aiqbench analysis
This research identifies a functional role for the corpus-mean direction in transformer residual streams, demonstrating that it acts as a critical reference point for MLP gate operating points across various architectures. By showing that removing this specific directional component drastically alters firing rates while random directions do not, the study reveals how models implicitly build constants to regulate their internal distributions rather than relying solely on explicit bias parameters.
Transformer MLP Gate Thresholds Are Couplings to a Carried Reference Direction
arXiv:2609.31956v1 Announce Type: cross Abstract: 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 $\rho \leq 0.09$ 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 reference costs 8-42$\times$ 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.
Abstract: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 $\rho \leq 0.09$ 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 reference costs 8-42$\times$ 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.
18 pages, 4 tables. Code and data: this https URL. An earlier version of this paper is archived on Zenodo, doi:https://doi.org/10.5281/zenodo.21498411%3B this version supersedes it and corrects several reported values
Computation and Language (cs.CL); Machine Learning (cs.LG)
arXiv:2609.31956 [cs.CL]
(or arXiv:2609.31956v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2609.31956 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 333 words
Related coverage
Performance Profiling on AMD GPUs – Part 5: Profiling-Driven Kernel Optimization with an AI Code-Assist Tool
AMD · Jul 16, 2026
Running Variational Quantum Eigensolver with Qiskit Aer on AMD Instinct
AMD · May 29, 2026
Lattice-Based Cryptography Explained
Quantum Zeitgeist · Aug 15, 2026
Deconfusing Corrigibility
AI Alignment Forum · Oct 17, 2026