Rigorous mathematical derivations, original research paper deconstructions, and continuous physical intuition bridging classical mechanics, thermodynamics, and large-scale AI engineering.
Modern deep learning is often presented as empirical alchemy. But through the lens of continuous physics — phase spaces, Hamiltonian mechanics, and entropy — neural networks reveal an astonishing, elegant mathematical symmetry.
Transformers are typically introduced as sequential query-key-value projections. But modern statistical physics proves that self-attention is a continuous-state associative memory network that minimizes a Lyapunov energy function in a single update step.
Backpropagation is often treated as mysterious magic. In this engineering deep dive, we build a complete, micrograd-style reverse-mode automatic differentiation engine in pure Python with zero external libraries.
Serving modern Large Language Models is memory-bandwidth bound rather than compute bound. We derive the exact byte equations for KV-cache memory footprints, compare Multi-Head vs. Grouped-Query Attention, and explore PagedAttention paging algorithms.
Fine-tuning full foundation models requires terabytes of VRAM for Adam states. LoRA proves that task adaptation lives on a tiny low-rank manifold. We decompose the linear algebra, intrinsic dimensionality, and weight-merging mechanics.
Curated mathematical derivations, interactive lab releases, and research breakdowns. 100% free, client-side executable, and engineered for thinkers and builders.
