Beyond Coordinate Gauge: An Audited Protocol for Detecting Donor-Specific Functional Fingerprints after Neural Collapse
Independently trained neural networks lack a shared neuron-index reference frame, necessitating coordinate-invariant methods for comparison. The study introduces an audited protocol using verified affine-correct alignment to map donor network heads into recipient coordinates. Donor-specific functional fingerprints remain distinguishable after Neural Collapse convergence, with all 20 ordered pairs correctly identified. Statistical significance was confirmed with an exact permutation p-value of 0.
Analysis
TL;DR
- Independently trained neural networks lack a shared neuron-index reference frame, necessitating coordinate-invariant methods for comparison.
- The study introduces an audited protocol using verified affine-correct alignment to map donor network heads into recipient coordinates.
- Donor-specific functional fingerprints remain distinguishable after Neural Collapse convergence, with all 20 ordered pairs correctly identified.
- Statistical significance was confirmed with an exact permutation p-value of 0.0083, robust against leakage audits.
- While detectability is established, the study does not prove transplantability or causal persistence of these functional variations.
Why It Matters
This research addresses a fundamental challenge in mechanistic interpretability: how to compare internal representations across independently trained models that have converged to similar geometric structures. By demonstrating that unique functional signatures persist even after Neural Collapse, it provides a rigorous framework for auditing and analyzing model individuality, which is crucial for understanding reproducibility and generalization in deep learning.
Technical Details
- Problem Context: Investigates whether trajectory-specific functional variation persists after networks converge to the low-dimensional geometry characteristic of Neural Collapse.
- Methodology: Utilized five independently trained networks on the MNIST dataset. Applied a verified affine-correct alignment mapping to resolve coordinate freedom between donor and recipient networks.
- Experimental Design: Conducted 20 ordered donor-recipient pair comparisons. Implemented recipient-level baseline correction to isolate donor-specific signals.
- Validation: Performed a leakage audit to ensure results were not artifacts of data contamination. Used exact permutation testing to assess statistical significance.
- Results: Achieved 100% correct identification of donor-recipient pairs with a p-value of 0.0083, confirming detectability under the tested conditions.
Industry Insight
- Researchers should account for coordinate freedom when performing cross-model analysis or interpretability studies, as standard index-based comparisons may be invalid.
- The development of audited alignment protocols can enhance the reliability of mechanistic interpretability findings, particularly in studies involving model ensembles or transfer learning.
- Future work must extend beyond detectability to investigate transplantability and causal persistence to fully understand the utility of these functional fingerprints in practical applications.
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