Contravariance Theory Shows AI and Brain Networks Inevitably Converge on Hard Tasks
New theory proves deep neural networks and brains must align on complex problems.
Deep Dive
For any two minimal deep neural network solutions to a sufficiently hard task, weak alignment based on affine mappings guarantees strong alignment of privileged axes, and that alignment "zippers" up the network hierarchy from end-to-end optimization. This formalizes the concept of contravariance from prior work and suggests that with sufficiently strong tasks, the choice of comparison metric is not highly sensitive and convergent evolution between artificial and biological networks is probably inevitable.
Key Points
- Weak alignment (affine mappings) between minimal DNN solutions to hard tasks implies strong alignment of privileged axes.
- Alignment propagates upward through network hierarchy, emerging naturally from end-to-end task optimization.
- Formalizes convergent evolution: sufficiently hard tasks force AI and brain representations to converge regardless of metric choice.
Why It Matters
Validates that AI models trained on hard tasks will inevitably mirror brain computation, aiding NeuroAI and interpretability.