2024/11/02 by Miria Feng, Feng, Miria, Zachary Frangella +3 · 1 citation
Computer Science · Neuroscience · #Advanced Neural Network Applications #Brain Tumor Detection and Classification #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2411.01088
openalex publication_date 2024/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the CRONOS algorithm for convex optimization of two-layer neural networks. CRONOS is the first algorithm capable of scaling to high-dimensional datasets such as ImageNet, which are ubiquitous in modern deep learning. This significantly improves upon prior work, which has been restricted to downsampled versions of MNIST and CIFAR-10. Taking CRONOS as a primitive, we then develop a new algorithm called CRONOS-AM, which combines CRONOS with alternating minimization, to obtain an algorithm capable of training multi-layer networks with arbitrary architectures. Our theoretical analysis proves that CRONOS converges to the global minimum of the convex reformulation under mild assumptions. In addition, we validate the efficacy of CRONOS and CRONOS-AM through extensive large-scale numerical experiments with GPU acceleration in JAX. Our results show that CRONOS-AM can obtain comparable or better validation accuracy than predominant tuned deep learning optimizers on vision and language tasks with benchmark datasets such as ImageNet and IMDb. To the best of our knowledge, CRONOS is the first algorithm which utilizes the convex reformulation to enhance performance on large-scale learning tasks.