Adversarial evaluation of large-language-model agents is usually expressed as event counts: attack-success rate, policy-violation rate, refusal-failure rate, pass percentage, or robustness score. These measures are necessary, but they do not show whether a safety intervention removed a load-bearing failure mode or merely suppressed the measured cases. This paper presents a model-agnostic framework for training and evaluating LLM agents using pressure-indexed persistent homology. The framework is intentionally reduced to two core constructs: topological robustness, meaning stable policy-compliant structure under increasing adversarial pressure, and topological anti-fragility, meaning before/after structural improvement after controlled adversarial hardening. Agent conduct is represented as a finite metric space of responses, decisions, and tool-call trajectories annotated by engineered pressure. Filtering this space by pressure yields summaries that distinguish a pressure-persistent safe core from recurrent unsafe structures. We also introduce a held-out release gate to reduce Goodhart-style overfitting to the development attack suite. To make the proposal empirically testable, we report a reproducible instrumented pilot with 1,440 generated agent traces. The pilot is not an external validation over production LLMs; it is a controlled proof of concept with known ground truth. The contribution is a structural complement to red-teaming: a way to ask whether an agent was actually hardened under adversarial load or merely adapted to the measured attacks.
Keywords — LLM agents, AI safety, adversarial robustness, topological data analysis, persistent homology, red-teaming
1.Research problem
Adversarial evaluation of LLM agents is usually expressed as event counts, which do not show whether an intervention removed a load-bearing failure mode or merely suppressed the measured cases.
2.Contribution
A model-agnostic framework using pressure-indexed persistent homology to train and evaluate LLM agents.
Two core constructs: topological robustness and topological anti-fragility.
A held-out release gate to reduce Goodhart-style overfitting to the development attack suite.
3.Architecture, methodology & evidence status
Evidence & statusThis is a preprint hosted on Research Square and has not undergone peer review. It is an independent research contribution; its claims and any reported experiments should be read as such. The proposal is made empirically testable through a specified protocol; reported work is a synthetic controlled pilot rather than validation on production agents.
The abstract above is the authoritative summary of the work as posted at the official source. This archival record does not add results, figures or claims beyond those in the published/posted manuscript. For the complete methodology, results and references, consult the official record or the archived PDF.
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Shirbint, E., & Rybalov, A. (2026). A Topological Robustness and Anti-Fragility Framework for LLM Agents. Research Square. https://doi.org/10.21203/rs.3.rs-9932131/v1
Emanuel Shirbint, and Alexander Rybalov. 2026. “A Topological Robustness and Anti-Fragility Framework for LLM Agents.” Research Square. https://doi.org/10.21203/rs.3.rs-9932131/v1.
@misc{shirbint2026topologicalrobustnessllmagents,
title = {A Topological Robustness and Anti-Fragility Framework for LLM Agents},
author = {Emanuel Shirbint and Alexander Rybalov},
year = {2026},
doi = {10.21203/rs.3.rs-9932131/v1},
url = {https://doi.org/10.21203/rs.3.rs-9932131/v1},
note = {Not peer-reviewed}
}
TY - PREPRINT
AU - Emanuel Shirbint
AU - Alexander Rybalov
TI - A Topological Robustness and Anti-Fragility Framework for LLM Agents
PY - 2026
DO - 10.21203/rs.3.rs-9932131/v1
UR - https://doi.org/10.21203/rs.3.rs-9932131/v1
N1 - Not peer-reviewed
ER -