decision boundary

The set of points in input space at which a classifierclassifier, n.: A program or model that sorts inputs into categories, for example flagging an email as spam or a chatbot message as harmful. Many AI safety filters are classifiers. is indifferent between two or more classes — where their scores or posterior probabilities are equal — dividing the space into decision regions, each assigned to one class. For logistic regressionlogistic regression, n.: A simple, widely used method for yes-or-no predictions that outputs a probability — say, a 70% chance a customer cancels — by passing a weighted sum of inputs through an S-shaped curve., linear SVMssupport 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. and linear discriminant analysislinear discriminant analysis, n.: A statistical method for telling known groups apart. It finds the weighted mix of measurements on which groups differ most relative to their spread, then uses it to sort new items or compress many measurements into a few. the boundary is a hyperplane; quadratic discriminant analysis gives curved quadric surfaces; decision treesdecision tree, n.: A model that makes a prediction by asking a series of yes-or-no questions about the input, like a flowchart, with each answer leading to the next question until it reaches a final answer. give axis-aligned, piecewise boundaries; and k-nearest neighborsk-nearest neighbors, n.: Predicting something about a new example by finding the few most similar examples already known and going with their majority answer, or their average., kernel methods and neural networks can produce arbitrarily complex ones. Flexibility reflects capacity: a boundary that wraps around individual training points signals 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., one too rigid for the data signals underfittingunderfitting, n.: When a model is too simple, or trained too little, to capture the real pattern in the data, so it does poorly even on the examples it learned from.. Plotting boundaries on two-dimensional toy data is a standard way to compare classifiers, and adversarial examplesadversarial example, n.: An input altered on purpose, often too slightly for people to notice, so that an AI model gets it badly wrong — like a panda photo that a classifier confidently calls a gibbon. exploit inputs lying close to a boundary.

The tree's decision boundary is a staircase, while the SVM's is a smooth curve.