Detailed explanation of how Python calculates weights based on a given model

In deep learning, model weights (or parameters) are obtained through training processes. However, sometimes we may need to manually calculate or check these weights. This is often useful when understanding how the model works, debugging, or performing model analysis.

Below I will use a simple example to show how to calculate and extract weights based on a given model structure. Here we choose a basic neural network model and use TensorFlow and Keras as deep learning frameworks.

1. Examples of neural network models (TensorFlow and Keras frameworks)

Step Overview

Define the model structure: We define a simple neural network model.
Compile the model: Specify the optimizer and loss function.
Training the model(Optional): Use training data to train the model (you can skip it here because we mainly focus on weights).
Extract weights: Extract weights from the model.

Complete code example

import tensorflow as tf
from  import Sequential
from  import Dense
import numpy as np
 
# 1. Define the model structuremodel = Sequential([
    Dense(units=64, activation='relu', input_shape=(10,)),  # Input layer, 10 input features, 64 neurons    Dense(units=32, activation='relu'),                     # Hidden layer, 32 neurons    Dense(units=1, activation='linear')                     # Output layer, 1 neuron (for regression task)])
 
# 2. Compile the model(optimizer='adam', loss='mean_squared_error')
 
# 3. Training the model (optional)# Here we generate some random data to train the model, but this is not necessary because we mainly focus on weightsX_train = (100, 10)  # 100 samples, 10 features per sampley_train = (100, 1)   # 100 samples, 1 output per sample 
# Train the model (you can comment out this line because we mainly focus on weights)# (X_train, y_train, epochs=10, batch_size=10)
 
# 4. Extract weights# Get the weight of each layerfor layer in :
    # Check if it is the Dense layer    if isinstance(layer, Dense):
        # Get weights and biases        weights, biases = layer.get_weights()
        print(f"Layer {} - Weights:\n{weights}\nBiases:\n{biases}")

Code explanation

Define the model structure：

model = Sequential([
    Dense(units=64, activation='relu', input_shape=(10,)),
    Dense(units=32, activation='relu'),
    Dense(units=1, activation='linear')
])

Here we define a simple fully connected neural network, including an input layer, a hidden layer and an output layer.

Compile the model：

(optimizer='adam', loss='mean_squared_error')

Use the Adam optimizer and mean square error loss function to compile the model.

Training model (optional)：

X_train = (100, 10)
y_train = (100, 1)
(X_train, y_train, epochs=10, batch_size=10)

For demonstration, we generate some random data and train the model. But in actual use, we may use our own dataset.

Extract weights：

for layer in :
    if isinstance(layer, Dense):
        weights, biases = layer.get_weights()
        print(f"Layer {} - Weights:\n{weights}\nBiases:\n{biases}")

Iterate through each layer of the model, check whether it is a Dense layer, and extract its weights and biases.

Things to note

Weight initialization: When the model is initialized, the weights and biases are initialized randomly. The training process adjusts these weights to minimize the loss function.
Weight extraction timing: Weights can be extracted before, during or after training. The weights after training are more practical because they have been adjusted through the training data.
Weights of different layers: Different types of layers (such as convolutional layers, recurrent layers, etc.) have different weight structures, but the extraction methods are similar, all throughget_weights()method.

With the above code, we can easily extract and check the weights of the neural network model, which is very helpful for understanding how the model works and debugging.

2. Example of scikit-learn library training linear regression model

In Python, calculating weights based on a given machine learning model usually involves training the model and extracting its internal parameters. The following is a detailed example of using the scikit-learn library to train a linear regression model and extract its weights. The weights (also called coefficients) in the linear regression model indicate the extent to which each feature affects the target variable.

Step Overview

Prepare data: Create or load a dataset containing features and target variables.
Dividing datasets: Divide the dataset into a training set and a test set (although in this example we mainly focus on the training set).
Training the model: Use the training set to train a linear regression model.
Extract weights: Extract weights from trained models.

Code Example

# Import the necessary librariesimport numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
 
# Prepare data# Suppose we have a simple two-dimensional feature dataset and a target variable# In actual applications, data may come from files, databases, or APIsX = ([[1, 1], [1, 2], [2, 2], [2, 3]])  # Feature Matrixy = (X, ([1, 2])) + 3  # Target variable, here we manually set a linear relationship 
# To simulate the real situation, we add some noisey += (0, 0.1, )
 
# Divide datasets# In this example, we use all the data directly as the training set, because the focus is on extracting weightsX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.0, random_state=42)
 
# Train the modelmodel = LinearRegression()
(X_train, y_train)
 
# Extract weightsweights = model.coef_  # Get the coefficients (weights) of the modelintercept = model.intercept_  # Get the intercept of the model 
# Output resultprint("The weight (coefficient):", weights)
print("Model intercept:", intercept)
 
# Verification model (optional)# Use the test set or training set to make predictions and calculate the errory_pred = (X_train)  # Here we use the training set for prediction, for the sake of presentation onlyprint("Predicted values on the training set:", y_pred)
print("Real value on the training set:", y_train)
 
# Calculate mean square error (MSE) as a performance evaluation indexfrom  import mean_squared_error
mse = mean_squared_error(y_train, y_pred)
print("Mean Square Error (MSE) on Training Set:", mse)

Code explanation

Import library: We imported numpy for data processing and scikit-learn for machine learning models training and evaluation.
Prepare data: We have created a simple 2D feature dataset manuallyXand a target variabley, and some noise was added to simulate the real situation.
Dividing datasets: Although in this example we use all the data directly as the training set, we usually divide the data set into a training set and a test set. Here we usetrain_test_splitfunctions are divided, buttest_sizeSet to 0.0 means there is no test set.
Training the model:We useLinearRegressionThe class creates a linear regression model and uses the training setX_trainandy_trainCarry out training.
Extract weights:After training is completed, we extract the weights (coefficients) and intercepts from the model.
Output result: Print weight and intercept.
Verification model(Optional): Use the training set to make predictions and calculate mean square error (MSE) as a performance evaluation indicator. This step is optional and is mainly used to show how to use the model for prediction and evaluation.

Reference value and practical significance

This example shows how to train a simple linear regression model using Python and scikit-learn libraries and extract its weights. Weights are very important in machine learning models because they represent the extent to which features affect the target variables. In practical applications, understanding these weights can help us understand which features are most important for model prediction, so as to perform follow-up work such as feature selection and model optimization. Additionally, this example can serve as a starting point for learning scikit-learn and machine learning basics.

This is the end of this article about how Python calculates weights based on a given model. For more related content on Python calculation of weights, please search for my previous articles or continue browsing the related articles below. I hope everyone will support me in the future!