Kinetic AI

A unified library for game-theoretic LLM training: Magnetic Mirror Descent, Deep Equilibrium Models, and Mechanism Design.

The Thesis

Current AI systems are trained via dictatorial optimization — a single loss function forces updates on every parameter. But real-world deployment environments are adversarial, multi-agent, and strategic. Game theory, not optimization, is the correct mathematical framework.

Kinetic AI implements the transition from static optimization to dynamic equilibrium:

Everything above traces to committed runs under results/ (config hashes + seeds). The research process is spec-driven and adversarially reviewed — see CLAUDE.md, research/specs/, and docs/decisions/. Paper: paper/kinetic_ai.tex. Site: site/. Researcher app: apps/web + app/server.py (see apps/web/DEPLOY.md).

Installation

pip install -e ".[all]"

Quick Start

Strategy-Space MMD on Rock-Paper-Scissors

import torch
from kinetic_ai.games.payoff import rock_paper_scissors
from kinetic_ai.games.qre import nash_conv
from kinetic_ai.optim.bregman import NegativeEntropy
from kinetic_ai.optim.mmd import mmd_strategy_update

game = rock_paper_scissors()
bregman = NegativeEntropy()

s1 = torch.tensor([0.7, 0.2, 0.1])  # Biased initial strategy
s2 = torch.tensor([0.1, 0.7, 0.2])
ref = torch.ones(3) / 3  # Uniform reference (magnet)

for step in range(500):
    # Sequential (alternating) updates with reduced learning rate
    # ensure convergence. Simultaneous updates require tighter stepsizes.
    g1 = game.utility_gradient(1, s1, s2)
    s1 = mmd_strategy_update(s1, g1, ref, bregman, lr=0.1, tau=0.05)
    
    g2 = game.utility_gradient(2, s2, s1)
    s2 = mmd_strategy_update(s2, g2, ref, bregman, lr=0.1, tau=0.05)

print(f"NashConv: {nash_conv(game, s1, s2):.6f}")  # Converges to τ-regularized QRE (≈Nash for RPS)

DEQ Layer with Anderson Acceleration

import torch
import torch.nn as nn
from kinetic_ai.config import DEQConfig, SolverType
from kinetic_ai.models.deq_layer import DEQLayer

transform = nn.Linear(32, 16)
def f(z, x):
    return torch.tanh(transform(torch.cat([z, x], dim=-1)))

deq = DEQLayer(f, DEQConfig(solver=SolverType.ANDERSON, max_iter=50))
z_star = deq(torch.randn(1, 16))  # Finds equilibrium state

Token Auction

import torch
from kinetic_ai.config import AuctionConfig, AuctionType
from kinetic_ai.mechanisms.auctions import TokenAuction

auction = TokenAuction(AuctionConfig(
    auction_type=AuctionType.WEIGHTED_AGGREGATION,
    vocab_size=1000,
))

bids = torch.tensor([2.0, 5.0, 1.0])
dists = torch.softmax(torch.randn(3, 1000), dim=-1)
result = auction.run_auction(bids, dists)
print(f"Selected token: {result.sampled_token}")

Architecture

kinetic_ai/
├── optim/          # Magnetic Mirror Descent + Bregman divergences
├── models/         # Deep Equilibrium Layers (Anderson, Broyden, Picard)
├── mechanisms/     # Token auctions, mechanism design
├── games/          # Game definitions, QRE computation, self-play
├── eval/           # Convergence diagnostics, statistical testing
└── config.py       # Config-driven experiment system

Running Tests

pytest tests/ -v                    # All tests
pytest tests/ -v -m "not slow"      # Skip slow convergence tests

Running the Full Simulation

python simulate.py

References

1. Sokota et al. "A Unified Approach to RL, QRE, and Two-Player Zero-Sum Games" (NeurIPS 2023)
2. Bai et al. "Deep Equilibrium Models" (NeurIPS 2019)
3. Duetting et al. "Mechanism Design for Large Language Models" (WWW 2024, Best Paper)
4. Wu et al. "Self-Play Preference Optimization for Language Model Alignment" (2024)
5. McKelvey & Palfrey "Quantal Response Equilibria for Normal Form Games" (1995)

License

MIT