Making Large Language Models More Flexible to Changing Contingencies through Tracking Induction

Experimental study examining whether tracking inductions can reduce rule-based insensitivity to contingencies in six frontier LLMs: GPT 5.2, Gemini 3 Flash, Grok 4.1 Fast, DeepSeek V3.2, Qwen3 235B, and Kimi K2. Using a 3×3 factorial design (Rule: none, correct, incorrect × Induction: none, direct tracking, metaphorical tracking) across 2,160 sessions, models played a rock-paper-scissors task whose contingencies reversed without warning at trial 41. Replicating prior findings, rules produced insensitivity in all six models, near-complete in GPT 5.2, Grok, and DeepSeek (sensitivity index between .03 and .10). Inductions reduced this insensitivity when rules were present, with minimal effects in their absence. Direct tracking, two sentences appended to the system prompt, was effective in every model. Metaphorical tracking (explorer, researcher, and programmer) was more variable: superior in Gemini, ineffective in Grok, and detrimental in Kimi K2. First evidence that tracking-based prompting can modulate LLM rigidity.