How Do Small Coding Agents Use Code Graphs and Embeddings?
Coding agents are given embedding search and code-graph tools on the premise that a repository's structure is something the model lacks and the tool supplies. We test that premise on SWE-bench Verified with small open-weight models, stratifying tasks by a deterministic hop depth (the shortest code-graph path from code the issue mentions to code the gold patch changes) that a companion paper defines and validates. First, we ablate a localization agent's tool set (grep only; +embedding search; +graph tools; all) on a depth-balanced 160-task split and on all 500 tasks for ten models (six Qwen3 sizes from 0.6B to 32B with five decodings each, an FP8 control, three Gemma 4 sizes; 79k episodes). Structured tools double grep-only accuracy for Qwen3-8B and Gemma 4 E4B; their gain peaks at 17-21 points at 1.7-4B and falls to 4-5 points at 32B (odds ratio 0.77-0.82 per doubling of parameters). From 8B up, about half of that gain is the form of the submission rather than finding the target; the fall from 14B to 32B is a fall in tool uptake at equal grep-only accuracy; and the same 4B size gains or does not gain from a tool depending on the checkpoint. Each extra hop multiplies the odds of correct localization by 0.50-0.67 at every size, and no tool set flattens that gradient: traces show the graph tools' gain is name lookup at hop 0 and one expansion at hop 1, and agents chain expansions in only 12-14% of episodes. A fixed repair model resolves 6-13 of 160 tasks from these localizations (oracle 26). Second, linear probes find direct call edges decodable under a within-anchor, degree-stratified protocol (AUC 0.74; 0.61-0.66 inside agent conversations), but below a lexical baseline (0.99), with two-hop edges at 0.57. Small agents carry a one-hop, largely lexical picture of their repository, in weights and in use. We release the agent, probes, logs and traces.