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You're modeling a dataset where the number of features...
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See plansWhen p (features) exceeds n (examples), you’re in an underdetermined regime: for any reasonable model class there are infinitely many parameter settings that fit the training data perfectly, so ordinary least-squares-style fitting breaks down both mathematically (XᵀX is singular and non-invertible) and conceptually — the model can memorize noise as easily as signal, and nothing in the raw optimization objective distinguishes the two. This is the sharp end of the curse of dimensionality: as p grows relative to n, the feature space becomes so sparse that almost any labeling becomes linearly separable, which is a symptom of overfitting capacity, not learned structure.
The fix is to inject an inductive bias the pure loss doesn’t provide. Regularized linear models — Ridge (which adds λI to make XᵀX invertible and shrinks coefficients), Lasso (which zeroes out most coefficients and does implicit feature selection), and Elastic Net (a blend) — are the standard first move because they explicitly trade a little bias for a lot of variance reduction. The other lever is dimensionality reduction before modeling: PCA, random projections, or domain-driven feature selection to cut p down toward or below n. Genomics, text classification on sparse vocabularies, and wide categorical-heavy tabular data are the classic settings where this comes up, and the failure mode to watch for is running feature selection on the full dataset before the train/test split, which silently leaks test information back into the model.