Ancient Algorithms
Tested Against Modern ML
We tested whether the King Wen I-Ching sequence's anti-habituation properties improve neural network training. The answer is no. The sequence has genuine statistical structure—confirmed by Monte Carlo analysis against 100,000 random baselines—but these properties destabilize gradient-based optimization rather than helping it.
By Augustin Chan with AI · Published January 2025 · Updated June 2026
Symbolic Reasoning Frameworks Modulate LLM Risk Aversion in Multi-Agent Strategic Settings
The Diplomacy-style simulation now has a preprint. In a seven-player Warring States variant, large language models turn out to be inherently risk-averse as strategic agents — and symbolic reasoning frameworks, applied as reflective prompts, measurably shift that bias and each framework's winner distribution. The guided agent never won, but framework choice changed its territorial performance. The effect runs through the act of reflection itself, not the framework's semantic content.
Research Materials
Research Paper
Negative result: the King Wen sequence has genuine statistical properties but they do not improve neural network training. Tested via LR modulation, curriculum ordering, and seed sensitivity analysis on two platforms.
Phase 1 — arXiv Preprint
Published in cs.LG (Machine Learning). The paper reports a rigorous negative result: the King Wen sequence's anti-habituation properties are statistically real but do not help neural network training. Includes experiments on two platforms with a 30-seed sensitivity analysis.
Phase 2 — arXiv Preprint
The Diplomacy-style simulation. In a seven-player Warring States variant, symbolic reasoning frameworks applied as reflective prompts modulate LLMs' inherent risk aversion and shift each framework's winner distribution. The guided agent never won, but framework choice changed its territorial performance — an effect that runs through reflection itself, not semantic content.
Results
Experimental Findings
LR Modulation
King Wen surprise profile as learning rate modulation degrades performance at all amplitudes (0.15, 0.3, 0.5). Worse than both random and Shao Yong controls.
Curriculum Ordering
As data ordering strategy, King Wen is the worst non-sequential ordering on CUDA and within noise on MLX. Random shuffle beats everything.
Statistical Properties
The sequence genuinely has anti-habituation structure: high transition distance, negative autocorrelation, yang balance. Confirmed vs 100K random permutations.
Why It Doesn't Work
The sequence's high variance—the property that makes it statistically distinctive—destabilizes gradient-based optimization. Negative autocorrelation disrupts optimizer momentum. Anti-habituation is premature for models still in early learning. A fixed 3,000-year-old sequence cannot adapt to the learner's state.
Phase 2 Design
The Oracle Changes the Board
All seven states are language-model agents with historical personas. The only variable is the symbolic framework Han — the weakest state — reflects through each round before it issues orders. Four conditions were run across a seven-player Diplomacy variant: a baseline with no oracle, the King Wen I-Ching (yarrow), tarot, and a scrambled-text ablation that preserves the ritual's structure but strips its meaning.
Han never wins, and its survival rate is flat across every condition. But the framework it reflects through reshapes which other state dominates — and because the framework's content (hexagram themes, tarot postures) does not predict Han's actions, the effect runs through the act of reflection itself, not the symbols' meaning.
| Framework Han reflects through | Who dominates the board | Han's own outcome |
|---|---|---|
| Baseline (no oracle) | Yan dominates (7/11) | Never wins |
| King Wen I-Ching (yarrow) | Yan & Chu co-dominate; Qin suppressed (0/10) | Never wins; survival flat |
| Tarot | Qin dominates (5/10, p = 0.006) | Higher peak territory, still no win |
| Scrambled text (ablation) | Qi dominates (5/10, p = 0.006) | Never wins |
The finding: the oracle changes the board, not the oracle-user. A symbolic framework injected into one weak agent modulates its inherent risk aversion and ripples outward to reshape outcomes for every other agent in the system. Full results in arXiv:2606.07552.
Why Han?
The ultimate underdog test case
Historical Constraints
- 疆Smallest territory of the seven Warring States
- 貧Poor resources and strategic depth
- 困Strategically boxed in by Qin, Wei, and Chu
- 亡First to fall to Qin (230 BC)
AI Opportunity
Early 3-state trials eliminated Han in 93% of games, confirming the need for full 7-state geopolitical complexity. The published Phase 2 run (arXiv:2606.07552) settled the survival question: the guided agent never won, and survival stayed flat across frameworks. The real finding is subtler — the symbolic framework an agent reflects through measurably shifts its risk aversion and territorial performance, even when the framework's semantic content does not predict its moves.
Potential Strategies
- Overcome extreme geopolitical constraints
- Form strategic alliances
- Engineer asymmetric strategies
- Leverage espionage and diplomacy
Scaling the Experiment
Alternative Test States
For testing a new learning algorithm, you want a historically disadvantaged but initially viable state. These candidates could serve as interesting underdogs:
Wei
Once Mighty, Then Declined
Challenge: Reverse-engineer successful Qin deterrence
Opportunity: Test long-term planning and strategic correction
Yan
Isolated and Slow to Act
Challenge: Build stable power base in the north
Opportunity: Use unconventional warfare and early alliances
Zhao
Brave but Overwhelmed
Challenge: Balance tactical vs. strategic skills
Opportunity: Leverage military talent with better strategy
Qi
Economic Powerhouse
Challenge: Translate wealth into lasting dominance
Opportunity: Leverage Jixia Academy and salt monopoly
Chu
Complex Geopolitics
Challenge: Manage vast territory effectively
Opportunity: Test complex alliance dynamics
Qin
Test Restraint
Challenge: Test restraint, not power
Opportunity: Avoid over-aggression and maintain stability
Recommendation: Use Han as the Test Bed
Han is historically the most constrained—minimal land, minimal power, first to die. If your AI can lead Han to survive or even dominate, you have a powerful system.
Scaling Strategy: Start with Han (baseline AI), then scale to Wei/Yan (advanced challenge), Zhao/Chu (complex geopolitics), and Qin (test restraint, not power).