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.

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.

With the top-ranked PTM candidates, we further learn to enrich task repr.

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.

Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen domains after fine-tuning on multiple training domains. However, maximally exploiting a zoo of PTMs is challenging since fine-tuning all possible combinations of PTMs is computationally prohibitive while accurate selection of PTMs requires tackling the possible data distribution shift for OoD tasks. In this work, we propose ZooD, a paradigm for PTMs ranking and ensemble with feature selection. Our proposed metric ranks PTMs by quantifying inter-class discriminability and inter-domain stability of the features extracted by the PTMs in a leave-one-domain-out cross-validation manner. The top-K ranked models are then aggregated for the target OoD task. To avoid accumulating noise induced by model ensemble, we propose an efficient variational EM algorithm to select informative features. We evaluate our paradigm on a diverse model zoo consisting of 35 models for various OoD tasks and demonstrate: (i) model ranking is better correlated with fine-tuning ranking than previous methods and up to 9859x faster than brute-force fine-tuning; (ii) OoD generalization after model ensemble with feature selection outperforms the state-of-the-art methods and the accuracy on most challenging task DomainNet is improved from 46.5\% to 50.6\%. Furthermore, we provide the fine-tuning results of 35 PTMs on 7 OoD datasets, hoping to help the research of model zoo and OoD generalization.