Towards a Definition of Disentangled Representations (1812.02230v1)

Abstract: How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of the world into disjoint parts of its representation. However, there is no generally agreed-upon definition of disentangling, not least because it is unclear how to formalise the notion of world structure beyond toy datasets with a known ground truth generative process. Here we propose that a principled solution to characterising disentangled representations can be found by focusing on the transformation properties of the world. In particular, we suggest that those transformations that change only some properties of the underlying world state, while leaving all other properties invariant, are what gives exploitable structure to any kind of data. Similar ideas have already been successfully applied in physics, where the study of symmetry transformations has revolutionised the understanding of the world structure. By connecting symmetry transformations to vector representations using the formalism of group and representation theory we arrive at the first formal definition of disentangled representations. Our new definition is in agreement with many of the current intuitions about disentangling, while also providing principled resolutions to a number of previous points of contention. While this work focuses on formally defining disentangling - as opposed to solving the learning problem - we believe that the shift in perspective to studying data transformations can stimulate the development of better representation learning algorithms.

• The paper introduces a formal definition of disentangled representations using group theory and symmetry transformations.
• It demonstrates how data transformations can be decomposed into independent, invariant subspaces, as shown in a grid world example.
• The study suggests aligning ML models with symmetry principles can lead to more robust, efficient learning in complex settings.

Towards a Definition of Disentangled Representations

The paper "Towards a Definition of Disentangled Representations" by Higgins et al. investigates the notion of disentangled representations in machine learning, proposing a formal framework rooted in group and representation theory. The work is motivated by the need to address the shortcomings of current machine learning models that lack data efficiency and robustness synonymous with biological intelligence.

Overview of Disentangled Representations

Disentangled representation learning aims to improve data efficiency by separating data into independent, meaningful components. Despite its potential, a concrete definition has been elusive, complicating the evaluation and progression of related research. Higgins et al. argue that symmetry transformations, ubiquitous in physics and potentially applicable to data, provide a foundation to define disentangled representations.

Core Contributions

1. Symmetry Transformations Insight: Building on principles from physics, the authors suggest that data transformations which modify only certain properties while leaving others invariant embody a form of exploitable structure. This perspective aligns with past successes in physics using group theory to understand world structures.
2. Formal Definition: Disentangled representation is characterized via group and representation theory. A vector representation is deemed disentangled if it can be decomposed into independent subspaces, each invariant to certain transformations yet susceptible to a specific transformation subgroup.
3. Theoretical Observations: The formalism suggests numerous clarifications to prevailing debates. For example, it asserts that a disentangled representation need not conform to a unique axis alignment, and each subspace can be multi-dimensional based on the symmetry group's structure.

Strong Results and Claims

• Worked Example: The paper describes a grid world scenario where transformations (translations and color changes) have an underlying symmetry group structure. Using a CCI-VAE model, the authors demonstrate how current approaches approximate these transformation groups, validating the relevance of their new definition.
• Linearity Consideration: In contrast to previous discussions, the paper distinguishes linear disentangled representations as a subset, emphasizing that while linearly transforming subspaces could be beneficial for certain tasks, they are not a necessity for disentanglement.

Implications and Future Directions

Practical Implications: Aligning representation learning with symmetry transformations could lead to more robust models capable of rapidly generalizing across varied tasks. This framework allows machine learning models to mimic human-like intelligence in efficiently adapting and understanding unseen scenarios.

Theoretical Implications: The paper posits that the focus should shift from purely statistical independence structures to active perception, aiding in uncovering world symmetries and transforming them into computational models. This shift could reshape approaches to unsupervised learning.

Future Exploration: While the framework sets a foundational premise, it opens avenues for exploration into active learning methodologies to identify useful group decompositions. Further empirical verification is necessary to validate and refine these theoretical constructs in more complex environments beyond toy datasets.

Conclusion

Higgins et al. provide a rigorous approach to disentangled representation learning through symmetries and group theory. This work offers a structured theoretical base to resolve previous ambiguities in the field, potentially accelerating advancements in crafting machine learning systems with human-like representational powers. The emphasis on structurally informed representations marks a critical step towards more intelligent, efficient learning algorithms.