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Abhishek Chakraborty

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Machine Learning Computer Vision Cryptography and Security Information Theory math.IT math.OC

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preprint2026arXiv

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization

Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in general norm geometries and develop three complementary algorithms. For smooth non-convex objectives, we introduce Distance-Adaptive Muon, whose trust-region radius is set from the radius explored by the trajectory, and prove a stationarity guarantee under a bounded-trajectory assumption. We then turn to star-convex objectives, a tractable model of the favorable global geometry often used to reason about the empirical loss landscapes of deep neural networks, where objective-gap guarantees are possible. In this setting, we first introduce Scale-Calibrated Muon, which keeps Muon's exponential moving average but sets the step length from a local descent certificate computed from the current gradient and momentum. For this method, we prove a last-iterate O(1/T) objective-gap bound under a bounded initial sublevel-set assumption, where the corresponding radius parameter appears only in the analysis and not in the algorithm. Finally, we develop Distance-Free Muon, a recentered trust-region method that uses a scalar distance certificate and a majorized one-dimensional search to select the trust-region radius without requiring the unknown distance from the initialization to a global minimizer. Experiments on Transformer language modeling (GPT-124M/WikiText-103) and image classification (ViT-Tiny/CIFAR-100) show that the proposed adaptive scaling rules reduce sensitivity to manual scale tuning and match or improve tuned fixed-scale Muon baselines under the tested budgets.

preprint2022arXiv

DynaMarks: Defending Against Deep Learning Model Extraction Using Dynamic Watermarking

The functionality of a deep learning (DL) model can be stolen via model extraction where an attacker obtains a surrogate model by utilizing the responses from a prediction API of the original model. In this work, we propose a novel watermarking technique called DynaMarks to protect the intellectual property (IP) of DL models against such model extraction attacks in a black-box setting. Unlike existing approaches, DynaMarks does not alter the training process of the original model but rather embeds watermark into a surrogate model by dynamically changing the output responses from the original model prediction API based on certain secret parameters at inference runtime. The experimental outcomes on Fashion MNIST, CIFAR-10, and ImageNet datasets demonstrate the efficacy of DynaMarks scheme to watermark surrogate models while preserving the accuracies of the original models deployed in edge devices. In addition, we also perform experiments to evaluate the robustness of DynaMarks against various watermark removal strategies, thus allowing a DL model owner to reliably prove model ownership.

preprint2022arXiv

Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descent

We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear interpolation, we hypothesize that the search space is a Reproducing Kernel Hilbert Space (RKHS). We develop first and second-order variants of stochastic mirror descent employing (i) \emph{pseudo-gradients} and (ii) complexity-reducing projections. Compressive projection in the first-order scheme is executed via kernel orthogonal matching pursuit (KOMP), which overcomes the fact that the vanilla RKHS parameterization grows unbounded with the iteration index in the stochastic setting. Moreover, pseudo-gradients are needed when gradient estimates for cost are only computable up to some numerical error, which arise in, e.g., integral approximations. Under constant step-size and compression budget, we establish tradeoffs between the radius of convergence of the expected sub-optimality and the projection budget parameter, as well as non-asymptotic bounds on the model complexity. To refine the solution's precision, we develop a second-order extension which employs recursively averaged pseudo-gradient outer-products to approximate the Hessian inverse, whose convergence in mean is established under an additional eigenvalue decay condition on the Hessian of the optimal RKHS element, which is unique to this work. Experiments demonstrate favorable performance on inhomogeneous Poisson Process intensity estimation in practice.

preprint2016arXiv

Graph Fourier Transform based on Directed Laplacian

In this paper, we redefine the Graph Fourier Transform (GFT) under the DSP$_\mathrm{G}$ framework. We consider the Jordan eigenvectors of the directed Laplacian as graph harmonics and the corresponding eigenvalues as the graph frequencies. For this purpose, we propose a shift operator based on the directed Laplacian of a graph. Based on our shift operator, we then define total variation of graph signals, which is used in frequency ordering. We achieve natural frequency ordering and interpretation via the proposed definition of GFT. Moreover, we show that our proposed shift operator makes the LSI filters under DSP$_\mathrm{G}$ to become polynomial in the directed Laplacian.