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Memoization

Memoization is an optimization in which a function remembers the results of calls it has already performed: when invoked again with the same inputs, it returns the stored result instead of recomputing it. It is caching applied to functions, and it shines when computation is expensive and inputs repeat frequently.

Definition

How it works

The mechanism relies on a lookup table (typically a hash map) that maps a function's arguments to its output. On every call the function checks the table: if the input-result pair exists, it reuses it; otherwise it computes, stores and returns. It only works reliably with pure functions, meaning functions that always produce the same output for the same input and have no side effects.

Applications

In AI, memoization appears in agent frameworks that avoid re-running tool calls already executed with identical parameters, in evaluation systems that reuse previously computed scores, and in feature engineering pipelines. In classic programming it is the technique that makes dynamic programming tractable, from computing Fibonacci numbers to aligning DNA sequences in bioinformatics.

History & etymology

The term was coined by Donald Michie, the British AI pioneer, in his 1968 Nature paper Memo Functions and Machine Learning. It derives from the Latin memorandum, a thing to be remembered: Michie deliberately chose memoization rather than memorization to describe turning a function into a memo function that remembers its own results.

How it's used in Grace

Grace's problem solving trains you to recognize when a computation needs to be redone and when it can be reused: the same principle as memoization, applied to your AI workflows. The daily gym with its 0-100 score shows how much efficiency you gain with each iteration.

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