# Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology

arXiv: https://arxiv.org/abs/2605.22886 · HTML: https://mlsanity.com/paper/2605.22886/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 14 of 14)

- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [On the Importance of Gradients for Detecting Distributional Shifts in the Wild](https://mlsanity.com/paper/2110.00218/) (2021)
- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Sionna: An Open-Source Library for Next-Generation Physical Layer Research](https://mlsanity.com/paper/2203.11854/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Deep Learning-Based Communication Over the Air](https://mlsanity.com/paper/1707.03384/) (2017)
- [Deep Transfer Learning Based Downlink Channel Prediction for FDD Massive MIMO Systems](https://mlsanity.com/paper/1912.12265/) (2019)
- [Online Meta-Learning For Hybrid Model-Based Deep Receivers](https://mlsanity.com/paper/2203.14359/) (2022)
- [Maximum Mean Discrepancy on Exponential Windows for Online Change Detection](https://mlsanity.com/paper/2205.12706/) (2022)
- [An Adaptive and Robust Deep Learning Framework for THz Ultra-Massive MIMO Channel Estimation](https://mlsanity.com/paper/2211.15939/) (2022)
- [Neural network-based CUSUM for online change-point detection](https://mlsanity.com/paper/2210.17312/) (2022)
- [Resilient-By-Design: A Resiliency Framework for Future Wireless Networks](https://mlsanity.com/paper/2410.23203/) (2024)
- [Design and Analysis of Resilient Vehicular Platoon Systems over Wireless Networks](https://mlsanity.com/paper/2405.08706/) (2024)
- [A Universal Neural Receiver that Learns at the Speed of Wireless](https://mlsanity.com/paper/2602.15458/) (2026)

## Abstract (arXiv)

AI-native wireless receivers based on deep learning exhibit remarkable performance under stationary channel conditions, yet their resilience to distributional shifts remains poorly characterized by conventional metrics such as bit error rate (BER). To overcome these limitations, this paper proposes a novel real-time metric, the Topological Resilience Index (TRI), grounded in persistent homology and persistence exponents. TRI quantifies the structural stability of a neural network receiver's parameter space during online adaptation to non-stationary channels. Specifically, TRI captures resilience through three complementary dimensions: (i) validation-loss resilience measuring model-channel mismatch, grounded in the topological persistence of loss-landscape sublevel sets; (ii) channel impulse response (CIR) distribution shift, tracking geometric drift of CIR vectors from the calibration reference distribution; and (iii) channel manifold topology, quantified by the spectral gap of the Gaussian kernel matrix normalized by the Olivier-Ricci curvature norm. We establish theoretical guarantees showing that TRI is bounded, monotonic under performance degradation, and Lipschitz-stable with respect to perturbations in channel distributions measured in Wasserstein distance. Simulation results for an OFDM deep-learning receiver adapting across ten ITU-R inter-environment transitions at three shift rates demonstrate that TRI provides a consistent mean warning lead of more than one OFDM symbol over gradient-norm and validation-loss baselines, whereas the gradient-norm baseline achieves zero lead in every scenario. Furthermore, the proposed TRI-guided burst re-adaptation reduces post-shift BER by 80% relative to no adaptation within 200 OFDM symbols.