In the context of deep learning, the primary objective is rarely to recover the exact true underlying parameters of the data generation process. Instead, the focus is on discovering parameter values that result in highly accurate predictions. Even though optimization landscapes for deep networks are complex, algorithms like stochastic gradient descent perform exceptionally well. This practical success is largely due to the fact that deep models possess numerous different parameter configurations that all lead to excellent predictive performance.

Accurate Prediction vs. Parameter Recovery in Deep Networks

In machine learning, it is generally not possible to find a single, unique set of true parameters for deep neural networks. Even for simpler linear models, recovering the exact underlying parameters is only achievable if all input features are linearly independent. Because multiple parameter configurations can yield the same model behavior, the ability to exactly recover ground truth parameters should not be taken for granted.

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When training a model such as linear regression from scratch on a synthetic dataset, the true underlying parameters are perfectly known. This provides a unique opportunity to evaluate the success of the training loop by directly comparing the ground truth weights and bias with the parameters learned by the model. While exactly recovering the true parameters is generally difficult or impossible for deep networks because unique solutions often do not exist, stochastic gradient descent typically discovers parameter configurations that yield highly accurate predictions.

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