Learn EqLM
Seven short explainers that bridge game theory, equilibrium computation, and practical training. Every number comes from validated findings. Start anywhere.
Why Game-Theoretic Training
The foundational thesis: equilibrium learning dynamics in multi-agent systems.
Magnetic Mirror Descent and Last-Iterate Convergence
How MMD reaches equilibrium where standard GDA cycles.
Equilibrium Language Models — Depth as a Fixed Point
How DEQ transformers enable equilibrium computation inside the model.
The Honest Scaling Story: Two Misses, Then Parity
How the width gap appeared, widened, and was closed by changing the training regime.
Token Auctions: Where They Win and Where They Don't
Truthful per-token model selection — a scoring-time win with an honest closed-loop boundary.
Preference Optimization: an Under-Dosed Magnet and an Unexpectedly Stable Architecture
What DPO does to unseen phenomena, and why the equilibrium model barely moves.
The Closure Contract and Reproducibility
How findings are verified and signed off.
How to Read
Each section pairs a real finding (or set of findings) with its meaning. We don't explain the theory first and then show the evidence; instead, we start with the discovery and build backward.
What you'll find: The claim, the numbers (with experiment IDs like F1, F22), and the implication for future work or understanding. No invented examples. Every number is traceable to research/memory/findings.md.
One sentence per section: Each ends with a takeaway—the one thing that should stick. Use these to navigate and decide where to dive deeper.