TPV: Parameter Perturbations Through the Lens of Test Prediction Variance

Devansh Arpit
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:3754-3795, 2026.

Abstract

We introduce test prediction variance (TPV)—the first-order sensitivity of a trained model’s outputs to parameter perturbations—as a unifying framework for analyzing post-training robustness. TPV’s trace form $\mathrm{Tr}(H_{\mathrm{eff}}C)$ separates the geometry of the trained model $H_{\mathrm{eff}}$ from the perturbation covariance $C$, placing SGD noise, label noise, quantization, and pruning under a single lens. The resulting expressions recover the wide-minima hypothesis for SGD and quantization noise, and yield a distinct Jacobian-spectral characterization for label noise connecting label-noise TPV with benign overfitting in nonlinear networks. Theoretically, we prove that training-set TPV converges to its test-set counterpart in the overparameterized limit, irrespective of generalization performance, providing the first result that prediction variance under local parameter perturbations can be inferred from training inputs alone. Empirically, this stability holds far more broadly, including at very low widths. Further, TPV correlates well with test loss, enabling practical applications: JBR, a label-free pruning criterion derived from TPV geometry matching state-of-the-art baselines; and training-set based model selection signal for in-distribution and transfer learning scenarios. https://github.com/devansharpit/TPV/tree/main

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-arpit26a, title = {{TPV}: Parameter Perturbations Through the Lens of Test Prediction Variance}, author = {Arpit, Devansh}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {3754--3795}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/arpit26a/arpit26a.pdf}, url = {https://proceedings.mlr.press/v306/arpit26a.html}, abstract = {We introduce test prediction variance (TPV)—the first-order sensitivity of a trained model’s outputs to parameter perturbations—as a unifying framework for analyzing post-training robustness. TPV’s trace form $\mathrm{Tr}(H_{\mathrm{eff}}C)$ separates the geometry of the trained model $H_{\mathrm{eff}}$ from the perturbation covariance $C$, placing SGD noise, label noise, quantization, and pruning under a single lens. The resulting expressions recover the wide-minima hypothesis for SGD and quantization noise, and yield a distinct Jacobian-spectral characterization for label noise connecting label-noise TPV with benign overfitting in nonlinear networks. Theoretically, we prove that training-set TPV converges to its test-set counterpart in the overparameterized limit, irrespective of generalization performance, providing the first result that prediction variance under local parameter perturbations can be inferred from training inputs alone. Empirically, this stability holds far more broadly, including at very low widths. Further, TPV correlates well with test loss, enabling practical applications: JBR, a label-free pruning criterion derived from TPV geometry matching state-of-the-art baselines; and training-set based model selection signal for in-distribution and transfer learning scenarios. https://github.com/devansharpit/TPV/tree/main} }
Endnote
%0 Conference Paper %T TPV: Parameter Perturbations Through the Lens of Test Prediction Variance %A Devansh Arpit %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-arpit26a %I PMLR %P 3754--3795 %U https://proceedings.mlr.press/v306/arpit26a.html %V 306 %X We introduce test prediction variance (TPV)—the first-order sensitivity of a trained model’s outputs to parameter perturbations—as a unifying framework for analyzing post-training robustness. TPV’s trace form $\mathrm{Tr}(H_{\mathrm{eff}}C)$ separates the geometry of the trained model $H_{\mathrm{eff}}$ from the perturbation covariance $C$, placing SGD noise, label noise, quantization, and pruning under a single lens. The resulting expressions recover the wide-minima hypothesis for SGD and quantization noise, and yield a distinct Jacobian-spectral characterization for label noise connecting label-noise TPV with benign overfitting in nonlinear networks. Theoretically, we prove that training-set TPV converges to its test-set counterpart in the overparameterized limit, irrespective of generalization performance, providing the first result that prediction variance under local parameter perturbations can be inferred from training inputs alone. Empirically, this stability holds far more broadly, including at very low widths. Further, TPV correlates well with test loss, enabling practical applications: JBR, a label-free pruning criterion derived from TPV geometry matching state-of-the-art baselines; and training-set based model selection signal for in-distribution and transfer learning scenarios. https://github.com/devansharpit/TPV/tree/main
APA
Arpit, D.. (2026). TPV: Parameter Perturbations Through the Lens of Test Prediction Variance. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:3754-3795 Available from https://proceedings.mlr.press/v306/arpit26a.html.

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