Scaled weight decay for Muon (Muon-SW) has been reported to train language models more efficiently than constant decoupled weight decay, but such comparisons usually reuse one learning-rate (LR) and weight-decay (WD) setting for both methods. We re-run the comparison under the MAI-Base-2 protocol: LR and WD are tuned jointly through their product for each method, on a source-scaled mixture-of-experts (MoE) scaling ladder (1.9M to 15M active parameters) that holds tokens per active parameter and data repetition fixed across sizes. We find: (1) Most of the gain is a tuning gap. At the shared setting Muon-SW wins by 0.035 bits per byte (BPB), a 1.52x compute saving; after both methods are tuned, the gap is 0.0026 BPB (95% CI [0.0018, 0.0034]), a 1.03x saving, so about 90% of the advantage disappears. (2) The small advantage that remains is real: at the smallest size, all four paired seeds favour Muon-SW at the tuned settings. (3) That advantage grows with model size: across an 8x range of active parameters, the tuned gap rises from 0.0036 to 0.0051 BPB while the untuned gap shrinks from 0.035 to 0.024, so the surviving share rises from about 10% to 21%. (4) The best weight decay moves with scale: the optimal LRWD product grows for both methods, faster for Muon-SW (ratio 1.40 to 1.91), and a law fitted on the two smallest sizes overshoots the third by 1.3-1.5x, costing up to 0.002 BPB. The whole study runs on one NVIDIA T4 GPU; we release the code and all run results.
Monitoring a model's chain of thought (CoT) is useful for safety only if the final answer depends on the written steps. Prior measurements use natural tasks where true reasoning is unknown. We measure it against an exact ground truth on a synthetic box-swap task where every intermediate state is known. We replace one step inside a model's own chain with a wrong but valid state and check whether the answer follows the edit. We evaluate 25 open-weight models--Qwen3 (0.6B-14B, base and post-trained), Gemma 3 (1B-12B), Llama 3 (1B-8B), and 8 OLMo 2 checkpoints--on 7,200 items each. We find five results: (1) Reliance rises with size and saturates. In Qwen3, answer reliance rises from 16-18% at 0.6B to 97-100% at 14B; a logistic in log N fits well (R^2 = 0.89), and Gemma 3 and Llama 3 follow this trend. (2) Capability is the main driver. Across all models, reliance and step accuracy correlate at r = 0.99; equally capable models are equally reliant, regardless of family. (3) Size still matters at matched correctness. On problems solved correctly before the edit, reliance increases with size among capable models (rho = 0.80, p = 0.002). (4) Post-training does not change reliance. Base and post-trained Qwen3 differ by at most 0.03 from 4B upward; a large gap at 1.7B matches a large capability gap. (5) No model up to 14B solves the task internally. Without written steps, every capable model is at chance once a problem has four or more swaps. OLMo 2 checkpoints never become capable, making the training-token axis a limitation. On tasks requiring step-by-step computation, scale makes the chain of thought more load-bearing, supporting CoT monitoring in this regime.