Can Neural Networks Be Turing Machines? Exploring the Limits of AI Computation

Featuring Dr Keith Duggar

In a recent conversation, AI researchers Keith Nolan, Paul Szerlip, and Andrew Critch debated a fascinating question at the intersection of computer science and artificial intelligence: Can neural networks function as Turing machines?

The discussion centered around whether the neural network architectures used in modern AI systems are fundamentally limited to finite state automata, or if they could in principle perform the kind of unbounded computation that Turing machines are capable of. As Nolan explained, a Turing machine can be thought of as "nothing more than a finite state machine that has an expandable read-write memory" - a simple yet powerful model that can carry out any computable task.

While artificial neural networks excel at complex pattern recognition and function approximation within a fixed computational budget, it remains an open question whether they can be made to operate like Turing machines with an unbounded memory. "The problem we run into is training, training the neural networks to do something useful with unbounded read-write memory," noted Szerlip. "Like we don't usually do that."

Critch offered a more optimistic take, suggesting that the apparent inability of neural nets to perform Turing-complete computation may be "an accident of particular definitions and the way that we've been structuring neural architectures" rather than a fundamental limitation. He posited that by allowing feedback connections in the network, "suddenly you can get access to that higher order computation."

The trio also considered the pragmatic implications of this question for the future of AI system design. Szerlip highlighted the work of researchers like François Chollet who advocate building AI via "purely discrete program search," as well as neuro-symbolic approaches that combine the strengths of deep learning and symbolic reasoning. Nolan suggested that techniques from category theory could help in designing domain-specific languages with the right semantics to enable "the next generation of neural networks."

Ultimately, the conversation raised more questions than answers, but it illuminated the significant gap between the current capabilities of neural networks and the aspiration of creating AI systems that can flexibly learn and reason like humans. As Szerlip put it, "there's no theoretical reason why a neural network can't be a Turing machine - we just haven't figured out how to train neural networks that function in that way yet, at least not efficiently or for general purpose."

What do you think - are neural networks fundamentally constrained by their finite automata-like structure, or is Turing-complete AI achievable with the right advances in architecture and training? Let us know your thoughts in the comments.

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