Process-Tensor Tomography of SGD: Measuring Non-Markovian Memory via Back-Flow of Distinguishability

Vasileios Sevetlidis, George Pavlidis
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2521-2529, 2026.

Abstract

We model neural training as a classical multi-time map from controllable interventions—batch choices, augmentations, and optimizer micro-steps—to model predictions on a fixed probe set. On this basis, we introduce a simple, model-agnostic witness of training memory based on back-flow of distinguishability. In a controlled two-step protocol, we compare predictive distributions after one intervention versus two; a positive increase $\Delta_{\mathrm{BF}} = D_2 - D_1 > 0$, with $D\in{\mathrm{TV}, \mathrm{JS}, \mathrm{H}}$, certifies observable-level non-Markovianity. Across controlled SGD experiments, we observe consistent positive back-flow with tight bootstrap confidence intervals, stronger effects under higher momentum, larger batch overlap, and more micro-steps, and marked collapse under a \emph{causal break} that resets optimizer state. The witness is inexpensive, requires no architectural changes, and is robust across TV/JS/Hellinger. We position this as a measurement contribution: a practical diagnostic, and empirical evidence, that real training often deviates from the Markov idealization in ways that matter for optimizer behavior, data order, and schedule design.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-sevetlidis26a, title = { Process-Tensor Tomography of SGD: Measuring Non-Markovian Memory via Back-Flow of Distinguishability }, author = {Sevetlidis, Vasileios and Pavlidis, George}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2521--2529}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/sevetlidis26a/sevetlidis26a.pdf}, url = {https://proceedings.mlr.press/v300/sevetlidis26a.html}, abstract = { We model neural training as a classical multi-time map from controllable interventions—batch choices, augmentations, and optimizer micro-steps—to model predictions on a fixed probe set. On this basis, we introduce a simple, model-agnostic witness of training memory based on back-flow of distinguishability. In a controlled two-step protocol, we compare predictive distributions after one intervention versus two; a positive increase $\Delta_{\mathrm{BF}} = D_2 - D_1 > 0$, with $D\in{\mathrm{TV}, \mathrm{JS}, \mathrm{H}}$, certifies observable-level non-Markovianity. Across controlled SGD experiments, we observe consistent positive back-flow with tight bootstrap confidence intervals, stronger effects under higher momentum, larger batch overlap, and more micro-steps, and marked collapse under a \emph{causal break} that resets optimizer state. The witness is inexpensive, requires no architectural changes, and is robust across TV/JS/Hellinger. We position this as a measurement contribution: a practical diagnostic, and empirical evidence, that real training often deviates from the Markov idealization in ways that matter for optimizer behavior, data order, and schedule design. } }
Endnote
%0 Conference Paper %T Process-Tensor Tomography of SGD: Measuring Non-Markovian Memory via Back-Flow of Distinguishability %A Vasileios Sevetlidis %A George Pavlidis %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-sevetlidis26a %I PMLR %P 2521--2529 %U https://proceedings.mlr.press/v300/sevetlidis26a.html %V 300 %X We model neural training as a classical multi-time map from controllable interventions—batch choices, augmentations, and optimizer micro-steps—to model predictions on a fixed probe set. On this basis, we introduce a simple, model-agnostic witness of training memory based on back-flow of distinguishability. In a controlled two-step protocol, we compare predictive distributions after one intervention versus two; a positive increase $\Delta_{\mathrm{BF}} = D_2 - D_1 > 0$, with $D\in{\mathrm{TV}, \mathrm{JS}, \mathrm{H}}$, certifies observable-level non-Markovianity. Across controlled SGD experiments, we observe consistent positive back-flow with tight bootstrap confidence intervals, stronger effects under higher momentum, larger batch overlap, and more micro-steps, and marked collapse under a \emph{causal break} that resets optimizer state. The witness is inexpensive, requires no architectural changes, and is robust across TV/JS/Hellinger. We position this as a measurement contribution: a practical diagnostic, and empirical evidence, that real training often deviates from the Markov idealization in ways that matter for optimizer behavior, data order, and schedule design.
APA
Sevetlidis, V. & Pavlidis, G.. (2026). Process-Tensor Tomography of SGD: Measuring Non-Markovian Memory via Back-Flow of Distinguishability . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2521-2529 Available from https://proceedings.mlr.press/v300/sevetlidis26a.html.

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