# Provable Adaptation across Multiway Domains via Representation Learning

arXiv: https://arxiv.org/abs/2106.06657 · HTML: https://mlsanity.com/paper/2106.06657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 12 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (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)
- [Feature-Critic Networks for Heterogeneous Domain Generalization](https://mlsanity.com/paper/1901.11448/) (2019)
- [Learning to Compose Domain-Specific Transformations for Data Augmentation](https://mlsanity.com/paper/1709.01643/) (2017)
- [Deep Multi-task Representation Learning: A Tensor Factorisation Approach](https://mlsanity.com/paper/1605.06391/) (2016)
- [A Unified Perspective on Multi-Domain and Multi-Task Learning](https://mlsanity.com/paper/1412.7489/) (2014)
- [Tensor Completion Made Practical](https://mlsanity.com/paper/2006.03134/) (2020)
- [Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties](https://mlsanity.com/paper/1310.4977/) (2013)

## Built on by (most cited first, 3 of 3)

- [Linear Speedup in Personalized Collaborative Learning](https://mlsanity.com/paper/2111.05968/) (2021)
- [Text Descriptions are Compressive and Invariant Representations for Visual Learning](https://mlsanity.com/paper/2307.04317/) (2023)
- [Multi-dimensional domain generalization with low-rank structures](https://mlsanity.com/paper/2309.09555/) (2023)

## Abstract (arXiv)

This paper studies zero-shot domain adaptation where each domain is indexed on a multi-dimensional array, and we only have data from a small subset of domains. Our goal is to produce predictors that perform well on unseen domains. We propose a model which consists of a domain-invariant latent representation layer and a domain-specific linear prediction layer with a low-rank tensor structure. Theoretically, we present explicit sample complexity bounds to characterize the prediction error on unseen domains in terms of the number of domains with training data and the number of data per domain. To our knowledge, this is the first finite-sample guarantee for zero-shot domain adaptation. In addition, we provide experiments on two-way MNIST and four-way fiber sensing datasets to demonstrate the effectiveness of our proposed model.