Yes, a Turing machine can theoretically simulate a neural network, as neural networks are mathematical models that can be described algorithmically. A Turing machine, being a universal model of computation, can simulate any algorithm, including the training and inference processes of neural networks.
However, the simulation might be inefficient. Neural networks typically operate in parallel, handling large amounts of data simultaneously, while Turing machines work sequentially. This difference in architecture means the simulation could be computationally expensive and slow.
Despite the inefficiency, this theoretical capability demonstrates that neural networks are within the scope of classical computation, affirming their computability and algorithmic foundations.