Chain of Thought (CoT) lifts the expressive ceiling of bounded-depth Transformers, with characterizations tying the number of CoT steps to circuit complexity classes. What remains largely missing are concrete instantiations with explicit, depth-bounded constructions, and the traversal procedures such characterizations presuppose.
arXiv:2608. 30273v1 Announce Type: cross Abstract: The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory.
By Ravi Tandon
arXiv:2606. 19697v1 Announce Type: cross Abstract: The increasing popularity of \emph{reasoning} models -- language models that output a series of reasoning or thought tokens before producing an answer -- is justified, in part, by theoretical results showing that chain-of-thought (CoT) transformers can simulate Turing machines, and thus perform arbitrary computation.
By Yanhong Li, Anej Svete, Ashish Sabharwal, William Merrill
arXiv:2609. 04046v1 Announce Type: cross Abstract: What can a single layer of self-attention compute?
By Rajmohan Rajaraman, Ravi Sundaram, Amanuel Tesfaye
arXiv:2603.21676v2 Announce Type: replace-cross
Abstract: Standard Transformers have a fixed computational depth, limiting their ability to generalize to tasks that require variable-depth reasoning....
By Hung-Hsuan Chen
arXiv:2608.31067v1 Announce Type: new
Abstract: Learning generalizable algorithmic computations remains a challenge for neural networks, as reflected in persistent failures on compositional and lengt...
By Takuya Ito, Ruchir Puri, Murray Campbell, Parikshit Ram