TextNCA: Neural Cellular Automata for Language Modeling via Hierarchical Local Attention

Can a strictly local, iterated, weight-shared computation primitive support language modelling, and which of those three properties actually drives the model's behaviour? We define TextNCA, a 1D causal windowed-attention realisation of the Neural Cellular Automaton primitive, and study a hierarchical variant that cascades three stages with windows w \in {8, 32, 128} and T_s shared-weight iterations per stage, all on WikiText-103 at roughly 30M parameters and 60k training steps. The model does not match a parameter-matched Transformer at this scale (Hier-TextNCA 60.3 vs.\ Transformer-6L 52.8 and Transformer-12L 44.7 PPL), so we treat it as an analytical probe rather than a proposed alternative. The behaviour we observe is largely explained by the staged narrow-to-wide schedule: a non-iterating sliding-window Transformer that reuses the same schedule comes within +4.1 PPL of the iterated model, while reversing, flattening, or breaking the monotonic ordering of the schedule costs between +16.7 and +70.8 PPL. Iteration adds a smaller bounded benefit on top of the schedule, with a clear optimum at T_s{=}4 and a U-shaped degradation beyond it. The GRU gate and learned per-step embeddings are required for that benefit to appear, and training with random T_s yields an inference-time iteration-count knob at the cost of substantially higher absolute PPL. We position the work as a controlled reading of which parts of NCA-style computation carry the weight in language modelling.