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A single-layer perceptron catches isolated fraud anomal...
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See plansThe instinct to reach for more data treats this as an estimation problem, but it’s a representational one. A single-layer perceptron — one affine transformation followed by a threshold — is mathematically constrained to drawing exactly one straight hyperplane through feature space, no matter how many training examples it sees. More data makes that one hyperplane better-positioned; it can never make the model capable of drawing a shape it structurally cannot represent.
Coordinated fraud, where feature A is individually benign, feature B is individually benign, but the combination is fraudulent, is the classic XOR pattern in disguise. The fraudulent cases sit in opposite corners of the feature space from each other, and the innocuous cases sit in the other two corners. Try drawing one straight line that puts both fraudulent corners on one side and both innocuous corners on the other — it’s not that a particular training run fails to find such a line, it is that no such line exists. This is a structural impossibility, not a convergence problem, and no amount of additional labeled data, hyperparameter tuning, or extended training changes the shape of what a linear model can express.
The fix is architectural, not statistical: insert a hidden layer with a non-linear activation function between input and output. A network with even one non-linear hidden layer can compose several linear boundaries together, which lets it carve out arbitrary, non-convex regions of feature space — including the specific opposite-corner pattern that coordinated fraud produces. This is the textbook justification for why depth (or at minimum, one non-linearity) exists at all: it’s not an optimization convenience, it’s what makes certain decision boundaries representable in the first place.