# Transfer Learning in Nonparametric Regression with Deep ReLU Networks

arXiv: https://arxiv.org/abs/2608.20255 · HTML: https://mlsanity.com/paper/2608.20255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 71 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Covid-19: Automatic detection from X-Ray images utilizing Transfer Learning with Convolutional Neural Networks](https://mlsanity.com/paper/2003.11617/) (2020)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery](https://mlsanity.com/paper/1908.01842/) (2019)
- [How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model](https://mlsanity.com/paper/2307.02129/) (2023)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [Adaptive and Robust Multi-Task Learning](https://mlsanity.com/paper/2202.05250/) (2022)
- [Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness](https://mlsanity.com/paper/2303.17765/) (2023)
- [A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization](https://mlsanity.com/paper/2102.07148/) (2021)
- [Hypothesis Transfer Learning via Transformation Functions](https://mlsanity.com/paper/1612.01020/) (2016)
- [Quantile regression with deep ReLU Networks: Estimators and minimax rates](https://mlsanity.com/paper/2010.08236/) (2020)
- [Deep Conditional Transformation Models](https://mlsanity.com/paper/2010.07860/) (2020)
- [Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure](https://mlsanity.com/paper/2401.12272/) (2024)
- [Representation Learning Beyond Linear Prediction Functions](https://mlsanity.com/paper/2105.14989/) (2021)
- [Position: A Theory of Deep Learning Must Include Compositional Sparsity](https://mlsanity.com/paper/2507.02550/) (2025)

## Abstract (arXiv)

This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the mathcal L2 error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.