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Reusing the Task-specific Classifier as a Discriminator: Discriminator-free Adversarial Domain Adaptation

Lin Chen, Huaian Chen, Zhixiang Wei, Xin Jin, Xiao Tan, Yi Jin, Enhong Chen

arXiv:2204.03838v1cs.CV

TL;DR

Existing adversarial UDA methods often add discriminators but do not effectively use predicted discriminative information. This paper reuses the task-specific classifier with NWD in DALN, achieving competitive performance across datasets and enabling NWD-based improvements for existing methods.

  • Problem

    Existing adversarial UDA methods typically add a discriminator but may fail to leverage predicted discriminative information effectively.

  • Method

    DALN reuses the task-specific classifier as an implicit discriminator and couples it with NWD to jointly perform domain alignment and category distinguishment.

  • Results

    DALN outperforms existing state-of-the-art methods across varied datasets, while NWD improves existing UDA methods as a plug-and-play regularizer.

  • Takeaways & Limitations

    NWD provides a generic regularizer that can make existing UDA methods more competitive without requiring an additional discriminator.

  • Takeaways & Limitations

    The theoretical guarantee assumes an ideal classifier satisfying the K-Lipschitz constraint and a sufficiently small ideal joint-hypothesis risk.

Abstract

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Adversarial learning has achieved remarkable performances for unsupervised domain adaptation (UDA). Existing adversarial UDA methods typically adopt an additional discriminator to play the min-max game with a feature extractor. However, most of these methods failed to effectively leverage the predicted discriminative information, and thus cause mode collapse for generator. In this work, we address this problem from a different perspective and design a simple yet effective adversarial paradigm in the form of a discriminator-free adversarial learning network (DALN), wherein the category classifier is reused as a discriminator, which achieves explicit domain alignment and category distinguishment through a unified objective, enabling the DALN to leverage the predicted discriminative information for sufficient feature alignment. Basically, we introduce a Nuclear-norm Wasserstein discrepancy (NWD) that has definite guidance meaning for performing discrimination. Such NWD can be coupled with the classifier to serve as a discriminator satisfying the K-Lipschitz constraint without the requirements of additional weight clipping or gradient penalty strategy. Without bells and whistles, DALN compares favorably against the existing state-of-the-art (SOTA) methods on a variety of public datasets. Moreover, as a plug-and-play technique, NWD can be directly used as a generic regularizer to benefit existing UDA algorithms. Code is available at https://github.com/xiaoachen98/DALN.

1. Introduction

UDA addresses performance decline caused by domain shifts by transferring knowledge from labeled source domains to unlabeled target domains. DALN reuses the task-specific classifier as an implicit discriminator, while NWD unifies domain alignment with category distinguishment and supports competitive performance.

  • UDA transfers knowledge from a labeled source domain to an unlabeled target domain under domain shift.
  • Existing adversarial UDA methods commonly use additional classifiers or discriminators, but ambiguous predictions can hinder adaptation optimization.
  • DALN reuses the original task-specific classifier as an implicit discriminator for unified domain alignment and category distinguishment.
  • NWD combines Nuclear norm and 1-Wasserstein distance to encourage prediction determinacy and diversity while providing guidance for discrimination.
  • DALN requires no additional domain discriminator, and NWD can also serve as a plug-and-play regularizer for existing UDA methods.
  • The method reports competitive performance across public datasets, including 80.6% average accuracy on a synthetic-to-real setting.

2. Related Works

Prior UDA work mainly uses moment matching or adversarial learning, with adversarial methods relying on extra discriminators or classifier pairs. DALN instead couples the original task-specific classifier with NWD to construct an implicit discriminator without clipping or gradient penalties.

  • UDA methods are broadly categorized into moment matching and adversarial learning approaches.
  • Additional-discriminator methods distinguish source and target features to reduce domain discrepancy through adversarial learning.
  • Bi-classifier methods use the disparity between two task-specific classifiers as an implicit discriminator, but their approaches include classifier-disagreement measures such as L1 distance or sliced Wasserstein discrepancy.
  • DALN reuses the original task-specific classifier and couples it with NWD to implicitly construct a discriminator or critic.
  • The implicit discriminator satisfies the K-Lipschitz constraint without additional weight clipping or gradient penalty strategies.

3. Method

The method reuses the task-specific classifier as a discriminator and introduces NWD to align domains while preserving category structure. DALN combines these components with supervised source classification and provides a theoretical target-risk bound.

  • Classifier reuse: DALN reuses the original task-specific classifier as a discriminator, avoiding an explicit domain discriminator while enabling adversarial UDA.The classifier is coupled with a discrepancy to perform domain alignment and category distinguishment through one objective.
  • Classifier reuse: Self-correlation matrices use diagonal terms for intra-class correlation and off-diagonal terms for inter-class correlation or confusion.Source predictions tend toward larger intra-class and smaller inter-class correlation, whereas target predictions show the opposite pattern under source-only training.
  • Classifier reuse: The correlation discrepancy is represented by Ia − Ie = 2∥Z∥F − b, yielding a classifier-based critic with high source and low target scores.Here Z is the classifier prediction matrix, and Ia + Ie = b.
  • Nuclear-norm Wasserstein discrepancy: NWD replaces the Frobenius norm with the nuclear norm, encouraging prediction diversity while retaining a Wasserstein-based domain discrepancy.The resulting critic is D = ∥C∥∗ and jointly supports category-level distinguishment and feature-level alignment.
  • Nuclear-norm Wasserstein discrepancy: The implicit discriminator satisfies the K-Lipschitz constraint, so training requires neither additional weight clipping nor gradient penalties.The empirical NWD is estimated by maximizing the domain critic loss, and a gradient reversal layer supports single-backpropagation training.
  • Optimization and guarantee: DALN optimizes supervised source classification together with the NWD objective, while theory bounds target risk using source risk and the introduced NWD.The balance parameter λ combines Lcls and Lnwd, and the paper states that proofs and empirical target-risk details are provided in supplementary materials.

4. Experiments

The experiments evaluate DALN and NWD across several UDA benchmarks, showing strong classification performance and improved feature discriminability and prediction behavior.

  • Experimental setup: DALN and NWD are evaluated on Office-Home, Office-31, ImageCLEF, and VisDA-2017, alongside comparisons with SOTA methods and existing UDA regularizers.The study also tests NWD with DANN, CDAN, MDD, and MCC.
  • Comparison results: 80.6% average accuracy is achieved by DALN on VisDA-2017 despite the synthetic-to-real domain shift.Combining NWD with DANN, CDAN, MDD, and MCC improves their performances by 22.6%, 7.5%, 5.2%, and 4.9%, respectively.
  • Comparison results: On Office-Home, DALN improves over existing SOTA methods by 2.9% on A→R and 2.2% on C→R, while NWD raises DANN’s average accuracy by 7.9%.NWD combined with MCC reaches 72.6%, a 3.2% improvement.
  • Comparison results: On Office-31, DALN attains SOTA performance on five adaptation subtasks and improves average accuracy over WDGRL by 11.8%.Using NWD as a regularizer improves typical methods by at least 0.6%, while DANN’s average accuracy increases by 4.9%.
  • Insight analysis: Confusion matrices show that DALN produces larger main-diagonal values, while adding NWD to DANN and MDD considerably decreases off-diagonal elements.These patterns indicate fewer category confusions in the evaluated target-domain task.
  • Insight analysis: The analyses examine determinacy, diversity, and t-SNE feature distributions to compare prediction certainty, category coverage, and learned feature structure.The t-SNE visualizations distinguish source and target features using blue and red points.

5. Conclusions

The paper concludes that reusing the task-specific classifier as a discriminator, together with NWD, yields a discriminator-free adversarial UDA model with transferable and discriminative representations.

  • Contributions: DALN reuses the task-specific classifier as a discriminator and uses NWD to provide definite guidance for adversarial UDA.The resulting model targets transferable representations while promoting prediction determinacy and diversity.
  • Contributions: NWD functions as a plug-and-play regularizer for existing UDA methods and helps them achieve more competitive performance.The conclusion reports effectiveness across experiments on a variety of datasets.

Supplementary Material

The supplementary material develops the Lipschitz analysis underlying the implicitly constructed discriminator and the theoretical treatment of NWD.

  • K-Lipschitz constraint: The supplementary material proves that the implicitly constructed discriminator D = ∥C∥* satisfies the K-Lipschitz constraint.The classifier is analyzed as a fully connected layer followed by softmax.
  • K-Lipschitz constraint: For the fully connected layer Lc(f) = Wf + b, the Lipschitz constant is bounded by the Frobenius norm ∥W∥F.The layer maps input features to outputs, with W as the weight matrix and b as the bias vector.
  • K-Lipschitz constraint: The spectral norm ∥W∥2 is identified as the Lipschitz constant of the linear layer, while the Frobenius norm aggregates its singular values.The supplementary derivation relates σmax to the spectral norm and σi to the singular values used in the Frobenius norm.
  • Definitions: A K-Lipschitz function is defined through a constant K that bounds changes between distinct inputs in the relevant metric spaces.The supplementary material states this definition for mappings between compact subsets of Euclidean spaces.
  • K-Lipschitz constraint: The softmax mapping is shown to satisfy a 1-Lipschitz constraint.The proof bounds entries of the softmax Jacobian using prediction probabilities in the range from 0 to 1.

B. Generalization Bound

The analysis establishes that target risk is bounded by NWD between source and target feature distributions, with empirical NWD measures converging to their expected counterparts under stated assumptions.

  • Discrepancy control: The NWD term is obtained by bounding the classifier-related discrepancy with 2KW1(νs, νt).This connects the discrepancy between source and target classification errors to Wasserstein distance in representation space.
  • Risk bound: Theorem 2 bounds expected target risk using source error, the NWD between source and target features, and the ideal joint-hypothesis risk.The bound is derived for classifiers satisfying the K-Lipschitz constraint.
  • Risk bound: The expected target risk is therefore controlled by expected NWD measures on the source and target domain distributions.
  • Empirical convergence: Under T1(η*) assumptions, empirical NWD measures converge to expected measures for independently sampled source and target features.The convergence result applies when sample sizes satisfy the theorem’s stated lower-bound condition.
  • Empirical convergence: The finite-sample theorem gives a high-probability statement uniformly over classifiers under the assumptions of the preceding lemmas.It uses source and target sample sizes Ns and Nt and probability at least 1 − δ.

C. Implementation details

DALN is implemented with standard pretrained ResNet feature extractors, a task-dependent fully connected classifier, a gradient reversal layer, and SGD optimization.

  • Platform: The implementation uses PyTorch on a Tesla-V100 32 GB GPU.
  • Architecture: ResNet50 or ResNet101 pretrained on ImageNet serves as the feature extractor, with a bottleneck replacing the final fully connected layer.
  • Architecture: The classifier is a task-dependent fully connected layer, and the gradient reversal layer follows the existing setting.
  • Optimization: Training uses the SGD optimizer.

D. Detailed results on VisDA-2017

On VisDA-2017, DALN achieves an average accuracy of 80.6% and outperforms existing SOTA methods, while NWD substantially improves several established UDA algorithms.

  • Overall performance: 80.6% average accuracy is achieved by DALN on VisDA-2017, outperforming existing SOTA methods.
  • NWD integration: 22.6%, 7.5%, 5.2%, and 4.9% are the reported improvements from adding NWD to DANN, CDAN, MDD, and MCC, respectively.
  • Category behavior: The reported gains are especially evident for bus, car, person, and truck categories.The passage attributes these improvements to distinguishing confusing pairs such as bus versus car and train versus truck.

E. Extra experiments on DomainNet

On DomainNet, a complex benchmark with 0.6 million images, 345 categories, and 6 subdomains, DALN outperforms previous SOTA methods in average accuracy across 30 sub-experiments.

  • Dataset: DomainNet contains 0.6 million images, 345 categories, and 6 subdomains.
  • Experimental setup: The experiment comprises 30 sub-experiments with a batch size of 64.
  • Results: DALN outperforms previous SOTA methods in average accuracy on DomainNet.The passage presents this result as evidence of DALN’s performance on complex datasets.

F. Insight Analysis

The insight analyses examine DALN’s decision boundaries, feature transferability, prediction correlations, convergence, and parameter sensitivity. Across these analyses, DALN handles target-domain imbalance, learns transferable representations, and converges rapidly under suitable parameter ranges.

  • Toy examples: DALN classifies both source and target samples effectively on balanced toy data and achieves better classification performance than MDD.DANN misclassifies some upper-moon samples, whereas MDD and DALN classify both domains successfully.
  • Toy examples: Under target-domain class imbalance, DALN learns a favorable decision boundary while DANN and MDD misclassify samples from both moons.
  • Transferability: DALN achieves the lowest proxy A-distance on Office-31 task A→W, while adding NWD to DANN or MDD considerably decreases their proxy A-distances.Smaller proxy A-distance denotes better transferability.
  • Prediction correlations: DALN concentrates target self-correlation values on the main diagonal, increasing intra-class correlation and decreasing inter-class correlation.
  • Convergence: DALN converges rapidly with competitive accuracy, and minimizing NWD also decreases maximum mean discrepancy on Office-31 tasks A→W and W→A.

G. Limitations

The method has two reported training limitations: computing the Nuclear norm through SVD takes time, and performance peaks early before slowly declining.

  • SVD-based Nuclear-norm computation adds training time, and performance peaks early before slowly declining.
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