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Controllable Invariance through Adversarial Feature Learning
Qizhe Xie, Zihang Dai, Yulun Du, Eduard Hovy, Graham Neubig
TL;DR
The paper asks how to preserve task-relevant content while removing information about a specified detrimental attribute. It formulates representation learning as an adversarial minimax game and reports invariant representations with improved performance across three benchmark tasks.
Problem
Controllably learning representations that preserve meaningful task information while eliminating noisy or detrimental variation remains an open problem.
Method
An encoder, discriminator, and predictor jointly learn an invariant representation through an adversarial minimax game.
Results
The framework induces invariant representations and improves performance across fair classification, language-independent generation, and lighting-independent image classification.
Takeaways & Limitations
The approach provides a generic framework for learning representations invariant to a specified factor or trait across tasks from different domains.
Takeaways & Limitations
Although the framework theoretically allows continuous and structured attributes, the paper focuses mainly on discrete labels with multiple choices.
Abstract
from arXiv · showhide
Learning meaningful representations that maintain the content necessary for a particular task while filtering away detrimental variations is a problem of great interest in machine learning. In this paper, we tackle the problem of learning representations invariant to a specific factor or trait of data. The representation learning process is formulated as an adversarial minimax game. We analyze the optimal equilibrium of such a game and find that it amounts to maximizing the uncertainty of inferring the detrimental factor given the representation while maximizing the certainty of making task-specific predictions. On three benchmark tasks, namely fair and bias-free classification, language-independent generation, and lighting-independent image classification, we show that the proposed framework induces an invariant representation, and leads to better generalization evidenced by the improved performance.
1 Introduction
The paper frames controllable invariance as an open representation-learning problem and proposes a generic adversarial framework to remove attribute-specific variation. It addresses limitations of pairwise distribution-based criteria while targeting improved generalization across diverse tasks.
- Controllably preserving meaningful variation while eliminating noisy signals remains an open representation-learning problem.
- Dedicated architectures can induce invariance, but changing invariance requirements may require designing a new architecture for each task.
- Probabilistic and discrepancy-based methods explicitly target nuisance or domain variation, including through MMD, adversarial costs, and CMD.
- Pairwise distribution divergences express invariance only between attribute-value pairs, requiring O(n2) pairs for multinomial attributes.
- The proposed framework uses an encoder, discriminator, and predictor in a minimax game, with theoretical equilibrium analysis and evaluation on three benchmark tasks.
2 Adversarial Invariant Feature Learning
The framework encodes observations and attributes into representations that retain information useful for predicting targets while concealing undesired attributes. Its minimax objective balances attribute uncertainty against task-prediction certainty, with scope extending theoretically beyond the paper’s discrete-label focus.
- The task predicts target y from observation x while seeking predictions invariant to an intrinsic attribute s.
- The paper distinguishes settings where s and y are marginally independent from biased settings where a latent variable links them.
- The encoder produces h = E(x, s), intended to preserve variations needed for y while removing information about s.
- The discriminator predicts s from h while the encoder conceals s, creating an adversarial game over the representation.
- In theory, s may be continuous or structured, but the paper focuses mainly on discrete labels with multiple choices.
- The objective weights attribute-prediction likelihood by γ while minimizing the negative target-prediction likelihood.
3 Theoretical Analysis
The analysis reduces the adversarial game to an encoder objective that filters information about s while preserving predictability of y. Its equilibrium depends on whether s and y are independent: the objectives can align or compete.
- For a fixed encoder, the optimal discriminator and predictor recover the conditional distributions ˜p(s | h) and ˜p(y | h).
- The encoder-only objective combines γ log ˜q(s | h) with −log ˜q(y | h), equivalently weighting conditional uncertainty about s against prediction of y.The objective follows after substituting the optimal discriminator and predictor into the minimax formulation.
- Maximizing uncertainty about s given h filters s-information, while the opposing entropy term increases certainty in predicting y from h.
- Win-win equilibrium: When s is irrelevant to prediction, both objectives can be optimized simultaneously, yielding a win-win equilibrium independent of γ with sufficient model capacity.Lighting-invariant image classification is given as an example.
- Competing equilibrium: When s and y are dependent, invariance and prediction compete; γ controls their relative strengths in the final equilibrium.The paper cites sensitive factors such as gender and age in fair classification as an example.
4 Parametric Instantiation of the Proposed Framework
The framework is instantiated for multilingual sentence generation and classification using task-specific neural encoders, predictors, and discriminators. Training can alternate adversarial components or jointly use gradient reversal.
- Sentence Generation: Multilingual machine translation tests sentence generation, with source language s, source sentence x, and target-language translation y.
- Sentence Generation: Separate language-specific LSTM encoders produce hidden-state representations, while one LSTM predictor serves all languages.
- Sentence Generation: The sentence predictor uses an attention-based autoregressive LSTM, and the discriminator uses an LSTM with a softmax language classifier.
- Classification: Classification experiments use feedforward neural networks for all three players, with s provided to the encoder as an embedding vector.
- Training alternates adversarial components or jointly trains all three with a gradient reversal layer; alternating updates provide more control over encoder–discriminator balance.
5 Experiments
Experiments evaluate invariant representations across fair classification, multilingual translation, and lighting-independent image classification. The framework removes nuisance information while preserving task performance and improves several benchmark results.
- Experimental Tasks: Experiments cover fair classification, language-independent generation through multilingual translation, and lighting-independent image classification.The tasks span fairness, language, and vision settings.
- Fair Classification: On German, the model reaches 0.744 accuracy versus 0.727 for VFAE and 0.723 for LFR; on Adult, it reaches 0.844 versus 0.813 and 0.823.Health performance remains barely above the majority baseline for all models because 85% of the data shares one label.
- Fair Classification: On Adult, biased-category accuracy is 0.788 versus 0.748 for the unconstrained baseline; on German, it is 0.676 versus 0.648.These results support learning a more unbiased representation despite similar or lower overall accuracy.
- Multilingual Translation: The model outperforms the baseline multilingual system on both languages, with a 0.6 BLEU score improvement for French-to-English.Removing the discriminator worsens performance, while separate encoders make cross-lingual representation learning easier.
- Image Classification: Identity-classification accuracy reaches 89% versus 85% for the best MMD baseline on Extended Yale B.The dataset contains 38 identities under five lighting conditions, with lighting treated as the factor to remove.
- Image Classification: Lighting-prediction accuracy falls from 0.96 to 0.57, while t-SNE clusters shift from lighting conditions toward individual identities.Both measurements indicate that the learned representation filters lighting information.
6 Related Work
Related work includes domain adaptation, fair representation learning, disentangled representations, and adversarial independence learning. These approaches motivate invariant representations but often rely on pairwise distribution matching or restrictive assumptions.
- Invariant Representations: Domain adaptation and fair classification learn representations invariant to domains or nuisance variables using adversarial costs, discrepancy measures, or distribution regularization.Examples include standard binary adversarial cost, CMD, LFR, and VFAE.
- Disentangled Representations: Disentangled representation learning separates different influencing factors of the input into distinct representation components.The related objective is to make each component marginally independent of the others.
- Limitations of Prior Work: Pairwise regularization scales poorly for attributes with many values because expressing invariance requires a combinatorial number of distribution pairs.An adversarial framework for categorical or continuous variables also assumes the attribute is irrelevant to prediction, limiting applicability.
7 Conclusion
The paper proposes a generic adversarial framework for representations invariant to specified factors or traits. Theory and experiments across three domains show invariant representations, better generalization, and improved task performance.
- Conclusion: The framework casts representation learning as an adversarial game among an encoder, discriminator, and predictor.It is intended to learn invariance to a specified factor or trait across different settings.
- Conclusion: Theoretical analysis characterizes the optimal equilibrium of the minimax game, while experiments evaluate the framework on three tasks from different domains.The reported outcome is an invariant representation with better generalization and improvements on all three tasks.
A Supplementary Material: Proofs
The proofs derive optimal discriminator and predictor distributions for a fixed encoder by solving their respective optimization problems. The optimal discriminator and predictor match the corresponding conditional distributions.
- Optimal discriminator: The optimal discriminator outputs q∗D(s | h) = ˜p(s | h).
- Optimal discriminator: For a fixed encoder, the discriminator optimization is solved using a Lagrangian dual formulation with equality constraints.The dual variables λ(h) are introduced for the constraints enforcing valid conditional distributions.
- Optimal discriminator: The proof obtains the discriminator solution by differentiating the constrained objective, summing over s, and substituting the resulting dual variable.The derivation uses the optimality equation and λ(h) = −˜q(h) before substitution.
- Optimal predictor: Similarly, differentiating with respect to qM(y | h) yields the optimal predictor M(y | h) = ˜p(y | h).