New paper: "Gauge-Invariant Diagnostics for Hidden Representational Structure in Transformer Language Models"
Can a transformer hide internal state that doesn't show up in its output distribution? I formalize this using fiber bundle geometry and test it on Phi-2. Result: no.
The setup: if a model's internal activations form a fiber bundle over its output distributions, there could be "holonomy" -- the model traverses different internal paths but arrives at the same output, with hidden residual structure. I define four falsifiable criteria and test all of them.
All negative. Outputs never converge enough for the holonomy gate to trigger. Path information is retained at 100% accuracy at every layer -- never compressed. Scrubbing path info from activations changes output logits -- the model uses it. No hidden structure.
What looks like "processing depth" in mid-layer divergence profiles is largely explained by token recency, not semantic abstraction. This matters for anyone interpreting layer-wise activation patterns.
Along the way I propose a three-tier gauge-invariance classification for interpretability metrics. If your metric changes under a basis rotation, it's not measuring the computation. A lot of published geometric findings in interp fail this test.
Paper: github.com/anderswrk/represe…
Full code, results, and plots: github.com/anderswrk/represe…
Looking for an arXiv cs.LG endorsement — DM me if you can help.
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