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arXiv · 2610.09621

When does a network's training history predict its future learning better than its current state? Evidence from a response probe and a forecasting screen

Martin Hofmann·Patrick Mäder
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Abstract

Networks that behave alike now can still learn differently when training continues. Work on loss of plasticity and critical periods shows that the path to a state shapes what follows; it does not show whether the path carries information that a measurement of the state itself misses. We ask when the training history of a network predicts its future learning better than its current state. In a main study, small multilayer perceptrons were trained under three history regimes (42 histories), and future learning was measured at four checkpoints by a short probe: a copy of the network trained for 100 updates on a new task. Before the prediction result was read, the protocol checked the probe. It responded monotonically to a function-preserving rescaling of hidden units, repeated measurements agreed (intraclass correlation 0.940, [0.903, 0.997], in the least reliable class, mean of three repeats), and a re-initialisation of units was visible directly after it but not 100 to 200 updates later. A history state of at most four dimensions did not improve on a calibrated model of the current state (gain -21.4%, 90% interval [-91.9, 8.1]; required in advance: 10%). A companion screen on 1,560 synthetic regression runs asked the same question for a target further away, the final error of the run. There, history models forecast better than the current validation error after 12 of up to 240 epochs (compact state 30.3%, [15.8, 39.4], a contextual comparison) and were not distinguishable from it after 48. In both studies the history was informative only while the current state was not yet informative about the target; this reading was formed after the results.

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Martin Hofmann, Patrick Mäder. 2026-10-07. When does a network's training history predict its future learning better than its current state? Evidence from a response probe and a forecasting screen. https://arxiv.org/abs/2610.09621

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