arXiv AI

A Geometric Unification of Concept Learning with Concept Cones

arXiv:2512. 07355v2 Announce Type: replace Abstract: Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge.

arXiv Machine Learning
1d ago

Beyond Linear Concepts: Discovering and Aligning Non-Linear Concept Manifolds in Large Language Models

The paper extends mechanistic interpretability of large language models by modeling concepts as low‑dimensional non‑linear manifolds rather than linear subspaces. It introduces a concept‑based alignment (CBA) score to compare these manifolds across layers and models, revealing block structures in intermediate layers, a shift from syntax‑dominated to mixed syntactic‑semantic concepts, and training‑dependent multilingual sharing. The study also shows that alignment patterns differ across model families and training stages, with adjacent stages aligning more closely than distant ones.

By Tido Specht, Elias Benedict Krey, Nils Neukirch, Nils Strodthoff