequence length n increases?

A sequential processing model needs to maintain a summary of a long stream of numerical inputs. The design requires that more recent inputs have a significantly stronger influence on the final summary than inputs from the distant past. Which of the following state update functions, where h_i is the state at step i and input_i is the current input, best achieves this goal?

A model is designed to process a long sequence of information by reading one element at a time and updating a single, continuous memory state. The new memory state at each step is calculated as a function of the previous memory state and the current input element. What is a fundamental limitation of this processing method for tasks requiring an understanding of relationships across the entire sequence?