Graflib

Visualize the Connections.

Navigate complex subjects with interactive knowledge graphs. We transform intricate topics into intuitive, explorable networks to accelerate your learning.

Explore Graphs

How It Works

A simple way to dive deep into any subject.

Select a Topic

Choose from our growing library of subjects, from abstract mathematics to cutting-edge AI.

Explore Connections

Pan, zoom, and click on nodes to uncover relationships and dependencies between different concepts.

Deepen Understanding

Read concise, expert explanations for each concept, complete with formulas and key insights.

Explore Our Knowledge Graphs

Click any card to launch the interactive visualization.

Positional Encoding

ML & AI

Uncover the ingenuity of positional encoding. See how this critical step injects the concept of order into models that otherwise perceive text as just an unordered bag of words. Learn how unique vectors, generated from sine and cosine waves, provide a distinct 'address' for each token, empowering the model to understand syntax and context based on relative position.

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Inner Product

Mathematics

Explore the power of the inner product. See how this fundamental operation takes two vectors and distills their geometric relationship into a single number, revealing concepts like length, distance, and angle. Understand how it provides the essential test for orthogonality, forming the very foundation of vector projection and geometric measurement.

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Quantum Operators

Physics

Unlock the dynamics of the quantum realm. ⚛️ See how these fundamental tools act as the mathematical representation of physical observables, like energy, position, and momentum. Understand how an operator, when applied to a quantum state, extracts the possible outcomes of a measurement—its special values known as eigenvalues. Discover how they form the very foundation of quantum prediction, governing everything from the results of experiments to the evolution of a system through time via the Schrödinger equation.

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Our Mission

We believe that the best way to learn is by visualizing the connections. Traditional books often present linked concepts far apart, leaving learners to connect the dots on their own. Our mission is to build a platform that makes these connections explicit, tangible, and beautiful, empowering anyone to explore and understand the rich tapestry of knowledge.