Bhaskar Ranjan Karn | Searcharxiv

arXiv2026

Hybrid Topological Data Analysis and LSTM Networks for Enhanced Network Intrusion Detection Using CIC-IDS2017 Dataset

Network intrusion detection systems (NIDS) are crucial in cybersecurity infrastructure, needing advanced techniques to detect hostile activity in network traffic. This research introduces a hybrid approach that combines Topological Data Analysis (TDA) with Long Short-Term Memory (LSTM) networks to improve anomaly detection in network security. Our multi-layered design combines TDA's persistent homology with LSTM networks to capture topological characteristics of network traffic patterns and simulate temporal sequences. We assessed our methodology using the CIC-IDS2017 dataset, which includes over 2.8 million labelled flows, 77 network variables, and 14 attack categories that reflect modern threat landscapes such as DDoS, brute force, web attacks, penetration, and botnet activities. Integrating Betti curves and persistence diagrams with deep learning architectures enhances feature extraction performance. Our hybrid TDA+LSTM model has an AUC of 1.000 and F1-score of 1.000, with 5-fold cross-validation producing a mean AUC of 1.000 $\pm$ 0.000 and mean F1 of 0.999 $\pm$ 0.001. An ablation research demonstrates the complimentary contributions of topological (F1=0.990) and temporal characteristics (F1=1.000). Comparative research shows that the suggested strategy beats TDA+Random Forest (F1=0.994) and Isolation Forest (F1=0.835) baselines in several attack categories.

cs.CR↗

arXiv2026

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Complex dynamical systems governed by holomorphic maps such as $z^2 + c$ exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these structures from data requires methods that respect the underlying complex-analytic geometry, yet Multi-Layer Perceptrons (MLPs) within Neural Ordinary Differential Equations (Neural ODEs) lack complex-analytic priors, violate the Cauchy--Riemann conditions, and function as opaque approximators incapable of yielding governing equations. We introduce Holomorphic KAN-ODE, a framework that replaces the MLP with a Kolmogorov-Arnold Network (KAN) whose learnable B-spline activations reside on network edges, and incorporates Cauchy--Riemann equations as a differentiable regularization to preserve holomorphic structure. We evaluate on six families of complex dynamical systems spanning polynomial and transcendental classes. With only 280 parameters ($16\times$ fewer than the MLP baseline), the network achieves velocity-field $R^2 > 0.95$ on all six systems, correctly identifies all six governing symbolic families through automatic spline-to-formula fitting, and reconstructs Julia set fractal boundaries with up to 98.0\% agreement. Crucially, the model exhibits only 4\% MSE degradation under 10\% observation noise versus $15.2\times$ for MLPs, and achieves 90.4\% improvement in transfer learning from quadratic to cubic dynamics. While the MLP attains lower pointwise reconstruction error due to its larger capacity, the KAN uniquely provides interpretable symbolic equations, enforced holomorphic structure, and superior noise resilience, capabilities that are entirely absent in black-box architectures. These results establish KANs as a parameter-efficient, interpretable alternative to MLPs for physics-informed discovery of holomorphic dynamics.

cs.LG↗