Code
import math
class Value:
def __init__(self, data, _children=(), _op=''):
self.data = data
self.grad = 0.0
self._backward = lambda :None
self._prev = set(_children)
self._op = _op
def __repr__(self):
return f"Value(data={self.data}, grad={self.grad})"
def __add__(self, other):
other = other if isinstance(other, Value) else Value(other)
out = Value(self.data + other.data, (self, other), '+')
def _backward():
self.grad += 1.0 * out.grad
other.grad += 1.0 * out.grad
out._backward = _backward
return out
def __radd__(self, other):
return self + other
def __mul__(self, other):
other = other if isinstance(other, Value) else Value(other)
out = Value(self.data * other.data, (self, other), '*')
def _backward():
self.grad += other.data * out.grad
other.grad += self.data * out.grad
out._backward = _backward
return out
def __rmul__(self, other): # karpathy knows too much
return self * other
def __truediv__(self, other):
return self * other**-1
def __sub__(self, other):
return self + (other * -1) #LOL
def __pow__(self, other):
assert isinstance(other, (int, float))
out = Value(self.data ** other, (self, ), f'**{other}')
def _backward():
self.grad += other * self.data**(other-1) * out.grad
out._backward = _backward
return out
def tanh(self):
x = self.data
t = (math.exp(2*x)-1)/(math.exp(2*x)+1)
out = Value(t, (self, ), 'tanh')
def _backward():
self.grad += (1 - t**2) * out.grad
out._backward = _backward
return out
def exp(self):
x = self.data
out = Value(math.exp(x), (self, ), 'exp')
def _backward():
self.grad += out.data * out.grad
out._backward = _backward
return out
def backward(self):
"""implements topological sort and calls the _backward method in a reversed order"""
topo = []
visited = set()
def build_topo(v):
if v not in visited:
visited.add(v)
for child in v._prev:
build_topo(child)
topo.append(v)
build_topo(self)
self.grad = 1.0
for node in reversed(topo):
node._backward() import random
class Neuron:
def __init__(self, nin):
# nin = number of inputs
self.w = [Value(random.uniform(-1,1)) for _ in range(nin)]
self.b = Value(random.uniform(-1,1))
def parameters(self):
return self.w + [self.b]
def __call__(self, x):
# this is wild; you can call an instance of Neuron as n(x) :O
# x are the inputs, we are taking a dot product:
act = sum((wi*xi for wi, xi in zip(self.w, x)), self.b) # sum can take an optional starting value: self.b
out = act.tanh()
return out
class Layer:
def __init__(self, nin, nout):
self.neurons = [Neuron(nin) for _ in range(nout)]
def __call__(self, x):
outs = [n(x) for n in self.neurons]
return outs[0] if len(outs) == 1 else outs
def parameters(self):
return [p for neuron in self.neurons for p in neuron.parameters()]
class MLP:
def __init__(self, nin, nouts):
sz = [nin] + nouts
self.layers = [Layer(sz[i], sz[i+1]) for i in range(len(nouts))]
def __call__(self, x):
for layer in self.layers:
x = layer(x)
return x
def parameters(self):
return [p for layer in self.layers for p in layer.parameters()] n = MLP(3, [4,4,1])
xs = [
[2.0, 3.0, -1, 0],
[3.0, -1.0, 0.5],
[0.5, 1.0, 1.0],
[1.0, 1.0, -1.0]
]
ys = [1.0, -1.0, -1.0, 1.0] for k in range(20):
ypred = [n(x) for x in xs]
loss = sum((yout - ygt)**2 for ygt, yout in zip(ys, ypred))
for p in n.parameters(): # without this, you accumulate the gradients and create an artificial momentum.
p.grad = 0.0
loss.backward()
for p in n.parameters():
p.data += -0.01 * p.grad
print(k, loss.data)0 6.827977524064868 1 6.564699072251051 2 6.231394384341386 3 5.851082578630887 4 5.468387820425157 5 5.114416471232759 6 4.795337579218638 7 4.5056247601912105 8 4.237419335600638 9 3.9834296130886995 10 3.7377002240069004 11 3.4958631215074445 12 3.2552411075315213 13 3.0149114257272585 14 2.775727346928721 15 2.5401826675264108 16 2.3119463645904297 17 2.0950143399155294 18 1.8927285043107416 19 1.7071191357642472
ypred| Value | (data=0.5774378654478666 grad=-0.8451242691042669) | Value | (data=-0.708228299005086 grad=0.583543401989828) | Value | (data=-0.2457719356156506 grad=1.5084561287686988) | Value | (data=0.06481569752237379 grad=-1.8703686049552524) |
References
https://www.youtube.com/watch?v=VMj-3S1tku0&list=PLAqhIrjkxbuWI23v9cThsA9GvCAUhRvKZ
ttt
Andrej Karpathy Video
Code
Pulling the dataset we will be working on:
curl https://raw.githubusercontent.com/karpathy/char-rnn/master/data/tinyshakespeare/input.txt -o input.txtReading it into python
with open('input.txt', 'r', encoding='utf-8') as f:
text = f.read()Data inspection
print("length of dataset in characters: ", len(text))
print("length of data: ", len(data))length of dataset in characters: 1115394 length of data: 1115394
print(text[:1000])First Citizen: Before we proceed any further, hear me speak. All: Speak, speak. First Citizen: You are all resolved rather to die than to famish? All: Resolved. resolved. First Citizen: First, you know Caius Marcius is chief enemy to the people. All: We know't, we know't. First Citizen: Let us kill him, and we'll have corn at our own price. Is't a verdict? All: No more talking on't; let it be done: away, away! Second Citizen: One word, good citizens. First Citizen: We are accounted poor citizens, the patricians good. What authority surfeits on would relieve us: if they would yield us but the superfluity, while it were wholesome, we might guess they relieved us humanely; but they think we are too dear: the leanness that afflicts us, the object of our misery, is as an inventory to particularise their abundance; our sufferance is a gain to them Let us revenge this with our pikes, ere we become rakes: for the gods know I speak this in hunger for bread, not in thirst for revenge.
chars = sorted(list(set(text)))
vocab_size = len(chars)
print(''.join(chars))
print(vocab_size)!$&',-.3:;?ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz 65
Tokeniser
stoi = { ch:i for i,ch in enumerate(chars) }
itos = { i:ch for i,ch in enumerate(chars) }
encode = lambda s: [stoi[c] for c in s]
# defines function taking in string, outputs list of ints
decode = lambda l: ''.join([itos[i] for i in l])
# input: list of integers, outputs string
print(encode("hello world"))
print(decode(encode("hello world")))[46, 43, 50, 50, 53, 1, 61, 53, 56, 50, 42] hello world
import torch
data = torch.tensor(encode(text), dtype=torch.long)
print(data.shape, data.dtype)
print(data[:1000])
torch.Size([1115394]) torch.int64
tensor([18, 47, 56, 57, 58, 1, 15, 47, 58, 47, 64, 43, 52, 10, 0, 14, 43, 44,
53, 56, 43, 1, 61, 43, 1, 54, 56, 53, 41, 43, 43, 42, 1, 39, 52, 63,
1, 44, 59, 56, 58, 46, 43, 56, 6, 1, 46, 43, 39, 56, 1, 51, 43, 1,
57, 54, 43, 39, 49, 8, 0, 0, 13, 50, 50, 10, 0, 31, 54, 43, 39, 49,
6, 1, 57, 54, 43, 39, 49, 8, 0, 0, 18, 47, 56, 57, 58, 1, 15, 47,
58, 47, 64, 43, 52, 10, 0, 37, 53, 59, 1, 39, 56, 43, 1, 39, 50, 50,
1, 56, 43, 57, 53, 50, 60, 43, 42, 1, 56, 39, 58, 46, 43, 56, 1, 58,
53, 1, 42, 47, 43, 1, 58, 46, 39, 52, 1, 58, 53, 1, 44, 39, 51, 47,
57, 46, 12, 0, 0, 13, 50, 50, 10, 0, 30, 43, 57, 53, 50, 60, 43, 42,
8, 1, 56, 43, 57, 53, 50, 60, 43, 42, 8, 0, 0, 18, 47, 56, 57, 58,
1, 15, 47, 58, 47, 64, 43, 52, 10, 0, 18, 47, 56, 57, 58, 6, 1, 63,
53, 59, 1, 49, 52, 53, 61, 1, 15, 39, 47, 59, 57, 1, 25, 39, 56, 41,
47, 59, 57, 1, 47, 57, 1, 41, 46, 47, 43, 44, 1, 43, 52, 43, 51, 63,
1, 58, 53, 1, 58, 46, 43, 1, 54, 43, 53, 54, 50, 43, 8, 0, 0, 13,
50, 50, 10, 0, 35, 43, 1, 49, 52, 53, 61, 5, 58, 6, 1, 61, 43, 1,
49, 52, 53, 61, 5, 58, 8, 0, 0, 18, 47, 56, 57, 58, 1, 15, 47, 58,
47, 64, 43, 52, 10, 0, 24, 43, 58, 1, 59, 57, 1, 49, 47, 50, 50, 1,
46, 47, 51, 6, 1, 39, 52, 42, 1, 61, 43, 5, 50, 50, 1, 46, 39, 60,
43, 1, 41, 53, 56, 52, 1, 39, 58, 1, 53, 59, 56, 1, 53, 61, 52, 1,
54, 56, 47, 41, 43, 8, 0, 21, 57, 5, 58, 1, 39, 1, 60, 43, 56, 42,
47, 41, 58, 12, 0, 0, 13, 50, 50, 10, 0, 26, 53, 1, 51, 53, 56, 43,
1, 58, 39, 50, 49, 47, 52, 45, 1, 53, 52, 5, 58, 11, 1, 50, 43, 58,
1, 47, 58, 1, 40, 43, 1, 42, 53, 52, 43, 10, 1, 39, 61, 39, 63, 6,
1, 39, 61, 39, 63, 2, 0, 0, 31, 43, 41, 53, 52, 42, 1, 15, 47, 58,
47, 64, 43, 52, 10, 0, 27, 52, 43, 1, 61, 53, 56, 42, 6, 1, 45, 53,
53, 42, 1, 41, 47, 58, 47, 64, 43, 52, 57, 8, 0, 0, 18, 47, 56, 57,
58, 1, 15, 47, 58, 47, 64, 43, 52, 10, 0, 35, 43, 1, 39, 56, 43, 1,
39, 41, 41, 53, 59, 52, 58, 43, 42, 1, 54, 53, 53, 56, 1, 41, 47, 58,
47, 64, 43, 52, 57, 6, 1, 58, 46, 43, 1, 54, 39, 58, 56, 47, 41, 47,
39, 52, 57, 1, 45, 53, 53, 42, 8, 0, 35, 46, 39, 58, 1, 39, 59, 58,
46, 53, 56, 47, 58, 63, 1, 57, 59, 56, 44, 43, 47, 58, 57, 1, 53, 52,
1, 61, 53, 59, 50, 42, 1, 56, 43, 50, 47, 43, 60, 43, 1, 59, 57, 10,
1, 47, 44, 1, 58, 46, 43, 63, 0, 61, 53, 59, 50, 42, 1, 63, 47, 43,
50, 42, 1, 59, 57, 1, 40, 59, 58, 1, 58, 46, 43, 1, 57, 59, 54, 43,
56, 44, 50, 59, 47, 58, 63, 6, 1, 61, 46, 47, 50, 43, 1, 47, 58, 1,
61, 43, 56, 43, 0, 61, 46, 53, 50, 43, 57, 53, 51, 43, 6, 1, 61, 43,
1, 51, 47, 45, 46, 58, 1, 45, 59, 43, 57, 57, 1, 58, 46, 43, 63, 1,
56, 43, 50, 47, 43, 60, 43, 42, 1, 59, 57, 1, 46, 59, 51, 39, 52, 43,
50, 63, 11, 0, 40, 59, 58, 1, 58, 46, 43, 63, 1, 58, 46, 47, 52, 49,
1, 61, 43, 1, 39, 56, 43, 1, 58, 53, 53, 1, 42, 43, 39, 56, 10, 1,
58, 46, 43, 1, 50, 43, 39, 52, 52, 43, 57, 57, 1, 58, 46, 39, 58, 0,
39, 44, 44, 50, 47, 41, 58, 57, 1, 59, 57, 6, 1, 58, 46, 43, 1, 53,
40, 48, 43, 41, 58, 1, 53, 44, 1, 53, 59, 56, 1, 51, 47, 57, 43, 56,
63, 6, 1, 47, 57, 1, 39, 57, 1, 39, 52, 0, 47, 52, 60, 43, 52, 58,
53, 56, 63, 1, 58, 53, 1, 54, 39, 56, 58, 47, 41, 59, 50, 39, 56, 47,
57, 43, 1, 58, 46, 43, 47, 56, 1, 39, 40, 59, 52, 42, 39, 52, 41, 43,
11, 1, 53, 59, 56, 0, 57, 59, 44, 44, 43, 56, 39, 52, 41, 43, 1, 47,
57, 1, 39, 1, 45, 39, 47, 52, 1, 58, 53, 1, 58, 46, 43, 51, 1, 24,
43, 58, 1, 59, 57, 1, 56, 43, 60, 43, 52, 45, 43, 1, 58, 46, 47, 57,
1, 61, 47, 58, 46, 0, 53, 59, 56, 1, 54, 47, 49, 43, 57, 6, 1, 43,
56, 43, 1, 61, 43, 1, 40, 43, 41, 53, 51, 43, 1, 56, 39, 49, 43, 57,
10, 1, 44, 53, 56, 1, 58, 46, 43, 1, 45, 53, 42, 57, 1, 49, 52, 53,
61, 1, 21, 0, 57, 54, 43, 39, 49, 1, 58, 46, 47, 57, 1, 47, 52, 1,
46, 59, 52, 45, 43, 56, 1, 44, 53, 56, 1, 40, 56, 43, 39, 42, 6, 1,
52, 53, 58, 1, 47, 52, 1, 58, 46, 47, 56, 57, 58, 1, 44, 53, 56, 1,
56, 43, 60, 43, 52, 45, 43, 8, 0, 0])
n = int(0.9*len(data))
train_data = data[:n]
val_data = data[n:]Understanding the context influence of n+1th token
block_size = 8
print(train_data[:block_size])
x = train_data[:block_size]
y = train_data[1:block_size+1]
for t in range(block_size):
context = x[:t+1]
target = y[t]
print(f"at input {context}\n" +
f"target {target}")tensor([18, 47, 56, 57, 58, 1, 15, 47]) at input tensor([18]) target 47 at input tensor([18, 47]) target 56 at input tensor([18, 47, 56]) target 57 at input tensor([18, 47, 56, 57]) target 58 at input tensor([18, 47, 56, 57, 58]) target 1 at input tensor([18, 47, 56, 57, 58, 1]) target 15 at input tensor([18, 47, 56, 57, 58, 1, 15]) target 47 at input tensor([18, 47, 56, 57, 58, 1, 15, 47]) target 58
Note that within the block_size of 8, there are 8 total examples.