Solving the Clustering Reasoning Problems by Modeling a Deep-Learning-Based Probabilistic Model

TL;DR

PMoC tackles visual abstract reasoning, focusing on clustering-style Bongard problems (Bongard-Logo). It introduces two architectures: SBSD, which enforces distributional similarity via the Sinkhorn distance between latent representations, and PMoC, which reframes the task as estimating the probability that a sample belongs to a latent distribution $p_i'(z|y)$ using a two‑module setup with $f_ heta(z|x)$ and $g_ \omega(\mu,\sigma^2|z)$, later evolving to PMoC 2.0 that directly estimates $p_i'(z_{ij'}|y)$ with a Transformer-Encoder and Lipschitz-regularized training. Empirical results show PMoC achieves high reasoning accuracies on Bongard-Logo (around 92% in the standard setting; SBSD around 84%), with data augmentation boosting performance further (up to approximately 98% in some categories). The study argues for the value of probabilistic clustering approaches in visual reasoning and suggests that indirect modeling and dataset expansion can unlock greater capabilities in few-shot reasoning tasks with deep networks.

Abstract

Visual abstract reasoning problems pose significant challenges to the perception and cognition abilities of artificial intelligence algorithms, demanding deeper pattern recognition and inductive reasoning beyond mere identification of explicit image features. Research advancements in this field often provide insights and technical support for other similar domains. In this study, we introduce PMoC, a deep-learning-based probabilistic model, achieving high reasoning accuracy in the Bongard-Logo, which stands as one of the most challenging clustering reasoning tasks. PMoC is a novel approach for constructing probabilistic models based on deep learning, which is distinctly different from previous techniques. PMoC revitalizes the probabilistic approach, which has been relatively weak in visual abstract reasoning.

Figures (10)

• Figure 1: Bongard case
• Figure 2: Feedforward process of SBSD
• Figure 3: Framework of PMoC.
• Figure 4: Feedforward process of $f_\theta(z_{ij}|x_{ij})$
• Figure 5: Parameterizes process of $p_i'(z|y)$