Unsupervised Discovery of Steerable Factors When Graph Deep Generative Models Are Entangled

TL;DR

The paper tackles unsupervised graph editing for pretrained graph deep generative models, identifying entangled latent spaces as a barrier to controllable graph generation. It introduces GraphCG, a model-agnostic framework that learns semantic directions by maximizing mutual information within an energy-based model, producing sequences of edited graphs without labeled factors. Key contributions include a formal MI-based learning objective, an EBMs-based implementation with a NoICE variant (GraphCG-NCE), extensive experiments on molecular graphs and point clouds, and qualitative demonstrations of seven steerable factors across multiple datasets. The work offers a practical pathway for controllable graph generation with limited supervision, enabling scalable editing of molecular structures and 3D shapes for applications in chemistry and geometry processing.

Abstract

Deep generative models (DGMs) have been widely developed for graph data. However, much less investigation has been carried out on understanding the latent space of such pretrained graph DGMs. These understandings possess the potential to provide constructive guidelines for crucial tasks, such as graph controllable generation. Thus in this work, we are interested in studying this problem and propose GraphCG, a method for the unsupervised discovery of steerable factors in the latent space of pretrained graph DGMs. We first examine the representation space of three pretrained graph DGMs with six disentanglement metrics, and we observe that the pretrained representation space is entangled. Motivated by this observation, GraphCG learns the steerable factors via maximizing the mutual information between semantic-rich directions, where the controlled graph moving along the same direction will share the same steerable factors. We quantitatively verify that GraphCG outperforms four competitive baselines on two graph DGMs pretrained on two molecule datasets. Additionally, we qualitatively illustrate seven steerable factors learned by GraphCG on five pretrained DGMs over five graph datasets, including two for molecules and three for point clouds.

Figures (12)

• Figure 1: (a) The learning phase. Given two latent codes ${\bm{z}}^u$ and ${\bm{z}}^v$, we edit the four latent representations along $i$-th and $j$-th direction with step size $\alpha$ and $\beta$ respectively. The goal of GraphCG, is to align the positive pair ($\bar{{\bm{z}}}^u_{i, \alpha}$ and $\bar{{\bm{z}}}^v_{i, \alpha}$), and contrast them with $\bar{{\bm{z}}}^u_{j, \beta}$ and $\bar{{\bm{z}}}^v_{j, \beta}$ respectively. (b) The inference phase. We will first sample an anchor molecule and adopt the learned directions in the learning phase for editing. With step size $\alpha \in [-3, 3]$, we can generate a sequence of molecules. Specifically, after decoding, there is a functional group change shown up: the number of hydroxyl groups decreases along the sequence in the decoded molecules.
• Figure 2: This illustrates the sequence monotonic ratio (SMR) on calibrated Tanimoto similarity (CTS). \ref{['eq:SMR_each_sequence', 'eq:SMR_each_direction']} are the SMR on each sequence and each direction respectively, where $M$ is the number of generated sequences for the $i$-th direction and $\{ s(\bar{{\bm{x}}}') \}_i^m$ is the CTS of the $m$-th generated sequence with the $i$-th direction. \ref{['eq:top_K_SMR']} is the average of top-K SMR on $D$ directions.
• Figure 3: GraphCG for molecular graph editing. We visualize the output molecules and CTS in four directions with two sequences each, where each sequence consists of five steps. The five steps correspond to five step sizes: -3, -1.8, 0, 1.8, and 3, where 0 marks the anchor molecule (center point of reach sequence). \ref{['fig:path_generation_example_hiervae_main_a']} visualizes how the number of halogens (marked in green) decreses from -3 to 3. \ref{['fig:path_generation_example_hiervae_main_b']} visualizes how the number of hydroxyls (marked in red) decreases from -3 to 3. \ref{['fig:path_generation_example_hiervae_main_c']} visualizes how the number of amides (marked in red and blue) increases from -3 to 3. \ref{['fig:path_generation_example_hiervae_main_d']} visualizes how the number of chains (marked in green) increases from -3 to 3. Notably, certain properties change with molecular structures accordingly, like topological polar surface area (tPSA) and the number of rotatable bonds (NRB).
• Figure 4: GraphCG for point clouds editing. We show four editing sequences, where each sequence consists of five point clouds, and the center one is the anchor point clouds, i.e., with step size 0. The other four point clouds correspond to step size with -3, -1.8, 1.8, and 3, respectively. \ref{['fig:airplane_data_2_dir_14_engine_removal']} and \ref{['fig:airplane_data_2_dir_14_engine_add']} refer the same semantic direction, and they are showing how to steer the factor engine: the number of engines will be decreased and increased with the negative (left) and positive (right) step size respectively. Similarly, \ref{['fig:car_data_2_dir_8', 'fig:chair_data_2_dir_8']} illustrate the effect of the steerable factors on the car size and the chair leg height.
• Figure 5: \ref{['fig:original_tanimoto_similarity_sequence']} is the original Tanimoto similarity sequence w.r.t. the anchor molecule, i.e., step size with 0 in the figure. Yet, this is not easy to compute the monotonicity. We thus propose the calibrated Tanimoto similarity sequence, by taking the deduction from 2 for output molecules with positive step size, as shown in \ref{['fig:calibrated_tanimoto_similarity_sequence']}.