Contravariance Theory: Strong Alignment for Minimal Solutions to Hard Tasks
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Abstract (arXiv)
A series of results from the NeuroAI over the past fifteen years have raised core questions both about how to compare Deep Neural Network (DNN) models to the brain, and about how much convergent evolution to expect between artificial networks and real brain networks. Here, we show that for any two minimal DNN solutions to a sufficiently hard task: (i) "weak" alignment of network representations based on affine mappings guarantees "strong" alignment of privileged axes, and (ii) alignment "zippers" up the network hierarchy, causing the emergence of privileged axes from end-to-end task optimization. These results formalize the notion of contravariance from Cao and Yamins [2024], and illustrate important consequences for the theory of NeuroAI: with sufficiently strong tasks, choice of metric for inter-network comparison is not all that sensitive, and that convergent evolution is probably inevitable.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 6 of its 54 references that are in the map. First posted on arXiv 9 Jul 2026.
Builds on
6 of 54 references.
References · 6
- 2023Soft Matching Distance: A metric on neural representations that captures single-neuron tuningcited by 18
- 2024Evaluating Representational Similarity Measures from the Lens of Functional Correspondencecited by 12
- 2025Layers at Similar Depths Generate Similar Activations Across LLM Architecturescited by 12
- 2025Bridging Critical Gaps in Convergent Learning: How Representational Alignment Evolves Across Layers, Training, and Distribution Shiftscited by 6
- 2025Inducing Dyslexia in Vision Language Modelscited by 2
- 2026What Capable Agents Must Know: Selection Theorems for Robust Decision-Making under Uncertaintycited by 2
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Citing papers per year: 2026: 2.
2 papers.