Transductively Informed Inductive Program Synthesis

TL;DR

Transductively Informed Inductive Program Synthesis (TIIPS) introduces a cooperative framework that unifies inductive and transductive reasoning for program synthesis. An inductive generator proposes subprograms while a transductive guidance module provides targeted intermediate-output predictions only when progress stalls, forming a nested loop with up to $T$ outer iterations. Empirical results on string and list manipulation show TIIPS solving more tasks and achieving closer semantic and syntactic alignment to ground truth than ExeDec or a purely inductive baseline, with notable robustness in out-of-distribution settings. The work demonstrates that selectively applying transductive guidance can catalyze inductive search, reduce overhead, and improve generalization, suggesting broader implications for general-purpose synthesis and planning across domains.

Abstract

Abstraction and reasoning in program synthesis has seen significant progress through both inductive and transductive paradigms. Inductive approaches generate a program or latent function from input-output examples, which can then be applied to new inputs. Transductive approaches directly predict output values for given inputs, effectively serving as the function themselves. Current approaches combine inductive and transductive models via isolated ensembling, but they do not explicitly model the interaction between both paradigms. In this work, we introduce \acs{tiips}, a novel framework that unifies transductive and inductive strategies by explicitly modeling their interactions through a cooperative mechanism: an inductive model generates programs, while a transductive model constrains, guides, and refines the search to improve synthesis accuracy and generalization. We evaluate \acs{tiips} on two widely studied program synthesis domains: string and list manipulation. Our results show that \acs{tiips} solves more tasks and yields functions that more closely match optimal solutions in syntax and semantics, particularly in out-of-distribution settings, yielding state-of-the-art performance. We believe that explicitly modeling the synergy between inductive and transductive reasoning opens promising avenues for general-purpose program synthesis and broader applications.

Figures (9)

• Figure 1: arc tasks that exemplify cases best addressed by (a) inductive, (b) transductive, or (c) hybrid approaches.
• Figure 2: Compositional generalization results across both domains. End-to-end test accuracy reflects the proportion of test tasks that are successfully solved.
• Figure 3: Tasks solved by tiips and ExeDec in the list manipulation domain, grouped according to their intent match and syntactical overlap. The x-axis denotes intent match, calculated as the overlap between the predicted/executed and ground truth subtask outputs. The y-axis shows syntactical overlap, reflecting the syntactic match between predicted programs and ground truth solutions. As a result, correctly solved tasks--both in terms of semantics and implementation--tend to appear in the top-right region. Values are averaged across all compositional generalization categories. This analysis covers over 6,900 solved tasks averaged across all compositional generalization categories.
• Figure 4: Number of calls to the transductive guidance model. tiips calls the transductive guidance model significantly fewer times than ExeDec.
• Figure A.1: String manipulation functions.