How do diffusion models learn and generalize on abstract rules for reasoning?
Keywords: Generative model, Reasoning, Raven’s Progressive Matrix, Diffusion, Scaling law, Stochastic interpolant
TL;DR: Diffusion and autoregressive model exhibit complementary capability when trained on rules: diffusion excel at ab initio generation while autoregression excel at pattern completion.
Abstract: Diffusion models excel in generating and completing patterns in images.
But how good is their ability to learn hidden rules from samples and to generate and reason according to such rules or even generalize to similar rules?
We trained a wide family of unconditional diffusion models on Raven's progression matrix task to precisely study this. We quantified their capability to generate structurally consistent samples and complete missing parts according to hidden rules.
We found diffusion models can synthesize novel samples consistent with rules without memorizing the training set, much better than GPT2 trained on the same data. They memorized and recombined local parts of the training samples to create new rule-conforming samples.
When tasked to complete the missing panel with inpainting techniques, advanced sampling techniques were needed to perform well. Further, their pattern completion capability can generalize to rules unseen during training.
Further, through generative training on rule data, a robust rule representation rapidly emerged in the diffusion model, which could linearly classify rules at 99.8\% test accuracy.
Our results suggest diffusion training is a useful paradigm for reasoning and learning representations for downstream tasks even for abstract rules data.
Primary Area: applications to neuroscience & cognitive science
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Submission Number: 11638
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