benign overfitting
In plain wordsWhen a model fits its training data perfectly — even the errors and noise — yet still predicts well on new data, defying the textbook warning that this always backfires.
The phenomenon in which a model interpolates noisy training data — reaching zero training error even on mislabeled or noisy examples — yet still attains near-optimal test performance. Peter Bartlett and colleagues characterized when this happens in overparameterized linear regression: the minimum-norm interpolating solution generalizes well if the data covariance has many small, roughly equal directions in which the noise can be absorbed harmlessly, while a few important directions carry the signal. Analogous results hold for kernel methods, two-layer networks and max-margin classification. Later work distinguishes benign overfitting (the excess risk vanishes), 'tempered' overfitting (bounded but nonzero harm, as seen in many neural networks) and catastrophic overfitting. The concept reconciles classical theory with the practice of training deep networks to zero training loss and accounts for part of the second descent in double descentdouble descent, n.: A surprising pattern where a model's error on new data first falls, then rises, then falls again as the model grows bigger — contradicting the old rule that oversized models always do worse.; whether real deep networks overfit benignly or merely temperately remains open.
Origin
Named by Peter L. Bartlett, Philip M. Long, Gábor Lugosi and Alexander Tsigler in 'Benign Overfitting in Linear Regression' (arXiv June 2019; PNAS 2020), building on studies of interpolation by Mikhail Belkin and colleagues (2018). Neil Mallinar and colleagues proposed the benign–tempered–catastrophic taxonomy in 2022.
Related
- double descentdouble descent, n.: A surprising pattern where a model's error on new data first falls, then rises, then falls again as the model grows bigger — contradicting the old rule that oversized models always do worse.
- overparameterizationoverparameterization, n.: Giving a model far more adjustable settings than it would seem to need — often more than it has training examples. Classic theory predicted this would backfire; in deep learning it usually helps.
- overfittingoverfitting, n.: When a model learns its training examples too well — quirks and noise included — so it does great on data it has seen but poorly on anything new, like a student who memorizes answers without understanding.
- implicit regularizationimplicit regularization, n.: The hidden preferences of a training method itself: even with no explicit rule against complexity, the way a model is trained tends to steer it toward simpler solutions.
- generalization gapgeneralization gap, n.: The difference between how well a model does on the examples it trained on and how well it does on new ones. A big gap means it memorized rather than learned.
- memorizationmemorization, n.: When an AI model stores specific pieces of its training data — a paragraph, a phone number, an image — closely enough to reproduce them, instead of only learning general patterns.
- overfittingoverfitting, n.: When a model learns its training examples too well — quirks and noise included — so it does great on data it has seen but poorly on anything new, like a student who memorizes answers without understanding.
Sources
- Bartlett, P. L., Long, P. M., Lugosi, G. & Tsigler, A. (2020). Benign overfitting in linear regression. PNAS 117(48), 30063–30070.
- Mallinar, N. et al. (2022). Benign, Tempered, or Catastrophic: A Taxonomy of Overfitting. NeurIPS 2022.
Mentioned in
overfittingoverfitting, n.: When a model learns its training examples too well — quirks and noise included — so it does great on data it has seen but poorly on anything new, like a student who memorizes answers without understanding., generalization gapgeneralization gap, n.: The difference between how well a model does on the examples it trained on and how well it does on new ones. A big gap means it memorized rather than learned., double descentdouble descent, n.: A surprising pattern where a model's error on new data first falls, then rises, then falls again as the model grows bigger — contradicting the old rule that oversized models always do worse., implicit regularizationimplicit regularization, n.: The hidden preferences of a training method itself: even with no explicit rule against complexity, the way a model is trained tends to steer it toward simpler solutions., overparameterizationoverparameterization, n.: Giving a model far more adjustable settings than it would seem to need — often more than it has training examples. Classic theory predicted this would backfire; in deep learning it usually helps.