Foundations + Research

Xiaojing Yangfrom foundations to applied systems

A bilingual knowledge base on mathematics, statistics, machine learning, NLP, LLMs, model evaluation, and applied AI research. The goal is simple: make the foundations reusable, then connect them to real experiments.

Foundations

The concepts I want to keep sharp

This track is where existing high-quality resources become my own explanations, notes, examples, and interview-ready mental models.

Mathematics

Linear algebra, calculus, optimization, graphs, and representation spaces explained through ML and NLP examples.

Statistics

Probability, distributions, confidence intervals, bootstrap testing, hypothesis tests, and uncertainty in evaluation.

Machine Learning

Splits, generalization, model selection, cross-validation, losses, regularization, and practical training workflows.

NLP & LLMs

Tokenization, embeddings, Transformers, fine-tuning, prompting, sequence models, and language-specific evaluation.

Research Engineering

Experiment repositories, config-driven pipelines, logging, annotation sheets, demos, and reproducible analysis.

Research & Applications

Broad enough for future work, concrete enough for real projects

This track avoids boxing the blog into one thesis topic. It groups research by capability: building, evaluating, explaining, retrieving, and applying AI systems.

Multilingual AI

Machine translation, multilingual NLP, low-resource adaptation, terminology, domain adaptation, and language variation.

Model Evaluation

Metrics, benchmark design, statistical testing, ablations, error analysis, human evaluation, and robustness.

Explainability & Responsible AI

Interpretability, bias analysis, attribution, model auditing, SHAP/LIME, Shapley values, and controlled evaluation.

Retrieval & Knowledge Systems

Information retrieval, RAG, long documents, graph retrieval, evidence grounding, and document intelligence.

Applied ML Systems

Data pipelines, classification, forecasting, information extraction, deployment, product demos, and applied analytics.

Latest notes

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Posts may be in English, Chinese, or bilingual. Foundations posts often start from strong public resources; research posts connect those foundations to my own experiments.

FoundationsRetrieval & Knowledge SystemsEN

What Is RAG? From Retrieval to Grounded Answers

From documents, chunks, and embeddings to retrieval, reranking, evidence completeness, augmentation, and generation: a complete visual foundation for RAG.

FoundationsRetrieval & Knowledge Systems中文

什么是 RAG?从检索到有证据依据的回答

从文档、Chunk 和 Embedding,到检索、重排序、证据完整性、上下文增强与生成:系统理解 Retrieval-Augmented Generation 的完整基础流程。

This blog complements my portfolio.

Portfolio pages show what I built. These notes explain the foundations, decisions, experiments, and tradeoffs behind the work.