Symbol k
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Because a genuine tensor decomposition composes with itself, the rank number converts directly into an asymptotic cost exponent, and DeepMind’s own paper does not spell out what that conversion yields — this is the article’s own arithmetic, shown rather than asserted. Applying Strassen’s 2×2 trick twice to reach 4×4 gives an algorithm whose cost scales as ; applying it k times to reach a 2^k 2^k matrix costs 7^k multiplications for n = 2^k , the same exponent however you slice the recursion. A genuine rank-48 4×4 decomposition, applied the same way, would scale as instead:
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Equation 2 · Technological Evolution
Mathematicians Finished the Job After an Evolutionary Search Beat 56 Years of Human Proofs
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Because a genuine tensor decomposition composes with itself, the rank number converts directly into an asymptotic cost exponent, and DeepMind’s own paper does not spell out what that conversion yields — this is the article’s own arithmetic, shown rather than asserted. Applying Strassen’s 2×2 trick twice to reach 4×4 gives an algorithm whose cost scales as ; applying it k times to reach a 2^k 2^k matrix costs 7^k multiplications for n = 2^k , the same exponent however you slice the recursion. A genuine rank-48 4×4 decomposition, applied the same way, would scale as instead:
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