# Half the Nonlinearity Is Wasted: Measuring and Reallocating the Transformer's MLP Budget

arXiv: https://arxiv.org/abs/2603.03459 · HTML: https://mlsanity.com/paper/2603.03459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [MoEfication: Transformer Feed-forward Layers are Mixtures of Experts](https://mlsanity.com/paper/2110.01786/) (2021)
- [Neural Redshift: Random Networks are not Random Functions](https://mlsanity.com/paper/2403.02241/) (2024)
- [Bilinear MLPs enable weight-based mechanistic interpretability](https://mlsanity.com/paper/2410.08417/) (2024)
- [Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wild](https://mlsanity.com/paper/2503.10065/) (2025)

## Abstract (arXiv)

We investigate when transformer MLP nonlinearity is actually necessary. A gate with d+1 parameters decides when to replace the full MLP with a linear surrogate. Through systematic investigation across six models (162M-2.8B parameters), two architectures, and three corpora, we establish that nonlinearity need cannot be predicted from token identity: cross-corpus correlation is zero (r < 0.05). The routing decision is fully contextual. Despite weak per-instance predictability, the gate exploits a heavily skewed distribution where most MLP computations are near-linear, achieving 25-56% linear routing at <1% perplexity cost in GPT-2. In GPT-2 Large, 11 of 36 layers beat baseline with gating and no layer exceeds 3.7% all-linear cost. This success is architecture-dependent: Pythia models show higher costs, though Pythia-2.8B's full 32-layer sweep reveals one layer that narrowly beats baseline. As a proof of concept, we progressively replace middle-layer MLPs with frozen linear matrices: 5 of 24 layers linearize at zero cost. With a full training budget, 4 linearized layers yield a 10.2% perplexity improvement -- and a two-phase gated approach pushes this to 17.3%, beating a vanilla fine-tuning control and confirming that the nonlinear MLPs at these layers were actively harmful.