Neuromorphic visual scene understanding with resonator networks

Analysing a visual scene by inferring the configuration of a generative model is widely considered the most flexible and generalizable approach to scene understanding. Yet, one major problem is the computational challenge of the inference procedure, involving a combinatorial search across object identities and poses. Here we propose a neuromorphic solution exploiting three key concepts: (1) a computational framework based on vector symbolic architectures (VSAs) with complex-valued vectors, (2) the design of hierarchical resonator networks to factorize the non-commutative transforms translation and rotation in visual scenes and (3) the design of a multi-compartment spiking phasor neuron model for implementing complex-valued resonator networks on neuromorphic hardware. The VSA framework uses vector binding operations to form a generative image model in which binding acts as the equivariant operation for geometric transformations. A scene can therefore be described as a sum of vector products, which can then be efficiently factorized by a resonator network to infer objects and their poses. The hierarchical resonator network features a partitioned architecture in which vector binding is equivariant for horizontal and vertical translation within one partition and for rotation and scaling within the other partition. The spiking neuron model allows mapping the resonator network onto efficient and low-power neuromorphic hardware. Our approach is demonstrated on synthetic scenes composed of simple two-dimensional shapes undergoing rigid geometric transformations and colour changes. A companion paper demonstrates the same approach in real-world application scenarios for machine vision and robotics. The inference procedure for analysing a visual scene presents a computational challenge. Renner, Supic and colleagues develop a neural network model, the hierarchical resonator, to determine the generative factors of variation of objects in simple scenes. The resonator was implemented on neuromorphic hardware, using a spike-timing code for complex numbers.