‘‘Extreme edge” ¹ devices, such as smart sensors, are a uniquely challenging environment for the deployment of machine learning. The tiny energy budgets of these devices lie beyond what is feasible for conventional deep neural networks, particularly in high-throughput scenarios, requiring us to rethink how we approach edge inference. In this work, we propose ULEEN, a model and FPGA-based accelerator architecture based on weightless neural networks (WNNs). WNNs eliminate energy-intensive arithmetic operations, instead using table lookups to perform computation, which makes them theoretically well-suited for edge inference. However, WNNs have historically suffered from poor accuracy and excessive memory usage. ULEEN incorporates algorithmic improvements and a novel training strategy inspired by binary neural networks (BNNs) to make significant strides in addressing these issues. We compare ULEEN against BNNs in software and hardware using the four MLPerf Tiny datasets and MNIST. Our FPGA implementations of ULEEN accomplish classification at 4.0–14.3 million inferences per second, improving area-normalized throughput by an average of 3.6× and steady-state energy efficiency by an average of 7.1× compared to the FPGA-based Xilinx FINN BNN inference platform. While ULEEN is not a universally applicable machine learning model, we demonstrate that it can be an excellent choice for certain applications in energy- and latency-critical edge environments.