# Towards Provable and Scalable Training of Quantized Neural Networks with Ising Optimization

arXiv: https://arxiv.org/abs/2506.18240 · HTML: https://mlsanity.com/paper/2506.18240/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)

## Abstract (arXiv)

Training quantized neural networks remains fundamentally challenging due to non-convex loss landscapes and discrete parameter spaces. We introduce an exact Quadratic Constrained Binary Optimization (QCBO) framework with provable guarantees. We first characterize the stratified topology of network zero-loss level sets: generic interior strata are smooth, yet globally optimal components can remain disconnected even under overparameterization. To address this non-convex obstruction, we compile finite-depth architectures with parameter codebooks and Forward Interval Propagation (FIP)-bounded states into bounded QCBOs, yielding an exact completely positive convex formulation that preserves the global discrete optimum with zero relaxation gap. To overcome monolithic sample scaling, we formulate sample-wise Decomposed Lower-Bound Optimization (DLBO) to reduce each Ising call from dataset to single-sample scale. The DLBO moment hierarchy also forms a Hamiltonian-locality hierarchy, with order two giving an auxiliary-free pairwise QUBO oracle and higher orders trading interaction locality for tighter bounds. Strictly feasible discrete parameters are recovered via Spectral--ADMM and randomized rounding. Experiments on a coherent Ising machine achieve 94.95% accuracy on binary Fashion-MNIST (coats vs. sandals) at 1.1-bit precision, demonstrating resilience against low-bit representational collapse. Multi-class DLBO evaluations on 3-class Fashion-MNIST, 3-class Wine, and 3-class Digits further validate scalable convergence.