:%20The%20Key%20Bottleneck%20on%20In-context%20Retrieval&subtitle=This%20paper%20investigates%20the%20gap%20in%20representation%20powers%20of%20Recurrent%20Neural%20Networks%20(RNNs)%20and%20Transformers%20in%20the%20context%20of%20solving%20algorithmic%20problems.%20We%20focus%20on%20understanding%20whether%20RNNs%2C%20known%20for%20their%20memory%20efficiency%20in%20handling%20long%20sequences%2C%20can%20match%20the%20performance%20of%20Transformers%2C%20particularly%20when%20enhanced%20with%20Chain-of-Thought%20(CoT)%20prompting.%20Our%20theoretical%20analysis%20reveals%20that%20CoT%20improves%20RNNs%20but%20is%20insufficient%20to%20close%20the%20gap%20with%20Transformers.%20A%20key%20bottleneck%20lies%20in%20the%20inability%20of%20RNNs%20to%20perfectly%20retrieve%20information%20from%20the%20context%2C%20even%20with%20CoT:%20for%20several%20tasks%20that%20explicitly%20or%20implicitly%20require%20this%20capability%2C%20such%20as%20associative%20recall%20and%20determining%20if%20a%20graph%20is%20a%20tree%2C%20we%20prove%20that%20RNNs%20are%20not%20expressive%20enough%20to%20solve%20the%20tasks%20while%20Transformers%20can%20solve%20them%20with%20ease.%20Conversely%2C%20we%20prove%20that%20adopting%20techniques%20to%20enhance%20the%20in-context%20retrieval%20capability%20of%20RNNs%2C%20including%20Retrieval-Augmented%20Generation%20(RAG)%20and%20adding%20a%20single%20Transformer%20layer%2C%20can%20elevate%20RNNs%20to%20be%20capable%20of%20solving%20all%20polynomial-time%20solvable%20problems%20with%20CoT%2C%20hence%20closing%20the%20representation%20gap%20with%20Transformers.)
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