Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for a new target task, especially when the sample size m of the training data for the latter is low. In this work, we rigorously analyze the potential benefit of transfer learning in terms of sample efficiency. Specifically, taking an optimal transport viewpoint of transfer learning, we find that when the data dimension d is higher than 3, the sample complexity for transfer learning is O(m−(α+1)/d), with α indicating the smoothness of the data distribution, as opposed to the O(m−p/d) sample complexity for direct learning with p indicating the smoothness of the optimal target model. Our finding theoretically supports a better sample efficiency for transfer learning, when the target task is optimizing over a family of not-so-smooth models (i.e., highly complex networks with the possible use of non-smooth activation functions). Using image classification as an example, we numerically demonstrate the sample efficiency for transfer learning, that is, in the data hungry regime, the model performance can be significantly improved by transfer learning.
Transfer learning involves taking information and insight from one problem domain and applying it to a new problem domain. Although widely used in practice, theory for transfer learning remains less well-developed. To address this, we prove several novel results related to transfer learning, showing the need to carefully select which sets of information to transfer and the need for dependence between transferred information and target problems. Furthermore, we prove how the degree of probabilistic change in an algorithm using transfer learning places an upper bound on the amount of improvement possible. These results build on the algorithmic search framework for machine learning, allowing the results to apply to a wide range of learning problems using transfer.
Transfer learning is particularly useful in settings with limited training data, and within image classification it is common to transfer learn upon massive datasets like ImageNet , CIFAR-100, or COCO . Qualitatively, it seems a transfer learning dataset should have both more classes and more examples per class than the fine tuning dataset; however, a quantitative method to choose the best transfer learning dataset does not currently exist. In this paper, we design TLDChoiceNet, a model to choose the best transfer learning dataset given a fine tuning dataset by predicting the test-set accuracy after fine-tuning. A simple version 1 achieves 0.154 MSE on the test dataset, while a version 2 leveraging an ImageNet pre-trained ResNet50 v2 embedding with per-class information attains a 5X lower MSE of 0.031. We further design two metrics that enable an unsupervised method of choosing an optimal transfer learning dataset: distribution distance (DD), which linearly regresses against fine-tune accuracy with an R2 of 0.89, and average class correlation (ACC), which improves the R2 to 0.97. Our results underscore that a dataset's low-level statistics can explain the transfer learning effect, and that using a pre-trained ImageNet can embed different classes further apart in latent feature space.
Multi-task learning is effective for related applications, but its performance can deteriorate when the target sample size is small. Transfer learning can borrow strength from related studies; yet, many existing methods rely on restrictive bounded-difference assumptions between the source and target models. We propose SMART, a spectral transfer method for multi-task linear regression that instead assumes spectral similarity: the target left and right singular subspaces lie within the corresponding source subspaces and are sparsely aligned with the source singular bases. Such an assumption is natural when studies share latent structures and enables transfer beyond the bounded-difference settings. SMART estimates the target coefficient matrix through structured regularization that incorporates spectral information from a source study. Importantly, it requires only a fitted source model rather than the raw source data, making it useful when data sharing is limited. Although the optimization problem is nonconvex, we develop a practical ADMM-based algorithm. We establish general, non-asymptotic error bounds and a minimax lower bound in the noiseless-source regime. Under additional regularity conditions, these results yield near-minimax Frobenius error rates up to logarithmic factors. Simulations confirm improved estimation accuracy and robustness to negative transfer, and analysis of multi-modal single-cell data demonstrates better predictive performance. The Python implementation of SMART, along with the code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/smart.