Universal Computation: Biological and Artificial Neural Substrates

Architectural Divergence: Centralized vs Distributed Computation

The Church-Turing thesis establishes that computation is substrate-independent—any algorithm implementable on a Turing machine can be executed by any universal computer. Neural networks, both artificial and biological, serve as computational substrates. Yet their architectures diverge radically.

Artificial networks organize neurons into sequential layers where each neuron connects to every neuron in adjacent layers. The MNIST digit recognition network exemplifies this: 784 input neurons feed into hidden layers of 16 neurons each, culminating in 10 output neurons. Learning proceeds through backpropagation, which propagates error signals backward through all layers, computing how sensitive the cost function is to each of the 13,000 parameters. Gradient descent then adjusts all weights simultaneously based on this global error signal, nudging the entire parameter space toward lower cost values through thousands of synchronized iterations.

Biological networks follow different principles. The octopus possesses 500 million neurons—approaching the complexity of cats, dogs, and parrots—yet only one-third reside in the central brain. Two-thirds inhabit the eight arms. This distributed architecture enables remarkable autonomy: severed arms respond to stimuli an hour after separation, with information bypassing the central brain entirely. Suckers and arms perform local analysis and decision-making. Similarly, blindsight patients with damaged primary visual cortex V1 consciously report complete blindness yet unconsciously navigate obstacles and flinch at approaching objects—visual processing persists through alternative pathways that bypass conscious cortical routes.

The Credit Assignment Problem: Local vs Global Learning

Backpropagation requires global knowledge. The algorithm recursively applies the chain rule from calculus to compute gradients layer by layer, determining the relative proportions of parameter changes that most rapidly decrease cost. Every weight adjustment depends on error signals propagated from the output layer backward through the entire network.

This is biologically implausible. Individual neurons lack access to global loss functions. They cannot know how their activation contributes to final network error. Real brains must solve the credit assignment problem differently—likely through local learning rules where synaptic modifications depend only on locally available information.

The octopus arm demonstrates this local intelligence. With 333 million neurons in peripheral ganglia, arms execute sensory-motor loops without routing information to the central brain. A severed arm functioning independently is impossible under centralized backpropagation—no global error signal reaches it, yet it continues processing. What learning principles enable this distributed intelligence?

Substrate Independence in Theory, Constraints in Practice

Universal approximation theorems confirm that neural networks—given sufficient neurons—can approximate any continuous function. Biological and artificial networks are both universal approximators. Any computation one performs, the other theoretically can too.

Yet practical implementations diverge due to substrate properties. Silicon transistors enable deterministic, energy-efficient, centralized computation where backpropagation is tractable—computing gradients for 13,000 parameters simultaneously is feasible. Biological networks evolved under different constraints: metabolic cost per neuron, physical volume, developmental wiring programs, and local electrochemical signaling. These constraints favor distributed processing and peripheral autonomy.

Can we import biological principles—local learning rules, distributed intelligence, peripheral autonomy—into artificial systems? Or does the determinism of silicon versus the stochasticity of biological signaling create fundamental architectural trade-offs? Universal computation guarantees functional equivalence, not architectural equivalence. The substrate may be irrelevant to what can be computed, but decisive for how computation is organized.