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

Abstract: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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Optics (physics.optics)

arXiv:2506.18240 [cs.LG]

(or arXiv:2506.18240v5 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2506.18240 Focus to learn more arXiv-issued DOI via DataCite

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