How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural 文章

arXiv:2606.19379v1 Announce Type: cross Abstract: Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity. Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from near-linear (>0.99) to strongly nonlinear (<0.3) between adjacent blocks, and is not set by the activation function: same-width GELU models GPT-2 and Pythia-160m have sharply different profiles, so recoverability is a learned property of individual trained blocks, not an architectural one.