# Combining Induction and Transduction for Abstract Reasoning

arXiv: https://arxiv.org/abs/2411.02272 · HTML: https://mlsanity.com/paper/2411.02272/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 62 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 30 of 31)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [Chain of Code: Reasoning with a Language Model-Augmented Code Emulator](https://mlsanity.com/paper/2312.04474/) (2023)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [WorldCoder, a Model-Based LLM Agent: Building World Models by Writing Code and Interacting with the Environment](https://mlsanity.com/paper/2402.12275/) (2024)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain](https://mlsanity.com/paper/2305.07141/) (2023)
- [Top-Down Synthesis for Library Learning](https://mlsanity.com/paper/2211.16605/) (2022)
- [Modular meta-learning](https://mlsanity.com/paper/1806.10166/) (2018)
- [Code Repair with LLMs gives an Exploration-Exploitation Tradeoff](https://mlsanity.com/paper/2405.17503/) (2024)
- [VisualPredicator: Learning Abstract World Models with Neuro-Symbolic Predicates for Robot Planning](https://mlsanity.com/paper/2410.23156/) (2024)
- [Learning adaptive planning representations with natural language guidance](https://mlsanity.com/paper/2312.08566/) (2023)
- [H-ARC: A Robust Estimate of Human Performance on the Abstraction and Reasoning Corpus Benchmark](https://mlsanity.com/paper/2409.01374/) (2024)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [Reasoning Abilities of Large Language Models: In-Depth Analysis on the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2403.11793/) (2024)
- [Deep Amortized Inference for Probabilistic Programs](https://mlsanity.com/paper/1610.05735/) (2016)
- [Neural-guided, Bidirectional Program Search for Abstraction and Reasoning](https://mlsanity.com/paper/2110.11536/) (2021)
- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (2024)
- [From Perception to Programs: Regularize, Overparameterize, and Amortize](https://mlsanity.com/paper/2206.05922/) (2022)
- [ANPL: Towards Natural Programming with Interactive Decomposition](https://mlsanity.com/paper/2305.18498/) (2023)
- [A Neurodiversity-Inspired Solver for the Abstraction & Reasoning Corpus (ARC) Using Visual Imagery and Program Synthesis](https://mlsanity.com/paper/2302.09425/) (2023)
- [Solving ARC visual analogies with neural embeddings and vector arithmetic: A generalized method](https://mlsanity.com/paper/2311.08083/) (2023)
- [A Divide-Align-Conquer Strategy for Program Synthesis](https://mlsanity.com/paper/2301.03094/) (2023)
- [Do Large Language Models Solve ARC Visual Analogies Like People Do?](https://mlsanity.com/paper/2403.09734/) (2024)

## Built on by (most cited first, 30 of 53)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [ArcMemo: Abstract Reasoning Composition with Lifelong LLM Memory](https://mlsanity.com/paper/2509.04439/) (2025)
- [RLAD: Training LLMs to Discover Abstractions for Solving Reasoning Problems](https://mlsanity.com/paper/2510.02263/) (2025)
- [Is That Your Final Answer? Test-Time Scaling Improves Selective Question Answering](https://mlsanity.com/paper/2502.13962/) (2025)
- [Product of Experts with LLMs: Boosting Performance on ARC Is a Matter of Perspective](https://mlsanity.com/paper/2505.07859/) (2025)
- [LoopViT: Scaling Visual ARC with Looped Transformers](https://mlsanity.com/paper/2602.02156/) (2026)
- [Generating Computational Cognitive Models using Large Language Models](https://mlsanity.com/paper/2502.00879/) (2025)
- [BOTS: A Unified Framework for Bayesian Online Task Selection in LLM Reinforcement Finetuning](https://mlsanity.com/paper/2510.26374/) (2025)
- [EasyARC: Evaluating Vision Language Models on True Visual Reasoning](https://mlsanity.com/paper/2506.11595/) (2025)
- [ARC-GEN: A Mimetic Procedural Benchmark Generator for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.00162/) (2025)
- [Shoot First, Ask Questions Later? Building Rational Agents that Explore and Act Like People](https://mlsanity.com/paper/2510.20886/) (2025)
- [MIR-Bench: Can Your LLM Recognize Complicated Patterns via Many-Shot In-Context Reasoning?](https://mlsanity.com/paper/2502.09933/) (2025)
- [MiGrATe: Mixed-Policy GRPO for Adaptation at Test-Time](https://mlsanity.com/paper/2508.08641/) (2025)
- [Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models](https://mlsanity.com/paper/2608.09696/) (2026)
- [Diverse Inference and Verification for Advanced Reasoning](https://mlsanity.com/paper/2502.09955/) (2025)
- [Think Visually, Reason Textually: Vision-Language Synergy in ARC](https://mlsanity.com/paper/2511.15703/) (2025)
- [Your Reasoning Benchmark May Not Test Reasoning: Revealing Perception Bottleneck in Abstract Reasoning Benchmarks](https://mlsanity.com/paper/2512.21329/) (2025)
- [Transferability for General Reasoning: An Automated Curriculum for Multi-Domain RLVR](https://mlsanity.com/paper/2606.25178/) (2026)
- [Benchmarking Abstract and Reasoning Abilities Through A Theoretical Perspective](https://mlsanity.com/paper/2505.23833/) (2025)
- [CausalARC: Abstract Reasoning with Causal World Models](https://mlsanity.com/paper/2509.03636/) (2025)
- [Program Synthesis via Test-Time Transduction](https://mlsanity.com/paper/2509.17393/) (2025)
- [Symbol-Equivariant Recurrent Reasoning Models](https://mlsanity.com/paper/2603.02193/) (2026)
- [Twin: Playing an Unknown Game with a Test-Time Digital Twin](https://mlsanity.com/paper/2608.14490/) (2026)
- [ARC-AGI Without Pretraining](https://mlsanity.com/paper/2512.06104/) (2025)
- [Shedding Light in Task Decomposition in Program Synthesis: The Driving Force of the Synthesizer Model](https://mlsanity.com/paper/2503.08738/) (2025)
- [Cognitive maps are generative programs](https://mlsanity.com/paper/2504.20628/) (2025)
- [From Reasoning to Generalization: Knowledge-Augmented LLMs for ARC Benchmark](https://mlsanity.com/paper/2505.17482/) (2025)

## Abstract (arXiv)

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC by training neural models for induction (inferring latent functions) and transduction (directly predicting the test output for a given test input). We train on synthetically generated variations of Python programs that solve ARC training tasks. We find inductive and transductive models solve different kinds of test problems, despite having the same training problems and sharing the same neural architecture: Inductive program synthesis excels at precise computations, and at composing multiple concepts, while transduction succeeds on fuzzier perceptual concepts. Ensembling them approaches human-level performance on ARC.