Backpropagation is a method used in artificial neural networks to adjust the weights of the network based on the error between the predicted output and the actual output. The adjustment process involves calculating the gradient of the error with respect to each weight in the network, and then updating the weights in the opposite direction of the gradient to minimize the error. This process is repeated for each training example in the dataset until the error is minimized.

Other methods that exist for the adjustment process include:

- Gradient descent: a general optimization algorithm that can be used to minimize any differentiable function, not just the error function in neural networks. It works by iteratively adjusting the parameters in the direction of steepest descent of the function.
- Stochastic gradient descent: a variant of gradient descent that updates the parameters based on a randomly selected subset of training examples, rather than all examples at once. This can speed up convergence and reduce memory requirements.
- Conjugate gradient: an optimization algorithm that uses conjugate directions to iteratively minimize a function. It can be more efficient than gradient descent for certain types of functions.
- Levenberg-Marquardt: an optimization algorithm commonly used in nonlinear least squares problems, such as fitting a neural network to data. It combines aspects of gradient descent and Gauss-Newton methods to iteratively adjust the parameters.
- Quasi-Newton: a family of optimization algorithms that approximate the Hessian matrix (second derivative) of a function using only gradient information. They can be more efficient than gradient descent for certain types of functions.
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