Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the systematic ``generalization gap'', where the train error becomes an unreliable proxy for test error. Existing approaches either argue this gap is benign through complex analysis or sacrifice data to a validation set. In contrast, we introduce decoupled descent (DD), a novel theory-based training algorithm that satisfies a train-test identity -- enforcing the train error to asymptotically track the test error for stylized Gaussian mixture models. Within this specific regime, leveraging approximate m...
| Authors | Max Lovig |
|---|---|
| Primary category | math.ST |
| Published | 30 April 2026 |
| Last updated at source | 30 April 2026 |
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