Topological Neural Discrete Representation Learning \`a la Kohonen

Unsupervised learning of discrete representations from continuous ones in neural networks (NNs) is the cornerstone of several applications today. Vector Quantisation (VQ) has become a popular method to achieve such representations, in particular in the context of generative models such as Variational Auto-Encoders (VAEs). For example, the exponential moving average-based VQ (EMA-VQ) algorithm is often used. Here we study an alternative VQ algorithm based on the learning rule of Kohonen Self-Organising Maps (KSOMs; 1982) of which EMA-VQ is a special case. In fact, KSOM is a classic VQ algorithm which is known to offer two potential benefits over the latter: empirically, KSOM is known to perform faster VQ, and discrete representations learned by KSOM form a topological structure on the grid whose nodes are the discrete symbols, resulting in an artificial version of the topographic map in the brain. We revisit these properties by using KSOM in VQ-VAEs for image processing. In particular, our experiments show that, while the speed-up compared to well-configured EMA-VQ is only observable at the beginning of training, KSOM is generally much more robust than EMA-VQ, e.g., w.r.t. the choice of initialisation schemes. Our code is public.