Creating a Multilayer Perceptron from Scratch
The article walks through building and manually computing a simple 3-layer multilayer perceptron (MLP) from scratch, covering both forward propagation and backpropagation step by step Key architectural decisions include using sigmoid activation functions for both hidden and output layers, MSE loss for a binary classification task, and random initial weights between 0 and 1 The backpropagation process is broken into seven distinct steps: differentiating the loss function, differentiating the acti
Analysis
TL;DR
- The article walks through building and manually computing a simple 3-layer multilayer perceptron (MLP) from scratch, covering both forward propagation and backpropagation step by step
- Key architectural decisions include using sigmoid activation functions for both hidden and output layers, MSE loss for a binary classification task, and random initial weights between 0 and 1
- The backpropagation process is broken into seven distinct steps: differentiating the loss function, differentiating the activation function, computing output deltas, calculating output gradients, computing hidden neuron deltas, calculating hidden weight gradients, and updating weights and biases
- A 3x3x3x1 MLP with 1,000 training examples over 100 iterations requires over 14 million calculations for just 28 parameters, illustrating the computational scale of modern AI
- The author demonstrates that even a single training example shows measurable improvement (loss decreased by 0.0027835127), validating the learning mechanism
Why It Matters
This article provides a rare, transparent walkthrough of MLP mechanics at the arithmetic level, making it an invaluable educational resource for AI practitioners and students who want to move beyond API-level understanding. It bridges the gap between theoretical concepts and practical implementation, helping readers appreciate both the simplicity of core neural network principles and the immense computational demands of scaling them to modern models like GPT-5.
Technical Details
- Architecture: A fully connected 3-layer network (functionally 2 computational layers, excluding the input layer), with 3 hidden neurons and 1 output neuron, designed as a binary classifier
- Activation Functions: Sigmoid chosen for both hidden and output layers due to its straightforward differentiability during backpropagation; ReLU discussed as an alternative for hidden layers
- Loss Function: Mean Squared Error (MSE), simplified to squared error for a single training example; the author notes that the gradient of loss drives learning, not the loss value itself
- Backpropagation Steps: (1) Differentiate MSE to get 2(predicted − actual), (2) differentiate sigmoid activation, (3) compute output delta by multiplying the two derivatives, (4) scale output delta by hidden layer outputs to get output gradients, (5) propagate output delta backward through output weights and apply sigmoid derivative for hidden deltas, (6) scale hidden deltas by hidden layer inputs for hidden weight gradients, (7) update weights using learning rate of 0.1
- Bias Handling: Biases are updated differently from weights since they are added rather than multiplied; the gradient for bias equals the delta value directly (equivalent to delta × 1)
- Scale Comparison: The author contrasts the manual MLP with GPT-5's estimated 2–5 trillion parameters trained on hundreds of billions of examples, highlighting the exponential growth in computational requirements
Industry Insight
- Understanding the first principles of MLPs through manual computation builds intuition that translates directly to debugging and optimizing larger, more complex neural architectures in production
- The article reinforces that architectural simplicity (e.g., choice of activation function, learning rate) has outsized impact on training dynamics, a principle that scales to modern deep learning systems
- The computational scale comparison serves as a reminder that while the core mechanics of learning remain unchanged, the engineering challenge has shifted from algorithmic design to infrastructure and optimization at massive scale
Disclaimer: The above content is generated by AI and is for reference only.