Autograd：逆伝播のための自動微分
スカラー計算グラフを定義し、.backward()を呼び出して、葉テンソルの.gradを確認しながら、勾配がネットワークを通って流れる仕組みを理解します。
「Autograd：逆伝播のための自動微分」はCoddyKit上の無料Machine Learning Academyレッスンです。 これはレッスン2/4です。 下記で完全なレッスンを無料で読むことができます。その後、ブラウザ内の組み込みコードエディタと24時間対応のAIチューターでハンズオン演習できます。 これはMachine Learning Academy学習パスの一部であり、ウェブとCoddyKitアプリ全体で進捗が同期されます。 Machine Learning Academyコースには全4レッスンが含まれています。
このレッスンの一部はまだ翻訳されておらず、英語で表示されています。
What Is Automatic Differentiation?
Automatic differentiation (autograd) is the engine that computes gradients in PyTorch without requiring the programmer to derive them by hand. Unlike numerical differentiation (finite differences) or symbolic differentiation (algebra), autograd works by recording operations on tensors at runtime and replaying them in reverse. This makes it possible to train models of any architecture efficiently and correctly.
import torch
# A simple differentiable computation
x = torch.tensor(3.0, requires_grad=True)
y = x ** 2 + 2 * x + 1 # y = (x+1)^2
# Compute gradient dy/dx
y.backward()
print(x.grad) # tensor(8.) because dy/dx = 2x+2 = 2*3+2 = 8requires_grad: Enabling Gradient Tracking
Gradient tracking is disabled by default. Setting requires_grad=True tells PyTorch to record all operations on that tensor so gradients can be computed later. Leaf tensors (parameters) require gradients; intermediate tensors inherit gradient-tracking from their parents automatically. Model parameters created by nn.Module have requires_grad=True set automatically.
import torch
# Leaf tensor with gradient tracking
w = torch.tensor(2.0, requires_grad=True)
b = torch.tensor(0.5, requires_grad=True)
# Forward pass
x = torch.tensor(3.0) # input, no grad needed
y_pred = w * x + b # y = wx + b = 6.5
print(y_pred.requires_grad) # True (inherited)
print(w.is_leaf) # True
print(y_pred.is_leaf) # FalseThe Computation Graph
As you perform operations on tensors with requires_grad=True, PyTorch builds a dynamic computation graph (a directed acyclic graph of operations). Each node stores the operation and references to its inputs. When .backward() is called, PyTorch traverses this graph in reverse (from output to inputs) using the chain rule to compute partial derivatives for every leaf tensor. The graph is re-built fresh on each forward pass, enabling dynamic architectures.
import torch
a = torch.tensor(2.0, requires_grad=True)
b = torch.tensor(3.0, requires_grad=True)
# Build computation graph
c = a * b # c = 6
d = c + a # d = 8
e = d ** 2 # e = 64
# Inspect graph node
print(e.grad_fn) # <PowBackward0 object>
print(e.grad_fn.next_functions) # parents in the graphCalling .backward(): Computing Gradients
Calling .backward() on a scalar tensor triggers backpropagation through the entire computation graph, depositing gradients into the .grad attribute of each leaf tensor. If the output is not scalar, you must provide a gradient tensor of the same shape (the upstream gradient). Gradients accumulate by default — always call optimizer.zero_grad() (or tensor.grad.zero_()) before the next backward pass to avoid incorrect updates.
import torch
x = torch.tensor(4.0, requires_grad=True)
loss = (x - 1) ** 2 # minimum at x=1
loss.backward()
print(x.grad) # tensor(6.) = 2*(x-1) = 2*3 = 6
# Gradients accumulate! Reset before next pass
x.grad.zero_()
new_loss = (x - 2) ** 2
new_loss.backward()
print(x.grad) # tensor(4.) = 2*(x-2) = 2*2 = 4Gradient Flow Through Multiple Operations
The chain rule states that the derivative of a composition of functions is the product of derivatives. Autograd applies this mechanically through every operation in the graph. Understanding how gradients flow helps debug issues like vanishing gradients (products near zero) and exploding gradients (products greater than 1 repeated many times). Activation function choice (ReLU vs sigmoid) directly affects gradient magnitudes.
import torch
# Chain: z = sigmoid(wx + b), loss = (z - y_true)^2
def sigmoid(x):
return 1 / (1 + torch.exp(-x))
w = torch.tensor(0.5, requires_grad=True)
b = torch.tensor(0.0, requires_grad=True)
x = torch.tensor(2.0)
y_true = torch.tensor(1.0)
z = sigmoid(w * x + b)
loss = (z - y_true) ** 2
loss.backward()
print(f'dL/dw = {w.grad:.4f}') # gradient w.r.t. weight
print(f'dL/db = {b.grad:.4f}') # gradient w.r.t. biastorch.no_grad(): Disabling Gradient Tracking
During inference (prediction on new data), you do not need gradients — computing them wastes time and memory. Wrapping inference code with torch.no_grad() disables the computation graph entirely, speeding up forward passes and reducing memory usage by up to 50%. This is also used during evaluation loops to get validation metrics without influencing training.
import torch
x = torch.randn(100, requires_grad=True)
# With gradient tracking (training)
out = x ** 2
print(out.requires_grad) # True
# Without gradient tracking (inference)
with torch.no_grad():
out_no_grad = x ** 2
print(out_no_grad.requires_grad) # False
# Also used as a decorator
@torch.no_grad()
def predict(model, data):
return model(data)Gradient Accumulation Issue and zero_grad
PyTorch accumulates (adds) gradients into .grad each time .backward() is called. This is intentional for some advanced techniques, but during normal training it means you must zero gradients before each backward pass. The standard idiom uses the optimizer's zero_grad() method, which clears gradients for all parameters the optimizer manages. Forgetting this step leads to gradients growing unboundedly, corrupting updates.
import torch
import torch.nn as nn
import torch.optim as optim
model = nn.Linear(2, 1)
optimizer = optim.SGD(model.parameters(), lr=0.01)
for epoch in range(3):
optimizer.zero_grad() # clear old gradients
x = torch.randn(4, 2)
y_pred = model(x)
loss = y_pred.sum()
loss.backward() # compute new gradients
optimizer.step() # update weights
print(f'Epoch {epoch}: loss={loss.item():.3f}')Inspecting Gradient Values for Debugging
Inspecting gradient values is crucial for diagnosing training problems. You can access them via tensor.grad after calling backward. Plotting the gradient norm across layers reveals whether gradients vanish (near zero) or explode (very large) in deep networks. A common debugging hook is to print gradient statistics after every N batches to detect instability early in training.
import torch
import torch.nn as nn
model = nn.Sequential(
nn.Linear(4, 8),
nn.ReLU(),
nn.Linear(8, 1)
)
x = torch.randn(16, 4)
y_pred = model(x)
loss = y_pred.mean()
loss.backward()
# Inspect gradients of each parameter
for name, param in model.named_parameters():
if param.grad is not None:
norm = param.grad.norm().item()
print(f'{name}: grad_norm={norm:.4f}')Detaching Tensors from the Graph
Sometimes you want to use a computed tensor as a constant input to another computation — without letting gradients flow through it. .detach() returns a new tensor that shares data but is removed from the computation graph. This is used in target networks (reinforcement learning), stopping gradient flow in specific branches of a network, and converting tensors to NumPy arrays for plotting.
import torch
a = torch.tensor(3.0, requires_grad=True)
b = a * 2 # b depends on a
c = b.detach() # c is a constant copy of b's value
d = c * 5 # gradient does NOT flow back to a
d.backward()
# a.grad is None because c severed the graph
print(a.grad) # None
# Detach before converting to NumPy
np_val = b.detach().numpy()
print(np_val) # [6.0] (as NumPy array)Second-Order Gradients with create_graph
PyTorch supports higher-order differentiation. Passing create_graph=True to .backward() keeps the computation graph for the gradient computation itself, allowing you to differentiate through gradients. This is used in meta-learning (MAML), gradient penalty regularisation (Wasserstein GAN), and any technique that optimises with respect to gradients.
import torch
x = torch.tensor(2.0, requires_grad=True)
y = x ** 3 # y = x^3
# First derivative dy/dx = 3x^2
dy = torch.autograd.grad(y, x, create_graph=True)[0]
print(dy) # tensor(12., grad_fn=...)
# Second derivative d^2y/dx^2 = 6x
d2y = torch.autograd.grad(dy, x)[0]
print(d2y) # tensor(6.)Autograd in the Training Pipeline
Autograd is the foundation of every neural network training loop. The standard four-step pattern is: (1) zero gradients with optimizer.zero_grad(), (2) forward pass to compute predictions and loss, (3) backward pass with loss.backward() to compute gradients, and (4) optimizer step with optimizer.step() to update parameters. Understanding that autograd is doing the heavy calculus work lets you focus on model architecture and hyperparameters.
import torch
import torch.nn as nn
import torch.optim as optim
model = nn.Linear(1, 1)
optimizer = optim.SGD(model.parameters(), lr=0.1)
criterion = nn.MSELoss()
# Synthetic data: y = 3x + 1
X = torch.randn(20, 1)
y = 3 * X + 1 + 0.1 * torch.randn(20, 1)
for epoch in range(5):
optimizer.zero_grad() # (1) zero grads
y_pred = model(X) # (2) forward
loss = criterion(y_pred, y) # (2) loss
loss.backward() # (3) backward
optimizer.step() # (4) update
print(f'Epoch {epoch}: loss={loss.item():.4f}')Quick Check
Test your understanding of Machine Learning with Python concepts from this lesson.
Lesson Recap
In this lesson you learned: autograd builds a dynamic computation graph recording every operation on tensors with requires_grad=True, .backward() computes gradients via the chain rule and deposits them in .grad, and gradients accumulate so you must zero them before each training step. Next up we explore building a feedforward network with nn.Module.
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よくある質問
「Autograd：逆伝播のための自動微分」レッスンは無料ですか？
はい。「Autograd：逆伝播のための自動微分」の完全なテキストはこのウェブで無料で読めます。インタラクティブに演習し（組み込みコードエディタと24時間対応のAIチューター）、Machine Learning Academyコースの残りをアンロックするには、CoddyKit PROにアップグレードしてください。 Machine Learning Academyコースには全4レッスンが含まれています。
「Autograd：逆伝播のための自動微分」で何を学びますか？
スカラー計算グラフを定義し、.backward()を呼び出して、葉テンソルの.gradを確認しながら、勾配がネットワークを通って流れる仕組みを理解します。 ブラウザで直接実行するハンズオンコードでMachine Learning Academyを演習し、24時間対応のAIチューターがレッスンを進める中での質問に答えます。
Machine Learning Academyを始めるのに経験は必要ですか？
事前経験は必要ありません。CoddyKitのMachine Learning Academyは初級者から上級者向けに構成されているため、ここから始めるか最初から始めて、自分のペースで進むことができます。 これはレッスン2/4です。
「Autograd：逆伝播のための自動微分」レッスンにはどのくらい時間がかかりますか？
ほとんどのCoddyKitレッスンは約5～10分かかります。各レッスンはコンパクトでインタラクティブなので、着実に進歩し、ウェブとアプリ全体で正確に前回の場所から再開できます。
このMachine Learning Academyレッスンでコードを書いて実行できますか？
はい。すべてのMachine Learning Academyレッスンに組み込みコードエディタが含まれているため、ブラウザでリアルコードを書いて実行し、即座のAIフィードバックを取得できます。ローカル設定は不要です。
このコースのすべてのレッスン
- PyTorchテンソル：作成、演算、GPUへの転送
- Autograd：逆伝播のための自動微分
- nn.Moduleによるフィードフォワードネットワークの構築
- 学習ループ：損失、オプティマイザー、エポック