The Model Already Has a Dictionary: Cumulative SVD Features as a Training-Free Alternative to Sparse Autoencoders

Sparse autoencoders (SAEs) have become the prevailing paradigm for learning interpretable feature dictionaries from neural activations, but they require large activation corpora, introduce reconstruction errors, and vary across training seeds; consequently, public SAE releases remain largely confined to a few model families and activation sites. We ask how much of this feature dictionary can instead be recovered directly from the model's intrinsic weights. For each Transformer residual stream state, we construct an inherently overcomplete, model-intrinsic dictionary in a training-free manner by unifying two principles: accumulating historical module outputs across all upstream layers, and applying singular value decomposition (SVD) to attention head OV circuits $W_{OV}$ and MLP down projections $W_{\mathrm{down}}$ to extract compact, intra-module orthogonal read and write channels. The resulting dictionary reconstructs the accumulative residual activations exactly without training corpora or optimization. Across Gemma 3 (1B-27B) and Qwen3-8B, SAE features remain slightly easier to describe from activating contexts, while SVD attains full coarse topic coverage and captures complementary fine-grained semantics. Moreover, cumulative SVD features excel at sparse concept prediction and enable more selective attribute disentanglement alongside stronger factual relation steering under multi-feature composition. Extraction uses no corpus tokens and is about seven orders of magnitude more efficient than training a matched SAE pair. These findings position weight-derived feature dictionaries as a strong training-free baseline and a complementary source of concepts for SAE-based interpretability.