This paper studies the problem of class-incremental learning (CIL), a core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pretrained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration of PTMs into CIL has recently led to efficient approaches that treat the PTM as a fixed feature extractor combined with analytic classifiers, achieving state-ofthe-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading to suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), a novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-based training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded as the upper bound of CIL.

Federated continual learning (FCL) aims to maintain the model's performance on old tasks (i.e., stability) while enhancing its ability to acquire knowledge from current tasks (i.e., plasticity). With the development of pre-trained models (PTMs), fine-tuning PTMs on clients has become a promising approach to leveraging their extensive knowledge in FCL. In this paper, we propose MultiFCL, a novel FCL framework that fine-tunes PTMs to adapt to FCL while preserving their strong generalization capabilities. Specifically, to ensure the stability, MultiFCL introduces lightweight adapters for task adaption, which are subsequently frozen to prevent catastrophic forgetting. Moreover, by utilizing the semantic features of old tasks, MultiFCL performs multi-modal initialization of new task class prototypes. To enhance the plasticity, MultiFCL employs a multi-expert training mechanism that integrates multi-scale feature learning with multi-teacher dynamic self-distillation.

This paper studies the problem of class-incremental learning (CIL), a core setting within continual learning where a model learns a sequence of tasks, each containing a distinct set of classes. Traditional CIL methods, which do not leverage pre-trained models (PTMs), suffer from catastrophic forgetting (CF) due to the need to incrementally learn both feature representations and the classifier. The integration of PTMs into CIL has recently led to efficient approaches that treat the PTM as a fixed feature extractor combined with analytic classifiers, achieving state-of-the-art performance. However, they still face a major limitation: the inability to continually adapt feature representations to best suit the CIL tasks, leading to suboptimal performance. To address this, we propose AnaCP (Analytic Contrastive Projection), a novel method that preserves the efficiency of analytic classifiers while enabling incremental feature adaptation without gradient-based training, thereby eliminating the CF caused by gradient updates. Our experiments show that AnaCP not only outperforms existing baselines but also achieves the accuracy level of joint training, which is regarded as the upper bound of CIL.

Federated continual learning (FCL) aims to maintain the model's performance on old tasks (i.e., stability) while enhancing its ability to acquire knowledge from current tasks (i.e., plasticity). With the development of pre-trained models (PTMs), fine-tuning PTMs on clients has become a promising approach to leveraging their extensive knowledge in FCL. In this paper, we propose MultiFCL, a novel FCL framework that fine-tunes PTMs to adapt to FCL while preserving their strong generalization capabilities. Specifically, to ensure the stability, MultiFCL introduces lightweight adapters for task adaption, which are subsequently frozen to prevent catastrophic forgetting. Moreover, by utilizing the semantic features of old tasks, MultiFCL performs multi-modal initialization of new task class prototypes. To enhance the plasticity, MultiFCL employs a multi-expert training mechanism that integrates multi-scale feature learning with multi-teacher dynamic self-distillation.

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

Post-Translational Modifications (PTMs) are changes that occur in proteins after synthesis, influencing their structure, function, and cellular behavior. PTMs are essential in cell biology; they regulate protein function and stability, are involved in various cellular processes, and are linked to numerous diseases. A particularly interesting class of PTMs are chemical modifications such as phosphorylation introduced on amino acid side chains because they can drastically alter the physicochemical properties of the peptides once they are present. One or more PTMs can be attached to each amino acid of the peptide sequence. The most commonly applied technique to detect PTMs on proteins is bottom-up Mass Spectrometry-based proteomics (MS), where proteins are digested into peptides and subsequently analyzed using Tandem Mass Spectrometry (MS/MS).

Continual learning aims to incrementally acquire new concepts in data streams while resisting forgetting previous knowledge.With the rise of powerful pre-trained models (PTMs), there is a growing interest in training incremental learning systems using these foundation models, rather than learning from scratch. Existing works often view PTMs as a strong initial point and directly apply parameter-efficient tuning (PET) in the first session for adapting to downstream tasks.In the following sessions, most methods freeze model parameters for tackling forgetting issues. However, applying PET directly to downstream data cannot fully explore the inherent knowledge in PTMs.Additionally, freezing the parameters in incremental sessions hinders models' plasticity to novel concepts not covered in the first session. To solve the above issues, we propose a Slow And Fast parameter-Efficient tuning (SAFE) framework.In particular, to inherit general knowledge from foundation models, we include a transfer loss function by measuring the correlation between the PTM and the PET-applied model.After calibrating in the first session, the slow efficient tuning parameters can capture more informative features, improving generalization to incoming classes.Moreover, to further incorporate novel concepts, we strike a balance between stability and plasticity by fixing slow efficient tuning parameters and continuously updating the fast ones.Specifically, a cross-classification loss with feature alignment is proposed to circumvent catastrophic forgetting.During inference, we introduce an entropy-based aggregation strategy to dynamically utilize the complementarity in the slow and fast learners.Extensive experiments on seven benchmark datasets verify the effectiveness of our method by significantly surpassing the state-of-the-art.

After calibrating in the first session, the slow efficient tuning parameters can capture more informativefeatures, improving generalization to incoming classes. Moreover, to further incorporate novel concepts, we strikeabalance between stability and plasticity byfixing slowefficient tuning parameters and continuously updating the fast ones. Specifically, a cross-classification loss with feature alignment is proposed to circumvent catastrophic forgetting.