# Towards Causally Interpretable Wi-Fi CSI-Based Human Activity Recognition with Discrete Latent Compression and LTL Rule Extraction

arXiv: https://arxiv.org/abs/2604.22979 · HTML: https://mlsanity.com/paper/2604.22979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [SHARP: Environment and Person Independent Activity Recognition with Commodity IEEE 802.11 Access Points](https://mlsanity.com/paper/2103.09924/) (2021)
- [ReWiS: Reliable Wi-Fi Sensing Through Few-Shot Multi-Antenna Multi-Receiver CSI Learning](https://mlsanity.com/paper/2201.00869/) (2022)
- [Exposing the CSI: A Systematic Investigation of CSI-based Wi-Fi Sensing Capabilities and Limitations](https://mlsanity.com/paper/2302.00992/) (2023)
- [Accurate Passive Radar via an Uncertainty-Aware Fusion of Wi-Fi Sensing Data](https://mlsanity.com/paper/2407.04733/) (2024)

## Abstract (arXiv)

We address Human Activity Recognition (HAR) utilizing Wi-Fi Channel State Information (CSI) under the joint requirements of causal interpretability, symbolic controllability, and direct operation on high-dimensional raw signals. Deep neural models achieve strong predictive performance on CSI-based HAR (CHAR), yet rely on continuous latent representations that are opaque and difficult to modify; purely symbolic approaches, in contrast, cannot process raw CSI streams. We propose a fully automatic and strictly decoupled pipeline in which CSI magnitude windows are compressed by a categorical variational autoencoder with Gumbel-Softmax latent variables under a capacity-controlled objective, yielding a compact discrete representation. The encoder is then frozen and used as a deterministic mapping to one-hot latent trajectories. Causal discovery is performed on these trajectories to estimate class-conditional temporal dependency graphs. Statistically supported lagged dependencies are translated into Linear Temporal Logic (LTL) rules, producing a fully symbolic and deterministic classifier based solely on rule evaluation and aggregation, without any learned discriminative head. Because rules are defined over discrete latent variables, antenna-specific rule sets can in principle be combined at the symbolic level, enabling structured multi-antenna fusion without retraining the encoder. Results from CHAR Latent Temporal Rule Extraction (CHARL-TRE) indicate competitive performance while preserving explicit temporal and causal structure, showing that deterministic symbolic classification grounded in unsupervised discrete latent representations constitutes a viable alternative to end-to-end black-box models for wireless HAR.