Double descent is a striking phenomenon in modern machine learning that challenges the traditional bias–variance tradeoff. In classical learning theory, increasing model complexity beyond a certain point is expected to increase test error because the model starts to overfit the training data. However, in many contemporary models—from simple linear predictors to deep neural networks—a second descent in test error emerges as the model becomes even more overparameterized.
At its core, the double descent curve can be understood in three stages. In the first stage, as the model’s capacity increases, the error decreases because the model is better able to capture the underlying signal in the data. As the model approaches the interpolation threshold—where the number of parameters is roughly equal to the number of data points—the model fits the training data exactly. This exact fitting, however, makes the model extremely sensitive to noise, leading to a spike in test error. Surprisingly, when the model complexity is increased further into the highly overparameterized regime, the training algorithm (often stochastic gradient descent) tends to select from the many possible interpolating solutions one that exhibits desirable properties such as lower norm or smoothness. This implicit bias toward simpler, more generalizable solutions causes the test error to decrease again, producing the second descent.
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