Important machine learning equations

This blog post provides a comprehensive guide to the key mathematical equations that power machine learning, covering topics such as probability and information theory, linear algebra, optimization, and advanced ML concepts. The guide includes theoretical insights, equations, and practical implementations in Python, making it a valuable resource for anyone looking to deepen their understanding of machine learning and its underlying math.

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Some thoughts on LLMs and software development

The author is taking a break from managing a site and shares thoughts on the state of Large Language Models (LLMs) and AI, noting that surveys on their impact are flawed due to varying usage and capabilities. The author advises experimentation and caution, warning that LLMs can introduce significant security risks and create a huge increase in the attack surface of software systems, and that their limitations and potential for "hallucinations" should be carefully considered.

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Building your own CLI coding agent with Pydantic-AI

The author built a custom CLI coding agent using the Pydantic-AI framework and the Model Context Protocol (MCP), which allows the AI model to use various tools through a standardized interface, making the assistant highly extensible. The agent was customized to the author's internal context and project specifics, and its capabilities were expanded to include running tests, analyzing error messages, and suggesting targeted fixes, with the goal of creating a more efficient and effective coding workflow.

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Will AI Replace Human Thinking? The Case for Writing and Coding Manually

While AI can be a useful tool, over-reliance on it can lead to a loss of critical thinking and learning skills, making it essential to strike a balance between using AI and developing one's own competencies. Relying too heavily on AI can result in a plateau of knowledge and skills, and even lead to a decrease in productivity and creativity in the long run.

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Rendering a game in real time with AI

The author created an ASCII game called "Thunder Lizard" and explored the possibility of rendering it in real-time with AI-generated graphics, using models from fal.ai to achieve a frame rate of 10 FPS with around one second of latency. The author experimented with various image generation models and techniques, including ControlNet and image-to-image models, to find the right balance between speed, layout consistency, and visual quality, ultimately achieving a satisfactory result after trying numerous combinations of settings and techniques.

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CCPS: Calibrating LLM Confidence via Perturbation Stability – EMNLP 2025

CCPS, a novel method, analyzes internal representational stability in Large Language Models (LLMs) to improve confidence estimation by applying targeted perturbations and using a lightweight classifier to predict answer correctness. The results show that CCPS significantly outperforms current approaches, reducing errors and increasing accuracy, making it a more accurate and efficient solution for estimating LLM confidence and improving their trustworthiness.

ArXiv

LMAR: Language Model Augmented Retriever for Domain-Specific Knowledge Indexing

LMAR (Language Model Augmented Retriever) is a framework that addresses the challenges of domain-specific knowledge in Retrieval Augmented Generation systems by combining LLM-guided data synthesis with contrastive embedding adaptation and efficient text clustering. Experimental results show that LMAR outperforms baseline models while maintaining moderate hardware requirements and low latency, making it a practical and cost-effective solution for scalable domain-specific adaptation.

ArXiv

Monte Carlo Gradient Estimation in Machine Learning

This paper surveys methods for Monte Carlo gradient estimation, a core problem in machine learning that involves computing the gradient of an expectation with respect to parameters defining a distribution. The paper explores three strategies for estimating these gradients, their historical development, and potential generalizations, with the goal of supporting further advances in the field.

ArXiv

VLT observations of interstellar comet 3I/ATLAS II

The interstellar comet 3I/ATLAS was studied using VLT spectroscopy, revealing a dust-dominated coma with a constant red optical continuum slope and detections of CN emission and numerous Ni I lines, but no signs of other expected emissions. The production rates of CN and Ni were measured and found to have a steep heliocentric-distance scaling, with the Ni emission potentially driven by the carbonyl formation channel, suggesting a low-activation-energy release from dust rather than direct sublimation of metal phases.

ArXiv

Learning Facts at Scale with Active Reading

Large language models (LLMs) struggle to reliably learn and recall facts from their training data, but a new framework called Active Reading can improve their knowledge absorption by training them to study material with self-generated learning strategies. Active Reading has been shown to significantly outperform traditional methods, with models trained using this framework achieving state-of-the-art results on various benchmarks, including factual question answering.

ArXiv

Show HN: SwiftAI – open-source library to easily build LLM features on iOS/macOS

SwiftAI is a modern, type-safe Swift library for building AI-powered apps, providing a unified API that works seamlessly across different AI models, including Apple's on-device models and cloud-based services like OpenAI. The library offers features such as model-agnostic API, structured output, agent tool loop, conversations, and extensibility, making it easy to integrate AI capabilities into Swift applications.

Repo

Show HN: Unwrap_or_AI – replace unwrap() with AI guesses for errors

The unwrap_or_ai library is a revolutionary error handling system for Rust that utilizes artificial intelligence to create advanced error recovery, providing instant and intelligent fallback data. It offers seamless integration, production optimization, and adaptive learning, allowing developers to transform their error handling into intelligent success systems with minimal code changes.

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Show HN: Txtos for LLMs – 60 SEC setup, long memory, boundary guard, MIT

The WFGY project is a semantic reasoning engine designed to solve core AI problems such as hallucination, context drift, and logic failure, with a goal of igniting a new civilization layer built on semantic reasoning. The project includes various modules, such as TXT OS, Blah Blah Blah, and Blur Blur Blur, which provide semantic Q&A, image generation, and reasoning games, all running natively as .txt apps with no installation or dependencies required.

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Show HN: oLLM – LLM Inference for large-context tasks on consumer GPUs

The oLLM library is a lightweight Python tool for large-context language model inference, built on Huggingface Transformers and PyTorch, allowing models like Llama to run on consumer GPUs with 8GB VRAM. It achieves efficient inference by offloading data to SSD, chunking attention and MLP, and using fp16 precision, enabling tasks like analyzing large contracts, medical literature, and log files with significant performance improvements.

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Show HN: AgentCheck – Local AI-powered code review agents for Claude Code

AgentCheck is a local AI-powered code review tool that integrates into a developer's workflow, providing focused and actionable feedback on code changes before they are committed. It uses project-specific context and customizable agents to analyze staged changes, prioritize findings, and suggest concrete fixes, aiming to make human code reviews faster and more efficient.

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