Machine Learning Algorithms & Theories Index

The transformer model revolutionizes natural language processing (NLP) by processing entire sequences at once, leveraging techniques like self-attention mechanism, positional encodings, and multi-head attention.

An architectural deep dive and synthetic benchmark of FAPE, LPE, RPE, and RoPE. Learn how different Positional Encoding methods impact a Transformer's ability to handle sequences 20x longer than its training context.

Grouped-Query Attention (GQA) is a type of attention mechanisms designed to reduce the memory bandwidth requirements and latency during the decoding phase.

The Transformer architecture, introduced in the “Attention Is All You Need” paper, has revolutionized Natural Language Processing (NLP). Its core innovation, the self-attention mechanism, allows models to weigh the importance of different parts of the input sequence. However, the standard self-attention mechanism suffers from its computational complexity which scales quadratically (O(N²)) as the length of the input sequence N grows, creating a bottleneck especially in tasks with long N such as document summarization or high-resolution image processing. Attention approximation solve this challenge by reducing the complexity using various techniques.

Generative Adversarial Networks (GANs) are a class of deep learning architectures designed for generative modeling which focuses on generating new, realistic examples from original data.

An autoencoder (AE) is a type of artificial neural network used to copy inputs to outputs by learning unlabeled data through unsupervised learning.

From sequential data modeling with the chain rule to hands-on PyTorch simulations, learn why standard RNNs struggle with long-term dependencies and how the vanishing gradient problem manifests in real-time training.

While standard RNNs struggle with long-term dependencies, LSTMs leverage a sophisticated gating mechanism to maintain information flow. This article breaks down LLM Fine-tuningematical core of forget, input, and output gates, explains the additive gradient path that prevents vanishing gradients, and provides a PyTorch implementation comparing LSTM and RNN performance on long-sequence weather data.

A deep dive into LLM Fine-tuningematical mechanisms of GRUs, error signals, and how Signature GRUs (SigGRU) leverage temporal geometry for superior long-sequence forecasting.

Standard RNNs often miss the context required for complex sequence modeling. This guide breaks down the mechanics of Bidirectional RNNs (BRNNs), provides a mathematical walkthrough, and uses PyTorch simulations to compare BiLSTM and BiGRU performance across varying sequence lengths.

An in-depth technical exploration of DRNN architectures. Learn how to implement and optimize vertical, temporal, and I/O depth to handle high-dimensional sequential data in NLP and time-series forecasting.

While high-level frameworks make deep learning accessible, true mastery lies in understanding the underlying calculus and linear algebra. This guide breaks down Deep Feedforward Networks (DFNs) into their fundamental components—from He Initialization and ReLU activations to L2 regularization and Adam optimization—providing a step-by-step mathematical derivation and a robust Python implementation from scratch.

Regression is a common task in machine learning with variety of applications.

The learning problem of regression is to identify the most suitable approximate function (hypothesis) that can accurately map input values X to output values Y:

K-Nearest Neighbor (KNN) is often the first algorithm we learn, but mastering it requires navigating the bias-variance tradeoff and the curse of dimensionality. This technical guide explores the mechanics of unweighted vs. weighted KNN, compares six critical distance metrics (from Minkowski to Jaccard), and demonstrates how to leverage K-fold cross-validation and Grid Search to find LLM Fine-tuningematically optimal k for your dataset.

An in-depth technical guide to decision tree algorithms. Learn LLM Fine-tuningematical foundations of $E(D)$ and $G(D)$, explore how greedy algorithms find optimal splits, and see a comparative simulation of Exact vs. Histogram-based methods using Scikit-Learn.

An in-depth technical guide to Gradient Boosting Machines (GBM). This article bridges the gap between theoretical loss minimization—using negative gradients and pseudo-residuals—and practical application. We implement a custom GBM from scratch and benchmark industry leaders like XGBoost, LightGBM, and CatBoost against traditional Logistic Regression and Deep Learning models.

An in-depth technical exploration of Random Forest ensembles. This article covers the mechanics of bootstrapping and feature selection, explains Out-of-Bag (OOB) error estimation, and provides a head-to-head Python simulation comparing Random Forest complexity against Gradient Boosting Machines (XGBoost, LightGBM, CatBoost) for classification tasks.

Naive Bayes is often sidelined due to its native feature independence assumption. However, by leveraging specialized pipelines for Gaussian, Bernoulli, and Multinomial data—and combining them via stacking—you can build a high-efficiency classifier that handles complex, real-world datasets with minimal overhead.