On the Turing Completeness of Modern Neural Network Architectures
This provides foundational insights into the theoretical capabilities of widely used models in AI, which is important for researchers and practitioners in machine learning.
The paper tackles the problem of understanding the computational power of modern neural network architectures like Transformers and Neural GPUs, showing that both are Turing complete based solely on their internal dense representations without needing external memory.
Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.