Minimal prior knowledge needed for few augmentation steps

Determine the minimum amount of pre-training parametric knowledge, modeled as a partial subgraph G of a ground-truth knowledge graph G*, that suffices for a system to answer queries using only a small number of test-time augmentation steps (e.g., retrieval or verification queries). Formulate the requirement precisely for multi-step reasoning tasks such as s–t connectivity, and characterize thresholds or conditions under which constant expected augmentation is achievable across relevant graph families and observation models.

Background

The paper models multi-step reasoning as s–t connectivity on a knowledge graph G* and represents an LLM’s pre-training knowledge as a subgraph G. Test-time augmentation is abstracted as querying oracles on G*. The authors present upper and lower bounds showing phase transitions: dense, well-connected priors enable constant-query path finding, while sparse priors can force Ω(√n) or Ω(n) queries.

Despite these results for specific regimes (e.g., Erdős–Rényi graphs with retention), the broader question of how much pre-training knowledge is required to enable few augmentation steps remains only partially addressed and is posed explicitly in the abstract as unclear in general.