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You can cache K and V matrices, but for such huge matrices you'll still pay a ton of compute to calculate attention in the end even if the user just adds a five word question.
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The state of the system can be cached after the system prompt is calculated and all new chats start from that state. O(n^2) is not great but apparently its fine at these context lengths and I'm sure this is a factor in their minimum prompt cost. Advances like grouped query or multi head attention or sparse attention will eventually get rid of that exponential, hopefully.
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I would assume so too, so the costs would not be so substantial to Anthropic.
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