Research notes and engineering essays

Ideas on AI, mathematics,
and software systems.

Practical write-ups, experiments, and technical notes.

12 articlesAI and mathematicsLong-form technical writing

October 9, 2026•7 min read

Positive–Unlabeled Learning: A Short Survey

A phone number with several confirmed spam reports is a useful positive example. A number with no reports is harder to interpret: it might be benign, or it might be spam that nobody has reported yet. Treating every unreported number as negative turns missing information into a potentially incorrect…

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September 24, 2026•17 min read

Kiến trúc nền tảng MLOps nội bộ với ClearML và Label Studio

Một nền tảng AI nội bộ cần quản lý nhiều hơn các tác vụ huấn luyện. Dữ liệu thô phải được gán nhãn và quản lý phiên bản; mỗi thử nghiệm phải gắn với đúng mã nguồn, môi trường chạy và bộ dữ liệu; mô hình sau huấn luyện phải có thể truy ngược nguồn gốc. Khi hệ thống bị cô lập Internet, toàn bộ contain…

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August 24, 2026•23 min read

DAVE, MonkeyOCRv2, and DocPO: A Survey of Document VLM Training

Executive summary DAVE, MonkeyOCRv2, and DocPO address different stages of a document vision language model VLM lifecycle rather than competing as three interchangeable training recipes. Method Primary stage Main contribution Best use case DAVE Vision encoder pretraining and multi decoder alignment…

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August 20, 2026•12 min read

Uncertainty in Deep Learning: Deep Ensembles and MC Dropout

Why uncertainty matters A neural network can be confidently wrong. A softmax score of 0.99 only says that one logit is much larger than the others; it does not prove that the input resembles the training data or that the prediction is reliable. This distinction matters whenever a prediction drives a…

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August 3, 2026•8 min read

Navier–Stokes Equations: From Conservation Laws to Fluid Flow

Why these equations matter The Navier–Stokes equations describe how the velocity, pressure, density, and temperature of a fluid evolve. They sit behind weather prediction, aircraft design, blood flow simulation, ocean circulation, combustion, and the movement of water through a pipe. Their ingredien…

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July 24, 2026•30 min read

Data Studio Architecture and Data Storage Specification

Production AI data platforms need more than a file upload endpoint. This specification defines a complete, reproducible path from Hugging Face compatible repositories to immutable revisions, transactional metadata, content addressed storage, columnar indexes, and revision scoped serving. Live demo T…

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June 13, 2026•11 min read

Q-Learning from Scratch: Solving a Grid World with Python

Introduction Most machine learning models learn from labeled examples. Reinforcement learning is different: an agent interacts with an environment , observes the consequences of its actions, and learns which decisions produce the largest long term reward. In this tutorial, we will implement Q learni…

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January 22, 2026•5 min read

Bayesian Inference: Priors, Likelihoods, and Decisions

Why Bayesian inference matters Deterministic pipelines often fall apart when the data distribution shifts or the amount of evidence changes. Bayesian inference keeps a full probability distribution over uncertain quantities, so you can update beliefs as new observations arrive and keep downstream de…

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October 4, 2024•8 min read

Build a ChatGPT-like chatbot for free with Ollama and Open WebUI

Introduction Has the power of ChatGPT led you to explore large language models LLMs and want to build a ChatGPT like chatbot app? Do you want to create a chatbot with your own personal touch? Do you want to deploy a chatbot tool for your team at work to support daily tasks? This post shows you how t…

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March 2, 2023•11 min read

Linear Regression: Foundations, Estimation, and Diagnostics

Linear Regression: Foundations, Estimation, and Diagnostics Linear regression is a fundamental method for modeling the relationship between a continuous response variable and one or more explanatory variables. It is widely used for prediction, estimation, hypothesis testing, and the analysis of rela…

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February 28, 2023•7 min read

Hàm sigmoid dưới góc nhìn xác suất

Trong bài toán phân loại nhị phân, mô hình thường tạo ra một điểm số thực $z in mathbb R $. Tuy nhiên, một số thực bất kỳ chưa thể được diễn giải trực tiếp như xác suất. Hàm sigmoid giải quyết vấn đề này bằng cách ánh xạ $z$ vào khoảng $ 0, 1 $: $$ sigma z = frac 1 1 + e^ z . $$ Nếu đặt $$ P y=1 mid…

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February 17, 2022•6 min read

Giới thiệu về Variational Autoencoder

Introduction Xin chào mọi người, trong bài viết ngày hôm này mình sẽ cùng mọi người tìm hiểu về Variational Autoencoder VAE , một loại generative model trong deep learning. Trong vài năm gần đây, các mô hình generative đang thu hút được sự chú ý của các nhà nghiên cứu và đạt được một số kết quả đáng…

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