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Fast matrix multiplication saves multiplications through exact cancellation, but rounding sums that mix token rows can leave contributions from later tokens in earlier language model outputs. This threatens prefix invariance, which multiple-choice likelihood scoring relies on: a scored likelihood must depend only on it...
Backward-state policy is argued that it is part of the learning algorithm, and that neither check shows whether it is right, and should be specified and checked use by use, not settled by copy accuracy and final loss.
Algorithm realization becomes an independent low-precision axis with a global $\Phi$ optimum and measured fp8 relevance: an independent low-precision axis with a global $\Phi$ optimum and measured fp8 relevance.
The results support intervention at the shared QK locus rather than separate repair at each fault source, and support intervention at the shared QK locus rather than separate repair at each fault source.
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