Emergence of Invariance and Disentanglement in Deep Representations

Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and injecting noise during training naturally bias the network towards learning invariant representations. We then decompose the cross-entropy loss used during training and highlight the presence of an inherent overfitting term. We propose regularizing the loss by bounding such a term in two equivalent ways: One with a Kullbach-Leibler term, which relates to a PAC-Bayes perspective; the other using the information in the weights as a measure of complexity of a learned model, yielding a novel Information Bottleneck for the weights. Finally, we show that invariance and independence of the components of the representation learned by the network are bounded above and below by the information in the weights, and therefore are implicitly optimized during training. The theory enables us to quantify and predict sharp phase transitions between underfitting and overfitting of random labels when using our regularized loss, which we verify in experiments, and sheds light on the relation between the geometry of the loss function, invariance properties of the learned representation, and generalization error.Comment: Deep learning, neural network, representation, flat minima, information bottleneck, overfitting, generalization, sufficiency, minimality, sensitivity, information complexity, stochastic gradient descent, regularization, total correlation, PAC-Baye

Disentangling Disentanglement in Variational Autoencoders

We develop a generalisation of disentanglement in variational autoencoders (VAEs)—decomposition of the latent representation—characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the aggregate encoding of the data conforming to a desired structure, represented through the prior. Decomposition permits disentanglement, i.e. explicit independence between latents, as a special case, but also allows for a much richer class of properties to be imposed on the learnt representation, such as sparsity, clustering, independent subspaces, or even intricate hierarchical dependency relationships. We show that the β-VAE varies from the standard VAE predominantly in its control of latent overlap and that for the standard choice of an isotropic Gaussian prior, its objective is invariant to rotations of the latent representation. Viewed from the decomposition perspective, breaking this invariance with simple manipulations of the prior can yield better disentanglement with little or no detriment to reconstructions. We further demonstrate how other choices of prior can assist in producing different decompositions and introduce an alternative training objective that allows the control of both decomposition factors in a principled manner

Neural Block-Slot Representations

In this paper, we propose a novel object-centric representation, called Block-Slot Representation. Unlike the conventional slot representation, the Block-Slot Representation provides concept-level disentanglement within a slot. A block-slot is constructed by composing a set of modular concept representations, called blocks, generated from a learned memory of abstract concept prototypes. We call this block-slot construction process Block-Slot Attention. Block-Slot Attention facilitates the emergence of abstract concept blocks within a slot such as color, position, and texture, without any supervision. This brings the benefits of disentanglement into slots and the representation becomes more interpretable. Similar to Slot Attention, this mechanism can be used as a drop-in module in any arbitrary neural architecture. In experiments, we show that our model disentangles object properties significantly better than the previous methods, including complex textured scenes. We also demonstrate the ability to compose novel scenes by composing slots at the block-level

Adversarial Disentanglement with Grouped Observations

We consider the disentanglement of the representations of the relevant attributes of the data (content) from all other factors of variations (style) using Variational Autoencoders. Some recent works addressed this problem by utilizing grouped observations, where the content attributes are assumed to be common within each group, while there is no any supervised information on the style factors. In many cases, however, these methods fail to prevent the models from using the style variables to encode content related features as well. This work supplements these algorithms with a method that eliminates the content information in the style representations. For that purpose the training objective is augmented to minimize an appropriately defined mutual information term in an adversarial way. Experimental results and comparisons on image datasets show that the resulting method can efficiently separate the content and style related attributes and generalizes to unseen data.Comment: Accepted at the 34th AAAI Conference on Artificial Intelligence (AAAI-20

Topographic VAEs learn Equivariant Capsules

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks