Is it possible to cheaply fix the problem of module usage in gradient descent?

If a problem arises during gradient descent related to module usage (for example, incorrect gradient computation or instability), several inexpensive and simple solutions can often be applied:

• Check gradient computation: ensure all operations are differentiable and correctly connected to the computation graph.
• Use automatic differentiation: modern frameworks (PyTorch, TensorFlow) automatically compute gradients, reducing manual coding errors.
• Apply normalization or scaling: normalizing input data or gradients helps stabilize training.
• Change the learning rate: a too-large step can lead to divergence.
• Use ready-made optimizers: instead of manually updating parameters, apply optimizers from libraries.

These measures usually do not require significant costs and allow quick fixing of gradient descent issues without deep changes to architecture or algorithms.