add backprop.

This commit is contained in:
publicmatt 2024-02-22 08:41:04 -08:00
parent 0ed01f7a84
commit 6cf0186544
5 changed files with 621 additions and 145 deletions

View File

@ -39,168 +39,182 @@
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]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# inputs\n",
"x1 = Value(2.0, label='x1')\n",
"x2 = Value(0.0, label='x2')\n",
"\n",
"# weights\n",
"w1 = Value(-3.0, label='w1')\n",
"w2 = Value(1.0, label='w2')\n",
"\n",
"# bias\n",
"b = Value(6.2, label='b')\n",
"\n",
"h1 = x1 * w1\n",
"h1.label = 'h1'\n",
"h2 = x2 * w2\n",
"h2.label = 'h2'\n",
"\n",
"h = h1 + h2\n",
"h.label = 'h'\n",
"\n",
"n = h + b\n",
"n.label = 'n'\n",
"y = n.tanh()\n",
"y.label = 'y'\n",
"\n",
"draw_dot(y)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "543bd866-2ce7-4b9a-8d8b-55a160a7c83b",
"metadata": {},
"outputs": [], "outputs": [],
"source": [] "source": []
} }

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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

104
test/test_backprop.py Normal file
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@ -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

31
test/test_neuron.py Normal file
View File

@ -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

View File

@ -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