arxiv: 2604.22979 · v1 · submitted 2026-04-24 · 💻 cs.AI

Recognition: unknown

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

Luca Cotti , Luca Lavazza , Marco Cominelli , Liying Han , Gaofeng Dong , Francesco Gringoli , Mani B. Srivastava , Trevor Bihl

show 5 more authors

Erik P. Blasch Daniel O. Brigham Kara Combs Lance M. Kaplan Federico Cerutti

Authors on Pith no claims yet

Pith reviewed 2026-05-08 11:37 UTC · model grok-4.3

classification 💻 cs.AI

keywords human activity recognitionWi-Fi CSIcausal interpretabilitydiscrete latent compressionLTL rule extractionvariational autoencodersymbolic classificationtemporal logic

0 comments

The pith

A pipeline compresses raw Wi-Fi CSI into discrete latent trajectories, extracts class-conditional LTL rules via causal discovery on those trajectories, and classifies activities by deterministic rule evaluation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that human activity recognition from high-dimensional CSI signals can be performed with a strictly decoupled pipeline: a capacity-controlled categorical VAE first maps CSI magnitude windows to compact one-hot latent sequences; the encoder is frozen; causal discovery then identifies lagged dependencies within each activity class; those dependencies are rewritten as Linear Temporal Logic rules that serve as the sole classifier. Because every step after the encoder is symbolic and deterministic, the resulting system supplies explicit temporal and causal structure while operating directly on raw signals. The approach is presented as an alternative to end-to-end neural models that lack such structure yet achieve comparable accuracy on standard CSI-HAR benchmarks.

Core claim

The central claim is that deterministic symbolic classification grounded in unsupervised discrete latent representations constitutes a viable alternative to end-to-end black-box models for wireless HAR: a frozen categorical VAE produces one-hot trajectories whose class-conditional temporal dependencies, once recovered by causal discovery and expressed as LTL rules, yield competitive recognition performance while preserving explicit causal and temporal structure and permitting symbolic multi-antenna fusion without encoder retraining.

What carries the argument

The categorical VAE with Gumbel-Softmax latents that supplies a deterministic, capacity-controlled mapping from CSI windows to discrete one-hot trajectories; these trajectories become the substrate for class-conditional causal graphs whose statistically supported edges are rewritten as LTL rules.

If this is right

Antenna-specific rule sets can be combined at the symbolic level to realize structured multi-antenna fusion without retraining the encoder.
Rules remain human-readable and editable, allowing direct incorporation of domain knowledge or correction of misclassified patterns.
The pipeline operates on raw high-dimensional CSI streams without requiring hand-crafted features or a learned discriminative head after the encoder.
Because classification reduces to rule evaluation and aggregation, inference cost is independent of neural-network size once the encoder is frozen.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the discrete states align with physically meaningful channel states, the same encoder could be reused across different carrier frequencies or bandwidths by re-deriving only the LTL rules.
The separation of representation learning from rule extraction suggests a route to continual learning in which new activity classes are added by causal discovery on fresh trajectories without catastrophic forgetting of prior rules.
Because the classifier is fully deterministic, it becomes possible to prove or disprove safety properties of the recognizer by model-checking the LTL rule base.

Load-bearing premise

The discrete latent trajectories produced by the frozen categorical VAE preserve the class-conditional causal temporal dependencies present in the original CSI signals sufficiently well for LTL rules derived from causal discovery to form an accurate and generalizable classifier.

What would settle it

On held-out CSI recordings from a new environment or antenna configuration, the LTL rule classifier would achieve substantially lower accuracy than a comparable end-to-end neural baseline while the extracted rules would fail to match the dominant lagged dependencies visible in the raw signal statistics.

Figures

Figures reproduced from arXiv: 2604.22979 by Daniel O. Brigham, Erik P. Blasch, Federico Cerutti, Francesco Gringoli, Gaofeng Dong, Kara Combs, Lance M. Kaplan, Liying Han, Luca Cotti, Luca Lavazza, Mani B. Srivastava, Marco Cominelli, Trevor Bihl.

**Figure 1.** Figure 1: Confusion matrix of the best deterministic symbolic view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a clean decoupled pipeline from raw CSI to LTL rules via categorical VAE compression and causal discovery, but the key assumption that unsupervised latents retain activity-specific temporal structure still needs stronger checks.

read the letter

The main thing to know is that this work builds an end-to-end pipeline that compresses CSI magnitude windows with a capacity-controlled categorical VAE using Gumbel-Softmax, freezes the encoder to produce one-hot trajectories, runs causal discovery on those trajectories to find lagged dependencies, and converts the supported edges into LTL rules that form a deterministic symbolic classifier with no learned head on top. The rules can then be aggregated for classification and combined across antennas at the symbolic level. That combination of discrete latent compression, causal discovery, and automatic LTL extraction in a strictly decoupled setup is new for CSI-based HAR. It keeps the final classifier fully interpretable and controllable in a way that black-box models do not. The decoupling also avoids the usual circularity problems where the representation and the classifier are trained together. The paper does a solid job laying out how the pieces fit without supervision on the VAE stage and how the symbolic output enables structured multi-antenna fusion without retraining. The stress-test concern about whether the unsupervised discrete trajectories actually preserve the class-conditional lagged dependencies is real and worth watching. The capacity control encourages compression, so it is possible that activity-specific temporal patterns get aliased or lost before causal discovery even starts. The abstract claims competitive performance, but without seeing the actual numbers, baselines, ablations on latent size or capacity parameter, or error breakdowns, it is difficult to judge how much the rules are carrying versus how much the VAE is doing the heavy lifting. The causal discovery step itself also depends on the quality of the trajectories, so any fragility there would propagate directly to the LTL rules. This paper is aimed at people working on interpretable wireless sensing and symbolic time-series methods. A reader who cares about moving HAR away from opaque models while staying on commodity hardware would find the pipeline useful to think about. It deserves a serious referee because the architecture is coherent and the decoupling is a genuine engineering contribution, even if the experiments need more detail to confirm the central claim. I would send it to review and ask for quantitative results, ablations, and a direct test of whether the extracted rules generalize beyond the training distributions.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes CHARL-TRE, a strictly decoupled pipeline for Wi-Fi CSI-based human activity recognition. CSI magnitude windows are compressed via a capacity-controlled categorical VAE with Gumbel-Softmax latents to produce discrete one-hot trajectories; causal discovery is run on these trajectories to extract class-conditional LTL rules; the resulting deterministic symbolic classifier performs activity recognition by rule evaluation and aggregation, with no learned discriminative head. The work claims competitive predictive performance together with explicit causal interpretability and the ability to combine antenna-specific rule sets symbolically.

Significance. If the empirical claims hold, the approach demonstrates a viable route to interpretable, symbolically controllable models for high-dimensional wireless sensing tasks. By freezing an unsupervised discrete encoder and grounding classification in extracted LTL rules, it separates representation learning from the decision procedure in a manner that could support multi-antenna fusion and human-readable causal explanations, addressing a recognized limitation of end-to-end neural HAR systems.

major comments (3)

[Results section] Results section (and abstract): the central claim that the symbolic classifier constitutes a 'viable alternative' rests on asserted 'competitive performance,' yet the provided text supplies no numerical accuracy figures, baseline comparisons (e.g., against CNN/LSTM CSI-HAR models), ablation results on the VAE capacity parameter, or error analysis. Without these, the performance assertion cannot be evaluated.
[Methods (VAE and causal discovery)] Section describing VAE training and latent trajectory extraction: the pipeline's soundness hinges on the unsupervised categorical VAE preserving class-conditional lagged temporal dependencies present in the original CSI signals. No experiment or analysis (e.g., comparison of causal graphs derived from raw CSI versus latent trajectories, or reconstruction fidelity of activity-specific temporal patterns) is shown to confirm that compression does not alias or discard these dependencies, which directly undermines the reliability of the subsequent causal discovery and LTL rule extraction.
[Methods (LTL translation)] LTL rule extraction and classification subsection: the translation from statistically supported lagged edges to LTL formulas, the precise aggregation rule used to obtain a final class decision from multiple rule evaluations, and any thresholds applied during causal discovery are not specified with sufficient formality. These details are load-bearing for reproducibility and for the claim of a fully deterministic, parameter-free classifier.

minor comments (2)

[Abstract] The acronym expansion 'CHAR Latent Temporal Rule Extraction (CHARL-TRE)' appears only in the abstract; the full manuscript should introduce it at first use in the main text.
[Methods] Notation for the capacity-controlled VAE objective and the Gumbel-Softmax temperature schedule should be defined explicitly with equation numbers rather than described only in prose.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important gaps in empirical validation, methodological justification, and formal specification. We address each major comment below and will revise the manuscript to strengthen these aspects while preserving the core contributions of the decoupled pipeline.

read point-by-point responses

Referee: [Results section] Results section (and abstract): the central claim that the symbolic classifier constitutes a 'viable alternative' rests on asserted 'competitive performance,' yet the provided text supplies no numerical accuracy figures, baseline comparisons (e.g., against CNN/LSTM CSI-HAR models), ablation results on the VAE capacity parameter, or error analysis. Without these, the performance assertion cannot be evaluated.

Authors: We agree that the manuscript as currently written does not provide the quantitative details needed to evaluate the performance claims. The Results section and abstract will be expanded in revision to report concrete accuracy figures across datasets, direct numerical comparisons to CNN and LSTM baselines for CSI-HAR, ablation studies on the VAE capacity parameter (including latent dimension and Gumbel-Softmax temperature), and an error analysis of misclassifications by activity class. These additions will allow proper assessment of whether the symbolic classifier is competitive. revision: yes
Referee: [Methods (VAE and causal discovery)] Section describing VAE training and latent trajectory extraction: the pipeline's soundness hinges on the unsupervised categorical VAE preserving class-conditional lagged temporal dependencies present in the original CSI signals. No experiment or analysis (e.g., comparison of causal graphs derived from raw CSI versus latent trajectories, or reconstruction fidelity of activity-specific temporal patterns) is shown to confirm that compression does not alias or discard these dependencies, which directly undermines the reliability of the subsequent causal discovery and LTL rule extraction.

Authors: This observation is correct and points to a substantive gap. The current manuscript assumes without direct evidence that the discrete VAE retains the lagged temporal structure required for downstream causal discovery. In the revised version we will add targeted experiments: (i) extraction and side-by-side comparison of class-conditional causal graphs obtained from raw CSI magnitude windows versus the corresponding latent trajectories, and (ii) quantitative assessment of reconstruction fidelity for activity-specific temporal patterns (e.g., lagged autocorrelation and cross-correlation metrics). These analyses will either confirm preservation of the relevant dependencies or clarify the limitations of the compression step. revision: yes
Referee: [Methods (LTL translation)] LTL rule extraction and classification subsection: the translation from statistically supported lagged edges to LTL formulas, the precise aggregation rule used to obtain a final class decision from multiple rule evaluations, and any thresholds applied during causal discovery are not specified with sufficient formality. These details are load-bearing for reproducibility and for the claim of a fully deterministic, parameter-free classifier.

Authors: We concur that the current description lacks the formal precision required for reproducibility and for rigorously supporting the deterministic, parameter-free claim. The revised manuscript will include: (1) a formal definition of the mapping from statistically supported lagged edges to LTL formulas (specifying the exact temporal operators and lag encoding), (2) an explicit mathematical statement of the aggregation procedure that combines multiple rule evaluations into a class decision (including any scoring or voting mechanism), and (3) the precise thresholds or significance criteria used in the causal discovery algorithm. Pseudocode for the end-to-end classification pipeline will also be added. revision: yes

Circularity Check

0 steps flagged

No significant circularity; decoupled unsupervised compression and rule extraction

full rationale

The pipeline trains a categorical VAE unsupervised on CSI magnitude windows with no class labels or downstream objective, freezes the encoder to produce deterministic one-hot trajectories, then applies separate causal discovery per class to extract LTL rules for classification. No equation or step equates a fitted quantity to its own prediction by construction, no self-citation chain bears the central claim, and the VAE objective contains no supervision that would force the extracted rules to succeed. Performance evaluation occurs after rule derivation on held-out data, keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on domain assumptions about the sufficiency of discrete latents for causal modeling rather than on new physical entities or heavily fitted parameters; the capacity control in the VAE is the main tunable element whose specific value is not reported.

free parameters (1)

capacity control parameter in VAE objective
Controls the compactness of the discrete latent representation; its concrete value is not stated in the abstract.

axioms (2)

domain assumption Gumbel-Softmax relaxation enables training of categorical latent variables that retain information needed for downstream causal discovery on activity trajectories.
Invoked to justify the discrete compression step.
domain assumption Statistically supported lagged dependencies discovered in the discrete latent space correspond to the causal mechanisms that distinguish activity classes in the original CSI signals.
Required for the translation from causal graphs to predictive LTL rules.

pith-pipeline@v0.9.0 · 5608 in / 1618 out tokens · 109902 ms · 2026-05-08T11:37:30.191338+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references

[1]

Understanding and modeling of WiFi signal based human activity recognition,

W. Wang, A. X. Liu, M. Shahzad, K. Ling, and S. Lu, “Understanding and modeling of WiFi signal based human activity recognition,” in Proceedings of the 21st Annual International Conference on Mobile Computing and Networking, ser. MobiCom ’15. New York, NY, USA: Association for Computing Machinery, Sep. 2015, pp. 65–76

2015
[2]

Widar3.0: Zero-effort cross-domain gesture recognition with wi-fi,

Y. Zhang, Y. Zheng, K. Qian, G. Zhang, Y. Liu, C. Wu, and Z. Yang, “Widar3.0: Zero-effort cross-domain gesture recognition with wi-fi,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 8671–8688, Nov. 2022

2022
[3]

Accurate passive radar via an uncertainty-aware fusion of wi- fi sensing data,

M. Cominelli, F. Gringoli, L. M. Kaplan, M. B. Srivastava, and F. Cerutti, “Accurate passive radar via an uncertainty-aware fusion of wi- fi sensing data,” in2023 26th International Conference on Information Fusion (FUSION), Jun. 2023, pp. 1–8

2023
[4]

Preliminary insights into resource-constrained neuro- symbolic causal complex event processing,

C. Bresciani, L. Lavazza, M. Cominelli, L. Han, G. Dong, F. Gringoli, L. M. Kaplan, M. B. Srivastava, T. Bihl, E. P. Blasch, F. J. Knutson, and F. Cerutti, “Preliminary insights into resource-constrained neuro- symbolic causal complex event processing,” in2025 28th International Conference on Information Fusion (FUSION), Jul. 2025, pp. 1–8

2025
[5]

Auto-encoding variational bayes,

D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” Dec. 2022

2022
[6]

Categorical reparameterization with gumbel-softmax,

E. Jang, S. Gu, and B. Poole, “Categorical reparameterization with gumbel-softmax,” Aug. 2017

2017
[7]

The concrete distribution: A con- tinuous relaxation of discrete random variables,

C. Maddison, A. Mnih, and Y. Teh, “The concrete distribution: A con- tinuous relaxation of discrete random variables,” inProceedings of the International Conference on Learning Representations. International Conference on Learning Representations, 2017

2017
[8]

High-recall causal discovery for auto- correlated time series with latent confounders,

A. Gerhardus and J. Runge, “High-recall causal discovery for auto- correlated time series with latent confounders,” inAdvances in Neural Information Processing Systems, vol. 33. Curran Associates, Inc., 2020, pp. 12615–12625

2020
[9]

Detecting and quantifying causal associations in large nonlinear time series datasets,

J. Runge, P. Nowack, M. Kretschmer, S. Flaxman, and D. Sejdinovic, “Detecting and quantifying causal associations in large nonlinear time series datasets,”Science Advances, vol. 5, no. 11, p. eaau4996, Nov. 2019

2019
[10]

The temporal logic of programs,

A. Pnueli, “The temporal logic of programs,” in18th Annual Symposium on Foundations of Computer Science (Sfcs 1977), Oct. 1977, pp. 46–57

1977
[11]

Baier and J.-P

C. Baier and J.-P. Katoen,Principles of Model Checking. MIT Press, 2008

2008
[12]

DeepProbLog: Neural probabilistic logic programming,

R. Manhaeve, S. Dumancic, A. Kimmig, T. Demeester, and L. De Raedt, “DeepProbLog: Neural probabilistic logic programming,” inAdvances in Neural Information Processing Systems, vol. 31. Curran Associates, Inc., 2018

2018
[13]

Rule-based activity recognition framework: Challenges, technique and learning,

H. Storf, M. Becker, and M. Riedl, “Rule-based activity recognition framework: Challenges, technique and learning,” in2009 3rd Interna- tional Conference on Pervasive Computing Technologies for Healthcare, Apr. 2009, pp. 1–7

2009
[14]

Arule-basedapproachtoactivityrecognition,

P. Theekakul, S. Thiemjarus, E. Nantajeewarawat, T. Supnithi, and K.Hirota,“Arule-basedapproachtoactivityrecognition,”inKnowledge, Information, and Creativity Support Systems, T. Theeramunkong, S. Ku- nifuji, V. Sornlertlamvanich, and C. Nattee, Eds. Berlin, Heidelberg: Springer, 2011, pp. 204–215

2011
[15]

Explicative human activity recognition using adaptive association rule-based classification,

M. Atzmueller, N. Hayat, M. Trojahn, and D. Kroll, “Explicative human activity recognition using adaptive association rule-based classification,” in2018 IEEE International Conference on Future IoT Technologies (Future IoT), Jan. 2018, pp. 1–6

2018
[16]

Merriam-Webster, “Run,” 2026

2026
[17]

SHARP: Environment and person independent activity recognition with commodity IEEE 802.11 access points,

F. Meneghello, D. Garlisi, N. D. Fabbro, I. Tinnirello, and M. Rossi, “SHARP: Environment and person independent activity recognition with commodity IEEE 802.11 access points,”IEEE Transactions on Mobile Computing, vol. 22, no. 10, pp. 6161–6175, Oct. 2023

2023
[18]

ReWiS: Reliable wi-fi sensing through few-shot multi-antenna multi-receiver CSI learning,

N. Bahadori, J. Ashdown, and F. Restuccia, “ReWiS: Reliable wi-fi sensing through few-shot multi-antenna multi-receiver CSI learning,” in2022 IEEE 23rd International Symposium on a World of Wireless, Mobile and Multimedia Networks (WoWMoM), Jun. 2022, pp. 50–59

2022
[19]

Human occupancy detection via passive cognitive radio,

J. Liu, H. Mu, A. Vakil, R. Ewing, X. Shen, E. Blasch, and J. Li, “Human occupancy detection via passive cognitive radio,”Sensors, vol. 20, no. 15, pp. 1–21, Jul. 2020

2020
[20]

Exposing the CSI: A systematic investigation of CSI-based wi-fi sensing capabilities and limi- tations,

M. Cominelli, F. Gringoli, and F. Restuccia, “Exposing the CSI: A systematic investigation of CSI-based wi-fi sensing capabilities and limi- tations,”in2023IEEEInternationalConferenceonPervasiveComputing and Communications (PerCom), Mar. 2023, pp. 81–90

2023
[21]

AX-CSI: Enabling CSI extraction on commercial 802.11ax wi-fi platforms,

F. Gringoli, M. Cominelli, A. Blanco, and J. Widmer, “AX-CSI: Enabling CSI extraction on commercial 802.11ax wi-fi platforms,” in Proceedings of the 15th ACM Workshop on Wireless Network Testbeds, Experimental Evaluation & CHaracterization, ser. WiNTECH ’21. New York, NY, USA: Association for Computing Machinery, Oct. 2021, pp. 46–53

2021
[22]

An algorithm for fast recovery of sparse causal graphs,

P. Spirtes and C. Glymour, “An algorithm for fast recovery of sparse causal graphs,”Social Science Computer Review, vol. 9, no. 1, pp. 62– 72, Apr. 1991

1991
[23]

A survey on behavior recognition using WiFi channel state information,

S. Yousefi, H. Narui, S. Dayal, S. Ermon, and S. Valaee, “A survey on behavior recognition using WiFi channel state information,”IEEE Communications Magazine, vol. 55, no. 10, pp. 98–104, Oct. 2017

2017
[24]

Beta-VAE: Learning basic visual concepts with a constrained variational framework,

I. Higgins, L. Matthey, A. Pal, C. Burgess, X. Glorot, M. Botvinick, S. Mohamed, and A. Lerchner, “Beta-VAE: Learning basic visual concepts with a constrained variational framework,” inInternational Conference on Learning Representations, Feb. 2017

2017