Q-Compass: Grounding Sequence Mixing in Reinforcement Learning Navigation

We introduce Q-Compass, a drop-in replacement for the standard multi-head attention
mechanism that eliminates the Value projection matrix and regrounds sequence mixing in
reinforcement learning theory. Standard attention computes routing weights via query-key
similarity and mixes projected values—four projection matrices in total. Q-Compass instead
computes a navigation matrix Q(s, a) = softmax (state (x) · action(x)⊤/√r) and gathers directly
from x, requiring only three projections. The mechanism is formally identical to the Q(s, a)
function in RL: “in state s, how valuable is attending to position a?” We describe the mechanism,
analyse its parameter efficiency, and present Quatrix — the architecture built on Q-Compass
— along with Tesseractor, an earlier proof-of-concept that preceded Quatrix and validated
the core idea at small scale before the full multimodal architecture was developed. Both train
stably from random initialisation, demonstrating that the Value projection is not necessary for
gradient-based language modelling.