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import math
import random
from dreamcoder.utilities import *
class InvalidLoss(Exception):
pass
class DN(object):
'''differentiable node: parent object of every differentiable operation'''
def __init__(self, arguments):
self.gradient = None
if arguments != []:
self.data = None
self.arguments = arguments
# descendents: every variable that takes this variable as input
# descendents: [(DN,float)]
# the additional float parameter is d Descendent / d This
self.descendents = []
self.recalculate()
def __str__(self):
if self.arguments == []:
return self.name
return "(%s %s)" % (self.name, " ".join(str(x)
for x in self.arguments))
def __repr__(self):
return "DN(op = %s, data = %s, grad = %s, #descendents = %d, args = %s)" % (
self.name, self.data, self.gradient, len(self.descendents), self.arguments)
@property
def derivative(self): return self.differentiate()
def differentiate(self):
if self.gradient is None:
self.gradient = sum(partial * descendent.differentiate()
for descendent, partial in self.descendents)
return self.gradient
def zeroEverything(self):
if self.gradient is None and self.descendents == [] and (
self.data is None or self.arguments == []):
return
self.gradient = None
self.descendents = []
if self.arguments != []:
self.data = None
for x in self.arguments:
x.zeroEverything()
def lightweightRecalculate(self):
return self.forward(*[a.lightweightRecalculate()
for a in self.arguments])
def recalculate(self):
if self.data is None:
inputs = [a.recalculate() for a in self.arguments]
self.data = self.forward(*inputs)
# if invalid(self.data):
# eprint("I am invalid",repr(self))
# eprint("Here are my inputs",inputs)
# self.zeroEverything()
# eprint("Here I am after being zeroed",repr(self))
# raise Exception('invalid loss')
#assert valid(self.data)
partials = self.backward(*inputs)
for d, a in zip(partials, self.arguments):
# if invalid(d):
# eprint("I have an invalid derivative",self)
# eprint("Inputs",inputs)
# eprint("partials",partials)
# raise Exception('invalid derivative')
a.descendents.append((self, d))
return self.data
def backPropagation(self):
self.gradient = 1.
self.recursivelyDifferentiate()
def recursivelyDifferentiate(self):
self.differentiate()
for x in self.arguments:
x.recursivelyDifferentiate()
def updateNetwork(self):
self.zeroEverything()
l = self.recalculate()
self.backPropagation()
return l
def log(self): return Logarithm(self)
def square(self): return Square(self)
def exp(self): return Exponentiation(self)
def clamp(self, l, u): return Clamp(self, l, u)
def __abs__(self): return AbsoluteValue(self)
def __add__(self, o): return Addition(self, Placeholder.maybe(o))
def __radd__(self, o): return Addition(self, Placeholder.maybe(o))
def __sub__(self, o): return Subtraction(self, Placeholder.maybe(o))
def __rsub__(self, o): return Subtraction(Placeholder.maybe(o), self)
def __mul__(self, o): return Multiplication(self, Placeholder.maybe(o))
def __rmul__(self, o): return Multiplication(self, Placeholder.maybe(o))
def __neg__(self): return Negation(self)
def __truediv__(self, o): return Division(self, Placeholder.maybe(o))
def __rtruediv__(self, o): return Division(Placeholder.maybe(o), self)
def numericallyVerifyGradients(self, parameters):
calculatedGradients = [p.derivative for p in parameters]
e = 0.00001
for j, p in enumerate(parameters):
p.data -= e
y1 = self.lightweightRecalculate()
p.data += 2 * e
y2 = self.lightweightRecalculate()
p.data -= e
d = (y2 - y1) / (2 * e)
if abs(calculatedGradients[j] - d) > 0.1:
eprint(
"Bad gradient: expected %f, got %f" %
(d, calculatedGradients[j]))
def gradientDescent(
self,
parameters,
_=None,
lr=0.001,
steps=10**3,
update=None):
for j in range(steps):
l = self.updateNetwork()
if update is not None and j % update == 0:
eprint("LOSS:", l)
for p in parameters:
eprint(p.data, '\t', p.derivative)
if invalid(l):
raise InvalidLoss()
for p in parameters:
p.data -= lr * p.derivative
return self.data
def restartingOptimize(self, parameters, _=None, attempts=1,
s=1., decay=0.5, grow=0.1,
lr=0.1, steps=10**3, update=None):
ls = []
for _ in range(attempts):
for p in parameters:
p.data = random.random()*10 - 5
ls.append(
self.resilientBackPropagation(
parameters, lr=lr, steps=steps,
decay=decay, grow=grow))
return min(ls)
def resilientBackPropagation(
self,
parameters,
_=None,
decay=0.5,
grow=1.2,
lr=0.1,
steps=10**3,
update=None):
previousSign = [None] * len(parameters)
lr = [lr] * len(parameters)
for j in range(steps):
l = self.updateNetwork()
if update is not None and j % update == 0:
eprint("LOSS:", l)
eprint("\t".join(str(p.derivative) for p in parameters))
if invalid(l):
raise InvalidLoss()
newSigns = [p.derivative > 0 for p in parameters]
for i, p in enumerate(parameters):
if p.derivative > 0:
p.data -= lr[i]
elif p.derivative < 0:
p.data += lr[i]
if previousSign[i] is not None:
if previousSign[i] == newSigns[i]:
lr[i] *= grow
else:
lr[i] *= decay
previousSign = newSigns
return self.data
class Placeholder(DN):
COUNTER = 0
def __init__(self, initialValue=0., name=None):
self.data = initialValue
super(Placeholder, self).__init__([])
if name is None:
name = "p_" + str(Placeholder.COUNTER)
Placeholder.COUNTER += 1
self.name = name
@staticmethod
def named(namePrefix, initialValue=0.):
p = Placeholder(initialValue, namePrefix + str(Placeholder.COUNTER))
Placeholder.COUNTER += 1
return p
def __str__(self):
return "Placeholder(%s = %s)" % (self.name, self.data)
@staticmethod
def maybe(x):
if isinstance(x, DN):
return x
return Placeholder(float(x))
def forward(self): return self.data
def backward(self): return []
class Clamp(DN):
def __init__(self, x, l, u):
assert u > l
self.l = l
self.u = u
super(Clamp, self).__init__([x])
self.name = "clamp"
def forward(self, x):
if x > self.u:
return self.u
if x < self.l:
return self.l
return x
def backward(self, x):
if x > self.u or x < self.l:
return [0.]
else:
return [1.]
class Addition(DN):
def __init__(self, x, y):
super(Addition, self).__init__([x, y])
self.name = '+'
def forward(self, x, y): return x + y
def backward(self, x, y): return [1., 1.]
class Subtraction(DN):
def __init__(self, x, y):
super(Subtraction, self).__init__([x, y])
self.name = '-'
def forward(self, x, y): return x - y
def backward(self, x, y): return [1., -1.]
class Negation(DN):
def __init__(self, x):
super(Negation, self).__init__([x])
self.name = '-'
def forward(self, x): return -x
def backward(self, x): return [-1.]
class AbsoluteValue(DN):
def __init__(self, x):
super(AbsoluteValue, self).__init__([x])
self.name = 'abs'
def forward(self, x): return abs(x)
def backward(self, x):
if x > 0:
return [1.]
return [-1.]
class Multiplication(DN):
def __init__(self, x, y):
super(Multiplication, self).__init__([x, y])
self.name = '*'
def forward(self, x, y): return x * y
def backward(self, x, y): return [y, x]
class Division(DN):
def __init__(self, x, y):
super(Division, self).__init__([x, y])
self.name = '/'
def forward(self, x, y): return x / y
def backward(self, x, y): return [1.0 / y, -x / (y * y)]
class Square(DN):
def __init__(self, x):
super(Square, self).__init__([x])
self.name = 'sq'
def forward(self, x): return x * x
def backward(self, x): return [2 * x]
class Exponentiation(DN):
def __init__(self, x):
super(Exponentiation, self).__init__([x])
self.name = 'exp'
def forward(self, x): return math.exp(x)
def backward(self, x): return [math.exp(x)]
class Logarithm(DN):
def __init__(self, x):
super(Logarithm, self).__init__([x])
self.name = 'log'
def forward(self, x): return math.log(x)
def backward(self, x): return [1. / x]
class LSE(DN):
def __init__(self, xs):
super(LSE, self).__init__(xs)
self.name = 'LSE'
def forward(self, *xs):
m = max(xs)
return m + math.log(sum(math.exp(y - m) for y in xs))
def backward(self, *xs):
m = max(xs)
zm = sum(math.exp(x - m) for x in xs)
return [math.exp(x - m) / zm for x in xs]
if __name__ == "__main__":
x = Placeholder(10., "x")
y = Placeholder(2., "y")
z = x - LSE([x, y])
z.updateNetwork()
eprint("dL/dx = %f\tdL/dy = %f" % (x.derivative, y.derivative))
x.data = 2.
y.data = 10.
z.updateNetwork()
eprint("dL/dx = %f\tdL/dy = %f" % (x.differentiate(), y.differentiate()))
x.data = 2.
y.data = 2.
z.updateNetwork()
eprint("z = ", z.data, z)
eprint("dL/dx = %f\tdL/dy = %f" % (x.differentiate(), y.differentiate()))
loss = -z
eprint(loss)
lr = 0.001
loss.gradientDescent([x, y], steps=10000, update=1000)
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