# TILT: Target-induced loss tilting under covariate shift

arXiv: https://arxiv.org/abs/2605.14280 · HTML: https://mlsanity.com/paper/2605.14280/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 15 of 15)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Unsupervised Domain Adaptation with Residual Transfer Networks](https://mlsanity.com/paper/1602.04433/) (2016)
- [Domain Separation Networks](https://mlsanity.com/paper/1608.06019/) (2016)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [A new similarity measure for covariate shift with applications to nonparametric regression](https://mlsanity.com/paper/2202.02837/) (2022)
- [A One-step Approach to Covariate Shift Adaptation](https://mlsanity.com/paper/2007.04043/) (2020)
- [Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation](https://mlsanity.com/paper/2603.25466/) (2026)

## Built on by (most cited first, 1 of 1)

- [Domain Adaptation with Target Information via Doubly-Anchored Distributionally Robust Optimization](https://mlsanity.com/paper/2609.32730/) (2026)

## Abstract (arXiv)

We introduce and analyze Target-Induced Loss Tilting (TILT) for unsupervised domain adaptation under covariate shift. It is based on a novel objective function that decomposes the source predictor as f+b, fits f+b on labeled source data while simultaneously penalizing the auxiliary component b on unlabeled target inputs. The resulting fit f is deployed as the final target predictor. At the population level, we show that this target-side penalty implicitly induces relative importance weighting at the population level, but in terms of an estimand b^*f that is self-localized to the current error, and remains uniformly bounded for any source-target pair (even those with disjoint supports). We prove a general finite-sample oracle inequality on the excess risk, and use it to give an end-to-end guarantee for training with sparse ReLU networks. Experiments on controlled regression problems and shifted CIFAR-100 distillation show that TILT improves target-domain performance over source-only training, exact importance weighting, and relative density-ratio baselines, with a stable dependence on the regularization parameter.