Sources of Implicit Bias
When training a machine learning model, the optimization algorithm you choose — such as stochastic gradient descent (SGD) or standard gradient descent (GD) — does more than just find a solution that fits your data. Each algorithm has its own way of searching through the space of possible solutions, and this search process can introduce its own preferences, or implicit biases, into the final model. Even if you use the same model architecture and loss function, simply switching from GD to SGD can lead to different learned solutions, especially in settings where there are many possible solutions that fit the training data perfectly. This means that your choice of optimization algorithm is not just a technical detail; it can fundamentally shape the kind of patterns your model prefers to learn.
Think of optimization algorithms as different ways of exploring a landscape to find a low point. Some algorithms, like GD, carefully follow the steepest path downhill, while others, like SGD, take small, noisy steps. Because of these differences, GD might consistently find one type of low point, while SGD might land at another. These tendencies are not accidental — they reflect the algorithm's built-in preferences for certain types of solutions, even when many solutions fit the data equally well.
Formally, the inductive bias of an optimization algorithm is the tendency of the algorithm to select particular solutions among all possible solutions that minimize the loss. For example, in overparameterized linear models, GD tends to find the solution with minimum Euclidean norm, while SGD can favor solutions with different properties, such as those that generalize better or have lower complexity according to other measures. This bias is not explicitly programmed, but emerges from the dynamics of the optimization process itself.
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How do SGD and GD differ in the solutions they find?
Why does the choice of optimization algorithm affect the final model?
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When training a machine learning model, the optimization algorithm you choose — such as stochastic gradient descent (SGD) or standard gradient descent (GD) — does more than just find a solution that fits your data. Each algorithm has its own way of searching through the space of possible solutions, and this search process can introduce its own preferences, or implicit biases, into the final model. Even if you use the same model architecture and loss function, simply switching from GD to SGD can lead to different learned solutions, especially in settings where there are many possible solutions that fit the training data perfectly. This means that your choice of optimization algorithm is not just a technical detail; it can fundamentally shape the kind of patterns your model prefers to learn.
Think of optimization algorithms as different ways of exploring a landscape to find a low point. Some algorithms, like GD, carefully follow the steepest path downhill, while others, like SGD, take small, noisy steps. Because of these differences, GD might consistently find one type of low point, while SGD might land at another. These tendencies are not accidental — they reflect the algorithm's built-in preferences for certain types of solutions, even when many solutions fit the data equally well.
Formally, the inductive bias of an optimization algorithm is the tendency of the algorithm to select particular solutions among all possible solutions that minimize the loss. For example, in overparameterized linear models, GD tends to find the solution with minimum Euclidean norm, while SGD can favor solutions with different properties, such as those that generalize better or have lower complexity according to other measures. This bias is not explicitly programmed, but emerges from the dynamics of the optimization process itself.
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