Cutting-Edge LLM Interpretability Research

Base-16 to Base-2 Conversion Analysis (Problem #4682)

Problem: When base-16 number 66666 is written in base 2, how many digits (bits) does it have?

Analysis:

• Initial (incorrect) approach: The model first concluded 20 bits based on a simple heuristic, but quickly questioned it (Sentence 12, 'Uncertainty Management').
• Pivotal 'Thought Anchor': Sentence 13 ('Plan Generation') – 'Alternatively, maybe I can calculate the value... in decimal and then find out how many bits...' – had the highest counterfactual importance and drastically increased accuracy, signaling a critical re-evaluation.
• Self-correction & verification: The model computed the decimal value, converted to binary (yielding 19 bits), noted the discrepancy, and then re-checked arithmetic and re-verified binary conversion.
• Resolution: Sentence 66 ('Plan Generation') – 'Ah, perhaps because leading zeros are not counted.' – explained the discrepancy, leading to the correct 19-bit answer.
• Converging evidence: All three methods (resampling, receiver heads, attention suppression) highlighted Sentence 13 and other planning/uncertainty management sentences as crucial, demonstrating a structured, self-correcting reasoning process driven by 'thought anchors'.

Conclusion: This case study illustrates how Large Language Models use critical 'thought anchor' sentences, such as planning and uncertainty management, to navigate complex problems, self-correct from initial errors, and steer the overall reasoning trajectory towards a correct solution.