Inferring the position of objects and their rigid transformations is still an
open problem in visual scene understanding. Here we propose a neuromorphic
solution that utilizes an efficient factorization network based on three key
concepts: (1) a computational framework based on Vector Symbolic Architectures
(VSA) with complex-valued vectors; (2) the design of Hierarchical Resonator
Networks (HRN) to deal with the non-commutative nature of translation and
rotation in visual scenes, when both are used in combination; (3) the design of
a multi-compartment spiking phasor neuron model for implementing complex-valued
vector binding on neuromorphic hardware. The VSA framework uses vector binding
operations to produce generative image models in which binding acts as the
equivariant operation for geometric transformations. A scene can therefore be
described as a sum of vector products, which in turn can be efficiently
factorized by a resonator network to infer objects and their poses. The HRN
enables the definition of 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. In this work, we demonstrate our approach using synthetic scenes
composed of simple 2D shapes undergoing rigid geometric transformations and
color changes. A companion paper demonstrates this approach in real-world
application scenarios for machine vision and robotics.

提出了一种基于神经形态学的解决方案，使用基于向量符号体系结构的高效因式分解网络，实现物体位置和其刚性变换的推断。