Structure-unaware algorithms, such as naïve matrix multiplication, work for every possible input— including inputs overwhelmingly unlikely to be encountered.
Structure-aware algorithms, however, can leverage the much smaller set of possible inputs afforded by the manifold hypothesis to find faster ways to compute.
For instance, while multiplying two 1,000 by 1,000 arbitrary matrices together using naïve matrix multiplication takes on the order of one billion operations, if the matrices are circulant (for instance, if they are adjacency matrices of circulant graphs such as Möbius ladders or Paley graphs of prime order), the extra structure affords a self-reducing algorithm that takes on the order of merely 10 million operations.
VMind leverages existing structure on AI inputs to afford much faster algorithms than naïve AI compute.
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