Given known recurrent structure f(x) = w0 * f(x-1) + w1 * f(x-1)

pytorch_play.py

import torch as th
from torch.autograd import Variable 

## helpers 
def fromlist(list):
    return th.FloatTensor(list)

def const(t):
    return Variable(t)

def var(t):
    return Variable(t, requires_grad=True)

## training data
fibs = [1,1]
for i in range(8): 
	fibs.append( fibs[i] + fibs[i-1])

## variables
a0 = var(th.randn(1))
a1 = var(th.randn(1))
w = var(th.randn(2)) # optimal value = [1,1]

## some computation
def recurrent(x):
	if x == 0: return a0
	if x == 1: return a1 
	a = recurrent(x-1)
	b = recurrent(x-2)
	return w[0] * a + w[1] * b 

## training
print('initial', a0, a1, w)

rate = 0.001
for i in range(5000):
    ## supply last 5 values 
    for j in range(len(fibs)-5,len(fibs)):
        ## absolute diff. as loss
        loss = (recurrent(j) - fibs[j]).abs()
        ## calculate gradient
        loss.backward()
        ## update variables
        for v in [a0,a1,w]:
	        v.data -= rate * v.grad.data
	        v.grad.data.zero_()
        
print('final', a0, a1, w)

## loss
print([ (recurrent(i) - fibs[i]).abs().data[0] for i in range(len(fibs)) ])