to avoid render-blocking @import chain (#13) -->Empirical Lyapunov Stability: Growth-Ratio Energy Functions as Leading Indicators of Agent Task Failure — Vishal Verma Labs

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&larr; All articlesKey takeaways This paper presents the first empirical validation of Lyapunov stability analysis applied to LLM agent execution trajectories, featuring a 5-condition ablation study across 3,175 total runs. Evaluated across four benchmarks—τ³-bench (750 runs, customer service), SWE-bench Verified (481 runs including 333 multi-trial, software engineering), MINT (1,136 runs, reasoning and coding), and a custom local-model battery (808 runs across 4 open-weight models on consumer hardware via Ollama)—we demonstrate that growth-ratio normalization transforms a theoretically sound but practically useless raw energy derivative into a precise leading indicator of task failure. Cross-model validation across 5 model families (Gemini 2.5 Flash, Llama 3.2:3B, Phi-4-Mini, Qwen3:4B, Gemma4:E4B) confirms zero false positives and consistent guard behavior. Local model evaluation reveals a novel small-model self-sabotage pattern: naive turn-limiting outperforms unconstrained baselines by +17.5pp on average because small models destroy correct solutions in later turns. The implementation is released as state-harness, an open-source Rust/Python library with first-class LangGraph and CrewAI adapters, a CLI tool, and OpenTelemetry export.<br>Abstract

In our prior theoretical work [1], we proposed a physics-inspired framework for governing the semantic boundary layer of multi-agent AI systems, drawing on Lyapunov stability theory, Renormalization Group compression, and Vector Symbolic Architectures. That framework was a theoretical edifice—mathematically grounded but empirically unverified.

This paper presents its empirical validation through a 5-condition ablation study (3,175 total runs) isolating each mechanism’s contribution, with multi-trial validation (333 SWE-bench runs) confirming statistical robustness and cross-model validation across 5 model families including 4 open-weight local models.

We implement the proposed framework as state-harness , a hybrid Rust/Python runtime safety library, and evaluate it across four complementary benchmarks: τ³-bench [2] (customer-service agents, 750 runs), SWE-bench Verified [14] (software engineering agents, 481 runs), MINT [15] (multi-turn reasoning and coding, 1,136 runs), and a custom local-model battery (808 runs across 4 open-weight model families via Ollama on consumer hardware). Our central empirical finding is that the naive Lyapunov energy function V(k)=S(k)+λθ(k)V(k) = S(k) + \lambda\theta(k)V(k)=S(k)+λθ(k) produces unacceptable false positive rates (46%) because multi-turn conversations naturally exhibit ΔV≥0\Delta V \geq 0ΔV≥0 as context windows accumulate. We resolve this through growth-ratio normalization : monitoring the ratio V^(k)=S(k)/Sˉ\hat{V}(k) = S(k)/\bar{S}V^(k)=S(k)/Sˉ against a warmup baseline rather than raw token counts. This normalization transforms an unstable diagnostic signal into a precise leading indicator of task failure.

Our 5-condition ablation (Baseline → Lyapunov-only → Lyapunov+RG → Full-stack → Naive Cap) reveals four principal results: (1) on short/medium-loop benchmarks (MINT + τ³), the monitor achieves zero stability violations across 1,886 runs with The implementation is released as open-source: github.com/vishal-dehurdle/state-harness. Install via PyPI: pip install state-harness.

1. From Theory to Measurement: The Experimental Program

Our prior theoretical work [1] proposed that the catastrophic failure modes of production multi-agent systems—Token Tsunamis, semantic drift, and context dilution—can be formally modeled using the mathematical machinery of dynamical systems theory. That framework drew on Lyapunov stability theory, Renormalization Group compression, and Vector Symbolic Architectures to construct a physics-inspired governance layer for autonomous agents.

Theoretical frameworks, however elegant, require empirical validation. This paper provides it — evaluating all three mechanisms through a 5-condition ablation study that isolates each layer’s contribution.

Specifically, our prior work [1] proposed three mechanisms:

A Lyapunov energy function V(k)=S(k)+λθ(k)V(k) = S(k) + \lambda\theta(k)V(k)=S(k)+λθ(k) whose derivative ΔV(k)\Delta V(k)ΔV(k) indicates trajectory stability.

Renormalization Group decimation to compress high-entropy agent communications into scale-invariant macrostates.

Holographic Invariant Storage via Vector Symbolic Architectures to detect policy drift outside the LLM context window.

This paper empirically evaluates all three mechanisms through a 5-condition ablation study that isolates the contribution of each layer.

Our experimental program asks four questions:

QuestionMethodSectionQ1: Does the raw Lyapunov energy derivative ΔV≥0\Delta V \geq 0ΔV≥0 predict task failure, and why does it...