Foundation Lab

Efficiency: Quantization, Distillation, LoRA & Sparse MoE

Quantization + LoRA are standard for deploying and fine-tuning Llama-class models on modest GPUs

Concept 16 of 100EfficiencyPhase 8

Open New Notebook All Foundations

#16EfficiencyEfficiency

key equationW' = W + BA,\quad r \ll d

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 16 of 100EfficiencyEfficiency / Phase 8: Scaling, theory & multimodal

Current question

Geometric views of low-rank updates: LoRA as adding a small, oriented "slice" in weight space

W' = W + BA,\quad r \ll d

PredictionCommit before the demo.

Ask what should change when the equation is manipulated, then let the visualization test that expectation.

EvidenceCompare local witness and source.

Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.

InvariantName what survives notation changes.

The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.

Next moveContinue in the newer notebook.

This atlas page keeps the working demo; the domain notebook carries the fuller Intuition -> Math -> Code -> Demo sequence.

Open demo Inspect equation Open newer notebook Next foundation

Why It Matters for Modern Models

Quantization + LoRA are standard for deploying and fine-tuning Llama-class models on modest GPUs
Distillation compresses large base models into "small assistants"
MoE/Switch-style sparsity powers very large Google-scale models (likely Gemini)

What Tutorials Skip

What is still poorly explained in textbooks and papers:

Geometric views of low-rank updates: LoRA as adding a small, oriented "slice" in weight space
Intuitive trade-offs in quantization: how error propagates, why some layers are more sensitive

Interactive Visualization

Core Math (Optional Deep Dive)

If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.

Key Equation

W' = W + BA,\quad r \ll d

Distillation: train student $q_\psi$ to match teacher $p_\theta$ :

\mathcal L = T^2\,\mathrm{KL}(p_\theta^T(\cdot\mid x)\,\|\,q_\psi^T(\cdot\mid x))

Quantization: map float weights to low-bit integers: $\tilde w = \Delta \cdot \mathrm{round}(w/\Delta)$

LoRA: re-parameterize weight matrix as: $W' = W + BA$ , where $B\in\mathbb R^{d\times r}, A\in\mathbb R^{r\times d}, r\ll d$ — only train $A,B$ , freezing $W$ .