Some neural networks compute, others don't.

Area of Science:

• Computer Science
• Computational Theory
• Neuroscience

Background:

• The nature of computation in artificial neural networks (ANNs) is a subject of ongoing debate.
• Understanding whether ANNs align with classical computability theory is crucial for their theoretical grounding.
• Distinguishing computational processes in ANNs from biological neural systems remains a key challenge.

Purpose of the Study:

• To determine if neural networks, as studied in computer science, perform computations.
• To differentiate between classical and non-classical computation within neural networks.
• To assess whether biological brains perform computations in the theoretical sense.

Main Methods:

• Explication of computability theory principles.
• Analysis of neural network architectures and their functional properties.
• Comparative assessment of computational paradigms in artificial and biological neural systems.

Main Results:

• Many artificial neural networks demonstrably perform computations.
• Some neural networks exhibit classical computation, akin to digital computers.
• Other neural networks engage in non-classical computation, and biological brains may not compute theoretically.

Conclusions:

• Artificial neural networks can be understood as computational systems.
• The computational mechanisms vary, encompassing both classical and non-classical forms.
• The question of whether biological brains compute remains open, potentially falling outside theoretical computation.