Title:TriPLU: Bypassing the Gate with Direct Trilinear Product FFNs in Tiny Language Models

Abstract:We study whether tiny decoder-only language models benefit from feed-forward layers that directly multiply learned feature projections. TriPLU, a Trilinear Product Linear Unit, replaces the usual gated FFN branch with a product-only degree-3 branch that multiplies three projected streams coordinatewise. In a character-level TinyStories 1M-byte prefix study, TriPLU reaches a mean best validation loss of 1.0637, compared with 1.1017 for closely matched SwiGLU, 1.0780 for a degree-4 product control, and 1.1026 for a degree-2 control. In train-only Byte-BPE experiments, TriPLU also lowers validation and heldout bits per byte on TinyStories and WikiText-2 raw under low-learning-rate settings, with PMI-slice evidence suggesting gains on seen middle- and high-PMI adjacent-token pairs. Constant-learning-rate diagnostics show that product-branch normalization can reduce the high-learning-rate best-checkpoint gap, although final BPB still degrades under hot schedules. The resulting claim is deliberately narrow: direct product FFNs can improve fixed-budget small-model loss in specific low-compute regimes, but the branch is optimization-sensitive and does not establish FLOP-normalized efficiency, scaling behavior, or broad LLM performance.

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