This is an open, unconventional textbook covering mathematics, computing, and artificial intelligence from foundational principles. It's designed for practitioners seeking a deep understanding, moving beyond exam preparation and focusing on real-world application. The author, drawing from years of experience in AI/ML, has compiled notes that prioritize intuition, context, and clear explanations, avoiding dense notation and outdated material.
The compendium covers a broad range of topics, from vectors and matrices to machine learning, computer vision, and multimodal learning, with future chapters planned for areas like data structures and AI inference.
The compendium covers a broad range of topics, from vectors and matrices to machine learning, computer vision, and multimodal learning, with future chapters planned for areas like data structures and AI inference.
This article announces a new discrete mathematics course available on the freeCodeCamp.org YouTube channel, taught by Karol Kurek. Discrete mathematics is crucial for fields like machine learning and algorithms, enabling tasks such as finding shortest paths, encryption, and data compression. The course provides an introduction to key areas including combinatorics, number theory, prime numbers, and concepts like the pigeonhole principle and Chinese remainder theorem.
It also includes practical applications and implementations in Python. The course aims to equip learners with a strong foundation for further exploration in this evolving field.
It also includes practical applications and implementations in Python. The course aims to equip learners with a strong foundation for further exploration in this evolving field.
MIT researchers developed a new approach that rethinks how a classic method, known as Bayesian optimization, can be used to solve problems with hundreds of variables. In tests on realistic engineering-style benchmarks, like power-system optimization, the approach found top solutions 10 to 100 times faster than widely used methods.
Their technique leverages a foundation model trained on tabular data that automatically identifies the variables that matter most for improving performance, repeating the process to hone in on better and better solutions. The researchers’ tabular foundation model does not need to be constantly retrained as it works toward a solution, increasing the efficiency of the optimization process.
The technique also delivers greater speedups for more complicated problems, so it could be especially useful in demanding applications like materials development or drug discovery. The research will be presented at the International Conference on Learning Representations.
Their technique leverages a foundation model trained on tabular data that automatically identifies the variables that matter most for improving performance, repeating the process to hone in on better and better solutions. The researchers’ tabular foundation model does not need to be constantly retrained as it works toward a solution, increasing the efficiency of the optimization process.
The technique also delivers greater speedups for more complicated problems, so it could be especially useful in demanding applications like materials development or drug discovery. The research will be presented at the International Conference on Learning Representations.
This post introduces **GIST (Greedy Independent Set Thresholding)**, a new algorithm for selecting diverse and useful data subsets for machine learning. GIST tackles the NP-hard problem of balancing diversity (minimizing redundancy) and utility (relevance to the task) in large datasets.
**Key points:**
* **Approach:** GIST prioritizes minimum distance between selected data points (diversity) then uses a greedy algorithm to approximate the highest-utility subset within that constraint, testing various distance thresholds.
* **Guarantee:** GIST is guaranteed to find a subset with at least half the value of the optimal solution.
* **Performance:** Experiments demonstrate GIST outperforms existing methods (Random, Margin, k-center, Submod) in image classification and single-shot downsampling.
* **Application:** Already used to improve video recommendation diversity at YouTube.
**GIST provides a mathematically grounded and efficient solution for selecting high-quality data subsets for machine learning, crucial as datasets scale.**
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**Key points:**
* **Approach:** GIST prioritizes minimum distance between selected data points (diversity) then uses a greedy algorithm to approximate the highest-utility subset within that constraint, testing various distance thresholds.
* **Guarantee:** GIST is guaranteed to find a subset with at least half the value of the optimal solution.
* **Performance:** Experiments demonstrate GIST outperforms existing methods (Random, Margin, k-center, Submod) in image classification and single-shot downsampling.
* **Application:** Already used to improve video recommendation diversity at YouTube.
**GIST provides a mathematically grounded and efficient solution for selecting high-quality data subsets for machine learning, crucial as datasets scale.**
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A connection between descriptive set theory and computer science has been discovered, allowing problems in one field to be rewritten and solved in the other by Anton Bernshteyn.
Problems in descriptive set theory (measuring infinite graph colorings) are mathematically equivalent to problems in distributed algorithms (efficient network coloring).
Problems in descriptive set theory (measuring infinite graph colorings) are mathematically equivalent to problems in distributed algorithms (efficient network coloring).
A 12-week, 26-lesson curriculum all about Machine Learning, using primarily Scikit-learn and avoiding deep learning.
The `mlabonne/llm-course` GitHub page offers a comprehensive LLM education in three parts: **Fundamentals** (optional math/Python/NN basics), **LLM Scientist** (building LLMs – architecture, training, alignment, evaluation, optimization), and **LLM Engineer** (applying LLMs – deployment, RAG, agents, security). It’s a detailed syllabus with extensive resources for learning the entire LLM lifecycle, from theory to practical application.
The `mlabonne/llm-course` GitHub page offers a comprehensive LLM education in three parts: **Fundamentals** (optional math/Python/NN basics), **LLM Scientist** (building LLMs – architecture, training, alignment, evaluation, optimization), and **LLM Engineer** (applying LLMs – deployment, RAG, agents, security). It’s a detailed syllabus with extensive resources for learning the entire LLM lifecycle, from theory to practical application.
Researchers have refined the simplex method, a key algorithm for optimization, proving it can't be improved further and providing theoretical reasons for its efficiency.
Mathematicians are using Srinivasa Ramanujan's century-old formulae to push the boundaries of high-performance computing and verify the accuracy of calculations.
This book provides an introductory, textbook-like treatment of multi-armed bandits. It covers various algorithms and techniques for decision-making under uncertainty, with a focus on theoretical foundations and practical applications.
* **Multi-Armed Bandit Framework:** The document introduces the core concept of multi-armed bandits – a model for decision-making under uncertainty, often used as a simplified starting point for more complex reinforcement learning problems.
* **Applications:** It highlights several applications, including news website optimization, dynamic pricing, and medical trials.
* **Key Concepts:** Defines crucial concepts like arms, rewards, regret, exploration vs. exploitation, and different feedback mechanisms (bandit, full, partial).
* **Algorithms:** Presents and analyzes simple algorithms like Explore-First and Epsilon-Greedy.
* **Regret Bounds:** Focuses heavily on bounding the regret of these algorithms, which measures how much worse the algorithm performs compared to always choosing the best arm.
* **Adaptive Exploration:** Introduces the idea of improving performance through adaptive exploration strategies (adjusting exploration based on observed rewards).
* **Clean Event:** Introduces the concept of the "clean event" to simplify analysis by focusing on high probability events.
* **Table of Contents:** Shows a detailed table of contents, indicating the breadth of topics covered in the full book including Bayesian Bandits, Contextual bandits, Adversarial bandits and connection with economics.
* **Multi-Armed Bandit Framework:** The document introduces the core concept of multi-armed bandits – a model for decision-making under uncertainty, often used as a simplified starting point for more complex reinforcement learning problems.
* **Applications:** It highlights several applications, including news website optimization, dynamic pricing, and medical trials.
* **Key Concepts:** Defines crucial concepts like arms, rewards, regret, exploration vs. exploitation, and different feedback mechanisms (bandit, full, partial).
* **Algorithms:** Presents and analyzes simple algorithms like Explore-First and Epsilon-Greedy.
* **Regret Bounds:** Focuses heavily on bounding the regret of these algorithms, which measures how much worse the algorithm performs compared to always choosing the best arm.
* **Adaptive Exploration:** Introduces the idea of improving performance through adaptive exploration strategies (adjusting exploration based on observed rewards).
* **Clean Event:** Introduces the concept of the "clean event" to simplify analysis by focusing on high probability events.
* **Table of Contents:** Shows a detailed table of contents, indicating the breadth of topics covered in the full book including Bayesian Bandits, Contextual bandits, Adversarial bandits and connection with economics.
A new paper demonstrates that the simplex method, a widely used optimization algorithm, is as efficient as it can be, and explains why it performs well in practice despite theoretical limitations.
