| name | contravariance-theory-strong-alignment |
| description | Contravariance Theory methodology — formal proof that minimal DNN solutions to sufficiently hard tasks exhibit strong alignment: weak alignment of representations guarantees strong alignment of privileged axes, and alignment zippers up the network hierarchy, proving convergent evolution is inevitable. |
| version | 1.0.0 |
| author | Hermes Agent |
| license | MIT |
| metadata | {"hermes":{"tags":["neuroscience","neuroai","brain-dnn-alignment","contravariance","convergent-evolution","representational-alignment","privileged-axes"],"category":"ai_collection","arxiv_id":"2607.08561","arxiv_url":"https://arxiv.org/abs/2607.08561","published":"2026-07-09","authors":["Dan Yamins","Aran Nayebi"],"categories":["cs.LG","q-bio.NC"],"trigger_words":["contravariance","strong alignment","weak alignment","privileged axes","alignment zipper","convergent evolution","brain-dnn alignment","representational similarity","neuroai theory"]}} |
| created | 2026-07-12 |
| updated | 2026-07-12 |
Contravariance Theory: Strong Alignment for Minimal Solutions to Hard Tasks
arXiv: 2607.08561 | Published: 2026-07-09 | Authors: Dan Yamins, Aran Nayebi
Core Thesis
For any two minimal DNN solutions to a sufficiently hard task:
- Weak alignment ⇒ Strong alignment: Weak alignment of network representations based on affine mappings guarantees strong alignment of privileged axes
- Alignment zippers up the hierarchy: Alignment propagates up the network hierarchy, causing the emergence of privileged axes from end-to-end task optimization alone
These results formalize the notion of contravariance from Cao and Yamins [2024], with major consequences for NeuroAI theory:
- With sufficiently strong tasks, the choice of metric for inter-network comparison is not all that sensitive
- Convergent evolution between artificial and biological neural networks is probably inevitable
Key Concepts
Weak Alignment vs. Strong Alignment
- Weak alignment: Two networks' representations are related by an affine mapping (linear transform + bias). This is the standard measure in representational similarity analysis (RSA).
- Strong alignment: The networks' privileged axes (e.g., directions of maximum variance, task-relevant features) are aligned — a much stronger structural claim.
Contravariance
The principle that when two systems independently solve the same hard computational problem with minimal parameters, their internal representations must converge — they are "constrained" by the task into the same representational geometry.
Alignment Zipper
The phenomenon where alignment at lower layers propagates upward through the network hierarchy. Lower-layer alignment forces higher-layer alignment, creating a cascading convergence effect.
Theoretical Framework
Formal Setting
Given:
- Task T (sufficiently hard)
- Two minimal DNNs M1, M2 solving T
- f_i: representation function of layer i
- Affine mapping A s.t. f_2(x) ≈ A · f_1(x) (weak alignment)
Then:
1. Privileged axes of f_1, f_2 are strongly aligned
2. Alignment at layer i implies alignment at layer i+1 (zipper)
Implications for NeuroAI
-
Metric insensitivity: When comparing DNNs to brains, the specific similarity metric (CCA, CKA, RSA, etc.) matters less if the task is hard enough — all metrics will converge to the same conclusion.
