# Task-Aware QUBO Allocation for Mixed-Precision Quantization

arXiv: https://arxiv.org/abs/2609.22238 · HTML: https://mlsanity.com/paper/2609.22238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Rethinking Differentiable Search for Mixed-Precision Neural Networks](https://mlsanity.com/paper/2004.05795/) (2020)
- [Differentiable Joint Pruning and Quantization for Hardware Efficiency](https://mlsanity.com/paper/2007.10463/) (2020)
- [Is Quantum Optimization Ready? An Effort Towards Neural Network Compression using Adiabatic Quantum Computing](https://mlsanity.com/paper/2505.16332/) (2025)
- [Optimization of the quantization of dense neural networks from an exact QUBO formulation](https://mlsanity.com/paper/2510.16075/) (2025)

## Abstract (arXiv)

Mixed-precision quantization requires discrete allocation of weight and activation bit-widths, followed by recovery of the selected network. We develop a task-aware quadratic unconstrained binary optimization (QUBO) surrogate with separate weight and activation profiles, a bit-operation (BOP) cost, and selected structural priors. QUBO provides a network-wide allocation that can be refined through direct validation-based PROTES search. On a compact NAFBlock-based denoiser, the refined route achieves 37.192 dB after LSQ+ at 4.035% routed-layer BOPs, versus 37.092 dB at 4.101% for a HAWQ-style baseline. The repeated-search primary experiment shows that LSQ+ largely closes the quality gap between QUBO allocation and expensive direct refinement. An additional restoration architecture retains a larger recovered gain, indicating that refinement's value depends on architecture and recovery. We evaluate quality, achieved cost, routing stability and optimization expense together. Deployment measurements characterize a fake-quantized floating-point implementation; BOP reductions describe analytical allocation savings.