Analyzing 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 (VSA) with complex-valued vectors; (2) the design of Hierarchical Resonator Networks (HRN) to factorize the non-commutative transforms translation and rotation in visual scenes; (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 HRN 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 2D shapes undergoing rigid geometric transformations and color changes. A companion paper demonstrates the same approach in real-world application scenarios for machine vision and robotics.

翻译：通过推断生成模型的配置来分析视觉场景，被广泛认为是实现场景理解最灵活且可泛化的方法。然而，一个主要问题在于推理过程所面临的计算挑战，这涉及跨物体身份与姿态的组合搜索。本文提出了一种神经形态解决方案，其利用了三个关键概念：(1) 基于复数值向量的向量符号架构(VSA)计算框架；(2) 分层谐振子网络(HRN)的设计，用于分解视觉场景中非交换的平移与旋转变换；(3) 用于在神经形态硬件上实现复数值谐振子网络的多室发放脉冲相量神经元模型的设计。VSA框架利用向量绑定操作构建生成式图像模型，其中绑定操作充当几何变换的等变运算。因此，一个场景可被描述为向量乘积之和，随后可通过谐振子网络高效分解以推断物体及其姿态。HRN采用分区架构，其中向量绑定在一个分区内对水平与垂直平移具有等变性，在另一分区内对旋转与缩放具有等变性。脉冲神经元模型使得谐振子网络能够映射到高效、低功耗的神经形态硬件上。我们的方法在由经历刚性几何变换与颜色变化的简单二维形状构成的合成场景上进行了验证。一篇配套论文展示了该方法在机器视觉与机器人学的实际应用场景中的相同应用。