xLSTM: Extended Long Short-Term Memory — part 13/30

Cleaned-text code points [177404, 193404). Bibliography omitted here; source.md includes it.

For this matrix memory, the normalizer state is the weighted sum of key vectors, where each key vector is weighted by the input gate and all future forget gates. Again, the normalizer state keeps record of the strength of the gates. Since the dot product between query and normalizer state can be close to zero, we use the absolute value of this dot product and lower bound it by a threshold (typically 1.0) as done previously ( Sun et al., 2023 ) . 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