Transformer MLP Gate Thresholds Are Couplings to a Carried Reference Direction

Olli Tuomi

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 $w \cdot b_L$ to the carried mean direction, at 48-56$\times$ the explicit bias parameter, and the coupling is direction-specific: a random direction at matched norm orders the population's firing rates at Spearman $ρ\leq 0.09$ 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$\times$, dose-monotonically, at 23-59$\times$ 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…