Reader--Writer Coupling in Transformer MLPs

arXiv:2610.29340v1 Announce Type: new Abstract: A transformer MLP gives each hidden channel two roles: a reader that decides when the channel responds, and a writer that decides what it adds back to the residual stream. Read as a key--value memory, the layer can be measured one factor set at a time: the pairing of readers to writers is carried only by their shared index, invisible to any quantity computed from one factor set alone. Yet training couples the two factors through their joint update, so we ask what reading them together shows. The block supplies the joint instrument: the MLP writes back into the very stream it reads, so the exact Jacobian of its update is square, and its agreement with its own transpose resolves into reader--writer terms whose inner products give each channel, read as a couple, a signed pairing coordinate. Ranked by this coordinate, each block we measure has a small core of strongly coupled channels; where initialization gives either sign equally, the core is nearly all opposed: each writer points against the direction its reader responds to. This opposed core recurs from the smallest models trained from scratch to released checkpoints; its sign is in place within a few percent of training and holds while the coupling grows. Read as couples, most channels return their contribution against the reader that fired it, and the readers of later blocks take it up; few show in the logits. Training holds the couples in place: flipping the opposed writers moves the output toward common tokens, and a writer permuted onto another reader regrows to fit that reader while the reader stays.

Abstract:A transformer MLP gives each hidden channel two roles: a reader that decides when the channel responds, and a writer that decides what it adds back to the residual stream. Read as a key--value memory, the layer can be measured one factor set at a time: the pairing of readers to writers is carried only by their shared index, invisible to any quantity computed from one factor set alone. Yet training couples the two factors through their joint update, so we ask what reading them together shows. The block supplies the joint instrument: the MLP writes back into the very stream it reads, so the exact Jacobian of its update is square, and its agreement with its own transpose resolves into reader--writer terms whose inner products give each channel, read as a couple, a signed pairing coordinate. Ranked by this coordinate, each block we measure has a small core of strongly coupled channels; where initialization gives either sign equally, the core is nearly all opposed: each writer points against the direction its reader responds to. This opposed core recurs from the smallest models trained from scratch to released checkpoints; its sign is in place within a few percent of training and holds while the coupling grows. Read as couples, most channels return their contribution against the reader that fired it, and the readers of later blocks take it up; few show in the logits. Training holds the couples in place: flipping the opposed writers moves the output toward common tokens, and a writer permuted onto another reader regrows to fit that reader while the reader stays.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2610.29340 [cs.LG]

(or arXiv:2610.29340v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.29340 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Reader--Writer Coupling in Transformer MLPs