Rapid advances in deep learning have led to paradigm shifts in a number of fields, from medical image analysis to autonomous systems. These advances, however, have resulted in digital neural networks with large computational requirements, resulting in high energy consumption and limitations in real-time decision-making when computation resources are limited. Here, we demonstrate a meta-optic-based neural network accelerator that can off-load computationally expensive convolution operations into high-speed and low-power optics. In this architecture, metasurfaces enable both spatial multiplexing and additional information channels, such as polarization, in object classification. End-to-end design is used to co-optimize the optical and digital systems, resulting in a robust classifier that achieves 93.1% accurate classification of handwriting digits and 93.8% accuracy in classifying both the digit and its polarization state. This approach could enable compact, high-speed, and low-power image and information processing systems for a wide range of applications in machine vision and artificial intelligence.