Distilling models using the linear representation hypothesis
summary
Claim: neural nets that implicitly encode decision trees via the linear representation hypothesis admit extraction. Method: run many linear probes (ordinary least squares on the network activation vector) to recover gate vectors W and assemble a decision tree via pruning/search. Empirically recovers random trees from oversized models (tested on million-parameter nets on a V100); fails on parity (single-index behavior). Runtime scales polynomially in network size, tree size and probe norms. Open: broader circuits and practical robustness.
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chapters (6)
- 0:00Introduction
- 1:42Distillation and decision trees
- 3:28Structural assumptions
- 5:57Linear representation hypothesis
- 7:43Open questions and future
- 9:17Q&A
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