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.

Conformal Bayes combines Bayesian posterior predictives with conformal calibration to produce prediction sets that are both statistically valid and geometrically efficient. We study conformal Bayes under label shift from a unified perspective, identifying two complementary approaches that restore nominal target-domain coverage through importance-weighted conformal calibration but operate through independent mechanisms. \emph{Post-hoc calibration} tilts the posterior predictive toward the target domain and corrects the conformal threshold via an importance-weighted quantile, leaving the parameter posterior unchanged. \emph{In-training adaptation} tilts the parameter posterior itself to the target domain, producing a corrected predictive whose highest predictive density region serves as the highest predictive density (HPD)-based prediction set under the fitted target predictive; efficiency is model-dependent and does not imply finite-sample conditional optimality. Two controlled experiments isolate the regime-dependence of each strategy: in the low-dimensional, well-estimated regime Strategy~A produces the narrowest valid intervals, while in the high-dimensional, underdetermined regime Strategy~B achieves up to $43\%$ width reduction at unchanged coverage, under the stated source-sampling and label-shift assumptions.

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.

The deployment of data-driven models in 6G wireless networks is increasingly challenged by frequent distribution shifts that degrade performance over time. Unsupervised Domain Adaptation (UDA) offers an alternative approach by adapting the trained model to a shifted domain without requiring labels. However, UDA pipelines are often more complex than single-task training due to additional modules and optimization procedures, raising a practical question: do the benefits of adaptation come at a higher energy cost, and how does this trade-off compare to retraining when labeling effort is also considered? In this work, we investigate the energy consumption of UDA and compare it to single task. We further propose a way to determine the minimum number of target domains for which UDA becomes more energy-efficient than retraining, taking into account the labeling cost. Our results aim to clarify when UDA should be preferred over classical train-from-scratch approaches from an energy and labeling-aware perspective.

In domain adaption (DA), joint maximum mean discrepancy (JMMD), as a famous distribution-distance metric, aims to measure joint probability distribution difference between the source domain and target domain, while it is still not fully explored and especially hard to be applied into a subspace-learning framework as its empirical estimation involves a tensor-product operator whose partial derivative is difficult to obtain. To solve this issue, we deduce a concise JMMD based on the Representer theorem that avoids the tensor-product operator and obtains two essential findings. First, we reveal the uniformity of JMMD by proving that previous marginal, class conditional, and weighted class conditional probability distribution distances are three special cases of JMMD with different label reproducing kernels. Second, inspired by graph embedding, we observe that the similarity weights, which strengthen the intra-class compactness in the graph of Hilbert Schmidt independence criterion (HSIC), take opposite signs in the graph of JMMD, revealing why JMMD degrades the feature discrimination. This motivates us to propose a novel loss JMMD-HSIC by jointly considering JMMD and HSIC to promote discrimination of JMMD. Extensive experiments on several cross-domain datasets could demonstrate the validity of our revealed theoretical results and the effectiveness of our proposed JMMD-HSIC.

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature's label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to "drift" noisy samples back to label-consistent representations. During adaptation, we sample from each target feature's latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier's accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve.

Black-box Unsupervised Domain Adaptation (BUDA) aims to transfer source domain knowledge to an unlabeled target domain, without accessing the source data or trained source model. Recent diffusion models have significantly advanced the ability to generate images from texts. While they can produce realistic visuals across diverse prompts and demonstrate impressive compositional generalization, these diffusion-based domain adaptation methods focus solely on composition, overlooking their sensitivity to textual nuances. In this work, we propose a novel diffusion-based method, called Rectifying-reasoning Errors of Diffusion (RrED) for BUDA. RrED is a two-stage learning strategy under diffusion supervision to effectively enhance the target model via the decomposed text and visual encoders from the diffusion model. Specifically, RrED consists of two stages: DiffusionTarget model Rectification (DTR) and Self-rectifying Reasoning Model (SRM). In DTR, we decouple the image and text encoders within the diffusion model: the visual encoder integrates our proposed feature-sensitive module to generate inferentially-enhanced visuals, while the text encoder enables multi-modal joint fine-tuning.

Domain Adaptation of Black-box Predictors (DABP) transfers knowledge from a labeled source domain to an unlabeled target domain, without requiring access to either source data or source model. Common practices of DABP leverage reliable samples to suppress negative information about unreliable samples. However, there are still some problems: i) Excessive attention to reliable sample aggregation leads to premature overfitting; ii) Valuable information in unreliable samples is often overlooked. To address them, we propose a novel spatial learning approach, called Controlled Visual Hallucination via Thalamus-driven Decoupling Network (CVHTDN). Specifically, CVH-TDN is the first work that introduces the thalamus-driven decoupling network in the visual task, relying on its connection with hallucination to control the direction of sample generation in feature space. CVH-TDN is composed of Hallucination Generation (HG), Hallucination Alignment (HA), and Hallucination Calibration (HC), aiming to explore the spatial relationship information between samples and hallucinations. Extensive experiments confirm that CVH-TDN achieves SOTA performance on four standard benchmarks.

Unsupervised domain adaptive hashing has emerged as a promising approach for efficient and memory-friendly cross-domain retrieval. It leverages the model learned on labeled source domains to generate compact binary codes for unlabeled target domain samples, ensuring that semantically similar samples are mapped to nearby points in the Hamming space. Existing methods typically apply domain adaptation techniques to the feature space or the Hamming space, especially pseudo-labeling and feature alignment. However, the inherent noise of pseudolabels and the insufficient exploration of complementary knowledge across spaces hinder the ability of the adapted model. To address these challenges, we propose a Vision-language model assisted Pseudo-labeling and Dual Space adaptation (VPDS) method.

Large foundation models are typically trained on data from multiple domains, with the data mixture-the proportion of each domain used-playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach accurately predicts the loss of a model of size N trained with D tokens and a specific domain weight vector h.