# Beyond Either-Or Reasoning: Transduction and Induction as Cooperative Problem-Solving Paradigms

arXiv: https://arxiv.org/abs/2505.14744 · HTML: https://mlsanity.com/paper/2505.14744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 24 of 24)

- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [Planning with Large Language Models for Code Generation](https://mlsanity.com/paper/2303.05510/) (2023)
- [ADaPT: As-Needed Decomposition and Planning with Language Models](https://mlsanity.com/paper/2311.05772/) (2023)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Phenomenal Yet Puzzling: Testing Inductive Reasoning Capabilities of Language Models with Hypothesis Refinement](https://mlsanity.com/paper/2310.08559/) (2023)
- [Compositional Generalization via Neural-Symbolic Stack Machines](https://mlsanity.com/paper/2008.06662/) (2020)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Combining Induction and Transduction for Abstract Reasoning](https://mlsanity.com/paper/2411.02272/) (2024)
- [Learning to Infer Program Sketches](https://mlsanity.com/paper/1902.06349/) (2019)
- [Is Programming by Example solved by LLMs?](https://mlsanity.com/paper/2406.08316/) (2024)
- [Doing Experiments and Revising Rules with Natural Language and Probabilistic Reasoning](https://mlsanity.com/paper/2402.06025/) (2024)
- [Latent Programmer: Discrete Latent Codes for Program Synthesis](https://mlsanity.com/paper/2012.00377/) (2020)
- [ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis](https://mlsanity.com/paper/2307.13883/) (2023)
- [Building Intelligent Agents with Neuro-Symbolic Concepts](https://mlsanity.com/paper/2505.06191/) (2025)
- [A Divide-Align-Conquer Strategy for Program Synthesis](https://mlsanity.com/paper/2301.03094/) (2023)
- [LambdaBeam: Neural Program Search with Higher-Order Functions and Lambdas](https://mlsanity.com/paper/2306.02049/) (2023)
- [Generating Planning Feedback for Open-Ended Programming Exercises with LLMs](https://mlsanity.com/paper/2504.08958/) (2025)
- [Shedding Light in Task Decomposition in Program Synthesis: The Driving Force of the Synthesizer Model](https://mlsanity.com/paper/2503.08738/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Small-Scale System for Autoregressive Program Synthesis Enabling Controlled Experimentation](https://mlsanity.com/paper/2602.09112/) (2026)

## Abstract (arXiv)

Traditionally, in Programming-by-example (PBE) the goal is to synthesize a program from a small set of input-output examples. Lately, PBE has gained traction as a few-shot reasoning benchmark, relaxing the requirement to produce a program artifact altogether which allows transductive methods to directly the missing output sample. Transduction and induction are complementary reasoning modes--where induction derives general rules from examples, transduction leverages the examples directly to infer specific outputs without intermediate generalization. Yet existing approaches either treat them as mutually exclusive or couple them in hybrid structures where one paradigm dictates a fixed trajectory for the other -- undermining the latter's reasoning potential and creating cascading errors. We move away from these hierarchical models and introduce cooperative transductive-inductive problem solving: by interleaving both reasoning modes and ensuring neither unconditionally dominates the other, we preserve the search autonomy and reasoning capacity of each paradigm. We instantiate this concept in TIIPS. Across three PBE domains, TIIPS consistently outperforms state-of-the-art baselines and generates programs that more closely mirror ground-truth trajectories in both syntax and semantics, indicating a better match to the intended program behavior. Our findings highlight cooperative reasoning as a promising new direction for harnessing the full power of symbolic, inductive and neural, transductive reasoning.