Equation 4 · Part 3 · Mathematicians Finished the Job After an Evolutionary Search Beat 56 Years of Human Proofs
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What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
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The passage around this formula
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:
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
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Sources cited in the article section
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