Representing Latent Dimensions Using Compressed Number Lines

Humans use log-compressed number lines to represent different quantities, including elapsed time, traveled distance, numerosity, sound frequency, etc. Inspired by recent cognitive science and computational neuroscience work, we developed a neural network that learns to construct log-compressed number lines. The network computes a discrete approximation of a real-domain Laplace transform using an RNN with analytically derived weights giving rise to a log-compressed timeline of the past. The network learns to extract latent variables from the input and uses them for global modulation of the recurrent weights turning a timeline into a number line over relevant dimensions. The number line representation greatly simplifies learning on a set of problems that require learning associations in different spaces - problems that humans can typically solve easily. This approach illustrates how combining deep learning with cognitive models can result in systems that learn to represent latent variables in a brain-like manner and exhibit human-like behavior manifested through Weber-Fechner law.