TANGO: Token-Aggregated Nonlinear Gating Operators for Natural and Formal Language Modeling

Abstract:A standard Transformer block separates cross-token interaction in self-attention from a nonlinear feed-forward network applied independently at each position. We introduce the TANGO model (Token-Aggregated Nonlinear Gating Operators), which replaces these two sublayers with one cross-token gated residual update. Each source token produces a SwiGLU gate vector. Query-key similarities determine a weighted average of source gates for each destination, and the resulting gate rescales projected destination features. TANGO assigns a separate weight to every causally visible source and is quadratic in sequence length. The WANGO model (Windowed Aggregation of Nonlinear Gating Operators) retains the same unnormalized scores within a recent window and uses positive feature-map prefix statistics for older sources, giving linear sequence-length complexity for fixed window and feature dimensions. We compare TANGO and WANGO with Recurrent and Untied Transformer++, full-attention GAU, and FLASH. All models have approximately 44.3M nonembedding parameters and are trained in three matched runs. TANGO, WANGO, and Recurrent Transformer++ apply one shared block four times; the other architectures use four independent blocks. TANGO obtains the lowest mean validation negative log-likelihood on FineWeb-Edu, Lean, and DeepMind Mathematics, although it has the largest analytical forward-pass operation count. WANGO obtains the lowest mean FineWeb-Edu NLL among the architectures with computation linear in sequence length and outperforms Recurrent Transformer++ at nearly the same analytical forward-pass multiply-accumulate count.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2608.22117 [cs.LG]

(or arXiv:2608.22117v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.22117 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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