# Transformer MLP Gate Thresholds Are Couplings to a Carried Reference Direction

arXiv: https://arxiv.org/abs/2609.31956 · HTML: https://mlsanity.com/paper/2609.31956/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 30 of 30)

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- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
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- [On the Relationship Between Activation Outliers and Feature Death in Sparse Autoencoders](https://mlsanity.com/paper/2605.31518/) (2026)
- [Massive Spikes in LLMs are Bias Vectors: Mechanistic Uncovering and Spike-Free Quantization](https://mlsanity.com/paper/2606.02288/) (2026)
- [Understanding Gated Neurons in Transformers from Their Input-Output Functionality](https://mlsanity.com/paper/2505.17936/) (2025)
- [The Curse and Blessing of Mean Bias in FP4-Quantized LLM Training](https://mlsanity.com/paper/2603.10444/) (2026)
- [The Discrete Charm of the MLP: Binary Routing of Continuous Signals in Transformer Feed-Forward Layers](https://mlsanity.com/paper/2603.10985/) (2026)
- [Bug or Feature2: Weight Drift, Activation Sparsity and Spikes](https://mlsanity.com/paper/2605.17659/) (2026)
- [Comparing Linear Probes with Mahalanobis Cosine Similarity](https://mlsanity.com/paper/2606.19603/) (2026)

## Abstract (arXiv)

The corpus-mean direction of a transformer's residual stream is a component shared across all inputs, and is commonly removed by mean-centering before representational analysis. We present evidence that it is a functional component: the reference against which the MLP gate population sets its operating point. In Phi-2, an exact decomposition of resting gate pre-activations shows that at mid-stack layers the resting inhibition of >99.9% of gates is carried by the coupling w · bL to the carried mean direction, at 48-56× the explicit bias parameter, and the coupling is direction-specific: a random direction at matched norm orders the population's firing rates at Spearman ρ ≤ 0.09 where the reference reaches 0.95. (That 0.95 is near-tautological on its own; the paper derives its null.) Causally, removing the stream's projection on the reference multiplies above-threshold firing by about 9×, dose-monotonically, at 23-59× a norm-matched control; a random-initialised twin is flat, and replacement tests show that the direction carries the function and the magnitude does not. A direction-matched control makes the same point: noise injected along the reference costs 8-42× the same energy along a random direction. The decomposition replicates on four further families spanning both gate types (GELU with an explicit gate bias, bias-free SwiGLU), and the dose-response on two of them. Across an eight-model scan the mechanism is present in every GELU and SiLU family and absent only in OPT, where an opposing LayerNorm bias cancels the carried reference. Gate thresholds are implemented as couplings to a constant the network builds for the distribution it is reading, with the bias parameters contributing little; how much of that constant is carried in the stream and how much in parameters depends on the architecture.