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新论文 · v1arXiv:2611.01620

Chain-of-Thought Oversight Requires Separate Evidence for Faithfulness and Monitorability

Sichao Li, Sai Ma, Xiyang Hu, Chudi Zhong, Tongliang Liu

A common assumption in chain-of-thought (CoT) oversight is that a visible reasoning trace makes model behavior easier to monitor. We argue that this assumption can conflate distinct properties along a chain linking a model's internal computation, reasoning artifacts, outputs, and monitor judgments. We identify four properties along this chain: reasoning visibility (whether a trace is accessible), mechanistic faithfulness (whether a trace reflects internal computation), mechanistic localizability (whether a compact causal mechanism can be isolated), and behavioral monitorability (whether a monitor can detect the target behavior). Two complementary case studies across three open-weight reasoning models show why these distinctions matter. In the security vulnerability reasoning study, probes and activation ablations provide evidence of internal representation and causal influence, but a monitor with access to the reference answer does not outperform the majority-class baseline in a held-out test. In authority-hint factual reasoning study, a monitor correctly distinguishes changed from unchanged answers, but seven mechanistic analyses do not isolate a compact causal mechanism. These results show that evidence for one claim does not establish the others. We therefore propose an evidential-chain reporting standard. Each claim carries a licensing statement that specifies its target property, access tier, and artifact, and labels each required link as supported, unsupported, or assumed. These assessments determine whether the conclusion is licensed, conditionally licensed, or not licensed.

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cs.AI · cs.CR
arXiv ↗PDF ↗
新论文 · v1arXiv:2611.01257

A Numerical Refinement of an Exact Discrete Fourier Transform Bound

Zhihao Yao, Sichao Liu

We refine the numerical bounds in Kartal's instantiation of Sussman's exact discrete Fourier transform construction. For every integer n >= 1, the resulting algorithm computes the length-n transform with work O(n (log n)^(1 - delta)), where delta = 0.0030201659. The bound holds in an exact complex-arithmetic RAM model with a supplied canonical root of unity. This final exponent saving exceeds the earlier certified parameter C_0 = 0.00302016 by 5.9 x 10^(-9). We retain the underlying circuit, tighten rational bounds for sums of powers of its block and target ranks, and increase the fixed tensor power from 7760 to 11640. These bounds establish the inequalities for Sussman's recursion at the intermediate certificate parameter C = 0.00302016595. The gap C - delta absorbs the overhead of recursion and Fourier reduction. The resulting transform theorem is proved in Lean and checked against the reference problem statement.

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cs.CC · cs.DS
arXiv ↗PDF ↗