Toward Understanding Unlearning Difficulty: A Mechanistic Perspective and Circuit-Guided Difficulty Metric

• URL: http://arxiv.org/abs/2601.09624v1
• Date: Wed, 14 Jan 2026 16:55:58 GMT
• Title: Toward Understanding Unlearning Difficulty: A Mechanistic Perspective and Circuit-Guided Difficulty Metric
• Authors: Jiali Cheng, Ziheng Chen, Chirag Agarwal, Hadi Amiri,
• Abstract summary: Circuit-guided Unlearning Difficulty (CUD) is a metric that assigns each sample a continuous difficulty score using circuit-level signals.<n>We identify key circuit-level patterns that reveal a mechanistic signature of difficulty.
• Score: 36.2724900971511
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Machine unlearning is becoming essential for building trustworthy and compliant language models. Yet unlearning success varies considerably across individual samples: some are reliably erased, while others persist despite the same procedure. We argue that this disparity is not only a data-side phenomenon, but also reflects model-internal mechanisms that encode and protect memorized information. We study this problem from a mechanistic perspective based on model circuits--structured interaction pathways that govern how predictions are formed. We propose Circuit-guided Unlearning Difficulty (CUD), a {\em pre-unlearning} metric that assigns each sample a continuous difficulty score using circuit-level signals. Extensive experiments demonstrate that CUD reliably separates intrinsically easy and hard samples, and remains stable across unlearning methods. We identify key circuit-level patterns that reveal a mechanistic signature of difficulty: easy-to-unlearn samples are associated with shorter, shallower interactions concentrated in earlier-to-intermediate parts of the original model, whereas hard samples rely on longer and deeper pathways closer to late-stage computation. Compared to existing qualitative studies, CUD takes a first step toward a principled, fine-grained, and interpretable analysis of unlearning difficulty; and motivates the development of unlearning methods grounded in model mechanisms.

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