Barriers to Universal Reasoning With Transformers (And How to Overcome Them)
Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than those seen during training is understudied. We use recent theoretical frameworks for Transformer length generalization and find that -- under standard positional encodings and a finite alphabet -- Transformers with CoT cannot solve problems beyond $TC^0$, i.e. the expressivity benefits do not hold under the stricter requirement of length-generalizable learnability. However, if we allow the vocabulary to grow with problem size, we attain a length-generaliz...
| Authors | Oliver Kraus, Yash Sarrof, Yuekun Yao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 April 2026 |
| Last updated at source | 9 August 2026 |
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