LLM Inference — From Tokens to Claude

How does typing a prompt produce an answer? Covers everything from scratch: tokenization (BPE), embeddings, RoPE positional encoding, scaled dot-product attention, multi-head attention, transformer blocks (RMSNorm, SwiGLU, residuals), autoregressive decoding, KV cache, GQA, sampling strategies (temperature, top-p), context windows, scaling laws, and current trends — speculative decoding, MoE, Flash Attention, quantization. All interactive.

Video Encoding & Decoding — I/P/B Frames, GOP, Quantization & FFmpeg

How raw pixels become a compressed bitstream from first principles. Covers YCbCr color space, block partitioning, intra/inter prediction, I/P/B frame construction (encoding and decoding), GOP structure, the DCT, quantization (QP, rate-distortion), entropy coding (CABAC), and how FFmpeg ties it all together — with 5 interactive visualizations.

Camera Intrinsics & Extrinsics — The Full Projection Pipeline

How a 3D point in the world ends up as a pixel on your screen. Covers world coordinates, the extrinsic matrix [R|t], the intrinsic matrix K, perspective divide, and what a real camera's sensor actually does — all interactive.

3D Shape Representations — From Points to Neural Fields

A guided tour of every major 3D representation: point clouds, meshes, voxel grids, KD-trees, and tri-planes. Then: surface normals, signed distance functions, Chamfer & Hausdorff distances, explicit vs. implicit rendering, and eikonal regularization — all with live interactive visualizations.

Triangle Deformation: Local Frames, Jacobians & UV Parameterization

How does a 3D triangle become a 2D UV face — and how much is it distorted? Build intuition from local coordinate frames to the per-face Jacobian, SVD, and ARAP/ACAP energies, with interactive visualizations throughout.

Singular Value Decomposition — The Geometry of Linear Maps

Every matrix is secretly rotate → stretch → rotate. SVD reveals those three steps visually: an interactive 2D transform explorer, eigenvalue vs singular value spectrum comparison, live image compression with a rank slider, and a PCA scatter plot — all with the full math.

PLCC, SROCC, KRCC & RMSE — Correlation Metrics for IQA/VQA

How to evaluate whether a quality model agrees with human perception. Covers Pearson linear correlation, Spearman rank correlation, Kendall concordance, and RMSE — with interactive visualizations, Q&A format, and failure case analysis.

Neural Networks from Scratch — Layers, Activations & Loss Functions

Build every piece of a neural network using raw PyTorch tensors — no nn.Linear, no autograd. Covers the Linear layer forward/backward pass with full complexity analysis (O(BMN)), seven activation functions with their gradients, five loss functions from MSE to Softmax-CE, and a complete MLP training loop. Three interactive visualizations let you explore activations, watch forward-pass activations flow through a live network, and compare loss landscapes side by side.