LoRA layer from scratch with a merge test

Wrap attention projections with low-rank adapters, verify merged and unmerged outputs agree, and compare two ranks with full fine-tuning at matched steps and seeds.

The exercise happens on Self-directed project (reference implementation linked). Canonical link: https://github.com/microsoft/LoRA. Link check: link responded (5 Oct 2026). Opened from this app 0 times; opening is not counted as an attempt.

Supports: Turns the LoRA paper into implementation-level understanding for research-ML and ML-engineering roles.