# BettiSplit: Topology-Guided Privacy-Aware Split Learning Against Feature Inversion and Gradient Leakage

arXiv: https://arxiv.org/abs/2607.24556 · HTML: https://mlsanity.com/paper/2607.24556/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 27 Jul 2026.

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

- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [Split Learning over Wireless Networks: Parallel Design and Resource Management](https://mlsanity.com/paper/2204.08119/) (2022)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Federated Learning for Privacy Preservation in Smart Healthcare Systems: A Comprehensive Survey](https://mlsanity.com/paper/2203.09702/) (2022)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [Passive Inference Attacks on Split Learning via Adversarial Regularization](https://mlsanity.com/paper/2310.10483/) (2023)
- [Exploring the Privacy-Energy Consumption Tradeoff for Split Federated Learning](https://mlsanity.com/paper/2311.09441/) (2023)
- [SafeSplit: A Novel Defense Against Client-Side Backdoor Attacks in Split Learning (Full Version)](https://mlsanity.com/paper/2501.06650/) (2025)
- [The Impact of Cut Layer Selection in Split Federated Learning](https://mlsanity.com/paper/2412.15536/) (2024)
- [Training Latency Minimization for Model-Splitting Allowed Federated Edge Learning](https://mlsanity.com/paper/2307.11532/) (2023)
- [Robust Collaborative Inference with Vertically Split Data Over Dynamic Device Environments](https://mlsanity.com/paper/2312.16638/) (2023)

## Abstract (arXiv)

Split learning enables collaborative model training by partitioning neural networks across clients and servers. However, improper split placement can lead to severe privacy leakage through intermediate representations. In this work, we propose a topology-guided framework for privacy-aware split learning based on the persistent Betti complexity of smashed activations. Through comprehensive layer-wise analysis, we show that privacy risk in split learning is highly non-uniform across layers and exhibits sharp transition regions that are not captured by architectural depth alone. In particular, feature inversion fidelity increases from negligible reconstruction to as high as 0.98 SSIM at deeper, privacy-critical split points. We further demonstrate that Betti complexity consistently identifies representation regimes associated with elevated feature-space privacy leakage across architectures and datasets. Leveraging this observation, we introduce BettiSafe, a topology-guided split selection strategy that identifies privacy-sensitive layers without requiring explicit attack execution. BettiSafe improves resistance to feature inversion by 2 to 5 times compared to depth-based heuristics while preserving classification accuracy. In addition, Betti-based regularisation increases inversion difficulty by nearly 5 x without degrading model utility, enabling a favourable privacy utility tradeoff. Overall, our results highlight topological complexity as a promising structural descriptor for secure, adaptive, and representation-aware split learning in real-world collaborative systems