Paper critique: MLP size unaccounted for in Transformer logarithmic depth bounds

kfountou · x · 2026-09-21

A reader working through Transformers, Parallel Computation, and Logarithmic Depth flags that the MLPs in the MPC simulation have no bound on internal size — they are simply allowed to compute arbitrary functions. In the routing construction, this freedom lets the MLP decoder recover clean messages, discard corrupted copies, and remove duplicates, meaning part of the communication work is delegated to an MLP whose size and cost are never accounted for.

The stated bounds do not rule out an exponentially large implementation (though the paper's particular decoder may not need one). So the general MPC simulation alone does not establish an efficient polynomial-size-MLP implementation, let alone an end-to-end runtime advantage over RNNs — that would require bounding the size and depth of the local MLPs. The authors state the assumption explicitly, but the distinction matters.

Related event: Flaw Claimed in Transformer Logarithmic Depth Proof(3 posts)→

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