Loading
Life sciences · Preprint
arXiv · September 25, 2026
No summary has been generated for this record yet. What follows is drawn from its source metadata only.
Preprint.
No findings were extractable from the material analysed.
Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.
The source did not state who this applies to in practice.
Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.
This record has not been graded across any dimension yet. Treat the label above as provisional and read the source.
What is missing. This record has no bottom line, key findings, reported figures, evidence dimensions. That is a gap in the analysis, not a judgement about the study.
The flatness of the loss landscape at a minimizer is a widely used heuristic for reasoning about neural-network generalization, yet evidence for this relation is mostly empirical and controversial. We study this relation in a teacher-student tree committee machine, where both the ERM estimator and the Hessian spectrum are analytically tractable in the proportional high-dimensional limit. First, we use a zero-temperature Gibbs formulation to obtain predictions for the observables of the typical minimizers of the empirical loss. Secondly, we use Edwards-Jones formalism to derive the limiting Hessian resolvent around these typical minimizers. All predictions agree with finite-size gradient-descent simulations. Finally, we study three measures of flatness, namely the left and right edges and the spectral mean, and check if a decrease in generalization error as the dataset size is increased corresponds to an increase in flatness. We find that the answer strongly depends on the learning task and on the ratio of the number of parameters to the number of data points. In regression, the spectral mean and right edge correlate with the generalization error, while the left edge does so only in the overparametrized regime. In classification this correlation reliably holds only in the highly overparametrized phase, while for underparametrized networks it can even reverse.