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‎tiny_autograd_tutorial.ipynb‎

Lines changed: 191 additions & 25 deletions
Original file line numberDiff line numberDiff line change
@@ -39,15 +39,15 @@
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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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"execution_count": 33,
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"metadata": {},
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"outputs": [],
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"source": [
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"from __future__ import annotations\n",
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"\n",
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"import math\n",
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"from dataclasses import dataclass, field\n",
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"from typing import Callable, Set\n",
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"from typing import Callable\n",
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"\n",
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"\n",
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"@dataclass\n",
@@ -61,7 +61,7 @@
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" _backward: 역전파 시 실행할 함수\n",
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" \"\"\"\n",
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" data: float\n",
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" _prev: Set[Value] = field(default_factory=set, repr=False)\n",
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" _prev: set[Value] = field(default_factory=set, repr=False)\n",
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" _backward: Callable[[], None] = field(default=lambda: None, repr=False)\n",
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" grad: float = 0.0\n",
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"\n",
@@ -70,8 +70,48 @@
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" raise TypeError(\"Value.data must be a number\")\n",
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" self.data = float(self.data)\n",
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"\n",
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" def __repr__(self) -> str:\n",
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" return f\"Value(data={self.data:.6f}, grad={self.grad:.6f})\""
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" def __repr__(self) -> str:\n",
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" return f\"Value(data={self.data:.6f}, grad={self.grad:.6f})\"\n",
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" \n",
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" def __hash__(self) -> int:\n",
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" return id(self)\n",
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"\n",
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" def __eq__(self, other) -> bool:\n",
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" return self is other"
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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": 30,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[1]\n",
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"[1, 2]\n",
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"[1]\n",
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"[2]\n"
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]
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}
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],
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"source": [
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"def append_item(x, items=[]): # 가변 기본값\n",
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" items.append(x)\n",
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" return items\n",
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"\n",
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"def append_item2(x, items=None):\n",
105+
" if items is None:\n",
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" items = []\n",
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" items.append(x)\n",
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" return items\n",
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"\n",
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"print(append_item(1)) # [1]\n",
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"print(append_item(2)) # [1, 2] ← 이전 호출과 공유됨\n",
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"\n",
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"print(append_item2(1)) # [1]\n",
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"print(append_item2(2)) # [2]"
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]
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},
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{
@@ -88,7 +128,7 @@
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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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"execution_count": 34,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -120,6 +160,33 @@
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"Value.__radd__ = lambda self, other: self.__add__(other)"
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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": 36,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Value(data=5.0, grad=0.0)\n",
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"Value(data=5.0, grad=0.0)\n"
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]
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}
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],
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"source": [
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"hasattr(Value, \"__add__\") # True가 나와야 정상\n",
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"\n",
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"a = Value(3.0)\n",
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"\n",
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"# 왼쪽이 숫자라서, int.__add__가 Value를 모르면 a.__radd__(2)가 호출됨\n",
183+
"c1 = 2 + a # __radd__ 경유 → __add__ 재사용\n",
184+
"c2 = a + 2 # __add__\n",
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"\n",
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"print(c1)\n",
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"print(c2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
@@ -129,9 +196,20 @@
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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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"execution_count": 37,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"a = Value(data=2.0, grad=0.0)\n",
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"b = Value(data=3.0, grad=0.0)\n",
208+
"c = a + b = Value(data=5.0, grad=0.0)\n",
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"c의 부모 노드들: {Value(data=2.0, grad=0.0), Value(data=3.0, grad=0.0)}\n"
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]
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}
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],
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"source": [
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"# 간단한 덧셈 예제\n",
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"a = Value(2.0)\n",
@@ -158,7 +236,7 @@
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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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"execution_count": 38,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -175,6 +253,7 @@
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"\n",
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" def _backward() -> None:\n",
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" # Product rule 적용\n",
256+
" print(\"backward is called, self.grad = \", self.grad, \"other.grad = \", other.grad, \"out.grad = \", out.grad)\n",
178257
" self.grad += other.data * out.grad # d(a*b)/da = b\n",
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" other.grad += self.data * out.grad # d(a*b)/db = a\n",
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"\n",
@@ -194,9 +273,20 @@
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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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"execution_count": 45,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"x = Value(data=3.0, grad=0.0)\n",
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"y = Value(data=4.0, grad=0.0)\n",
285+
"z = x * y = Value(data=12.0, grad=0.0)\n",
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"w = z * 2 = Value(data=24.0, grad=0.0)\n"
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]
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}
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],
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"source": [
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"# 곱셈 예제\n",
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"x = Value(3.0)\n",
@@ -225,7 +315,7 @@
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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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"execution_count": 46,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -260,7 +350,7 @@
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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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"execution_count": 47,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -295,7 +385,7 @@
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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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"execution_count": 48,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -344,7 +434,7 @@
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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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"execution_count": 49,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -430,6 +520,12 @@
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" self.grad = 1.0\n",
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" for v in reversed(topo):\n",
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" v._backward()\n",
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" \n",
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" def __hash__(self) -> int:\n",
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" return id(self)\n",
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"\n",
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" def __eq__(self, other) -> bool:\n",
528+
" return self is other\n",
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"\n",
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" def __repr__(self) -> str:\n",
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" return f\"Value(data={self.data:.6f}, grad={self.grad:.6f})\""
@@ -448,9 +544,28 @@
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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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"execution_count": 51,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"=== Forward Pass ===\n",
555+
"a = 1.300000\n",
556+
"b = -0.700000\n",
557+
"c = a * b = -0.910000\n",
558+
"d = c + a = 0.390000\n",
559+
"e = tanh(b) = -0.604368\n",
560+
"out = d * e = -0.235703\n",
561+
"\n",
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"=== Backward Pass ===\n",
563+
"∂out/∂a = -0.181310\n",
564+
"∂out/∂b = -0.538130\n",
565+
"(Value(data=-0.235703, grad=1.000000), -0.18131033313514905, -0.5381296701591537)\n"
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]
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}
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],
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"source": [
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"# 복잡한 함수 예제\n",
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"def test_complex_function():\n",
@@ -481,7 +596,8 @@
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" \n",
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" return out, a.grad, b.grad\n",
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"\n",
484-
"result = test_complex_function()"
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"result = test_complex_function()\n",
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"print(result)"
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]
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},
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{
@@ -495,9 +611,34 @@
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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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"execution_count": 25,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"테스트 케이스: a=1.3, b=-0.7\n",
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" 자동미분: ∂f/∂a = -0.18131033, ∂f/∂b = -0.53812967\n",
624+
" 수치미분: ∂f/∂a = -0.18131033, ∂f/∂b = -0.53812967\n",
625+
" 상대오차: a = 9.15e-13, b = 1.26e-11\n",
626+
" 통과: True\n",
627+
"\n",
628+
"테스트 케이스: a=0.5, b=0.5\n",
629+
" 자동미분: ∂f/∂a = 0.69317574, ∂f/∂b = 0.82089438\n",
630+
" 수치미분: ∂f/∂a = 0.69317574, ∂f/∂b = 0.82089438\n",
631+
" 상대오차: a = 4.10e-12, b = 2.06e-11\n",
632+
" 통과: True\n",
633+
"\n",
634+
"테스트 케이스: a=-1.2, b=2.0\n",
635+
" 자동미분: ∂f/∂a = 2.89208274, ∂f/∂b = -1.41117607\n",
636+
" 수치미분: ∂f/∂a = 2.89208274, ∂f/∂b = -1.41117607\n",
637+
" 상대오차: a = 9.31e-11, b = 3.11e-10\n",
638+
" 통과: True\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
@@ -564,9 +705,34 @@
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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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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"=== 연산 그래프 구조 ===\n",
717+
"노드 개수: 5\n",
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"엣지 개수: 5\n",
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"\n",
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"노드 정보:\n",
721+
" Node 0: data=1.0000, grad=1.0000\n",
722+
" Node 1: data=3.0000, grad=0.0000\n",
723+
" Node 2: data=2.0000, grad=0.0000\n",
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" Node 3: data=6.0000, grad=0.0000\n",
725+
" Node 4: data=8.0000, grad=0.0000\n",
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"\n",
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"연결 정보:\n",
728+
" 2.0000 -> 6.0000\n",
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" 6.0000 -> 8.0000\n",
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" 2.0000 -> 8.0000\n",
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" 3.0000 -> 6.0000\n",
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" 8.0000 -> 1.0000\n"
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]
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}
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],
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"source": [
571737
"def trace_graph(root):\n",
572738
" \"\"\"연산 그래프 추적\"\"\"\n",
@@ -728,7 +894,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"display_name": "ai",
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"language": "python",
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"name": "python3"
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},
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.0"
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"version": "3.11.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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}

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