aiqbench analysis
This withdrawn preprint offered a theoretical analysis of generative models under finite training sets, proposing that stochastic processes effectively produce noisy convex combinations of training samples. However, the authors identified critical proof errors in the key theorems and subsequently withdrew the paper to avoid misleading readers. For a technical audience, the primary takeaway is the existence of these fundamental mathematical flaws rather than the proposed framework itself.
Generation Properties of Stochastic Interpolation under Finite Training Set
arXiv:2509.21925v3 Announce Type: replace Abstract: This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while the stochastic generative process manifests as training samples with added Gaussian noise. Beyond the idealized setting, we consider model estimation errors and introduce formal definitions of underfitting and overfitting specific to generative models. Our theoretical analysis reveals that, in the presence of estimation errors, the stochastic generation process effectively produces convex combinations of training samples corrupted by a mixture of uniform and Gaussian noise. Experiments on generation tasks and downstream tasks such as classification support our theory.
Abstract:This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while the stochastic generative process manifests as training samples with added Gaussian noise. Beyond the idealized setting, we consider model estimation errors and introduce formal definitions of underfitting and overfitting specific to generative models. Our theoretical analysis reveals that, in the presence of estimation errors, the stochastic generation process effectively produces convex combinations of training samples corrupted by a mixture of uniform and Gaussian noise. Experiments on generation tasks and downstream tasks such as classification support our theory.
We found proof errors affecting key theorems and wish to avoid misleading readers. We have submitted a substantially revised new paper, arXiv:2606.08554, retaining only two old theorems and adding five new ones
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2509.21925 [cs.LG]
(or arXiv:2509.21925v3 [cs.LG] for this version)
Full text under the publisher's open licence · 181 words
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