The Automaton Underneath: The Additive Input Pathway Is a Parasitic Attractor for State Tracking in Householder Linear RNN
Linear RNNs with input-dependent Householder-product transitions (DeltaNet/DeltaProduct-class) can provably represent hard state-tracking automata, yet trained models fail to length-generalize -- a gap recent work attributes to optimization, without a causal account. We give one, in a pre-registered, within-architecture causal ablation: the same model with one term deleted -- the additive input injection $b_t = W_b e_t$. With $b_t$, models fit length 32 and collapse out-of-distribution on parity, $S_4$, $A_5$, and non-solvable $S_5$ word problems (0.20 at position 512 on $S_5$). Without it -- input acting only through the orthogonal transitions -- the same architecture learns the exact au...
| Authors | Gunner Levi Howe |
|---|---|
| Primary category | cs.LG |
| Published | 16 July 2026 |
| Last updated at source | 16 July 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.