Localizing succession — the +1 / greater-than operator

The operator catalog lists succession / greater-than as a gap (“MLP-dominated; no clean attention head”). This puts data behind it. Task: a run of consecutive single-token numbers (“ 3 4 5 6 7”) → predict the next; the succession-NLL is the metric. With all attention intact, mean-ablate each layer’s MLP; with all MLPs intact, each layer’s attention — the layers whose ablation most raises succession-NLL are where the increment is computed.

model	runs	base NLL	MLP-dominance (ΣMLP / (ΣMLP+Σattn))	top succession-MLP (depth, ΔNLL)	top succession-attn (depth, ΔNLL)
gpt2	254	0.05	99%	L1 (0.09, +9.7); L0 (0.00, +9.7); L2 (0.18, +8.9)	L11 (1.00, +0.3); L9 (0.82, +0.0); L1 (0.09, +0.0)
gpt2-medium	254	0.04	100%	L0 (0.00, +10.8); L3 (0.13, +5.6); L2 (0.09, +5.0)	L21 (0.91, +0.0); L1 (0.04, +0.0); L19 (0.83, +0.0)
gpt2-large	254	0.05	95%	L7 (0.20, +6.9); L8 (0.23, +5.7); L9 (0.26, +5.6)	L0 (0.00, +1.4); L23 (0.66, +0.0); L14 (0.40, +0.0)

Finding: succession is overwhelmingly MLP-computed (95–100% MLP-dominance) and lives in the early–mid MLPs (GPT-2-small L0–L2, gpt2-large L7–9) — putting data behind the catalog’s “MLP-dominated, no clean attention head” gap. GPT-2 family only: the RoPE tokenizers (Gemma, Llama, Qwen) have no single-token numbers (they split ` 1` into multiple tokens), so consecutive number runs don’t exist — which is itself why succession studies use GPT-2.

MLP-dominance = the MLP layers’ share of the total (positive) ablation damage to succession; >50% confirms the catalog’s MLP-dominated claim, and the top-MLP layers say *where* the increment lives. ΔNLL = succession-NLL rise when that layer’s MLP / attention is mean-ablated. Provisional, single-token number runs (length 5). Data: succession_summary.json. Regenerate: succession.py. See the operator catalog gaps.