Transformers need depth scaling as the product of ceil(k/s) and log n terms for k-hop pointer chasing under cache size s, with a conjectured lower bound, proved upper bound via windowed pointer doubling, and an adaptive-oblivious error separation.
In The Thirteenth International Conference on Learning Representations (ICLR)
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How Much Cache Does Reasoning Need? Depth-Cache Tradeoffs in KV-Compressed Transformers
Transformers need depth scaling as the product of ceil(k/s) and log n terms for k-hop pointer chasing under cache size s, with a conjectured lower bound, proved upper bound via windowed pointer doubling, and an adaptive-oblivious error separation.