Reverse Synthetic Networks: Training-Free Models in Closed Form

Abstract

We introduce Reverse Synthetic Networks (RSN), in which the data synthesizes the model in closed form: every weight is computed from corpus statistics, with no loss function, no gradient, and no GPU. We separate a positive and a negative result. For discriminative tasks a fully synthesized classifier edges a tuned linear SVM on 20 Newsgroups (87.0% ensemble) and reaches 90.8% on digit recognition with zero training, in seconds on a CPU. For generation, the same paradigm has a hard ceiling: a battery of twelve closed-form enrichments all collapse to a Modified Kneser-Ney n-gram. Measured honestly in bits-per-byte against a locally-run GPT-2, the pure RSN reaches 1.97 BPB versus GPT-2-small's 1.04, and a 100M-token scaling study shows the ceiling is representational, not data-limited. RSN is a cheap, strong floor for discriminative work, not a path to the trained generative frontier, and we explain why.