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Shen Lin

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math.PR Artificial Intelligence Computer Vision Machine Learning

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preprint2026arXiv

CATA: Continual Machine Unlearning via Conflict-Averse Task Arithmetic

Vision-language models (VLMs) have shown remarkable ability in aligning visual and textual representations, enabling a wide range of multimodal applications. However, their large-scale training data inevitably raises concerns about privacy, copyright, and undesirable content, creating a strong need for machine unlearning. While existing studies mainly focus on single-shot unlearning, practical VLM deployment often involves sequential removal requests over time, giving rise to continual machine unlearning. In this work, we make the first attempt to study continual unlearning for VLMs and identify three key challenges in this setting: effectiveness in removing target knowledge, fidelity in preserving retained model utility, and persistence in preventing knowledge re-emergence under sequential updates. To address these challenges, we propose CATA, a conflict-averse task arithmetic method that represents each forget request as an unlearning task vector. By maintaining historical task vectors and performing sign-aware conflict-averse aggregation, CATA suppresses conflicting update components that may weaken previous forgetting effects. Extensive experiments under both single-shot and continual settings show that CATA outperforms baselines in terms of forgetting effectiveness, model fidelity, and forgetting persistence.

preprint2026arXiv

ICED: Concept-level Machine Unlearning via Interpretable Concept Decomposition

Machine unlearning in Vision-Language Models (VLMs) is typically performed at the image or instance level, making it difficult to precisely remove target knowledge without affecting unrelated semantics. This issue is especially pronounced since a single image often contains multiple entangled concepts, including both target concepts to be forgotten and contextual information that should be preserved. In this paper, we propose an interpretable concept-level unlearning framework for VLMs, which constructs a compact task-specific concept vocabulary from the forgetting set using a multimodal large language model. In addition to modality alignment, visual representations are decomposed into sparse, nonnegative combinations of semantic concepts, providing an explicit interface for fine-grained knowledge manipulation. Based on this decomposition, our method formulates unlearning as concept-level optimization, where target concepts are selectively suppressed while intra-instance non-target semantics and global cross-modal knowledge are preserved. Extensive experiments across both in-domain and out-of-domain forgetting settings demonstrate that our method enables more comprehensive target forgetting, better preserves non-target knowledge within the same image, and maintains competitive model utility compared with existing VLM unlearning methods.

preprint2025arXiv

Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$

We study the critical branching random walk on $\mathbb{Z}^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^d$ . We are interested in the occupation time in $K$ and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order $\|x\|^{4-d}$ in dimensions $d\leq 3$ , of order $\log\|x\|$ in dimension $d=4$ , and of order 1 in dimensions $d\geq 5$ . The corresponding weak convergences are also established. These results answer a question raised by Le Gall and Merle (Elect. Comm. in Probab. 11 (2006), 252-265).

preprint2022arXiv

Scaling limits of tree-valued branching random walks

We consider a branching random walk (BRW) taking its values in the $\mathtt{b}$ -ary rooted tree $\mathbb W_{ \mathtt{b}}$ (i.e. the set of finite words written in the alphabet $\{ 1, \ldots, \mathtt{b} \}$ , with $\mathtt{b}\! \geq \! 2$ ). The BRW is indexed by a critical Galton--Watson tree conditioned to have $n$ vertices; its offspring distribution is aperiodic and is in the domain of attraction of a $γ$ -stable law, $γ\in (1, 2]$ . The jumps of the BRW are those of a nearest-neighbour null-recurrent random walk on $\mathbb W_{ \mathtt{b}}$ (reflection at the root of $\mathbb W_{ \mathtt{b}}$ and otherwise: probability $1/2$ to move closer to the root of $\mathbb W_{ \mathtt{b}}$ and probability $1/(2\mathtt{b})$ to move away from it to one of the $\mathtt{b}$ sites above). We denote by $\mathcal R_{\mathtt{b}} (n)$ the range of the BRW in $\mathbb W_{ \mathtt{b}}$ which is the set of all sites in $\mathbb W_{\mathtt{b}}$ visited by the BRW. We first prove a law of large numbers for $\# \mathcal R_{\mathtt{b}} (n)$ and we also prove that if we equip $\mathcal R_{\mathtt{b}} (n)$ (which is a random subtree of $\mathbb W_{\mathtt{b}}$ ) with its graph-distance $d_{\mathtt{gr}}$ , then there exists a scaling sequence $(a_n)_{n\in \mathbb N}$ satisfying $a_n \! \rightarrow \! \infty$ such that the metric space $(\mathcal R_{\mathtt{b}} (n), a_n^{-1}d_{\mathtt{gr}})$ , equipped with its normalised empirical measure, converges to the reflected Brownian cactus with $γ$ -stable branching mechanism: namely, a random compact real tree that is a variant of the Brownian cactus introduced by N. Curien, J-F. Le Gall and G. Miermont.

preprint2016arXiv

Typical behavior of the harmonic measure in critical Galton-Watson trees

We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height $n$ by simple random walk on a critical Galton-Watson tree conditioned to have height greater than $n$ . We prove that, with high probability, the mass of the harmonic measure carried by a random vertex uniformly chosen from height $n$ is approximately equal to $n^{-λ}$ , where the constant $λ>1$ does not depend on the offspring distribution. This universal constant $λ$ is equal to the first moment of the asymptotic distribution of the conductance of size-biased Galton-Watson trees minus 1.

preprint2015arXiv

The range of tree-indexed random walk in low dimensions

We study the range $R_n$ of a random walk on the $d$ -dimensional lattice $\mathbb{Z}^d$ indexed by a random tree with $n$ vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension $d\leq3$ that $n^{-d/4}R_n$ converges in distribution to the Lebesgue measure of the support of the integrated super-Brownian excursion (ISE). An auxiliary result shows that the suitably rescaled local times of the tree-indexed random walk converge in distribution to the density process of ISE. We obtain similar results for the range of critical branching random walk in $\mathbb{Z}^d$ , $d\leq3$ . As an intermediate estimate, we get exact asymptotics for the probability that a critical branching random walk starting with a single particle at the origin hits a distant point. The results of the present article complement those derived in higher dimensions in our earlier work.

preprint2014arXiv

The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution

We study properties of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $α\in (1,2]$ . Here the harmonic measure refers to the hitting distribution of height $n$ by simple random walk on the critical Galton-Watson tree conditioned on non-extinction at generation $n$ . For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is roughly of order $n^{\frac{1}{α-1}}$ , most of the harmonic measure is supported on a boundary subset of size approximately equal to $n^{β_α}$ , where the constant $β_α\in (0,\frac{1}{α-1})$ depends only on the index $α$ . Using an explicit expression of $β_α$ , we are able to show the uniform boundedness of $(β_α, 1<α\leq 2)$ . These are generalizations of results in a recent paper of Curien and Le Gall (arXiv: 1304.7190).

preprint2013arXiv

The range of tree-indexed random walk

We provide asymptotics for the range R(n) of a random walk on the d-dimensional lattice indexed by a random tree with n vertices. Using Kingman's subadditive ergodic theorem, we prove under general assumptions that R(n)/n converges to a constant, and we give conditions ensuring that the limiting constant is strictly positive. On the other hand, in dimension 4 and in the case of a symmetric random walk with exponential moments, we prove that R(n) grows like n/(log n). We apply our results to asymptotics for the range of branching random walk when the initial size of the population tends to infinity.

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math.PR Artificial Intelligence Computer Vision Machine Learning

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arxivconfidence 95%

external id: arxiv:2512.24047:author:2:shen-lin

Imported May 21, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.14309:author:1:shen-lin

Imported May 20, 2026Synced May 21, 2026

arxivconfidence 95%

external id: arxiv:2605.18610:author:1:shen-lin

Imported May 20, 2026Synced May 21, 2026

Jean-François Le Gall2 works Junhao Dong2 works Li Xu2 works Jing Lin1 work

Shen Lin

Research overview

Is this your work?

8 publications

CATA: Continual Machine Unlearning via Conflict-Averse Task Arithmetic

ICED: Concept-level Machine Unlearning via Interpretable Concept Decomposition

Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$

Scaling limits of tree-valued branching random walks

Typical behavior of the harmonic measure in critical Galton-Watson trees

The range of tree-indexed random walk in low dimensions

The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution

The range of tree-indexed random walk

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Shen Lin

Research overview

Is this your work?

8 publications

CATA: Continual Machine Unlearning via Conflict-Averse Task Arithmetic

ICED: Concept-level Machine Unlearning via Interpretable Concept Decomposition

Yaglom theorem for critical branching random walk on Zd\mathbb{Z}^dZd

Scaling limits of tree-valued branching random walks

Typical behavior of the harmonic measure in critical Galton-Watson trees

The range of tree-indexed random walk in low dimensions

The harmonic measure of balls in critical Galton-Watson trees with infinite variance offspring distribution

The range of tree-indexed random walk

See the researcher in context

Building this map preview

Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$