arXiv subjects

Anupriya Kumari

Publications and source records attributed to Anupriya Kumari.

3 recordsLinked to original sources

arXiv2026

Function-Correcting Codes with Optimal Data Protection for Hamming Code Membership

This paper investigates single-error-correcting function-correcting codes (SEFCCs) for the Hamming code membership function (HCMF), which indicates whether a vector in $\mathbb{F}_2^7$ belongs to the [7,4,3]-Hamming code. Necessary and sufficient conditions for valid parity assignments are established in terms of distance constraints between codewords and their nearest non-codewords. It is shown that the Hamming-distance-3 relations among Hamming codewords induce a bipartite graph, a fundamental geometric property that is exploited to develop a systematic SEFCC construction. By deriving a tight upper bound on the sum of pairwise distances, we prove that the proposed bipartite construction uniquely achieves the maximum sum-distance, the largest possible minimum distance of 2, and the minimum number of distance-2 codeword pairs. Consequently, for the HCMF SEFCC problem, sum-distance maximisation is not merely heuristic-it exactly enforces the optimal distance-spectrum properties relevant to error probability. Simulation results over AWGN channels with soft-decision decoding confirm that the resulting max-sum SEFCCs provide significantly improved data protection and Bit Error Rate (BER) performance compared to arbitrary valid assignments.

cs.IT↗

arXiv2024

Rethinking Randomized Smoothing from the Perspective of Scalability

Machine learning models have demonstrated remarkable success across diverse domains but remain vulnerable to adversarial attacks. Empirical defense mechanisms often fail, as new attacks constantly emerge, rendering existing defenses obsolete, shifting the focus to certification-based defenses. Randomized smoothing has emerged as a promising technique among notable advancements. This study reviews the theoretical foundations and empirical effectiveness of randomized smoothing and its derivatives in verifying machine learning classifiers from a perspective of scalability. We provide an in-depth exploration of the fundamental concepts underlying randomized smoothing, highlighting its theoretical guarantees in certifying robustness against adversarial perturbations and discuss the challenges of existing methodologies.

cs.LG↗

arXiv2024

Strengthening Interpretability: An Investigative Study of Integrated Gradient Methods

We conducted a reproducibility study on Integrated Gradients (IG) based methods and the Important Direction Gradient Integration (IDGI) framework. IDGI eliminates the explanation noise in each step of the computation of IG-based methods that use the Riemann Integration for integrated gradient computation. We perform a rigorous theoretical analysis of IDGI and raise a few critical questions that we later address through our study. We also experimentally verify the authors' claims concerning the performance of IDGI over IG-based methods. Additionally, we varied the number of steps used in the Riemann approximation, an essential parameter in all IG methods, and analyzed the corresponding change in results. We also studied the numerical instability of the attribution methods to check the consistency of the saliency maps produced. We developed the complete code to implement IDGI over the baseline IG methods and evaluated them using three metrics since the available code was insufficient for this study.

math.NA↗