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Concept-Based Unsupervised Domain Adaptation

Xinyue Xu, Yueying Hu, Hui Tang, Yi Qin, Lu Mi, Hao Wang, Xiaomeng Li

TL;DR

CUDA tackles domain shift in Concept Bottleneck Models by learning domain-invariant concept embeddings through adversarial training with a relaxed uniform alignment, allowing concept distributions to differ across domains up to a threshold $\tau$. It provides a theoretical target-domain error bound that decomposes risk into a ground-truth-concept source error, a domain-discrepancy term $d_{\mathcal{H}\Delta\mathcal{H}}$, and a concept-prediction error term, plus $R \cdot \mathbb{E}_S[\|\widehat{\boldsymbol{c}} - \boldsymbol{c}\|_2]$; with $\tau = \log 2$ this yields uniform alignment. The method achieves significant improvements over state-of-the-art CBM and DA baselines on eight real-world datasets, while maintaining interpretability through explicit concept predictions. It thus establishes new benchmarks for concept-based domain adaptation and opens avenues for robust, interpretable deployment in real-world shifts.

Abstract

Concept Bottleneck Models (CBMs) enhance interpretability by explaining predictions through human-understandable concepts but typically assume that training and test data share the same distribution. This assumption often fails under domain shifts, leading to degraded performance and poor generalization. To address these limitations and improve the robustness of CBMs, we propose the Concept-based Unsupervised Domain Adaptation (CUDA) framework. CUDA is designed to: (1) align concept representations across domains using adversarial training, (2) introduce a relaxation threshold to allow minor domain-specific differences in concept distributions, thereby preventing performance drop due to over-constraints of these distributions, (3) infer concepts directly in the target domain without requiring labeled concept data, enabling CBMs to adapt to diverse domains, and (4) integrate concept learning into conventional domain adaptation (DA) with theoretical guarantees, improving interpretability and establishing new benchmarks for DA. Experiments demonstrate that our approach significantly outperforms the state-of-the-art CBM and DA methods on real-world datasets.

Concept-Based Unsupervised Domain Adaptation

TL;DR

CUDA tackles domain shift in Concept Bottleneck Models by learning domain-invariant concept embeddings through adversarial training with a relaxed uniform alignment, allowing concept distributions to differ across domains up to a threshold . It provides a theoretical target-domain error bound that decomposes risk into a ground-truth-concept source error, a domain-discrepancy term , and a concept-prediction error term, plus ; with this yields uniform alignment. The method achieves significant improvements over state-of-the-art CBM and DA baselines on eight real-world datasets, while maintaining interpretability through explicit concept predictions. It thus establishes new benchmarks for concept-based domain adaptation and opens avenues for robust, interpretable deployment in real-world shifts.

Abstract

Concept Bottleneck Models (CBMs) enhance interpretability by explaining predictions through human-understandable concepts but typically assume that training and test data share the same distribution. This assumption often fails under domain shifts, leading to degraded performance and poor generalization. To address these limitations and improve the robustness of CBMs, we propose the Concept-based Unsupervised Domain Adaptation (CUDA) framework. CUDA is designed to: (1) align concept representations across domains using adversarial training, (2) introduce a relaxation threshold to allow minor domain-specific differences in concept distributions, thereby preventing performance drop due to over-constraints of these distributions, (3) infer concepts directly in the target domain without requiring labeled concept data, enabling CBMs to adapt to diverse domains, and (4) integrate concept learning into conventional domain adaptation (DA) with theoretical guarantees, improving interpretability and establishing new benchmarks for DA. Experiments demonstrate that our approach significantly outperforms the state-of-the-art CBM and DA methods on real-world datasets.
Paper Structure (19 sections, 12 theorems, 71 equations, 5 figures, 6 tables, 1 algorithm)

This paper contains 19 sections, 12 theorems, 71 equations, 5 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Generalization Error Bound for CBMs
  5. Concept-Based Unsupervised Domain Adaptation
  6. Theoretical Analysis for CUDA
  7. Experiments
  8. Evaluation Setup
  9. Results
  10. Conclusion
  11. Notation Table
  12. Proof
  13. Proof of Generalization Error Bound for CBMs
  14. Proof of Theoretical Analysis for CUDA
  15. Experiments
  16. ...and 4 more sections

Key Result

Lemma 3.1

Let $\mathcal{H}$ be a hypothesis space where all hypotheses $h \in \mathcal{H}$ are $L$-Lipschitz continuous under the Euclidean norm $\| \cdot \|_2$ for some constant $L > 0$. Assume that for all $\boldsymbol{v} \in \mathcal{V}$, $\| \boldsymbol{v} \|_2$ is bounded. Then, for any $h_1, h_2 \in \ma where $\epsilon_S(h_1, h_2) = \mathbb{E}_{\boldsymbol{v} \sim \widetilde{\mathcal{D}}_S} \left[\lef

Figures (5)

  • Figure 1: Illustration of our key idea. Left: Ground-truth (GT) concept distributions (for each concept) (top) and data distributions (bottom). Right: Uniform alignment (top) and relaxed alignment (bottom) after adaptation. Our relaxed alignment allows for greater differences between source and target concept distributions; such flexibility leads to predicted concept distributions closer to the ground truth and therefore higher final classification accuracy.
  • Figure 2: Overview of our CUDA framework. The framework takes source and target domain images as inputs to first learn feature embeddings. Positive embeddings $\boldsymbol{v}_i^{(+)}$ and negative embeddings $\boldsymbol{v}_i^{(-)}$ are then derived from these feature embeddings. These are passed through the neural network $G_{concept}$ to obtain concept predictions $\widehat{\boldsymbol{c}}$, which are subsequently combined to construct the final concept embeddings $\boldsymbol{v}$. During training, adversarial training is employed: the domain classifier (discriminator) is trained first, followed by the concept embedding encoder and label predictor. These two steps are alternated throughout the training process.
  • Figure 3: Concept intervention performance with different ratios of intervened concepts on Watebirds datasets. The intervention ratio denotes the proportion of provided correct concepts.
  • Figure 4: The kernel density estimation (KDE) plots compare the distributions of two selected concept indices under three different scenarios: Ground-truth (GT), without relaxation (w/o Relax), and with relaxation (w/ Relax).
  • Figure 5: The full CUDA framework. It processes source and target domain images to learn feature embeddings, from which positive $\boldsymbol{v}_i^{(+)}$ and negative $\boldsymbol{v}_i^{(-)}$ embeddings are derived. These embeddings are passed through $G_{\text{concept}}$ to compute concept predictions $\widehat{\boldsymbol{c}}$ and construct final concept embeddings $\boldsymbol{v}$. Adversarial training alternates between optimizing the domain classifier (discriminator) with Eqn. \ref{['eq:min_D']} and optimizing the concept embedding encoder and label predictor with Eqn. \ref{['eq:min_EF']}, guided by adversarial training using Eqn. \ref{['eq:prediction_loss']}$\sim$\ref{['eq:relaxed_discriminator_loss']}.

Theorems & Definitions (19)

  • Lemma 3.1: Source Error with Predicted Concept Embeddings
  • Theorem 3.1: Target-Domain Error Bound for Concept-Based Models
  • Lemma 4.1: Optimal Discriminator
  • Theorem 4.1: Relaxed Alignment
  • Definition 4.1: Uniform Alignment
  • Lemma 4.2: Optimal Predictor
  • Theorem 4.2: Optimal Concept Embedding Encoder
  • Lemma 2.1: Source Error with Predicted Concept Embeddings
  • proof
  • Theorem 2.1: Target-Domain Error Bound for Concept-Based Models
  • ...and 9 more