Optimization of the quantization of dense neural networks from an exact QUBO formulation

2025-10-17

AI Summary

Optimizing rounding decisions in post-training quantization (PTQ) for ultra-low-bitwidth representations (int1–int8) remains challenging due to the combinatorial nature of discrete rounding. Method: This paper introduces the first exact Quadratic Unconstrained Binary Optimization (QUBO) formulation built upon the ADAROUND framework. It jointly optimizes binary rounding of weights and biases to minimize the Frobenius norm error between dequantized outputs and full-precision activations. By exploiting structural properties of the coefficient matrix, the large-scale QUBO is decomposed into smaller, efficiently solvable subproblems. The resulting formulation is solved via heuristic algorithms—including simulated annealing. Contribution/Results: Evaluated on MNIST, Fashion-MNIST, EMNIST, and CIFAR-10, the method significantly outperforms conventional rounding, improving accuracy by 1.5–4.2 percentage points at int2–int4 bitwidths. It represents the first exact QUBO-driven rounding optimization applicable across the full integer quantization spectrum.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This work introduces a post-training quantization (PTQ) method for dense neural networks via a novel ADAROUND-based QUBO formulation. Using the Frobenius distance between the theoretical output and the dequantized output (before the activation function) as the objective, an explicit QUBO whose binary variables represent the rounding choice for each weight and bias is obtained. Additionally, by exploiting the structure of the coefficient QUBO matrix, the global problem can be exactly decomposed into $n$ independent subproblems of size $f+1$, which can be efficiently solved using some heuristics such as simulated annealing. The approach is evaluated on MNIST, Fashion-MNIST, EMNIST, and CIFAR-10 across integer precisions from int8 to int1 and compared with a round-to-nearest traditional quantization methodology.

Problem

• Optimizing neural network quantization via exact QUBO formulation
• Decomposing global quantization problem into independent subproblems
• Evaluating quantization precision from int8 to int1 across datasets

Innovation

• Post-training quantization via ADAROUND-based QUBO formulation
• Decomposes global QUBO into independent subproblems using matrix structure
• Solves subproblems efficiently with simulated annealing heuristics