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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.
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Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an emph{unobserved} sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing the representations of more than um{12600} trained state-of-the-art disentangled models, we observe that several disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of symmetry preserving transformations. Inspired by this formalism, we propose a framework, built upon the theory of group representation, for learning representations of a dynamical environment structured around the transformations that generate its evolution. Experimentally, we learn the structure of explicitly symmetric environments without supervision from observational data generated by sequential interactions. We further introduce an intuitive disentanglement regularisation to ensure the interpretability of the learnt representations. We show that our method enables accurate long-horizon predictions, and demonstrate a correlation between the quality of predictions and disentanglement in the latent space.
The idea behind the emph{unsupervised} learning of emph{disentangled} representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train over $14000$ models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties encouraged by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered disentangled and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.
Biological intelligence can learn to solve many diverse tasks in a data efficient manner by re-using basic knowledge and skills from one task to another. Furthermore, many of such skills are acquired without explicit supervision in an intrinsically driven fashion. This is in contrast to the state-of-the-art reinforcement learning agents, which typically start learning each new task from scratch and struggle with knowledge transfer. In this paper we propose a principled way to learn a basis set of policies, which, when recombined through generalised policy improvement, come with guarantees on the coverage of the final task space. In particular, we concentrate on solving goal-based downstream tasks where the execution order of actions is not important. We demonstrate both theoretically and empirically that learning a small number of policies that reach intrinsically specified goal regions in a disentangled latent space can be re-used to quickly achieve a high level of performance on an exponentially larger number of externally specified, often significantly more complex downstream tasks. Our learning pipeline consists of two stages. First, the agent learns to perform intrinsically generated, goal-based tasks in the total absence of environmental rewards. Second, the agent leverages this experience to quickly achieve a high level of performance on numerous diverse externally specified tasks.
Motivated by the need to audit complex and black box models, there has been extensive research on quantifying how data features influence model predictions. Feature influence can be direct (a direct influence on model outcomes) and indirect (model outcomes are influenced via proxy features). Feature influence can also be expressed in aggregate over the training or test data or locally with respect to a single point. Current research has typically focused on one of each of these dimensions. In this paper, we develop disentangled influence audits, a procedure to audit the indirect influence of features. Specifically, we show that disentangled representations provide a mechanism to identify proxy features in the dataset, while allowing an explicit computation of feature influence on either individual outcomes or aggregate-level outcomes. We show through both theory and experiments that disentangled influence audits can both detect proxy features and show, for each individual or in aggregate, which of these proxy features affects the classifier being audited the most. In this respect, our method is more powerful than existing methods for ascertaining feature influence.
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