Lisa Bonheme

Théophile Champion, Marek Grześ, Lisa Bonheme et al.

Active inference is a theory of perception, learning and decision making, which can be applied to neuroscience, robotics, and machine learning. Recently, reasearch has been taking place to scale up this framework using Monte-Carlo tree search and deep learning. The goal of this activity is to solve more complicated tasks using deep active inference. First, we review the existing literature, then, we progresively build a deep active inference agent. For two agents, we have experimented with five definitions of the expected free energy and three different action selection strategies. According to our experiments, the models able to solve the dSprites environment are the ones that maximise rewards. Finally, we compare the similarity of the representation learned by the layers of various agents using centered kernel alignment. Importantly, the agent maximising reward and the agent minimising expected free energy learn very similar representations except for the last layer of the critic network (reflecting the difference in learning objective), and the variance layers of the transition and encoder networks. We found that the reward maximising agent is a lot more certain than the agent minimising expected free energy. This is because the agent minimising expected free energy always picks the action down, and does not gather enough data for the other actions. In contrast, the agent maximising reward, keeps on selecting the actions left and right, enabling it to successfully solve the task. The only difference between those two agents is the epistemic value, which aims to make the outputs of the transition and encoder networks as close as possible. Thus, the agent minimising expected free energy picks a single action (down), and becomes an expert at predicting the future when selecting this action. This makes the KL divergence between the output of the transition and encoder networks small.

Lisa Bonheme, Marek Grzes

The ability of Variational Autoencoders (VAEs) to learn disentangled representations has made them popular for practical applications. However, their behaviour is not yet fully understood. For example, the questions of when they can provide disentangled representations, or suffer from posterior collapse are still areas of active research. Despite this, there are no layerwise comparisons of the representations learned by VAEs, which would further our understanding of these models. In this paper, we thus look into the internal behaviour of VAEs using representational similarity techniques. Specifically, using the CKA and Procrustes similarities, we found that the encoders' representations are learned long before the decoders', and this behaviour is independent of hyperparameters, learning objectives, and datasets. Moreover, the encoders' representations in all but the mean and variance layers are similar across hyperparameters and learning objectives.

Lisa Bonheme, Marek Grzes

When training a variational autoencoder (VAE) on a given dataset, determining the optimal number of latent variables is mostly done by grid search: a costly process in terms of computational time and carbon footprint. In this paper, we explore the intrinsic dimension estimation (IDE) of the data and latent representations learned by VAEs. We show that the discrepancies between the IDE of the mean and sampled representations of a VAE after only a few steps of training reveal the presence of passive variables in the latent space, which, in well-behaved VAEs, indicates a superfluous number of dimensions. Using this property, we propose FONDUE: an algorithm which quickly finds the number of latent dimensions after which the mean and sampled representations start to diverge (i.e., when passive variables are introduced), providing a principled method for selecting the number of latent dimensions for VAEs and autoencoders.

Lisa Bonheme, Marek Grzes

Variational autoencoders (VAEs) are used for transfer learning across various research domains such as music generation or medical image analysis. However, there is no principled way to assess before transfer which components to retrain or whether transfer learning is likely to help on a target task. We propose to explore this question through the lens of representational similarity. Specifically, using Centred Kernel Alignment (CKA) to evaluate the similarity of VAEs trained on different datasets, we show that encoders' representations are generic but decoders' specific. Based on these insights, we discuss the implications for selecting which components of a VAE to retrain and propose a method to visually assess whether transfer learning is likely to help on classification tasks.

Peter Clapham, Lisa Bonheme, Marek Grzes

Variational Autoencoders (VAEs) often exhibit a polarised regime in which latent variables separate into active, passive, and mixed subsets. Existing criteria for identifying active dimensions depend on a Gaussian prior, limiting their applicability to variational models and specific priors. We propose a simple information-theoretic classification of the polarised regime based on the entropy of the mean representation. We show theoretically how this entropy couples to KL minimisation through entropy--variance bounds, and we relate the resulting criterion to Bonheme's active/passive conditions. We also clarify a key limitation: entropy of the mean alone cannot reliably distinguish active from mixed dimensions without additional signals from the variance representation. Empirically, we evaluate the entropy criterion on $β$-VAEs, identifiable VAEs, Least-Volume Autoencoders, and L2-regularised autoencoders, and find that it consistently recovers a polarised regime when such a regime is present across the model classes studied. Finally, we show that passive dimensions can yield small but consistent improvements on downstream tasks when latent codes are appropriately normalised, suggesting that collapse is often a matter of scale rather than absolute information removal.

Lisa Bonheme, Marek Grzes

The ability of Variational Autoencoders to learn disentangled representations has made them appealing for practical applications. However, their mean representations, which are generally used for downstream tasks, have recently been shown to be more correlated than their sampled counterpart, on which disentanglement is usually measured. In this paper, we refine this observation through the lens of selective posterior collapse, which states that only a subset of the learned representations, the active variables, is encoding useful information while the rest (the passive variables) is discarded. We first extend the existing definition to multiple data examples and show that active variables are equally disentangled in mean and sampled representations. Based on this extension and the pre-trained models from disentanglement lib, we then isolate the passive variables and show that they are responsible for the discrepancies between mean and sampled representations. Specifically, passive variables exhibit high correlation scores with other variables in mean representations while being fully uncorrelated in sampled ones. We thus conclude that despite what their higher correlation might suggest, mean representations are still good candidates for downstream tasks applications. However, it may be beneficial to remove their passive variables, especially when used with models sensitive to correlated features.