Learned, Then Lost: Measuring a Single Training Example's Counterfactual Effect on GPT-2 Pre-training

Forum topic · 小凯 · 2026-08-21

Summary

A new arXiv paper (2608.19168) by Zachary Speck and Asa Shepard measures the counterfactual contribution of a single training example to a finished model. The authors trained 32 GPT-2 models (124M parameters) from scratch on OpenWebText across four conditions and eight seeds. At step 200 of 9,536, one row of a 256-row batch was replaced with a context injection carrying a 194-token passage: fluent prose on a corpus-attested topic, gradient-matched fabricated prose, random keyboard characters, or no injection. Injected arms predicted the passage better 50 steps later (cross-entropy differences of 0.039 and 0.044 nats, consistent across all eight seeds, p<10^-4), but the effect decayed to undetectable by the final step, with minimum detectable effects of 0.025 and 0.079 nats. Geometric measurements taken after decay showed weight displacement reaching 44.1% of seed-to-seed distance while the loss-basin barrier reached only 3.0%, a roughly 15-fold gap. The authors conclude that a single example transiently relocates the model within its basin without moving it out, contributing no detectable lasting trace.

Overview

Field: Machine Learning Authors: Zachary Speck, Asa Shepard Published: 2026-08-19 arXiv: 2608.19168

Abstract

A single training example's contribution to a finished model is normally estimated rather than measured, because measuring it takes two expensive full pre-training runs that differ in one row of one batch. The authors ran that counterfactual 24 times at a small scale. They trained 32 GPT-2 models at 124M parameters from scratch on OpenWebText, over four conditions and eight seeds.

At step 200 of 9,536, at peak learning rate, one row of a 256-row batch was replaced with a fixed context injection carrying a 194-token passage. The three injected conditions were:

1. Fluent prose with a corpus-attested subject 2. Fluent prose with a fabricated subject matched to it within 0.14% on full-batch gradient delta 3. Random keyboard characters

The fourth condition was an uninjected twin.

Findings

Learning: 50 steps after injection, arms that saw the passage predicted it better than unseen arms, with cross-entropy differences of 0.039 and 0.044 nats, consistent across all eight of eight seeds (p<10^-4).
Decay: At the final step, no difference was detected for either passage (p=0.25 and p=0.71, against minimum detectable effects of 0.025 and 0.079 nats), and no difference between the two passages (p=0.54). All geometric measurements were taken after this decay.
Interpolation barrier: The pre-registered interpolation loss barrier contrast was +0.0068 (p=0.509), against a minimum detectable effect of 0.032 barrier units. Held-out cross-entropy was -0.00044 (p=0.310).
Geometry: Per-layer centered kernel alignment showed no detectable separation on any condition at any layer. Weight displacement reached 44.1% of seed-to-seed Euclidean distance and was 92% stabilized before the training midpoint, while the barrier reached only 3.0% of seed-to-seed barrier — a gap of roughly 15x, which is a lower bound.

Conclusion

The injection repositions the model *within* its loss basin without moving it out of the basin. A single example is learned from one exposure, then its effect decays away, leaving no detectable lasting trace on the finished model.

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Source: arXiv:2608.19168

*Auto-collected on 2026-08-21.*