SI: motion and evidence flux
Geometric motion during learning
The supplementary analyses connect changes of predictive margins to smooth geometric motion, including controlled smooth-path checks and observational training measurements.
Motion on a controlled learning path
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Direction matters as well as cost
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From smooth changes to answer flips
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Methods and interpretation
Controlled paths and observational checkpoints have different causal interpretations. Smooth-path identities depend on their stated differentiability and spectral conditions.
Procedure in the paper: Reconstruct the frozen smooth paths and training observations, measure metric speed, objective margins and resolved projectors, and evaluate each reported identity under its stated conditions.
Code and data
v0.1.0 · 25 KB · View source on GitHub ↗
The controlled 24-seed smooth-path study with generated data.
v0.1.0 · 57 KB · View source on GitHub ↗
Objective-rate and direction alignment on 80 examples at a fixed Pythia-70M checkpoint.
v0.1.0 · 146 KB · View source on GitHub ↗
Continuous score/chord bounds, induction motion and cross-seed discrete flip curves.
Each standalone package includes code, shared helpers, required small inputs and reference results, with setup and commands in its README. Model weights and public datasets are obtained separately where needed.
Download complete source (v0.1.0) for all experiments and the companion website.