Guided Symbiosis Theory

Machine-verified core (190 Lean 4 modules, 0 sorryAx) and GRPO-aligned model achieving +15.6% accuracy with a 37.2% reduction in reasoning tokens.

Project Details

Guided Symbiosis Theory (GST) is a mathematical framework that models AI alignment and trajectory safety as a deterministic state-space control problem on an infinite horizon (t -> infinity). It replaces soft constraints with strict mathematical boundaries derived from Pontryagin's Maximum Principle.

Key Artifacts & TRL Status (TRL 4+):

Formal Verification in Lean 4: Fully machine-checked the GST Core V2 optimal-control model (190 modules, 0 sorryAx).

Link: https://zenodo.org/records/23296683

Integration into a Real LLM (Symbiont): Mapped the GST objective into a reward system and fine-tuned DeepSeek-R1-Distill-Qwen-7B via GRPO on an H100 GPU. Achieved a strong early signal: +15.63% accuracy on MBPP with a 37.2% reduction in reasoning tokens.Full execution logs and raw run data are available upon request.

Open Science: Open-access research artifacts, papers, and formal codebases fully documented and DOI-indexed on Zenodo.

Led by Yaroslav Isachenkov (Chief Architect) under NGO Guided Symbiosis Theory (Kyiv, Ukraine).

Theory of Impact

Standard alignment approaches rely on soft constraints, RLHF, and prompt-level heuristics, which fail under heavy optimization pressure and instrumental convergence. GST mitigates catastrophic risk by modeling human oversight and safety metrics directly as phase-space state variables within optimal control equations on an infinite horizon (t→ ∞).

Core Hypothesis: Corrigibility is not an artificial behavioral constraint, but the unique mathematically stable phase-space condition for long-term agent-human symbiosis (t→ ∞). Any trajectory deviating from human oversight inevitably destabilizes the system's optimal control functional.

Causal Chain:

Formal Proofs: Machine-verified Lean 4 guarantees (0 sorryAx) eliminate mathematical and logical gaps in the core control equations prior to model fine-tuning or deployment.

Phase-Space Boundaries: Rather than attempting deterministic hard-filtering on stochastic neural outputs, the control layer defines valid phase-space constraints. Trajectories deviating from safety bounds destabilize the agent's optimal control functional.

Compute-Efficient Alignment: Embedding GST objective functions into policy optimization (GRPO) keeps model behavior within verified boundaries while reducing reasoning token overhead, making mathematical safety viable for frontier LLM scaling.

People

Yaroslav Isachenkov

Team Member

Grants Received– no grants recorded

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Funding Asks

Funding ask

Open

Minimum

$3,000

Ideal

$30,000

How the money will be spent

All requested funds will be directly allocated to H100 GPU compute resources for reward structure debugging, policy optimization, and scaling via GRPO.

Minimum Budget ($3,000): Reward Shaping & 7B Model Debugging

Initial runs highlighted the need for iterative reward shaping to fine-tune the integration of GST loss components. This baseline funding covers final H100 GPU compute passes required to address edge-case reward signals and stabilize output trajectories on 7B models (DeepSeek-R1-Distill-Qwen-7B).

Ideal Budget ($30,000): Scaling to ~70B Open Models

Full funding enables scaling the machine-verified GST core to larger ~70B parameter models across various architectures (Qwen, Llama).

Covers cluster-level H100 compute for full-scale fine-tuning, evaluation across extended benchmarks, and empirical verification of trajectory stability under heavy optimization pressure.

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