IC-523LLMs rely on observed facts close to the test case in input feature space (neighbor-based reasoning) rather than on an abstract rule, and this effect is localized
Jiachun Li, Pengfei Cao, Zhuoran Jin, Yubo Chen, Kang Liu, Jun Zhao
When observed facts are partitioned into in-neighborhood (IF), cross-neighborhood (CF), and out-neighborhood (OF) relative to the test input using Chebyshev distance, model accuracy on example inference follows IF > CF > OF across all five models, all four scenarios, and multiple fact counts. Removing neighbor facts (OF only) causes a significant accuracy drop compared to the baseline. The effect is universal: it holds for GPT-4o, Claude-3.5, Llama3-8B, and Llama2-13B across list transformation, real-world problems, code generation, and string transformation. A deductive-density analysis shows the benefit of neighbor facts is localized: at test radius eta=1 the model achieves over 0.9 deductive density, but this drops to around 0.5 in the full test space, indicating the model generalizes only within a small neighborhood of the test case.
Evidence
correlational
Key metric
GPT-4o (d=5, n=5): IF only 0.84/0.52/0.84/0.63, CF only 0.69/0.35/0.72/0.50, OF only 0.49/0.23/0.57/0.36, baseline 0.66/0.36/0.71/0.46 (LT/RP/CG/ST). Deductive density: over 0.9 at eta=1 (d=3), around 0.5 in full test space (d=5). Claude-3.5 (d=5, n=5): IF only 0.90/0.46/0.87/0.61, OF only 0.60/0.30/0.71/0.39.
Caveat
The neighborhood is defined using Chebyshev distance on the input vectors; the authors validate this choice against Euclidean, Manhattan, and Minkowski distances and find only Chebyshev produces the effect. The analysis is on synthetic single-digit integer vectors, and the models are treated as black boxes with no internal inspection.