Yanhong Li

Ruize Xu, Chenxiao Yang, Yanhong Li et al.

We demonstrate that a small transformer can learn to execute programs in MicroPy, a simplified yet computationally universal programming language. Given procedure definitions together with an expression to evaluate, the transformer predicts small-step execution using PENCIL scaffolding for space-efficient execution within a bounded context window. After training on randomly generated, meaningless MicroPy programs, the learned transformer generalizes to various human-written programs including bit copying and flipping, binary addition and multiplication, and SAT verification and solving. We note that the trained model can achieve out-of-distribution generalization; i.e., evaluate novel programs from distribution on programs. Since MicroPy can express any computation, our results provide empirical evidence that a standard transformer can be trained to act as a universal computer.

William Merrill, Hongjian Jiang, Yanhong Li et al.

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what makes LRNNs -- but not traditional, nonlinear RNNs -- as easy to parallelize in practice as transformers. We answer this question by providing a tight connection between types of RNNs and standard complexity classes. We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that transformers admit. Furthermore, we show that nonlinear RNNs can solve $\mathsf{L}$-complete problems (and even $\mathsf{P}$-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them as efficiently as transformers. Our theory also identifies fine-grained expressivity differences between recent popular LRNN variants: permutation-diagonal LRNNs are $\mathsf{NC}^1$-complete whereas diagonal-plus-low-rank LRNNs are more expressive ($\mathsf{PNC}^1$-complete). We provide further insight by associating each type of RNN with a corresponding automata-theoretic model that it can simulate. Together, our results reveal fundamental tradeoffs between nonlinear RNNs and different variants of LRNNs, providing a foundation for designing LLM architectures that achieve an optimal balance between expressivity and parallelism.