  The ability to recognize objects despite there being differences in
appearance, known as Core Object Recognition, forms a critical part of human
perception. While it is understood that the brain accomplishes Core Object
Recognition through feedforward, hierarchical computations through the visual
stream, the underlying algorithms that allow for invariant representations to
form downstream is still not well understood. (DiCarlo et al., 2012) Various
computational perceptual models have been built to attempt and tackle the
object identification task in an artificial perceptual setting. Artificial
Neural Networks, computational graphs consisting of weighted edges and
mathematical operations at vertices, are loosely inspired by neural networks in
the brain and have proven effective at various visual perceptual tasks,
including object characterization and identification. (Pinto et al., 2008)
(DiCarlo et al., 2012) For many data analysis tasks, learning representations
where each dimension is statistically independent and thus disentangled from
the others is useful. If the underlying generative factors of the data are also
statistically independent, Bayesian inference of latent variables can form
disentangled representations. This thesis constitutes a research project
exploring a generalization of the Variational Autoencoder (VAE), $\beta$-VAE,
that aims to learn disentangled representations using variational inference.
$\beta$-VAE incorporates the hyperparameter $\beta$, and enforces conditional
independence of its bottleneck neurons, which is in general not compatible with
the statistical independence of latent variables. This text examines this
architecture, and provides analytical and numerical arguments, with the goal of
demonstrating that this incompatibility leads to a non-monotonic inference
performance in $\beta$-VAE with a finite optimal $\beta$.
