Tiange Li, Yinan Li, Youming Qiao, Dacheng Tao, Yingjie Wang
In Grochow and Qiao (\emph{SIAM J. Comput.}, 2023), the complexity class Tensor Isomorphism (TI) was introduced and isomorphism problems for groups, algebras, and polynomials were shown to be TI-complete. In this paper, we study average-case algorithms for several TI-complete problems over finite fields, including algebra isomorphism, matrix code conjugacy, and $4$-tensor isomorphism. Our main results reveal a rich landscape of average-case complexities of Tensor Isomorphism problems, despite their equivalence in the worst-case setting. Over the finite field of order $q$, we devise (1) average-case \emph{polynomial-time} algorithms for algebra isomorphism and matrix code conjugacy that succeed for $1/Θ(q)$ fraction of inputs; (2) an average-case \emph{polynomial-time} algorithm for the $4$-tensor isomorphism that succeeds for $1/q^{Θ(1)}$ fraction of inputs; and (3) an average-case \emph{polynomial-time} algorithm for the orthogonal $3$-tensor isomorphism that succeed for $1-1/\poly(n)$ fraction of $n\times n\times n$ tensors. Our main technical contribution is to introduce the spectral properties of random matrices into algorithms for TI-complete problems. This leads to not only new algorithms but also new questions in random matrix theory over finite fields. To settle these questions, we need to extend both the generating function approach as in Neumann and Praeger (\emph{J. London Math. Soc.}, 1998) and the character sum method of Gorodetsky and Rodgers (\emph{Trans. Amer. Math. Soc.}, 2021).
Huazheng Wang, Yongcheng Jing, Haifeng Sun, Yingjie Wang, Jingyu Wang, Jianxin Liao, Dacheng Tao Nanyang Technological University
In this paper, we investigate knowledge forgetting in large language models with a focus on its generalisation—ensuring that models forget not only specific training samples but also related implicit knowledge. To this end, we begin by identifying a broader unlearning scope that includes both target data and logically associated samples, including rephrased, subject-replaced, relation-reversed, and one-hop reasoned data. We then conduct a rigorous evaluation of 15 state-of-the-art methods across three datasets, revealing that unlearned models still recall paraphrased answers and retain target facts in their intermediate layers. This motivates us to take a preliminary step toward more generalised implicit knowledge forgetting by proposing PERMU—a novel probability perturbation-based unlearning paradigm. PERMU simulates adversarial unlearning samples to eliminate fact-related tokens from the logit distribution, collectively reducing the probabilities of all answer-associated tokens. Experiments are conducted on a diverse range of datasets, including TOFU, Harry Potter, ZsRE, WMDP, and MUSE, using models ranging from 1.3B to 13B in scale. The results demonstrate that PERMU delivers up to a 50.40% improvement in unlearning vanilla target data while maintaining a 40.73% boost in forgetting implicit knowledge. Our code can be found in the supplementary material.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表