implicit regularization
In plain wordsThe 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.
The tendency of a training algorithm — rather than any explicit penalty in the lossloss function, n.: A score that measures how wrong a model's predictions are. Training means adjusting the model, step by step, to push this number down. — to favor particular solutions among the many that fit the training data, typically ones that are simple in some sense and generalize well. Examples: gradient descentgradient descent, n.: A method for training models by repeatedly nudging every setting a small step in whichever direction most reduces the error, like a hiker who cannot see the valley but keeps stepping wherever the ground tilts down. on an underdetermined least-squares problem started at zero converges to the minimum-norm solution; on linearly separable data with logistic or cross-entropycross-entropy, n.: A score of how surprised a model's predictions are by what actually happens; lower is better. Language models are trained mainly by driving this number down on real text. loss, the weight direction converges, slowly, to the maximum-margin classifier of a hard-margin support vector machinesupport vector machine, n.: A classic method that separates two groups of examples with the widest possible gap — like laying the broadest possible road between them. A mathematical shortcut lets it draw curved boundaries too.; in matrix factorization, gradient descent from small initialization favors low-rank solutions. The noise of stochastic gradient descentstochastic gradient descent, n.: A faster version of gradient descent that estimates which way is downhill from a small random sample of the training data at each step, instead of checking the whole dataset., large learning rateslearning rate, n.: How big a step a model takes each time it adjusts its settings during training. Too large and learning goes haywire; too small and it crawls., early stoppingearly stopping, n.: Stopping training at the point where the model does best on practice data it has not learned from, before it starts memorizing quirks of its training examples., architecture and initialization scale each add biases, for instance toward flatter minima or toward learning low-frequency functions first. Implicit regularization is a leading explanation for why overparameterizedoverparameterization, 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. networks generalize despite being able to memorize, though no complete account exists for deep networks.
Origin
The phrase had earlier uses outside neural networks, for example for the regularizing side effects of approximate computation (Michael Mahoney, 2012). Behnam Neyshabur, Ryota Tomioka and Nathan Srebro brought it into deep learning in 'In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning' (arXiv December 2014). Daniel Soudry and colleagues' proof that gradient descent converges to the max-margin direction (2017) and Suriya Gunasekar and colleagues' matrix-factorization results (2017) made 'implicit bias' a research program.
Usage note
Unrelated to the psychological notion of unconscious 'implicit bias'; see biasbias, n.: A word with several AI meanings: an adjustable number added inside a model; a systematic error in estimates; or unfair treatment of some groups of people by an AI system. for the word's many senses.
Related
- regularizationregularization, n.: Any technique that stops a model from memorizing its training examples too closely — often by penalizing complexity — so that it works better on new data.
- 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.
- 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.
- sharp and flat minimasharp and flat minima, n.: Two kinds of low points a trained model can settle into: narrow pits where small changes spoil performance, and broad basins where they barely matter. Broad basins are thought to generalize better, though this is debated.
- inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases.
- stochastic gradient descentstochastic gradient descent, n.: A faster version of gradient descent that estimates which way is downhill from a small random sample of the training data at each step, instead of checking the whole dataset.
- benign overfittingbenign overfitting, n.: When 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.
- regularizationregularization, n.: Any technique that stops a model from memorizing its training examples too closely — often by penalizing complexity — so that it works better on new data.
Sources
- Neyshabur, B., Tomioka, R. & Srebro, N. (2015). In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning. ICLR 2015 Workshop. arxiv.org/abs/1412.6614
- Soudry, D., Hoffer, E., Nacson, M. S., Gunasekar, S. & Srebro, N. (2018). The Implicit Bias of Gradient Descent on Separable Data. ICLR 2018. arxiv.org/abs/1710.10345
Mentioned in
generalizationgeneralization, n.: How well a model copes with new examples it has never seen, rather than just memorizing its training data, like a student who understands the method, not just the answers., 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., Occam's razorOccam's razor, n.: A rule of thumb for choosing between explanations: if two fit the evidence equally well, bet on the one that assumes less. In AI it motivates preferring simpler models, which are less likely to fit noise., regularizationregularization, n.: Any technique that stops a model from memorizing its training examples too closely — often by penalizing complexity — so that it works better on new data., stochastic gradient descentstochastic gradient descent, n.: A faster version of gradient descent that estimates which way is downhill from a small random sample of the training data at each step, instead of checking the whole dataset., weight decayweight decay, n.: A training rule that shrinks every weight slightly at each step, like a small tax on large numbers. It keeps models simpler and usually helps them work better on new data., benign overfittingbenign overfitting, n.: When 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., 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., edge of stabilityedge of stability, n.: A surprising pattern in how neural networks train: the error landscape keeps getting steeper until it is just steep enough to make training wobble, then stays balanced at that edge while the error still falls., hypothesis spacehypothesis space, n.: The full menu of possible models a learning method is allowed to choose from — for example, all straight lines. Learning means picking the item on the menu that best fits the data., neural collapseneural collapse, n.: A striking tidiness that appears when classifiers are trained for a long time: the network's internal summaries of each class shrink to single points arranged as evenly and as far apart as possible., neural tangent kernelneural tangent kernel, n.: A mathematical tool showing that extremely wide neural networks learn like a simpler, well-understood method, because their internal settings barely move during training. It explains some, but not all, of deep learning's behavior., 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., sharpness-aware minimizationsharpness-aware minimization, n.: A training method that looks for settings where the error stays low even if the settings are nudged a little, rather than settings that are merely low at one precise point., statistical learning theorystatistical learning theory, n.: The mathematics of when and why learning from examples works: how much data is needed, and how well a model trained on some examples will do on new ones., VC dimensionVC dimension, n.: A measure of how flexible a family of prediction rules is: the largest number of points it can label in every possible way. More flexible families need more data to learn reliably.