Unsupervised Learning of Compositional Energy Concepts (2111.03042v1)

Abstract: Humans are able to rapidly understand scenes by utilizing concepts extracted from prior experience. Such concepts are diverse, and include global scene descriptors, such as the weather or lighting, as well as local scene descriptors, such as the color or size of a particular object. So far, unsupervised discovery of concepts has focused on either modeling the global scene-level or the local object-level factors of variation, but not both. In this work, we propose COMET, which discovers and represents concepts as separate energy functions, enabling us to represent both global concepts as well as objects under a unified framework. COMET discovers energy functions through recomposing the input image, which we find captures independent factors without additional supervision. Sample generation in COMET is formulated as an optimization process on underlying energy functions, enabling us to generate images with permuted and composed concepts. Finally, discovered visual concepts in COMET generalize well, enabling us to compose concepts between separate modalities of images as well as with other concepts discovered by a separate instance of COMET trained on a different dataset. Code and data available at https://energy-based-model.github.io/comet/.

• The paper introduces COMET, a novel unsupervised approach to learn visual concepts as energy functions without relying on explicit labels.
• It employs a unified framework to decompose scenes into global and local factors, enabling flexible recombination and realistic scene generation.
• Experimental results demonstrate that COMET outperforms methods like beta-VAE and MONet, highlighting strong generalization across diverse datasets.

Unsupervised Learning of Compositional Energy Concepts

The paper "Unsupervised Learning of Compositional Energy Concepts" introduces a novel approach, termed COMET, for unsupervised learning of visual concepts represented as energy functions. The primary goal of the research is to discover and represent both global and local scene descriptors under a unified energy-based framework, allowing rich and flexible compositional generalization of visual concepts. The authors propose a model that does not rely on traditional supervisory signals during training, showing potential applications in image generation and cross-domain composition.

Model Framework

COMET operates by decomposing a scene into various factors, each represented as an energy function. An individual energy function evaluates the compatibility of a factor with a given scene by assigning energy values—low for compatible and high for incompatible configurations. A scene is then generated by summing up these energy functions and optimizing them to minimize the total energy. This framework allows for:

1. Encoding both global (e.g., lighting, viewpoint) and local (e.g., object shapes, colors) factors.
2. Direct manipulation and recombination of factors across datasets and modalities, promoting flexible compositionality in new scenes.

Key Contributions

1. Unified Approach for Decomposition: COMET provides a method to learn both global and local disentanglements from raw image data without requiring labeled supervision. This distinct approach departs from prior methods that often required either explicit segmentation or predefined factorized vector spaces.
2. Energy Function Composition: By representing visual factors as energy functions, the model can flexibly compose multiple factors. This compositional nature allows the model to handle scenes with varying numbers of factors and seamlessly integrate components from different datasets, leading to novel scene constructions.
3. Generalization Across Modalities: COMET demonstrates robustness in generalizing discovered components across different datasets, suggesting the potential for cross-modal applications. For instance, components identified in a synthetic dataset can be effectively recombined with components discovered in real-world datasets.

Experimental Validation

The authors validate COMET across multiple datasets like Falcor3D, CelebA-HQ, CLEVR, and custom-rendered datasets. They focus on assessing both global factor disentanglement and object-level decomposition. The analysis includes qualitative visualizations of the gradients of the energy functions, indicating the captured aspects of the images and quantitative comparisons using metrics like the BetaVAE metric, MIG, and MCC. The results underscore COMET's capacity to outperform existing approaches like the $\beta$-VAE and MONet, particularly regarding the richness and controllability of learned representations.

Discussion and Future Directions

The paper underscores the computational benefits of using energy functions over conventional generative decoders. Training COMET does not need to approximate complex distributions directly; rather, it optimizes over simpler, interpretable energy formulations. This approach has shown an exponential expressiveness over fixed-dimensional vector spaces traditionally used in factor disentanglement tasks.

Future research directions suggested include the scaling of COMET to more realistic and diverse datasets and the exploration of compositional generalization across entirely different domains (e.g., vision to audio). Further advancements could expand the model's applicability and enhance the understanding and manipulation of compositional structures in AI systems.

In conclusion, COMET proposes a promising new pathway for unsupervised concept learning by integrating energy-based models with compositional capabilities, setting the stage for broader applications in AI and cognitive modeling.