Learning Rate Decay: The Misnomer
At first glance, "Learning Rate Decay" might sound like an undesirable side effect or something that happens inadvertently during model training. However, it's actually a deliberate strategy used to improve the training process of models like Grok.
What is Learning Rate Decay?
Learning Rate Decay refers to the practice of systematically reducing the learning rate over time during the training of neural networks. The learning rate determines how much we adjust the model's weights with respect to the loss gradient.
Why Use Learning Rate Decay? - The Analogy
Imagine you're trying to find the deepest point in a vast, hilly landscape using a flashlight in the dark:
Initial Search: At the start, you want to take big steps to cover more ground quickly. This is like having a high learning rate at the beginning of training, allowing you to move across large valleys or hills to get a sense of where the deepest point might be.
Fine-tuning: Once you think you're close to the deepest point, you wouldn't want to keep taking those large steps; you might overshoot and climb out of the valley. Instead, you'd take smaller, more careful steps. This is akin to reducing the learning rate, allowing you to delicately navigate to the exact bottom.
The Role of Loss Gradient
The loss gradient tells you which way to step to decrease the loss function (which you want to minimize). If you imagine each step you take is guided by this gradient:
High Learning Rate: With a high learning rate, you might follow the gradient's direction but take such a large step that you move past the local minimum or even bounce out of the valley.
Decayed Learning Rate: By reducing the learning rate, you're essentially shortening your stride, which allows you to follow the gradient's direction more precisely, making sure you're moving towards lower points in the loss landscape.
Local Minimum vs. Global Minimum
Local Minimum: This is like finding a small dip in the landscape. It's the lowest point in your immediate vicinity, but there might be deeper points elsewhere. In neural network training, this means your model has found a configuration where further adjustments increase the loss, but it might not be the best overall solution.
Global Minimum: This is the absolute lowest point across the entire landscape, the best solution for your problem. The challenge is that with complex landscapes (like those in deep learning), there are many local minima, and finding the global one isn't guaranteed.
How Learning Rate Decay Helps:
Avoiding Local Minima: By starting with a high learning rate, you can jump out of shallow dips (local minima) that might trap you. As the learning rate decays, the steps become smaller, allowing you to settle into what might be the global minimum without overshooting.
Convergence: The decayed rate helps in converging to the global minimum by allowing for fine adjustments after the broad strokes made by higher learning rates.
Stability: It stabilizes training by reducing oscillations around the minimum, ensuring that each step taken is more likely to be towards reducing loss rather than accidentally increasing it due to too large of a step size.
In summary, learning rate decay is not an accidental degradation but a strategic approach in training models like Grok to navigate the complex loss landscape more effectively, aiming to find the global minimum rather than settling for a local one. This technique mimics the human-like approach of taking broad sweeps initially and then fine-tuning with precision as you get closer to your goal.