Deep Understanding of Neural Network Optimization: Implementing Adam, SGD, and RMSProp Algorithms from Scratch

This article introduces the ML-OptimizationTechniques project, a visual learning tool that builds neural network optimization algorithms from scratch using NumPy, helping users intuitively understand the working principles of core optimizers like Adam, SGD, and RMSProp. The project aims to address the limitations of using optimizers as black boxes, allowing learners to go beyond API calls and master the internal mechanisms of optimization algorithms.

Using PyTorch/TensorFlow optimizers as black boxes has limitations:

• Difficulty in hyperparameter tuning: Relies on experience or grid search, making it hard to judge parameter impacts;
• Weak problem diagnosis ability: Blind debugging when training fails to converge or oscillates;
• Lack of basis for algorithm selection: Different optimizers are suitable for different scenarios (e.g., SGD for simple convex problems, Adam for sparse gradients);
• Limited innovation: Mastering basic principles is necessary to keep up with cutting-edge progress.

Key highlights of ML-OptimizationTechniques:

• Pure NumPy implementation: All logic is transparent and readable, with no framework dependencies from forward propagation to parameter updates;
• Multi-optimizer comparison: Implements SGD, Momentum, RMSProp, and Adam, clearly showing design ideas and applicable scenarios;
• t-SNE visualization: Maps high-dimensional optimization trajectories to 2D for intuitive observation of search paths;
• LLM-assisted data generation: Uses large language models to automatically generate demonstration datasets.

Core principles of each optimizer:

• SGD: Randomly samples mini-batches and updates parameters along the negative gradient; simple and efficient but prone to oscillation or getting stuck in local optima;
• Momentum: Accumulates the exponentially weighted average of historical gradients, adds inertia, accelerates traversal of flat regions, and reduces oscillation;
• RMSProp: Maintains an exponentially moving average of squared gradients for each parameter, adaptively adjusting the learning rate;
• Adam: Combines Momentum (first-order moment) and RMSProp (second-order moment), uses bias correction to handle initial zero bias, and has strong generality.

t-SNE visualization helps understand:

• Differences in convergence speed: Momentum approaches the optimal solution faster than SGD, and adaptive methods are more stable;
• Causes of oscillation: Excessively high learning rates lead to oscillation near the optimal solution;
• Local optimum trap: Different initializations may converge to different local optima;
• Parameter space structure: Intuitively perceive complex terrains like saddle points, plateaus, and valleys.

The project supports cross-platform use (Windows/macOS/Linux) with minimum requirements: 4GB RAM (8GB recommended), 200MB disk space, and an Intel Core i3 processor. The tool runs independently; no Python environment installation is required—just download the installation package for your system and unzip it to use.

Recommended learning path:

1. Master the basics of calculus and linear algebra (gradients, matrix operations);
2. Start with SGD and manually derive parameter update formulas;
3. Learn Momentum, RMSProp, and Adam one by one, understanding the problems each algorithm solves and its design ideas;
4. Use visual tools to observe differences in algorithm performance;
5. Adjust parameters (learning rate, momentum coefficient, etc.) and experiment with their impact on the optimization process.

ML-OptimizationTechniques helps learners go beyond API calls and truly understand the working principles of optimizers. In today's era of widespread deep learning, mastering basic principles is a hallmark that distinguishes ordinary users from professional engineers, bringing long-term benefits to interviews, solving practical problems, and algorithm research.