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Peak-Then-Collapse and the Four Interface Channels of Knowledge-Graph Tool Use

We test the standard RLVR tool-use recipe -- GRPO on Qwen2.5-7B-Instruct -- on a deliberately minimal knowledge-graph tool API: four Freebase navigation verbs over Complex WebQuestions. Under a self-verifiable retrieval reward, the policy's tool-grounded answer rate climbs from $3.8\%$ to $9.6\%$ over 250 steps, then collapses to $0\%$ within a single 50-step window -- a \emph{peak-then-collapse} pattern replicated across four seeds. Across seven reward designs, we find four recurring failure modes: adding denser or more targeted proxy rewards shifts the failure mode rather than eliminating it. We argue that a key difference from Python interpreters, web search, and JSON APIs is interface feedback: their failures often leak natural-language signal the model saw in pretraining. A Python traceback names the failing line; an empty Freebase result \texttt{[]} does not. Stripping away that surface exposes a degradation regime that same-family reward redesigns do not fix. A direct oracle ablation rules out relation selection: injecting gold relations at every retrieval call lifts exact-match accuracy by only $+0.20$~pp, and $95.4\%$ of retrieval-dependent errors are retrieval-composition failures rather than answer-extraction failures. As a mitigation, one-iteration self-distillation reaches $40.0\%$ EM at 7B and is capacity-invariant: doubling capacity to 14B improves EM by only $0.25$~pp, and initialization barely matters -- the ceiling appears interface-bound within the 7B--14B range tested.

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