Quantization techniques commonly reduce the inference costs of neural networks by restricting the precision of weights and activations. Recent studies show that also reducing the precision of the accumulator can further improve hardware efficiency at the risk of numerical overflow, which introduces arithmetic errors that can degrade model accuracy. To avoid numerical overflow while maintaining accuracy, recent work proposed accumulator-aware quantization (A2Q), a quantization-aware training method that constrains model weights during training to safely use a target accumulator bit width during inference. Although this shows promise, we demonstrate that A2Q relies on an overly restrictive constraint and a sub-optimal weight initialization strategy that each introduce superfluous quantization error. To address these shortcomings, we introduce: (1) an improved bound that alleviates accumulator constraints without compromising overflow avoidance; and (2) a new strategy for initializing quantized weights from pre-trained floating-point checkpoints. We combine these contributions with weight normalization to introduce A2Q+. We support our analysis with experiments that show A2Q+ significantly improves the trade-off between accumulator bit width and model accuracy and characterize new trade-offs that arise as a consequence of accumulator constraints.

We present extensions to the Open Neural Network Exchange (ONNX) intermediate representation format to represent arbitrary-precision quantized neural networks. We first introduce support for low precision quantization in existing ONNX-based quantization formats by leveraging integer clipping, resulting in two new backward-compatible variants: the quantized operator format with clipping and quantize-clip-dequantize (QCDQ) format. We then introduce a novel higher-level ONNX format called quantized ONNX (QONNX) that introduces three new operators -- Quant, BipolarQuant, and Trunc -- in order to represent uniform quantization. By keeping the QONNX IR high-level and flexible, we enable targeting a wider variety of platforms. We also present utilities for working with QONNX, as well as examples of its usage in the FINN and hls4ml toolchains. Finally, we introduce the QONNX model zoo to share low-precision quantized neural networks.