MLP - What is MLP (Multi-Layer Perceptron) classifier? - ZhangZhihuiAAA

An MLP (Multi-Layer Perceptron) classifier is a type of artificial neural network used for supervised learning, particularly for classification tasks. It’s one of the simplest forms of deep learning models and serves as the foundation for more advanced neural architectures.

Let’s break it down clearly 👇

🧠 1. Structure of an MLP

An MLP is composed of layers of neurons (nodes):

Input layer: Receives the feature vectors (e.g., pixel values, measurements, etc.).
Hidden layers: Perform nonlinear transformations of the input using weights, biases, and activation functions.
Output layer: Produces the final class probabilities or predictions.

⚙️ 2. How It Works

Each neuron computes:

Then applies a nonlinear activation function:

Common activation functions:

The output layer often uses:

Softmax (for multi-class classification)
Sigmoid (for binary classification)

🔁 3. Training Process

Forward pass: Data flows through the network to produce predictions.
Loss computation: Measures prediction error (e.g., using cross-entropy loss).
Backward pass: Uses backpropagation to compute gradients.
Weight update: Adjusts weights via gradient descent or variants (e.g., Adam, SGD).

Over many iterations (epochs), the model learns to minimize the loss and improve classification accuracy.

📊 4. Example in scikit-learn

hidden_layer_sizes=(100,) → one hidden layer with 100 neurons
activation='relu' → ReLU used in hidden layers
solver='adam' → Adam optimizer
max_iter=300 → maximum number of training iterations

🧩 5. Key Characteristics

Feature	Description
Model type	Feedforward neural network
Learning type	Supervised
Handles	Nonlinear decision boundaries
Requires	Feature scaling (e.g., StandardScaler)
Strengths	Flexible, can approximate complex functions
Weaknesses	Can overfit, slower to train than linear models

✅ Summary

MLP Classifier = A feedforward neural network that learns nonlinear mappings from input features to output labels through layers of weighted connections and nonlinear activations, trained via backpropagation.

Would you like me to show a diagram of the MLP structure (with input, hidden, and output layers)? It helps visualize how data flows through the network.

In the example Python code, I only see Step 1, could you update the code to include all 4 steps?

Excellent question 👏 — let’s expand the MLPClassifier example to clearly show all 4 steps of the training process:

① Forward pass → ② Loss computation → ③ Backward pass → ④ Weight update

In scikit-learn, most of these steps are handled internally by the fit() method, but I’ll illustrate both the conceptual version (for understanding) and the practical version (for implementation).

🧩 Full Example: MLP Classifier (with all 4 steps explained)

import numpy as np
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.neural_network import MLPClassifier
from sklearn.metrics import accuracy_score, log_loss

# ================================
# Step 0. Prepare Data
# ================================
X, y = make_moons(n_samples=1000, noise=0.2, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# ================================
# Step 1. Initialize the model
# ================================
mlp = MLPClassifier(hidden_layer_sizes=(10, 10),
                    activation='relu',
                    solver='adam',
                    max_iter=1,          # We'll manually loop training steps
                    warm_start=True)     # Keep training across iterations

# We'll manually simulate multiple training epochs
n_epochs = 20
for epoch in range(n_epochs):
    # ================================
    # Step 2. Forward pass + Loss computation
    # ================================
    # (mlp.fit does forward pass, loss computation, backward pass, and weight update)
    mlp.fit(X_train, y_train)
    
    # Compute predictions and loss for monitoring
    y_pred_prob = mlp.predict_proba(X_test)
    loss = log_loss(y_test, y_pred_prob)
    acc = accuracy_score(y_test, mlp.predict(X_test))
    
    # ================================
    # Step 3. Backward pass (inside fit)
    # ================================
    # Internally, MLPClassifier computes gradients via backpropagation
    
    # ================================
    # Step 4. Weight update (inside fit)
    # ================================
    # Optimizer (Adam) updates the model weights based on gradients
    
    print(f"Epoch {epoch+1}/{n_epochs} - Loss: {loss:.4f}, Accuracy: {acc:.4f}")

🔍 What’s happening under the hood

Step	Process	Done by
1. Initialize model	Randomly initializes weights and biases	`MLPClassifier(...)`
2. Forward pass	Computes predictions	`fit()` internal forward pass
3. Loss computation	Measures how far predictions are from targets	`fit()` internal loss function (log-loss)
4. Backward pass + weight update	Uses backpropagation and Adam optimizer to adjust weights	`fit()` internal training loop

✅ Output Example

Would you like me to rewrite this same example using PyTorch, where you can explicitly see each step (forward, loss, backward, update) implemented manually? That version gives you full control over every part of the training loop.

Yes, I would. Thanks.

Perfect 👍 — PyTorch is an excellent choice for understanding what’s really happening inside an MLP.
Below is a complete, clear example that explicitly shows all 4 training steps — from forward pass to weight updates — using PyTorch.

🧠 Full Example: MLP Classifier in PyTorch (All 4 Steps)

import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.datasets import make_moons
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import accuracy_score

# ============================================
# Step 0. Prepare data
# ============================================
X, y = make_moons(n_samples=1000, noise=0.2, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# Convert to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32)
y_train = torch.tensor(y_train, dtype=torch.long)
X_test = torch.tensor(X_test, dtype=torch.float32)
y_test = torch.tensor(y_test, dtype=torch.long)

# ============================================
# Step 1. Initialize the model
# ============================================
class MLPClassifier(nn.Module):
    def __init__(self):
        super().__init__()
        self.hidden1 = nn.Linear(2, 10)   # input → hidden1
        self.hidden2 = nn.Linear(10, 10)  # hidden1 → hidden2
        self.output = nn.Linear(10, 2)    # hidden2 → output (2 classes)
        self.relu = nn.ReLU()

    def forward(self, x):
        x = self.relu(self.hidden1(x))
        x = self.relu(self.hidden2(x))
        x = self.output(x)
        return x

model = MLPClassifier()

# Define loss function and optimizer
criterion = nn.CrossEntropyLoss()   # classification loss
optimizer = optim.Adam(model.parameters(), lr=0.01)

# ============================================
# Step 2–4. Training loop
# ============================================
n_epochs = 50

for epoch in range(n_epochs):
    # ---- Step 2: Forward pass ----
    logits = model(X_train)         # predicted outputs (unnormalized)
    loss = criterion(logits, y_train)  # compute loss

    # ---- Step 3: Backward pass ----
    optimizer.zero_grad()           # reset gradients
    loss.backward()                 # compute gradients via backpropagation

    # ---- Step 4: Weight update ----
    optimizer.step()                # update weights using gradients

    # Compute accuracy on test set
    with torch.no_grad():
        test_logits = model(X_test)
        y_pred = torch.argmax(test_logits, dim=1)
        acc = accuracy_score(y_test, y_pred)

    print(f"Epoch {epoch+1}/{n_epochs} - Loss: {loss.item():.4f} - Accuracy: {acc:.4f}")

🔍 Step-by-Step Breakdown

Step	What Happens	PyTorch Code
1. Initialize model	Define layers, activations, and optimizer	`model = MLPClassifier()`, `optimizer = Adam(...)`
2. Forward pass	Data flows through network to compute predictions	`logits = model(X_train)`
3. Backward pass	Gradients are computed via backpropagation	`loss.backward()`
4. Weight update	Optimizer updates weights using computed gradients	`optimizer.step()`

🧾 Output Example

🧩 Key Takeaways

Forward pass: Model produces predictions.
Loss: Measures prediction error.
Backward pass: Computes gradients of loss w.r.t. weights.
Update: Adjusts weights to minimize loss.

I can't understand torch.argmax(test_logits, dim=1) in the example code above, could you explain it please?

Excellent question — that’s a key line in the prediction process 👏

Let’s break down exactly what

🧩 Step 1: What is `test_logits`?

After running the model on the test data:

Each column corresponds to one class (e.g., class 0 and class 1).

The values are called logits, meaning raw model outputs before softmax normalization — they can be any real numbers (positive or negative).

🧩 Step 2: What `torch.argmax(..., dim=1)` does

torch.argmax(tensor, dim=1) means:

“Find the index of the largest value along dimension 1 (the columns).”

So for each row (each test sample), it returns the index of the class with the highest score.

Example:

Sample 1 → class 0 (since 2.1 > 0.3)
Sample 2 → class 1 (since 3.4 > -1.2)
Sample 3 → class 0 (since 0.8 > -0.5)

Thus, this gives you the predicted class label for each input.

🧠 Step 3: How it fits into the example

Converts the raw output (test_logits) to class predictions (y_pred)
y_pred is a 1D tensor like [0, 1, 1, 0, ...]
These are then compared to the true labels (y_test) using accuracy metrics:

✅ Summary

Expression	Meaning
`test_logits`	Raw model outputs (one row per sample, one column per class)
`dim=1`	Operate across columns (choose class for each sample)
`torch.argmax(..., dim=1)`	Returns the class index with the largest score per sample
`y_pred`	Final predicted class labels

I'd like to know if the indexes returned by torch.argmax() match the actual classes (the labels).

Excellent — that’s a very thoughtful question 👏

Yes, the indexes returned by torch.argmax() match the class labels, but only if your model’s output layer and your training labels use the same class-index convention.
Let’s look carefully at what that means and when you might need to be careful.

🧩 1. How class labels work in PyTorch classification

In PyTorch, when you use:

this loss function expects:

Model outputs (logits): shape (batch_size, num_classes)
True labels (y_train): shape (batch_size,), each entry is an integer class index in [0, num_classes - 1]

Example:

and class index 1 corresponds to column 1.

⚙️ 2. What `torch.argmax(logits, dim=1)` returns

torch.argmax(logits, dim=1) returns the index of the largest logit per row — that is, the predicted class index.

Continuing the example above:

→ tensor([0, 1])

These indices directly match the target labels:

Predicted class 0 for first sample
Predicted class 1 for second sample

✅ So yes — the indexes line up exactly with your class labels.

⚠️ 3. When they might not match automatically

If your dataset labels are not 0-based integers — for example:

You must then remap your labels, e.g.:

✅ 4. Summary Table

Component	Representation	Example
Model output	2D tensor `[batch_size, num_classes]`	`[[z₀, z₁, z₂]]`
Label	Integer index of true class	`1` (means class 1)
`torch.argmax(logits, dim=1)`	Predicted class index	`1`
Relationship	Indexes align directly with label integers	✔️

🧠 In other words:

As long as your labels are integers from 0 to num_classes - 1,
the indices returned by torch.argmax() directly correspond to your actual class labels.


博客园 © 2004-2025 浙公网安备 33010602011771号浙ICP备2021040463号-3

导航

🧠 1. Structure of an MLP

⚙️ 2. How It Works

🔁 3. Training Process

📊 4. Example in scikit-learn

🧩 5. Key Characteristics

✅ Summary

You said:

ChatGPT said:

🧩 Full Example: MLP Classifier (with all 4 steps explained)

🔍 What’s happening under the hood

✅ Output Example

You said:

ChatGPT said:

🧠 Full Example: MLP Classifier in PyTorch (All 4 Steps)

🔍 Step-by-Step Breakdown

🧾 Output Example

🧩 Key Takeaways

ChatGPT said:

🧩 Step 1: What is test_logits?

🧩 Step 2: What torch.argmax(..., dim=1) does

🧠 Step 3: How it fits into the example

✅ Summary

ChatGPT said:

🧩 1. How class labels work in PyTorch classification

⚙️ 2. What torch.argmax(logits, dim=1) returns

⚠️ 3. When they might not match automatically

✅ 4. Summary Table

🧠 In other words:

🧩 Step 1: What is `test_logits`?

🧩 Step 2: What `torch.argmax(..., dim=1)` does

⚙️ 2. What `torch.argmax(logits, dim=1)` returns