arXiv:2505. 18113v2 Announce Type: replace Abstract: Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem.
By Halyun Jeong, Jack Xin, Penghang Yin
The paper proves that several decision and approximation problems for ReLU neural networks are computationally hard. For any number of layers λ≥2, deciding whether a network’s output is positive (and thus whether it is surjective) is W[ℓ−1]-hard when parameterized by the input dimension d. In particular, for two-layer networks, the related geometric problem of zonotope non‑containment is W[1]-hard in the ambient dimension, and computing or approximating the Lp‑Lipschitz constant is NP‑hard and W[ℓ−1]-hard with respect to d. The results also show that these problems remain hard when parameterized by the number of layers for constant d, implying that naive enumeration algorithms running in n^{(ℓ−1)d}·poly(N) time are essentially optimal under the Exponential Time Hypothesis.
By Vincent Froese, Moritz Grillo, Christoph Hertrich, Moritz Stargalla
arXiv:2607. 20811v1 Announce Type: new Abstract: In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions.
By Cornelius Brand, Robert Ganian, Mathis Rocton
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
By Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim, Gregory Cousins, Haitz S\'aez de Oc\'ariz Borde
arXiv:2607. 16568v1 Announce Type: new Abstract: Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program.
By Abdallah Khemais (ISITCOM, University of Sousse)
The paper presents a Quadratic Constrained Binary Optimization (QCBO) framework that provides provable guarantees for training quantized neural networks. It characterizes the topology of zero‑loss level sets, compiles finite‑depth architectures into bounded QCBOs, and introduces a sample‑wise Decomposed Lower‑Bound Optimization (DLBO) to scale Ising‑based optimization. Experiments on a coherent Ising machine show high accuracy on binary Fashion‑MNIST at 1.1‑bit precision and validate the approach on multi‑class datasets.
By Wenxin Li, Chuan Wang, Hongdong Zhu, Qi Gao, Yin Ma, Hai Wei, Kai Wen