TANGO: Treating Tokens as Operators

Abstract

Transformers separate cross-token mixing in self-attention from token-wise transformation in feed-forward networks. We ask whether combining these operations can lower predictive loss under fixed data and parameter budgets. To do so, we introduce the Token-Aggregated Nonlinear Gating Operator (TANGO) model. TANGO computes a nonlinear feature-wise gate at each source token. Attention averages these gates for each destination. The average modulates a linear projection of the destination and forms the diagonal core of a source-conditioned linear operator. We test this proposal by comparing full-prefix and windowed TANGO with looped and untied Transformers, the Gated Attention Unit (GAU), and Fast Linear Attention with a Single Head (FLASH) on web text, Lean formal mathematics, DeepMind Mathematics, and code. The comparison uses two parameter scales, two depths, and three seeds. Checkpoints are selected on development data and evaluated on held-out test data. At matched parameters and training data, full-prefix TANGO has the lowest mean test negative log-likelihood in all 16 settings. In eight additional combinations of size and dataset, its development loss never increases as depth rises from 4 to 8 to 16, whereas the looped Transformer's loss increases in four. Full-prefix TANGO is computationally expensive because it averages wide gates over every visible source. To reduce this cost, we evaluate a variant with three narrower gated-projection sets assigned to the first, middle, and last applications. Across four FineWeb-Edu settings, this variant achieves 3.26 to 3.45 times the throughput of TANGO and 75% to 96% that of the looped Transformer. Its mean development negative log-likelihood is lower than TANGO's in three settings and 0.023 higher in the fourth, while remaining lower than both Transformer baselines in all four.