Combining Induction and Transduction for Abstract Reasoning
Wen-Ding Li, Keya Hu, Carter Larsen, Yuqing Wu, Simon Alford, Caleb Woo, Spencer M. Dunn, Hao Tang, Michelangelo Naim, Dat Nguyen, Wei-Long Zheng, Zenna Tavares, Yewen Pu, Kevin Ellis – 2024
This paper is great at a minimum because it defines induction and transduction in a clean way and delineates between the two.
- Induction – learning an intermediate function for mapping from input to output, then applying that function at test time. So the direct output of induction is the function itself, not the final output of applying that function. In some sense inductive learning involves conjuring up various candidate functions and then evaluating them on the training data. Importantly, once the function is learned the original training data can hypothetically be discarded as they are not actively used in future predictions. Learn, then apply – it’s like studying for an exam that you won’t be allowed to bring any cheat sheets for.
- Transduction – outputs the answer directly without explicit construction of an intermediate mapping function. In this sense it’s more “direct” in nature, as the learner uses everything it’s seen so far to generate the answer at test time (all the training data), not just some function it’s learned. Transduction is naturally less explainable because there’s no intermediate step. It’s like showing up to an exam with all your prep material and figuring out in real-time how to answer the questions based on those materials.
