# Contravariance Theory: Strong Alignment for Minimal Solutions to Hard Tasks

arXiv: https://arxiv.org/abs/2607.08561 · HTML: https://mlsanity.com/paper/2607.08561/

## 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 (most cited first, 6 of 6)

- [Soft Matching Distance: A metric on neural representations that captures single-neuron tuning](https://mlsanity.com/paper/2311.09466/) (2023)
- [Evaluating Representational Similarity Measures from the Lens of Functional Correspondence](https://mlsanity.com/paper/2411.14633/) (2024)
- [Layers at Similar Depths Generate Similar Activations Across LLM Architectures](https://mlsanity.com/paper/2504.08775/) (2025)
- [Bridging Critical Gaps in Convergent Learning: How Representational Alignment Evolves Across Layers, Training, and Distribution Shifts](https://mlsanity.com/paper/2502.18710/) (2025)
- [Inducing Dyslexia in Vision Language Models](https://mlsanity.com/paper/2509.24597/) (2025)
- [What Capable Agents Must Know: Selection Theorems for Robust Decision-Making under Uncertainty](https://mlsanity.com/paper/2603.02491/) (2026)

## Built on by (most cited first, 2 of 2)

- [Cognitive Expert Language Models Better Align with the Corresponding Brain Systems](https://mlsanity.com/paper/2609.36239/) (2026)
- [Traversing the solution space of neural networks with Hessian Null Space Continuation](https://mlsanity.com/paper/2609.38081/) (2026)

## 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.