When Tools Lie: Reliability of Mathematical Agents Under Corrupted Tool Feedback
Kavienan Jegatheesan and Gayathri Lihinikaduarachchi (University of Moratuwa) test how math agents handle tool calls that silently return plausible wrong results, using a hidden interceptor that corrupts tool outputs.
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Setup. 31 problems, four verification designs: no verification, mandatory same-context reflection, optional fresh-context verification, and optional structural verification, with Claude Haiku and Sonnet.
Corruption hurts. Without verification, Haiku drops from 100% on clean items to 72.4% on corrupted ones, and Sonnet from 100% to 81.5%.
Mandatory reflection recovers it. Requiring reflection brings Haiku back to 100%, at a 3.2% false-distrust cost where correct tool outputs get flagged.
Optional checks depend on use. Optional verifiers help only when the model calls them, so verifier availability and verification policy act as separate factors.
Recovery. After explicit detection, restarting the problem succeeds in 100% of cases.
Abstract
Mathematical problem solving often requires deterministic computational steps that agents delegate to tools and implicitly trust. Yet tools can fail silently, returning plausible but incorrect results. How well can agents detect and correct corrupted tool call outputs? We study this through a controlled corruption framework where a hidden interceptor replaces tool call results with plausible incorrect information on targeted problems. We evaluate agents across 31 problems under four verification designs including no verification (baseline), mandatory same-context reflection, optional fresh-context verification, and optional structural verification. Without verification, corruption causes dramatic accuracy loss, from 100% down to 72.4%. Mandatory reflection fully recovers this performance to 100%. Optional verification improves accuracy only when models actively invoke it. Our results show that checking frequency is strongly associated with robustness differences, while unequal invocation prevents a controlled comparison of verifier quality. A supporting recovery experiment shows that full problem restart succeeds in 100% of cases after explicit detection. These findings demonstrate that verifier availability and verification policy are separate components of mathematical-agent reliability. Mandatory policies enforce verification while optional policies depend on the model's own choice to invoke it.