Abstract
Continual learning (CL), where a model is trained on a sequence of data tasks, is increasingly being adopted across key fields such as large language models and image recognition, yet it remains highly vulnerable to data poisoning that triggers learning divergence or severe excess risk. Despite these threats, a principled theoretical foundation in CL for understanding attack and defense remains lacking. In this paper, we develop a theoretical framework to analyze strategic attacks and defenses in regularization-based CL, a cornerstone of recent CL theory. By framing the adversary-defender interaction as an online zero-sum game, we first establish a fundamental performance limit: no defense succeeds when an adversary poisons a linear proportion of tasks by injecting unbounded noise or pattern shifts in regularization-based CL. We then analyze two possibly defensible scenarios: infrequent attacks and bounded noise per attack. For the former regime, we propose a task-to-task verification mechanism to detect data poisoning and reduce cumulative bias for learning convergence. For the latter regime, we derive a robust defense that minimizes the model's sensitivity to poisoned features, provably accelerating the convergence rate. Extensive experiments on realistic tasks further validate our theoretical results.
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Jun 1, 2026cs.LG
In dynamic environments, large language models need to keep adapting to new tasks, but continual learning often suffers from forgetting, limited transfer, and vulnerability to adversarial perturbations. To address this, we present AdvCL, which repurposes adversarial perturbations as a geometric control signal for stable continual adaptation. AdvCL combines three plug-in modules: Intra-Smooth promotes local smoothness via small adversarial perturbations; Proto-Clip uses similarity clipping to prevent excessive alignment to current task prototype; and Inter-Align applies directional alignment toward previous task prototype to reduce representational gaps. Experiments show consistent gains in both standard performance and robustness, with lower forgetting and stronger transfer. We further analyze key mechanisms by quantifying the sensitivity of Intra-Smooth to perturbation settings and the effect of Inter-Align on task similarity and geometric distance. In summary, the modules provide complementary gains when combined, and each can also be integrated individually into diverse CL paradigms, including replay, regularization, and dynamic architectures, thereby offering a geometric control mechanism for continual learning.
Ran Liu, Min Yu, Mingqi Liu +7
Apr 19, 2026cs.LG
Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years, the theoretical development of CL remains in its infancy. At the heart of developing CL theory lies the challenge that the data distribution varies across tasks, and we argue that properly addressing this challenge requires understanding this variation--dependency among tasks. To explicitly model task dependency, we consider nonlinear regression tasks and propose the assumption that these tasks are dependent in such a way that the data of the current task is a nonlinear transformation of previous data. With this model and under natural assumptions, we prove statistical recovery guarantees (more specifically, bounds on estimation errors) for several CL paradigms in practical use, including experience replay with data-independent regularization and data-independent weights that balance the losses of tasks, replay with data-dependent weights, and continual learning with data-dependent regularization (e.g., knowledge distillation). To the best of our knowledge, our bounds are informative in cases where prior work gives vacuous bounds.
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Sep 7, 2026cs.AI
The abundance of online data is at risk of unauthorized usage in training deep learning models. To counter this, various Data Availability Attacks (DAAs) have been devised to make data unlearnable for such models by subtly perturbing the training data. However, existing attacks often excel against either Supervised Learning (SL) or Self-Supervised Learning (SSL) scenarios. Among these, a model-free approach that generates a Convolution-based Unlearnable Dataset (CUDA) stands out as the most robust DAA across both SSL and SL. Nonetheless, CUDA's effectiveness against SSL is underwhelming and it faces a severe trade-off between image quality and its poisoning effect. In this paper, we conduct a theoretical analysis of CUDA, uncovering the sub-optimal gradients it introduces and elucidating the strategy it employs to induce class-wise bias for data poisoning. Building on this, we propose a novel poisoning method named Imperfect Restoration Poisoning (IRP), aiming to preserve high image quality while achieving strong poisoning effects. Through extensive comparisons of IRP with eight baselines across SL and SSL, coupled with evaluations alongside five representative defense methods, we showcase the superiority of IRP. Code: https://github.com/lyumingzhi/IRP
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