From Decorative to Load-Bearing: Task Difficulty Shapes the Causal Role of Chain-of-Thought
Chain-of-thought (CoT) monitoring is only meaningful if written reasoning causally constrains the answer. We introduce continuation-based causal testing, an ablation-patch intervention that perturbs one reasoning step, truncates the chain, and forces the model to continue from the corrupted prefix. It measures how load-bearing a CoT is for the final answer, a behavioral notion distinct from mechanistic faithfulness. Across Gemma-2-9B-IT, Llama-3.1-8B-Instruct, and DeepSeek-R1-Distill-Qwen-7B on GSM8K, MMLU, and BIG-Bench Hard, CoT load-bearingness tracks model-relative task difficulty: on easy tasks models silently bypass their own reasoning; on hard tasks they follow corrupted steps and propagate errors. A matched 2x2 analysis shows task difficulty dominates perturbation type: error propagation rises 16x from GSM8K to BBH multistep arithmetic, and a variance partition over 28,584 continuations attributes 98.8% of explained deviance to task difficulty versus 0.8% to perturbation type. Reasoning-specific RL suppresses error propagation and compresses the gradient. A four-variant judge-sensitivity analysis and blind two-annotator study (n=500) show the error-propagation vs. non-propagation label is invariant to judge prompt, with perfect inter-annotator agreement (Cohen's kappa = 1.00). This gradient creates a structural problem for CoT-based oversight and AI safety monitoring: where the trace is easy to read it carries little signal, and where it matters errors propagate before a monitor can intervene. Linear probes on hidden states separate silent bypass, self-correction, and error propagation, but additive activation steering provides limited causal control, flipping only about 25% of error-propagation cases at best. Behavioral mode is readable but not reliably controllable.