Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy.

Let g[1](zx) be g(zx) and W[1] be W for notation simplicity. Consider each dimension's scalar output ofg(zx), and it is denoted asg p (zx) where p is an index of the output dimension. For each AL round, a target modelΘis trained via stochastic gradient descent(SGD) using IN examples in the labeled setSL (Lines 3-5). The initial learning rate of0.1 is decayed by a factor of 0.1 at 50% and 75% of the total training iterations. Owing to the ability to find the best balance between purity and informativeness, MQ-Net achieves the highest accuracy on every AL round.

Noisy labels are inevitable in large real-world datasets.

Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy.

Real-world datasets for deep learning frequently suffer from the co-occurring challenges of class imbalance and label noise, hindering model performance. While methods exist for each issue, effectively combining them is non-trivial, as distinguishing genuine tail samples from noisy data proves difficult, often leading to conflicting optimization strategies. This paper presents a novel perspective: instead of primarily developing new complex techniques from scratch, we explore synergistically leveraging well-established, individually 'weak' auxiliary models - specialized for tackling either class imbalance or label noise but not both. This view is motivated by the insight that class imbalance (a distributional-level concern) and label noise (a sample-level concern) operate at different granularities, suggesting that robustness mechanisms for each can in principle offer complementary strengths without conflict. We propose Dual-granularity Sinkhorn Distillation (D-SINK), a novel framework that enhances dual robustness by distilling and integrating complementary insights from such 'weak', single-purpose auxiliary models. Specifically, D-SINK uses an optimal transport-optimized surrogate label allocation to align the target model's sample-level predictions with a noise-robust auxiliary and its class distributions with an imbalance-robust one. Extensive experiments on benchmark datasets demonstrate that D-SINK significantly improves robustness and achieves strong empirical performance in learning from long-tailed noisy data.