<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["es", "en"].<end_of_turn>
<start_of_turn>user
¿Cómo funciona el algoritmo de backpropagation?<end_of_turn>
<start_of_turn>model
Any function can be represented through a computational graph where each vertex represents an operation. For example, the function f(a, b, x) = sqrt(a*x + b) can be represented with the following graph:

A node v1 represents the value a, another node v2 represents the value x, and another node v3 represents the value b.
Then, a new v4 node represents a*x, another v5 node represents a*x + b, and a last v6 node represents sqrt(a*x+b).

In other words v1 := a, v2 := x, v3 := b. Then v4 := v1 * v2, v5 := v4 + v3, v6 := sqrt(v5). What we are doing is representing the function f as a composition of other simpler functions.

Then, when we need to compute the derivative of the function f with respect to a,b,x, we use Leibnitz's chain rule, which says that if df/dx = df/dg * dg/dx.

So, we can compute the derivative dv6/dv5, dv5/dv4 and dv5/dv3, and dv4/dv1, dv4/dv2, and in this way we can compute the derivative of f with respect to the three variables a,b,x in a particular point. To do this, we first make a forward pass, to compute f(a,b,x) at the given values, and then make a backward pass according to the chain rule.<end_of_turn><eos>