Transfer learning leverages knowledge from related source domains to improve learning in a target domain. Recent theoretical advances cover a broad range of regression settings within (generalized) linear models. Despite their diversity, these methods share two common constraints: they assume a known link function or linear structure and require direct access to raw source data. To move beyond these constraints, we propose a source-data-free transfer learning framework based on the single-index model (SIM). Instead of requiring raw source data, our method transfers only summary statistics derived from a generalized Stein's lemma in a one-time communication. This design preserves privacy and avoids side effects caused by dissimilarities of unknown nonlinear link functions across domains. To capture flexible, unknown nonlinearity, we employ a multilayer perceptron guided by the pre-estimated index from the transferred statistics, which significantly mitigates overfitting. Extensive experiments on synthetic data and a real-world application demonstrate consistent improvements over existing (generalized) linear model-based approaches. The proposed framework thus offers a practical, privacy-preserving, and nonlinear-adaptive solution for transfer learning.

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

Learning-to-learn or meta-learning focuses on developing algorithms that leverage prior experience to quickly acquire new skills or adapt to novel environments. A crucial component of meta-learning is representation learning, which aims to construct data representations capable of transferring knowledge across multiple tasks--a critical advantage in data-scarce settings. We study how representation learning can improve the efficiency of bandit problems. We consider T d-dimensional linear bandits that share a common low-dimensional linear representation. We provide provably fast, sample-efficient algorithms to address the two key problems in meta-learning: (1) learning a common set of features from multiple related bandit tasks and (2) transferring this knowledge to new, unseen bandit tasks.

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL.

Theoretical works on supervised transfer learning (STL)--where the learner has access to labeled samples from both source and target distributions--have for the most part focused on statistical aspects of the problem, while efficient optimization has received less attention. We consider the problem of designing an SGD procedure for STL that alternates sampling between source and target data, while maintaining statistical transfer guarantees without prior knowledge of the quality of the source data. A main algorithmic difficulty is in understanding how to design such an adaptive sub-sampling mechanism at each SGD step, to automatically gain from the source when it is informative, or bias towards the target and avoid negative transfer when the source is less informative. We show that, such a mixed-sample SGD procedure is feasible for general prediction tasks with convex losses, rooted in tracking an abstract sequence of constrained convex programs that serve to maintain the desired transfer guarantees. We instantiate these results in the concrete setting of linear regression with square loss, and show that the procedure converges, with 1/ T rate, to a solution whose statistical performance on the target is adaptive to the a priori unknown quality of the source. Experiments with synthetic and real datasets support the theory.

Self-play constitutes a fundamental paradigm for autonomous skill acquisition, whereby agents iteratively enhance their capabilities through self-directed environmental exploration (Silver et al., 2018). Conventional self-play frameworks exploit agent symmetry within zero-sum competitive settings (Balduzzi et al., 2019), yet this approach proves inadequate for open-ended learning scenarios characterized by inherent asymmetry. Human pedagogical systems exemplify asymmetric instructional frameworks wherein educators systematically construct challenges calibrated to individual learners' developmental trajectories (Bobbitt, 1918; Bengio et al., 2009). The principal challenge resides in operationalizing these asymmetric, adaptive pedagogical mechanisms within artificial systems capable of autonomously synthesizing appropriate curricula without predetermined task hierarchies. Here we present Heterogeneous Adversarial Play (HAP), an adversarial Automatic Curriculum Learning (ACL) framework that formalizes teacher-student interactions as a minimax optimization wherein task-generating instructor and problem-solving learner co-evolve through adversarial dynamics. In contrast to prevailing ACL methodologies that employ static curricula or unidirectional task selection mechanisms, HAP establishes a bidirectional feedback system wherein instructors continuously recalibrate task complexity in response to real-time learner performance metrics. Experimental validation across multi-task learning domains demonstrates that our framework achieves performance parity with state-of-the-art (SOTA) baselines while generating curricula that enhance learning efficacy in both artificial agents and human subjects.

This paper presents a methodology-centered transfer learning framework for fragility adaptation under domain shift, class imbalance, and scarce target labels while preserving engineering interpretability and supporting decision-making under uncertainty. Four transfer learning strategies (instance-based, parameter-based, hierarchical Bayesian, and multi-source) are demonstrated through three complementary case studies: (i) instance-based transfer learning via importance weighting, demonstrated on coastal bridge fragility using Hurricane Katrina observations; (ii) parameter-based transfer learning together with hierarchical Bayesian transfer learning, enabling partial pooling across strata and posterior uncertainty quantification, demonstrated on residential building fragility using Hurricane Ian observations; and (iii) multi-source transfer learning that fuses multiple analytical fragility models with learned source weights and regularized target-domain adaptation, demonstrated on seismic bridge fragility using observations from the 2001 Nisqually earthquake. Across these case studies, direct transfer of source models (i.e. using existing state-of-the-art models) fails under domain shift and severe class imbalance, while targeted adaptation substantially improves failure detection and predictive stability in low-data regimes. These findings highlight the need for systematic guidance on diagnostics, strategy selection, and uncertainty reporting when developing and adapting fragility models.

Multi-source transfer learning provides an effective solution to data scarcity in realworld supervised learning scenarios by leveraging multiple source tasks. In this field, existing works typically use all available samples from sources in training, which constrains their training efficiency and may lead to suboptimal results. To address this, we propose a theoretical framework that answers the question: what is the optimal quantity of source samples needed from each source task to jointly train the target model? Specifically, we introduce a generalization error measure based on K-L divergence, and minimize it based on high-dimensional statistical analysis to determine the optimal transfer quantity for each source task. Additionally, we develop an architecture-agnostic and data-efficient algorithm OTQMS to implement our theoretical results for target model training in multisource transfer learning. Experimental studies on diverse architectures and two real-world benchmark datasets show that our proposed algorithm significantly outperforms state-of-the-art approaches in both accuracy and data efficiency. The code is available at https://github.com/zqy0126/OTQMS.

While data-driven methods such as neural operator have achieved great success in solving differential equations (DEs), they suffer from domain shift problems caused by different learning environments (with data bias or equation changes), which can be alleviated by transfer learning (TL). However, existing TL methods adopted in DEs problems lack either generalizability in general DEs problems or physics preservation during training. In this work, we focus on a general transfer learning method that adaptively correct the domain shift and preserve physical relation within the equation. Mathematically, we characterize the data domain as product distribution and the essential problems as distribution bias and operator bias. APhysics-preserved Optimal Tensor Transport (POTT) method that simultaneously admits generalizability to common DEs and physics preservation of specific problem is proposed to adapt the data-driven model to target domain, utilizing the pushforward distribution induced by the POTT map. Extensive experiments in simulation and real-world datasets demonstrate the superior performance, generalizability and physics preservation of the proposed POTT method.

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the connections and the lack of accounting for feedback mediation. Such shortcomings limit its effective scaling to complex network architectures and tasks. To this end, here we introduce the Structural Projection Hebbian Representation (SPHeRe), a novel unsupervised learning method that integrates orthogonality and structural information preservation through a local auxiliary nonlinear block. The loss for structural information preservation backpropagates to the input through an auxiliary lightweight projection that conceptually serves as feedback mediation while the orthogonality constraints account for the boundedness of updating magnitude. Extensive experimental results show that SPHeRe achieves SOTA performance among unsupervised synaptic plasticity approaches on standard image classification benchmarks, including CIFAR-10, CIFAR-100, and Tiny-ImageNet. Furthermore, the method exhibits strong effectiveness in continual learning and transfer learning scenarios, and image reconstruction tasks show the robustness and generalizability of the extracted features. This work demonstrates the competitiveness and potential of Hebbian unsupervised learning rules within modern deep learning frameworks, demonstrating the possibility of efficient and biologically inspired learning algorithms without the strong dependence on strict backpropagation.