1 Context and Motivation Most existing methods for learning representations of 2D images leverages autoencoder architectures to learn a compressed latent representation that captures the overall content of the image. In simple cases such as the MNIST dataset, the latent space is structured around the digit identity, allowing for linear decoding of digit classes. However, if the dataset no longer guarantees consistent positional placement of the digits, the latent space becomes less structured and interpretable in terms of digit identity, thereby hindering downstream tasks such as classification and generation. This research is derived from a previous effort on spatial-temporal modelling with multiscale convolutional LSTMs, where it was observed that no meaningful representation of digit identity emerged. We believe that the lack of persistent identity encoding is the reason for the degradation in performance after occlusions.

2 Problem Statement This research aims to develop an unsupervised method for learning disentangled representations of position and structure in 2D images solely through pixel-space reconstruction objectives. Position refers to the spatial location of objects within the image, while structure pertains to the shape of the objects themselves. The goal is to produce 2 distinct latent vectors, each encoding positional and structural information respectively, with minimal information and functional overlap. Disentanglement quality will be evaluated quantitatively through probe analysis between latent vectors and ground-truth factors of variation, as well as qualitatively through latent space interpolations and visualisations.

3 Potential Issues Without explicit supervision on disentanglement objectives, the model may struggle to clearly separate positional and structural information. Each latent vector might still contain mixed information, as the model tries to optimize for reconstruction accuracy. Additionally, the model may not be able to encode separately objects in the same image as distinct entities without the use of slot-based mechanisms, leading to difficulty in generalisation.

4 Proposed Approach This research aims to address the former by introducing information and architectural asymmetry between the position and structure encoders to encourage orthogonal representations. Additionally, the latter will be addressed by encoding the image as a continuous field, allowing for the representation of multiple objects without explicit slot-based mechanisms, thereby achieving better generalisation. Exploratory experiments have been conducted on synthetic dataset of 2 randomly placed MNIST digits in a 64x64 image. The latent space is evaluated through linear probes predicting digit identity, centroid, and inter-digit distance from the position and structure latent vectors respectively. Preliminary results and qualitative visualisations indicate promising disentanglement of positional and structural information.

5 Additional Requirements This research does NOT require additional specialised hardware or software beyond what is currently available. Ethical approval is NOT necessary as the research does not involve human participants, material, or data.