Analytical Correction for Subsampling Bias in Drifting Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913075353878528 |
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| author | Zhang, Jiaru Deng, Zeyun Lu, Juanwu Wang, Ziran Zhang, Ruqi |
| author_facet | Zhang, Jiaru Deng, Zeyun Lu, Juanwu Wang, Ziran Zhang, Ruqi |
| contents | Drifting models are capable one-step generative models trained to follow a drifting field. The field combines attractive and repulsive softmax-weighted centroids over the data and current-generator distributions. In practice, only a minibatch of $n$ samples from each distribution is available, and each centroid is approximated by an empirical estimate. In this paper, we begin by showing that the minibatch centroid is in general a biased estimator of the target centroid, with a pointwise $O(1/n)$ bias arising from softmax self-normalization. Correcting this bias requires the expectation over the full distribution, which is intractable. We instead approximate the leading bias term from in-batch statistics and propose Analytical Bias Correction (ABC), a closed-form plug-in adjustment. We prove that ABC reduces the bias from $O(1/n)$ to $O(1/n^2)$, introduces no first-order increase in total variance, and preserves convex-hull containment of the corrected centroid. In practice, ABC requires only two additional lines of code and has negligible wall-time overhead under compiled execution. Toy experiments confirm the theoretical $O(1/n)$ and $O(1/n^2)$ scaling. On CIFAR-10, ABC reduces FID and trains faster, with the largest gains at small $n$, where the bias is most significant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27239 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytical Correction for Subsampling Bias in Drifting Models Zhang, Jiaru Deng, Zeyun Lu, Juanwu Wang, Ziran Zhang, Ruqi Machine Learning Drifting models are capable one-step generative models trained to follow a drifting field. The field combines attractive and repulsive softmax-weighted centroids over the data and current-generator distributions. In practice, only a minibatch of $n$ samples from each distribution is available, and each centroid is approximated by an empirical estimate. In this paper, we begin by showing that the minibatch centroid is in general a biased estimator of the target centroid, with a pointwise $O(1/n)$ bias arising from softmax self-normalization. Correcting this bias requires the expectation over the full distribution, which is intractable. We instead approximate the leading bias term from in-batch statistics and propose Analytical Bias Correction (ABC), a closed-form plug-in adjustment. We prove that ABC reduces the bias from $O(1/n)$ to $O(1/n^2)$, introduces no first-order increase in total variance, and preserves convex-hull containment of the corrected centroid. In practice, ABC requires only two additional lines of code and has negligible wall-time overhead under compiled execution. Toy experiments confirm the theoretical $O(1/n)$ and $O(1/n^2)$ scaling. On CIFAR-10, ABC reduces FID and trains faster, with the largest gains at small $n$, where the bias is most significant. |
| title | Analytical Correction for Subsampling Bias in Drifting Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.27239 |