Funny-Valen-Tine: Planning Solution Distribution Enhances Machine Abstract Reasoning Ability

TL;DR

This paper reframes visual abstract reasoning as learning a solution distribution over options and shows that existing end-to-end solvers optimize distributions constrained by primary and auxiliary samples rather than the true correct-solution distribution. It introduces Valen, a unified baseline for RPM and Bongard-Logo, and three distribution-planning methods—Tine (adversarial auxiliary samples), Funny (Gaussian-mixture density estimation with MI supervision), and SBR (Gaussian-mixture planning using metadata). Through extensive experiments on RAVEN, Bongard-Logo, and PGM, the authors demonstrate that explicit distribution planning significantly improves accuracy and interpretability, with Funny+Valen and SBR+Valen achieving state-of-the-art results in several settings, including near 100% on PGM. The work highlights the importance of auxiliary-sample quality and latent-distribution design for abstract reasoning models, and provides a practical framework with released code for broader evaluation and development. Overall, the proposed approach offers a principled path to more robust, explainable machine abstract reasoning in visual tasks.

Abstract

Visual abstract reasoning is core to image processing. We present Valen, a unified probability-highlighting baseline that excels on both RPM (progression) and Bongard-Logo (clustering) tasks. Analysing its internals, we find solvers implicitly treat each task as a distribution where primary samples fit and auxiliaries do not; hence the learning target is jointly shaped by both sets, not by correct solutions alone. To close the gap we first introduce Tine, an adversarial adapter that nudges Valen toward correct-solution density, but adversarial training is unstable. We therefore replace it with Funny, a fast Gaussian-mixture model that directly estimates the correct-solution density without adversarial games, and extend the same paradigm to SBR for progressive-pattern planning. Extensive experiments show explicit distribution planning is the key to stronger, interpretable abstract reasoning. Codes are available in: https://github.com/Yuanbeiming/Funny-Valen-Tine-Planning-Solution-Distribution-Enhances-Machine-Abstract-Reasoning-Ability

Figures (20)

• Figure 1: RAVEN instance (a) and PGM instance (b)
• Figure 2: Bongard-Logo instance
• Figure 3: The reasoning process of an effective RPM problem solver
• Figure 4: Representation extraction of matrix
• Figure 5: Enumeration results of incomplete matrix