The Canary in the Carry Chain: model checkpoints for the long Collatz step

Trained transformer checkpoints accompanying the paper "The Canary in the Carry Chain: Transformers Know the Schedule Before They Can Execute". The paper studies when a transformer that fails on an iterative algorithmic factored as $y = E(x, c(x))$ for a discrete controller $c(x)$ and an executor $E.$ 

This bundle contains the locally trained PyTorch state dicts that produced the published numbers in Sections 5, 6, 8, and 9 of the paper. Loadable with torch.load(path, map_location='cpu').

Included:

- output_mps/b32/: the main $3x+1$ base-32 seq2seq encoder (4 encoder + 1 decoder layers, d=512, 8 heads, FFN 2048, max length 16, 1000 epochs). This is the canonical interpretability subject. Every probe selectivity number, every MLP ablation row, and every cross-attention-mass and gradient-attribution number is computed on this checkpoint. Includes ck_0010.pt through ck_0050.pt and best.pt.

- output_do/: the GPT-style 5-layer causal decoder-only replication used in Section 10 of the paper. Same width, format [BOS] $n$ [SEP] $\kappa(n)$ [EOS], 300 epochs.

- output_ctrl/: the single-permutation-orbit control model used in the task matrix.

- results_final/output_eci_seeds/baseline_s123/: one seed of the 500-epoch baseline ECI replication.