Routing Absorption in Sparse Attention: Why Random Gates Are Hard to Beat

Abstract: Can a transformer learn which attention entries matter during training? In principle, yes: attention distributions are highly concentrated, and a small gate network can identify the important entries post-hoc with near-perfect accuracy. In practice, barely. When sparse attention is trained end-to-end, the model's Q/K/V projections co-adapt to whatever mask is imposed, absorbing the routing signal until learned gates perform little better than frozen random gates. We call this routing absorption and present four independent lines of evidence for it in a controlled 31M-parameter transformer: (1) differentiable soft gating converges to nearly the same perplexity whether the gate is learned or random (48.73 +/- 0.60 vs. 49.83 +/- 0.04 over 3 seeds); (2) hard top-k gating receives exactly zero gradient through the mask; (3) a gate distilled onto co-adapted Q/K/V achieves high F1 against oracle masks but catastrophic perplexity when deployed (601.6 vs. 48.6 on mask-agnostic Q/K/V); and (4) stochastic mask randomization during training fails to prevent co-adaptation (78.2 ppl deployed dense vs. 37.3 baseline). We connect routing absorption to the same phenomenon in Mixture-of-Experts, where random routing matches learned routing because experts co-adapt to any router, but show that attention exhibits a structurally more severe form: shared Q/K/V parameters enable cross-layer compensation pathways absent in MoE, where experts are self-contained modules. The implication is that end-to-end sparse attention methods employing per-query token-level gating face absorption pressure proportional to the parameter asymmetry between the gate and the model, and that post-hoc approaches, which decouple representation learning from sparsification, sidestep this entirely.