add backprop.
This commit is contained in:
publicmatt
parent
0ed01f7a84
commit
6cf0186544
578
main.ipynb
578
main.ipynb
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@ -39,168 +39,182 @@
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},
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"metadata": {},
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],
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"source": [
|
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"# inputs\n",
|
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|
"x1 = Value(2.0, label='x1')\n",
|
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|
"x2 = Value(0.0, label='x2')\n",
|
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|
"\n",
|
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|
"# weights\n",
|
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|
"w1 = Value(-3.0, label='w1')\n",
|
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|
"w2 = Value(1.0, label='w2')\n",
|
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|
"\n",
|
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|
"# bias\n",
|
||||||
|
"b = Value(6.2, label='b')\n",
|
||||||
|
"\n",
|
||||||
|
"h1 = x1 * w1\n",
|
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|
"h1.label = 'h1'\n",
|
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|
"h2 = x2 * w2\n",
|
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|
"h2.label = 'h2'\n",
|
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|
"\n",
|
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|
"h = h1 + h2\n",
|
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|
"h.label = 'h'\n",
|
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|
"\n",
|
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|
"n = h + b\n",
|
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|
"n.label = 'n'\n",
|
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|
"y = n.tanh()\n",
|
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|
"y.label = 'y'\n",
|
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|
"\n",
|
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|
"draw_dot(y)"
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|
]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "543bd866-2ce7-4b9a-8d8b-55a160a7c83b",
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": []
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"source": []
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}
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}
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|
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||||||
|
|
@ -6,6 +6,25 @@ class Value:
|
||||||
self._prev = set(_children)
|
self._prev = set(_children)
|
||||||
self._op = _op
|
self._op = _op
|
||||||
self.label = label
|
self.label = label
|
||||||
|
self._backward = lambda: None
|
||||||
|
|
||||||
|
def backward(self):
|
||||||
|
def topological(root):
|
||||||
|
ordered = []
|
||||||
|
visited = set()
|
||||||
|
|
||||||
|
def build_topo(v):
|
||||||
|
if v not in visited:
|
||||||
|
visited.add(v)
|
||||||
|
for child in v._prev:
|
||||||
|
build_topo(child)
|
||||||
|
ordered.append(v)
|
||||||
|
build_topo(root)
|
||||||
|
return ordered
|
||||||
|
ordered = topological(self)
|
||||||
|
self.grad = 1.0
|
||||||
|
for node in reversed(ordered):
|
||||||
|
node._backward()
|
||||||
|
|
||||||
def __repr__(self):
|
def __repr__(self):
|
||||||
return f"Value(data={self.data})"
|
return f"Value(data={self.data})"
|
||||||
|
|
@ -13,6 +32,11 @@ class Value:
|
||||||
def __add__(self, other):
|
def __add__(self, other):
|
||||||
out = Value(data=self.data + other.data,
|
out = Value(data=self.data + other.data,
|
||||||
_children=(self, other), _op='+')
|
_children=(self, other), _op='+')
|
||||||
|
|
||||||
|
def _backward():
|
||||||
|
self.grad = 1.0 * out.grad
|
||||||
|
other.grad = 1.0 * out.grad
|
||||||
|
out._backward = _backward
|
||||||
return out
|
return out
|
||||||
|
|
||||||
def __sub__(self, other):
|
def __sub__(self, other):
|
||||||
|
|
@ -23,4 +47,20 @@ class Value:
|
||||||
def __mul__(self, other):
|
def __mul__(self, other):
|
||||||
out = Value(data=self.data * other.data,
|
out = Value(data=self.data * other.data,
|
||||||
_children=(self, other), _op='*')
|
_children=(self, other), _op='*')
|
||||||
|
|
||||||
|
def _backward():
|
||||||
|
self.grad = other.data * out.grad
|
||||||
|
other.grad = self.data * out.grad
|
||||||
|
out._backward = _backward
|
||||||
|
return out
|
||||||
|
|
||||||
|
def tanh(self):
|
||||||
|
from math import exp
|
||||||
|
t = (exp(2 * self.data) - 1) / (exp(2 * self.data) + 1)
|
||||||
|
out = Value(data=t, _children=(self,),
|
||||||
|
_op='tanh', label='tanh')
|
||||||
|
|
||||||
|
def _backward():
|
||||||
|
self.grad = (1 - t**2) * out.grad
|
||||||
|
out._backward = _backward
|
||||||
return out
|
return out
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,104 @@
|
||||||
|
import pytest
|
||||||
|
from micrograd.engine import Value
|
||||||
|
|
||||||
|
|
||||||
|
def test_backward_tanh():
|
||||||
|
# inputs
|
||||||
|
x = Value(0.8814)
|
||||||
|
y = x.tanh()
|
||||||
|
y.grad = 1.0
|
||||||
|
y._backward()
|
||||||
|
|
||||||
|
assert pytest.approx(x.grad, 0.1) == 0.5
|
||||||
|
|
||||||
|
|
||||||
|
def test_large_backprop():
|
||||||
|
# inputs
|
||||||
|
x1 = Value(2.0, label='x1')
|
||||||
|
x2 = Value(0.0, label='x2')
|
||||||
|
|
||||||
|
# weights
|
||||||
|
w1 = Value(-3.0, label='w1')
|
||||||
|
w2 = Value(1.0, label='w2')
|
||||||
|
|
||||||
|
# bias
|
||||||
|
b = Value(6.8813735870195432, label='b')
|
||||||
|
|
||||||
|
h1 = x1 * w1
|
||||||
|
h1.label = 'h1'
|
||||||
|
h2 = x2 * w2
|
||||||
|
h2.label = 'h2'
|
||||||
|
|
||||||
|
h = h1 + h2
|
||||||
|
h.label = 'h'
|
||||||
|
|
||||||
|
n = h + b
|
||||||
|
n.label = 'n'
|
||||||
|
y = n.tanh()
|
||||||
|
y.label = 'y'
|
||||||
|
|
||||||
|
y.grad = 1.0
|
||||||
|
y._backward()
|
||||||
|
|
||||||
|
assert pytest.approx(n.grad, 0.001) == 0.5
|
||||||
|
assert h.grad == 0.0
|
||||||
|
|
||||||
|
n._backward()
|
||||||
|
assert pytest.approx(b.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(h.grad, 0.001) == 0.5
|
||||||
|
|
||||||
|
b._backward()
|
||||||
|
h._backward()
|
||||||
|
assert pytest.approx(h1.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(h2.grad, 0.001) == 0.5
|
||||||
|
|
||||||
|
h1._backward()
|
||||||
|
h2._backward()
|
||||||
|
assert pytest.approx(x1.grad, 0.001) == -1.5
|
||||||
|
assert pytest.approx(w1.grad, 0.001) == 1.0
|
||||||
|
|
||||||
|
assert pytest.approx(x2.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(w2.grad, 0.001) == 0.0
|
||||||
|
|
||||||
|
|
||||||
|
@pytest.mark.skip(reason="non-deterministic")
|
||||||
|
def test_auto_diff():
|
||||||
|
# inputs
|
||||||
|
x1 = Value(2.0, label='x1')
|
||||||
|
x2 = Value(0.0, label='x2')
|
||||||
|
|
||||||
|
# weights
|
||||||
|
w1 = Value(-3.0, label='w1')
|
||||||
|
w2 = Value(1.0, label='w2')
|
||||||
|
|
||||||
|
# bias
|
||||||
|
b = Value(6.8813735870195432, label='b')
|
||||||
|
|
||||||
|
h1 = x1 * w1
|
||||||
|
h1.label = 'h1'
|
||||||
|
h2 = x2 * w2
|
||||||
|
h2.label = 'h2'
|
||||||
|
|
||||||
|
h = h1 + h2
|
||||||
|
h.label = 'h'
|
||||||
|
|
||||||
|
n = h + b
|
||||||
|
n.label = 'n'
|
||||||
|
y = n.tanh()
|
||||||
|
y.label = 'y'
|
||||||
|
|
||||||
|
y.backward()
|
||||||
|
assert pytest.approx(n.grad, 0.001) == 0.5
|
||||||
|
assert h.grad == 0.0
|
||||||
|
|
||||||
|
assert pytest.approx(b.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(h.grad, 0.001) == 0.5
|
||||||
|
|
||||||
|
assert pytest.approx(h1.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(h2.grad, 0.001) == 0.5
|
||||||
|
|
||||||
|
assert pytest.approx(x1.grad, 0.001) == -1.5
|
||||||
|
assert pytest.approx(w1.grad, 0.001) == 1.0
|
||||||
|
|
||||||
|
assert pytest.approx(x2.grad, 0.001) == 0.5
|
||||||
|
assert pytest.approx(w2.grad, 0.001) == 0.0
|
||||||
|
|
@ -0,0 +1,31 @@
|
||||||
|
import pytest
|
||||||
|
from micrograd.engine import Value
|
||||||
|
|
||||||
|
|
||||||
|
# @pytest.mark.skip(reason="complicated assertion")
|
||||||
|
def test_big_neuron():
|
||||||
|
# inputs
|
||||||
|
x1 = Value(2.0, label='x1')
|
||||||
|
x2 = Value(0.0, label='x2')
|
||||||
|
|
||||||
|
# weights
|
||||||
|
w1 = Value(-3.0, label='w1')
|
||||||
|
w2 = Value(1.0, label='w2')
|
||||||
|
|
||||||
|
# bias
|
||||||
|
b = Value(6.8813735870195432, label='b')
|
||||||
|
|
||||||
|
h1 = x1 * w1
|
||||||
|
h1.label = 'h1'
|
||||||
|
h2 = x2 * w2
|
||||||
|
h2.label = 'h2'
|
||||||
|
|
||||||
|
h = h1 + h2
|
||||||
|
h.label = 'h'
|
||||||
|
|
||||||
|
n = h + b
|
||||||
|
n.label = 'n'
|
||||||
|
y = n.tanh()
|
||||||
|
y.label = 'y'
|
||||||
|
|
||||||
|
assert pytest.approx(y.data, 0.01) == 0.7071
|
||||||
|
|
@ -56,3 +56,16 @@ def test_operations():
|
||||||
add = v1 + v2
|
add = v1 + v2
|
||||||
assert mul._op == '*'
|
assert mul._op == '*'
|
||||||
assert add._op == '+'
|
assert add._op == '+'
|
||||||
|
|
||||||
|
|
||||||
|
def test_tanh():
|
||||||
|
t = Value(2.0).tanh()
|
||||||
|
assert t.data > 0
|
||||||
|
assert t.data < 1
|
||||||
|
|
||||||
|
t = Value(0.0).tanh()
|
||||||
|
assert t.data == 0
|
||||||
|
|
||||||
|
t = Value(-2.0).tanh()
|
||||||
|
assert t.data < 0
|
||||||
|
assert t.data > -1
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue