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Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation
Chen-Yu Lee, Tanmay Batra, Mohammad Haris Baig, Daniel Ulbricht
TL;DR
Unsupervised domain adaptation must transfer knowledge from labeled source data to unlabeled target data despite domain shift and limitations in existing alignment methods. The paper combines task-specific decision-boundary alignment with Wasserstein distance through sliced Wasserstein discrepancy, enabling efficient end-to-end training. Across digit and sign recognition, image classification, semantic segmentation, and object detection, the method is reported to improve performance over competing approaches, including MCD.
Problem
Unsupervised domain adaptation seeks knowledge transfer from labeled source data to unlabeled target data, while existing classifier discrepancy can help only when output probability measures overlap.
Method
The method combines task-specific decision-boundary alignment with Wasserstein distance, using sliced Wasserstein discrepancy to measure classifier-output dissimilarity and train efficiently end to end.
Results
The method outperforms competing approaches across the reported tasks, including a 2.8% average absolute accuracy improvement over MCD across four digit and sign-recognition settings.
Takeaways & Limitations
Sliced Wasserstein discrepancy provides a geometrically meaningful discrepancy for aligning domains through task-specific decision boundaries across classification, segmentation, and detection tasks.
Takeaways & Limitations
Explicit optimal-transport approaches can restrict practical use when balanced source-target pairs are unavailable and are difficult to extend to structured outputs such as pixel-wise segmentation.
Abstract
from arXiv · showhide
In this work, we connect two distinct concepts for unsupervised domain adaptation: feature distribution alignment between domains by utilizing the task-specific decision boundary and the Wasserstein metric. Our proposed sliced Wasserstein discrepancy (SWD) is designed to capture the natural notion of dissimilarity between the outputs of task-specific classifiers. It provides a geometrically meaningful guidance to detect target samples that are far from the support of the source and enables efficient distribution alignment in an end-to-end trainable fashion. In the experiments, we validate the effectiveness and genericness of our method on digit and sign recognition, image classification, semantic segmentation, and object detection.
1. Introduction
The paper addresses unsupervised domain adaptation under covariate shift, where models trained on source data may perform poorly on target data. It replaces limited classifier-output discrepancy alignment with a Wasserstein-based approach that uses task-specific decision boundaries.
- Domain shift can involve covariate, prior-probability, or concept shifts, including changes between synthetic and real data.
- Unsupervised domain adaptation uses labeled source data and unlabeled target data, with much prior work directly aligning their feature distributions.
- Within-network adversarial alignment uses two task-specific classifiers and their decision boundary, but L1 discrepancy helps only when their output probability measures overlap.
- The proposed method aligns feature distributions through the task-specific decision boundary and Wasserstein distance, enabling efficient end-to-end training with sliced Wasserstein discrepancy.
2. Related Work
Prior domain-adaptation methods align distributions through statistical moments, adversarial learning, task-specific classifiers, or optimal transport. The paper combines task-specific decision-boundary alignment with Wasserstein distance to avoid restrictive sample mappings and support broader tasks.
- Moment-matching methods use MMD, CMD, or AdaBN to align hidden representations or normalization statistics across domains.
- Adversarial approaches train domain discriminators and feature generators to make feature distributions domain invariant, and later extend alignment to pixel-level methods.
- MCD uses task-specific classifiers to maximize target-output discrepancy outside source support, then minimize it to move target representations inside source support relative to the decision boundary.
- Wasserstein distance supplies a geometrically meaningful probability-distribution discrepancy and has been applied in retrieval, style transfer, image warping, and generative modeling.
- JDOT and DeepJDOT explicitly map source and target samples in label space, which can restrict use when balanced pairs are unavailable and leaves structured outputs difficult to extend.
- The proposed framework combines decision-boundary alignment with Wasserstein distance, directly measuring target support relative to source without explicit one-to-one label-space mappings.
3. Method
The method trains a feature generator and two classifiers in an adversarial three-step framework for unsupervised domain adaptation. Sliced Wasserstein discrepancy replaces inefficient direct Wasserstein optimization with an end-to-end trainable classifier-output discrepancy.
- The framework introduces the adaptation setting, reviews optimal transport, and details sliced Wasserstein discrepancy training.
- A feature generator G and classifiers C1 and C2 map source and target inputs to classifier logits p1(y|x) and p2(y|x).
- First, G, C1, and C2 are trained on labeled source data to classify or regress source samples correctly using an applicable source loss.
- SWD computes classifier-output dissimilarity through radial projections on uniform measures over the unit sphere, providing geometrically meaningful guidance for detecting target samples far from source support.
- Second, G is frozen while the classifiers maximize target-output discrepancy to identify samples outside the support of task-specific decision boundaries.
- Third, the classifiers are frozen while G minimizes target-output discrepancy, producing target representations nearer the source support with respect to the decision boundary.
G LDIS(Xt) (3)
The method replaces direct optimization of classifier-output Wasserstein distance with a sliced, variational discrepancy that is efficient and differentiable. It integrates this discrepancy into adversarial domain adaptation by maximizing it with classifiers and minimizing it with the feature generator on target data.
- Optimal Transport and Wasserstein Distance: The Wasserstein discrepancy measures classifier-output distributions while accounting for probability-space geometry, including when their supports do not overlap.The method uses the 1-Wasserstein distance as its discrepancy measure in the domain-adaptation framework.
- Learning with Sliced Wasserstein Discrepancy: Training alternates source supervision, classifier maximization of target SWD, and feature-generator minimization of the same target discrepancy.Algorithm 1 initializes a feature generator and two classifiers, then repeats these steps until convergence.
- Learning with Sliced Wasserstein Discrepancy: Directly computing W1 between classifier logits requires solving a linear-programming optimal-transport problem, which is inefficient for end-to-end training.The logits are the discrete classifier outputs p1(y|x) and p2(y|x).
- Learning with Sliced Wasserstein Discrepancy: SWD approximates W1 by projecting classifier outputs onto one-dimensional directions, where the resulting optimal-transport problems have closed-form solutions.For discrete measures, the one-dimensional matching is obtained by sorting projected samples.
- Learning with Sliced Wasserstein Discrepancy: The closed-form sliced formulation reduces computational cost and makes the discrepancy differentiable for optimizing the feature generator and classifiers.The implementation uses M randomly sampled projections and a quadratic loss for c unless otherwise mentioned.
4. Experiments
Experiments evaluate SWD across digit and sign recognition, image classification, semantic segmentation, and object detection, using standard benchmarks and protocols. Across these settings, SWD consistently improves over source-only and competing adaptation methods, including MCD.
- Experimental scope: SWD is evaluated across digit and sign recognition, image classification, semantic segmentation, and object detection tasks.The method is intended to apply broadly without similarity assumptions in input or output space.
- Experimental setup: Experiments use five standard digit and traffic-sign datasets, with task-specific architectures, Adam optimization, mini-batches of 128, and gradient reversal training.The datasets are SVHN, MNIST, USPS, SYNSIG, and GTSRB.
- Digit and sign recognition: 2.8% absolute accuracy improvement on average over MCD is reported across four digit and traffic-sign domain shifts.SWD outperforms competing approaches in all reported settings, and M = 128 works well across cases.
- Comparison with adaptation strategies: Task-specific discrepancy-aware methods lead the evaluated tasks, supporting decision-boundary-guided transfer over simple pixel-, feature-, or output-distribution matching.The comparison identifies MCD, DeepJDOT, and SWD as leading approaches for the addressed tasks.
- Training design: SWD is end-to-end trainable with one discrepancy loss, unlike DeepJDOT’s multi-stage training and iterative linear-programming procedure.The method avoids assuming that the true optimal transport coupling between every mini-batch sample pair converges in label space.
- Segmentation and detection: 25% relative mAP improvement over MCD is reported for object detection despite shifts in image realism, object scales, and relative object positions.For semantic segmentation, SWD improves over source-only models with both VGG-16 and ResNet-101 backbones and consistently outperforms other recent approaches; it also improves over competing methods under the larger Synthia-to-Cityscapes viewpoint shift.
5. Conclusion
The paper presents SWD as a generic unsupervised domain adaptation approach that aligns distributions through task-specific classifier outputs and reports superior results across four task families.
- SWD aligns source and target distributions by measuring sliced Wasserstein discrepancy between task-specific classifiers.
- The Wasserstein connection provides geometrically meaningful embeddings for efficient distribution alignment.
- The method is evaluated on digit and sign recognition, image classification, semantic segmentation, and object detection.
Supplementary Material
A toy inter twinning moons experiment examines decision boundaries under rotation and translation shifts. SWD adapts more successfully than source-only training and MCD across the evaluated target regions.
- Toy experiment: The toy experiment uses source upper and lower moons labeled 0 and 1, with target samples shifted by rotation and translation.Figure 4 compares the resulting decision boundaries after convergence.
- Decision-boundary comparison: The source-only model classifies source samples perfectly but fails to generalize to target samples in regions 1 and 2.Its decision boundary fits the source distribution without adequately handling the target shifts.
- Decision-boundary comparison: MCD adapts its decision boundary correctly in region 1 but not in region 2.The method therefore handles the shifted target samples unevenly across regions.
- Decision-boundary comparison: SWD adapts nicely to the target samples and draws a correct decision boundary in all regions.This is the strongest outcome among the three decision-boundary comparisons in the toy example.