💻 computer science

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

The paper proposes a novel pipeline for Wi-Fi-based human activity recognition that converts high-dimensional raw CSI signals into discrete latent trajectories via a categorical variational autoencoder, subsequently extracting interpretable Linear Temporal Logic (LTL) rules through causal discovery to enable a symbolic, controllable, and transparent classification process.

Original authors: Luca Cotti, Luca Lavazza, Marco Cominelli, Liying Han, Gaofeng Dong, Francesco Gringoli, Mani B. Srivastava, Trevor Bihl, Erik P. Blasch, Daniel O. Brigham, Kara Combs, Lance M. Kaplan, Federico Cerut

Published 2026-04-28

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CC BY 4.0

Original authors: Luca Cotti, Luca Lavazza, Marco Cominelli, Liying Han, Gaofeng Dong, Francesco Gringoli, Mani B. Srivastava, Trevor Bihl, Erik P. Blasch, Daniel O. Brigham, Kara Combs, Lance M. Kaplan, Federico Cerutti

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out what someone is doing in another room just by listening to the "vibrations" of the house. You can’t see them, but you can hear the rhythmic thumping of footsteps, the sudden rustle of a chair, or the sharp clap of hands.

This paper, CHARL-TRE, is a way to do exactly that, but using Wi-Fi signals instead of sound.

The Problem: The "Black Box" Mystery

Usually, when scientists use AI to recognize activities (like walking, jumping, or sitting) via Wi-Fi, they use "Black Box" models. These are like a master chef who makes a delicious soup but refuses to give you the recipe. You know the soup is good (the AI is accurate), but if the soup tastes weird, you have no idea why. You can't fix a single ingredient; you just have to start over. This is dangerous in sensitive areas like elderly care or security, where we need to know why an AI thinks someone has fallen.

The Solution: The Three-Step Translator

The researchers created a pipeline that acts like a translator, turning messy, invisible Wi-Fi waves into a clear, logical "instruction manual." They do this in three steps:

1. The "Digital Sieve" (Compression)

Wi-Fi data is incredibly messy—it’s like trying to read a book while someone is shaking it. The first step uses a special AI (a Categorical VAE) that acts like a high-tech sieve. It shakes the messy data and catches only the most important "shapes."

Instead of keeping every tiny, vibrating detail, it turns the signal into a series of discrete symbols—think of these like LEGO bricks. Instead of a continuous, blurry wave, the AI now sees: "Brick A, then Brick B, then Brick C."

2. The "Detective" (Causal Discovery)

Now that we have our LEGO bricks, we need to see how they interact. The researchers use a "detective" tool called LPCMCI.

Imagine you notice that every time a "Thump" brick appears, a "Rustle" brick appears two seconds later. The detective doesn't just see a coincidence; it looks for cause and effect. It asks: "Does the Thump actually cause the Rustle, or are they both just happening at the same time because of something else?" It builds a map of these relationships.

3. The "Rulebook" (LTL Logic)

Finally, the system takes those detective notes and writes them down as clear, logical rules using a language called LTL (Linear Temporal Logic).

Instead of a mysterious math equation, the AI’s "brain" becomes a literal rulebook that looks like this:

Rule for Walking: "IF you see Brick 3, THEN in two seconds you will see Brick 2."
Rule for Sitting: "IF you see Brick 5, THEN you will NOT see Brick 1 for a while."

Why is this a big deal? (The "Why it Matters" Part)

It’s Transparent: If the AI misidentifies a "Jump" as a "Walk," a human can open the rulebook, see which rule was triggered, and understand exactly where the mistake happened. It’s no longer a black box; it’s a glass box.
It’s Controllable: If the rules are slightly wrong, you don't have to retrain the whole massive AI (which takes days and huge computers). You can just go into the rulebook and edit a line, like fixing a typo in a manual.
It’s Modular: If you add more Wi-Fi antennas, you don't have to rebuild the whole system. You just write new rules for the new antennas and "staple" them to the old rulebook.

Summary in a Nutshell

The researchers have moved from "The computer thinks you are walking" (unreliable and mysterious) to "The computer sees a pattern of signals that follows the logical rules of walking" (reliable, understandable, and easy to fix).

Technical Summary: Towards Causally Interpretable Wi-Fi CSI-Based Human Activity Recognition (CHARL-TRE)

1. Problem Statement

Human Activity Recognition (HAR) using Wi-Fi Channel State Information (CSI) is a high-dimensional, noisy, and temporally structured task. Current state-of-the-art approaches rely on Deep Neural Networks (DNNs), which achieve high accuracy but suffer from two major drawbacks:

Lack of Interpretability: They utilize continuous, distributed latent representations that act as "black boxes," making it impossible to inspect or modify decision-making logic.
Lack of Controllability: Because the representation learning and classification are entangled, one cannot easily inject symbolic rules or modify the model's behavior without retraining the entire system.

Existing neuro-symbolic attempts often require human-defined semantic features or external video data, which limits their autonomy and applicability to raw wireless signals.

2. Methodology

The authors propose CHARL-TRE (CHAR Latent Temporal Rule Extraction), a fully automatic, strictly decoupled pipeline that separates signal compression from symbolic reasoning. The process follows three distinct stages:

A. Discrete Latent Representation Learning (Unsupervised)

Model: A Categorical Variational Autoencoder (VAE) using Gumbel-Softmax reparameterization.
Mechanism: Instead of continuous Gaussian latents, the model learns a compact, discrete latent space. The encoder maps high-dimensional CSI magnitude windows into a sequence of hard one-hot encoded categorical variables.
Information Control: To prevent "posterior collapse" (where the latent space becomes uninformative), the authors use a capacity-controlled objective ( $\beta$ -VAE style), gradually increasing the information bottleneck during training.

B. Causal Discovery (Latent Space)

Algorithm: Once the encoder is frozen, the resulting binary latent trajectories are analyzed using Latent PCMCI (LPCMCI) with Partial Correlation (ParCorr) tests.
Goal: To identify class-conditional temporal dependencies. The algorithm determines how the activation of one latent variable at time $t$ causally influences another at time $t + \tau$ .
Significance of Polarity: The discovered dependencies are signed; a positive correlation implies an "activation" rule, while a negative correlation implies an "exclusion" rule.

C. Symbolic Rule Extraction and Classification (Deterministic)

LTL Translation: Statistically significant lagged dependencies are translated into Linear Temporal Logic (LTL) formulas. For example, a positive dependency from $X_s$ to $X_d$ with lag $\tau$ becomes $\square(X_s \to \bigcirc^\tau X_d)$ .
Two-Level Search: The system performs a search to select the most discriminative rules for each activity based on a discriminative margin (how much more a rule occurs in its target class vs. others).
Deterministic Classifier: Classification is performed by evaluating the log-likelihood ratio of the LTL rules. There is no learned discriminative head (no final softmax layer); the decision is made purely through rule aggregation and scoring.

3. Key Contributions

Strict Decoupling: The pipeline separates neural compression (unsupervised) from symbolic reasoning (causal/logical), allowing for modularity.
Fully Automatic Pipeline: Unlike previous neuro-symbolic models, this requires no human-defined features, semantic labels, or external video data; it operates directly on raw CSI.
Symbolic Multi-Antenna Fusion: Because the rules are discrete and logical, rule sets from different antennas can be combined via logical conjunction or voting without retraining the encoder.
Causal Interpretability: Every classification decision is traceable to a specific LTL formula, providing an explicit temporal "logic" for the recognized activity.

4. Results

Performance: The model achieved competitive accuracy (exceeding 70%) using a purely deterministic rule-based classifier.
Complexity Correlation: The confusion matrix showed that "quasi-stationary" activities (e.g., Sit, Stand, Squat) were recognized with high precision, whereas highly dynamic activities (e.g., Jump, Waving) were more difficult due to non-stationary latent trajectories.
Rule Budget: The study confirmed that the number of extracted rules ( $N$ ) serves as a reliable proxy for activity complexity; activities with fewer rules were more prone to error.
Fallback Mechanism: For activities where no strong symbolic rules were found (e.g., Empty), the system utilized a prototype-based fallback using mean latent activations.

5. Significance

This work demonstrates that semantic interpretability is not a prerequisite for symbolic reasoning. Even though the latent variables ( $z_{d,c}$ ) do not have human-understandable names (like "leg movement"), their temporal relationships are stable enough to form a rigorous, logical, and causal classification system. This provides a viable alternative to black-box models for mission-critical wireless sensing applications where transparency and controllability are required.