Neel Mishra

Neel Mishra, Pawan Kumar

In our work, we propose a novel yet simple approach to obtain an adaptive learning rate for gradient-based descent methods on classification tasks. Instead of the traditional approach of selecting adaptive learning rates via the decayed expectation of gradient-based terms, we use the angle between the current gradient and the new gradient: this new gradient is computed from the direction orthogonal to the current gradient, which further helps us in determining a better adaptive learning rate based on angle history, thereby, leading to relatively better accuracy compared to the existing state-of-the-art optimizers. On a wide variety of benchmark datasets with prominent image classification architectures such as ResNet, DenseNet, EfficientNet, and VGG, we find that our method leads to the highest accuracy in most of the datasets. Moreover, we prove that our method is convergent.

Neel Mishra, Kushagara Trivedi, Pawan Kumar

Distributed training of large neural networks is bottlenecked by full-precision gradient communication and by coordinatewise optimizers that ignore the matrix structure of weight tensors. We propose Sign-Muon, a 1-bit, matrix-aware optimizer that combines majority-vote sign aggregation from signSGD with the polar-step framework of Muon. Each worker forms a Muon-style direction by taking the polar factor of its momentum via a Newton--Schulz iteration, transmits only the entrywise signs, and aggregates by majority vote; an optional local polar step further enforces orthogonality at no extra communication cost. Under spectral-norm smoothness and bounded-variance stochastic gradients, the spectral-norm normalized sign step yields an $\mathcal{O}(1/\sqrt{T})$ nonconvex rate for an $\ell_1$-based stationarity measure. With unimodal symmetric noise, majority vote across $M$ workers cuts the stochastic term by $1/\sqrt{M}$, matching signSGD. In the $α$-$β$ model, distributed Sign-Muon needs only one integer sum-allreduce per iteration; all orthogonalization is local, giving a $32\times$ bandwidth reduction over float32 ($4\times$ for int8). Across 330 CIFAR-10/ResNet-50 configurations Sign-Muon attains the best validation accuracy (92.15\%); its 4-GPU majority-vote variant reaches 92.02\% with 37\% less training time at matched effective batch. On nanoGPT, Sign-Muon achieves lower perplexity and better anytime performance than other sign-based baselines, with favorable weak-scaling up to 16 GPUs.

Neel Mishra, Bamdev Mishra, Pratik Jawanpuria et al.

A novel first-order method is proposed for training generative adversarial networks (GANs). It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse. The method corresponds to a fixed-point method that ensures necessary contraction. To evaluate its effectiveness, numerical experiments are conducted on various datasets commonly used in image generation tasks, such as MNIST, Fashion MNIST, CIFAR10, FFHQ, and LSUN. Our method is capable of generating high-fidelity images with greater diversity across multiple datasets. It also achieves the highest inception score for CIFAR10 among all compared methods, including state-of-the-art second-order methods. Additionally, its execution time is comparable to that of first-order min-max methods.