Secure Time-Modulated Intelligent Reflecting Surface via Generative Flow Networks

Athina P. Petropulu; Zhihao Tao

REVIEW 3 major objections 5 minor 24 references

Secure Time-Modulated Intelligent Reflecting Surface via Generative Flow Networks

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A generative flow network can choose time-modulated reflecting-surface settings that serve multiple users while scrambling all other directions.

desk verdict GFlowNet for TM-IRS is a fresh, reproducible application, but the multi-user sum-rate claim is unsupported by the single-stream system model. read the letter →

arxiv 2506.14992 v1 pith:LHCXZYQX submitted 2025-06-17 eess.SP

Zhihao Tao , Athina P. Petropulu This is my paper · ORCID

classification eess.SP

keywords intelligentreflectingsurfacetimemodulationdirectionalphysicallayersecurityGFlowNetsOFDMMarkovdecisionprocess

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the configuration of a time-modulated intelligent reflecting surface (TM-IRS) — which switches individual reflecting elements on and off in time to shape the transmitted OFDM waveform — can be chosen by a generative flow network rather than by hand-crafted rules. The goal is directional modulation: signals stay readable at the directions of legitimate users and are scrambled everywhere else. The authors cast configuration selection as a Markov decision process whose terminal states are full TM-IRS parameter settings and train a GFlowNet to sample settings with probability proportional to the achievable sum rate. Experiments show low symbol error rates at two user directions with scrambling elsewhere, and convergence after training on fewer than 0.000001% of the roughly $10^{65}$ configuration space. A sympathetic reader would take the paper as evidence that generative sampling can replace rule-based beamforming for physical-layer security in multi-user OFDM links.

What carries the argument

The load-bearing object is the GFlowNet with trajectory-balance loss: a generative model that treats each complete TM-IRS parameter set as a terminal state of a deterministic, acyclic Markov decision process, with actions assigning one discretized value to one parameter at a time. Flow-matching training makes the forward policy sample terminal states with probability proportional to the reward function $R = C_{\mathrm{total}} \prod_{u=1}^U H(\xi_u - |\arg(V_0)_u|)$, so high sum-rate configurations that respect constellation phase constraints are visited frequently without exhaustive search. The discrete parameter space is roughly $10^{65}$ configurations, and the trained network generalizes beyond the $9 \times 10^5$ sampled trajectories.

What would settle it

Transmit two distinct data streams to the two users at $(40^\circ, 30^\circ)$ and $(-40^\circ, 30^\circ)$ using the same trained GFlowNet configuration and check whether each user decodes its own stream; because Eq. (7) contains a single data symbol $d(k)$, the received signals at both directions will carry the same broadcast data, so the multi-user claim would collapse unless separate streams are actually delivered.

Watch

Extended reading notes

Core claim

The central discovery is that a GFlowNet trained with the trajectory-balance objective can learn a stochastic policy over TM-IRS parameters (phase shifts, turn-on instants, and on-durations for each element) such that the sampling distribution is proportional to a sum-rate reward. The reward is the total achievable rate across authorized directions, multiplied by a Heaviside factor that enforces a per-user phase constraint on the main-tap coefficient $V_0$. In simulation with a $6 \times 6$ IRS and 16 subcarriers, the policy yields near-zero symbol error rate at the intended directions while scrambling other directions, matches the single-user rule-based baseline, and extends to a second user at $(-40^\circ, 30^\circ)$. The authors further use the policy's diversity to switch among four configurations over time, averaging out accidental low-SER sidelobes.

Load-bearing premise

The paper's multi-user claim depends on each legitimate user being served an independent data stream, but the system model transmits a single OFDM data symbol $d(k)$ identically in all directions with no described precoding or scheduling, so if users are not actually served independent messages, the sum-rate objective measures broadcasting the same data to several directions rather than multi-user communication.

Editorial extensions

If this is right

Training on $9 \times 10^5$ trajectories out of a roughly $10^{65}$-state space suffices to approximate the reward distribution, so exhaustive search is not needed for this class of configuration problems.
The stochastic sampling policy yields many distinct high-reward configurations, which lets the system switch TM patterns over time and average away directions that accidentally have low symbol error rate.
The same reward formulation extends from one legitimate user to multiple users by enforcing a phase constraint per user, as demonstrated for two users.
The approach matches the rule-based single-user baseline in desired-direction symbol error rate while also scrambling all other directions, making it a viable replacement for the existing closed-form design.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

One implication the paper leaves implicit: because the sampling policy is stochastic, an eavesdropper who knows the channel but not the sampling seed cannot predict which configuration is active, so the configuration space itself becomes a source of secret randomness; quantifying that secrecy gain would be a natural next step.
The efficiency result suggests the same flow-matching setup could handle other combinatorial parameter searches in physical-layer security, such as joint IRS phase and position selection or waveform design with discrete phase shifters, whenever an analytical reward is available.
The single-stream system model means the multi-user demonstration is, strictly speaking, a broadcast to several directions; to make the sum-rate claim a genuine multi-user throughput result, the transmitter would need per-user precoding or subcarrier allocation, which the paper does not describe.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a competent application of GFlowNets to a hard discrete parameter search for time-modulated IRS, with code and a fair single-user comparison. The advertised multi-user contribution is undercut by a real mismatch: the system model broadcasts one OFDM stream d(k) to all directions, so Eq. (10) sums per-user rates as if each user had an independent message when no independent messages exist. The two-user SER plot shows the same data decodable at two angles, which is a multi-direction broadcast, not multi-user transmission.

What is genuinely new: prior TM-IRS design [18] is rule-based and single-direction, and this is the first GFlowNet-based parameter selection for TM-IRS that I know of. The MDP and trajectory-balance machinery is standard, but the application and the diversity-based security enhancement are legitimately new. The paper does the right thing empirically for the single-user case: Fig. 2 shows comparable SER at the intended direction and scrambling elsewhere, and the dynamic switching between diverse configurations (Fig. 3) is a sensible use of the sampler's mode coverage. Code is on GitHub, which makes the simulation reproducible.

Soft spots, in order of severity. First, the multi-user sum-rate issue is load-bearing. Eq. (1) sends the same d(k) on every antenna; Eq. (7) is that same data convolved with V(i−k). There is no precoding, scheduling, or per-user subcarrier allocation. Every legitimate user receives the same message, so the total achievable rate is at most min_u C_u, not ∑ C_u. The stated objective of maximizing sum rate across authorized directions is not an information-theoretically valid multi-user metric. This does not affect the single-user results, but it invalidates the claim of supporting multiple independent users. It is fixable by adding transmit precoding or subcarrier assignment, or by reframing the contribution as multi-direction secure broadcast.

Second, the efficiency claim is under-evidenced. Converging in 9e5 trajectories out of ~10^65 configurations tells us little without comparison to random search, greedy search, or another generative baseline. The comparison to exhaustive search is trivially true; what matters is comparison to plausible heuristics.

Third, no error bars or seed variance are reported. For a stochastic sampler, single-run SER curves make it hard to know how robust the policy is. Minor: the two-user experiment reports SER, not the sum rate that the objective nominally optimizes.

The circularity worry raised in the stress-test is not a real issue: the reward and SER come from the same simulation model, but no fitted constants are hidden, which is normal for this line of work.

Overall, the paper is a solid, honest single-user study that overclaims on multi-user. I'd send it to review, but the multi-user framing needs a serious rewrite before acceptance.

Referee Report

3 major / 5 minor

Summary. The paper proposes a generative flow network (GFlowNet) based method for designing time-modulated intelligent reflecting surface (TM-IRS) parameters in an OFDM directional modulation system. The parameter selection is cast as a deterministic MDP, and a trajectory-balance GFlowNet is trained to sample TM-IRS configurations with probability proportional to a reward that combines the sum rate across authorized directions with a phase-constraint penalty. Simulations compare the angular SER profile with a rule-based design for a single user, show a two-user example, and illustrate a time-varying configuration strategy that randomizes low-SER leakage directions. The authors report convergence after 9e5 sampled trajectories out of a space of roughly 10^65 configurations and provide implementation code.

Significance. The paper introduces a novel application of GFlowNets to a physical-layer security problem, and the idea of using generative models to explore a huge discrete TM-IRS parameter space is interesting and potentially valuable. The single-user comparison to the rule-based method is a reasonable sanity check, and the diversity-based security enhancement via switching among sampled configurations is a thoughtful contribution. The availability of code and the self-contained simulation are strengths. However, the advertised multi-user support is not supported by the system model, as detailed in the major comments; the claimed sum-rate objective and the two-user SER demonstration only establish a common-message broadcast capability. If reframed or extended to independent user streams, the approach could be significant for secure multi-directional transmission.

major comments (3)

[Section II, Eq. (10) and Section IV, Fig. 4] The system model in Eq. (1) transmits a single OFDM data stream d(k), and Eq. (7) shows that the received symbol at every direction is a function of that same d(k). Consequently, all legitimate users receive the same common message, and the per-user rates C_u in Eq. (10) cannot be summed as independent user rates. For this common-message broadcast channel, the achievable rate is at most min_u C_u, not the sum. The optimization problem in Eq. (11) and the reward in Eq. (17) therefore do not maximize a valid multi-user sum rate. The two-user result in Fig. 4 merely shows that one common message is decodable at two angles. Please either extend the system model with per-user precoding, scheduling, or subcarrier allocation that creates independent data streams, or reframe the contribution as multi-directional common-message broadcast and replace the sum-rate objective with an appropriate common-rate metric.
[Section III-B, state representation] The state vector is described as s in R^{M x Q}, partitioned into M blocks with Q = Q1+Q2+Q3 entries, and later the text states that after 3M actions every block contains a single 1. This is inconsistent: each IRS element has three TM-IRS parameters (cmn, tau_o_mn, Delta_tau_mn), so there are 3M parameters. A one-hot representation would require either 3M blocks or a different encoding (e.g., a block size of Q1*Q2*Q3 per element). The stated network output dimension 2M x Q similarly reflects only M blocks. Please clarify the exact state, action, and network output dimensions; the current description is not reproducible.
[Section II, Eq. (8)] The SINR expression has a malformed denominator: "eta * sum_{i j=i-(K-1)} |V_j|^2 - |V0|^2 + sigma^2" leaves the summation range ambiguous and does not define V_j for indices outside [0, K-1]. Since the achievable rate C in Eq. (9) and hence the reward in Eq. (17) depend directly on this SINR, please rewrite the summation explicitly (e.g., as sum_{j=0, j != i}^{K-1} |V_{i-j}|^2) and specify the definition and range of V_l.

minor comments (5)

[Section IV] The claim that 9e5 trajectories out of roughly 10^65 configurations demonstrates "remarkable efficiency" would be more persuasive with a comparison against random sampling or a simple baseline; as presented, the decreasing TB loss does not by itself establish that the sampled configurations are near-optimal or that the search is more efficient than random search.
[Section IV, two-user experiment] The threshold xi_u = pi/5 is used for QPSK modulation, but Section II states that for M-PSK the threshold must be smaller than pi/M (pi/4 for QPSK). Please justify the specific choice and state whether it satisfies the required margin.
[Section III-B and Section IV] The procedure for sampling the four diverse TM-IRS configurations used in the time-varying security strategy is not described; please specify whether they are sampled from the trained forward policy and whether any temperature or filtering is applied.
[Abstract and throughout] The paper contains several typographical and spacing errors (e.g., "conﬁgured" in the abstract, inconsistent hyphenation of "sum rate" and "sum-rate"); a careful proofreading pass is needed.
[Section II, Eq. (5)-(7)] The notation V(l, Omega_mn, theta, phi) is later abbreviated to Vi-k without an explicit definition of the indexing convention; please define Vi-k consistently, including the range of l for a finite number of harmonics used in the simulations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the training reward is derived from the analytical model, and the SER evaluation is an independent metric on the same model rather than a renamed training target.

full rationale

The paper's derivation chain is self-contained: the GFlowNet reward in Eq. (17) is built directly from the analytical system model (R = C_total * product of Heaviside phase-constraint terms), where C_total is the sum-rate expression in Eqs. (8)-(10) derived from the received-signal model in Eq. (7). The GFlowNet is trained to sample TM-IRS configurations with probability proportional to this reward, and the reported SER is obtained by nearest-neighbor detection on the same received-signal expression. This is a standard optimization-and-evaluation loop rather than circularity: SER is an independent decision-theoretic metric, not the training objective, and no fitted parameter is renamed as a prediction. The comparison against the rule-based design of [18] is a baseline comparison, not a load-bearing derivation step; the self-citations ([6], [16], [18]) are background or baseline references and do not supply an unverified premise that the paper's own equations rely on. The skeptic's concern that Eq. (10) sums per-user rates while the model transmits a single OFDM data stream is a modeling-validity issue about whether 'multi-user support' is actually independent-stream multi-user transmission; it is a correctness concern, not a circularity of the derivation. No step reduces a claimed prediction to its input by construction, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the assumed exactness of the Fourier model, the validity of the SINR-based reward as a proxy for SER, the GFlowNet convergence guarantee, and the multi-user sum-rate setup. The most questionable axiom is the multi-user independence, since the system model does not provide a mechanism for independent user data streams.

free parameters (4)

Q1 (phase quantization levels) = 16
Discretization of the IRS phase shift c_mn; chosen by hand, determines the size of the search space and the achievable phase resolution.
Q2 (turn-on time quantization levels) = 8
Discretization of the normalized turn-on instant tau_o_mn; chosen by hand.
Q3 (on-duration quantization levels) = 8
Discretization of the normalized on-duration Delta tau_mn; chosen by hand.
Phase constraint threshold xi_u = pi/5 for QPSK
The allowed phase rotation of V0 per user; chosen by hand (must be below pi/4 for QPSK).

assumptions (6)

standard math The periodic switching function U_mn(t) has an exact Fourier series expansion (Eq. 2) with harmonics only at integer multiples of the subcarrier spacing f_s.
Standard Fourier series for a periodic square wave; used to derive the received signal model in Eq. (5)-(7).
domain assumption The SINR expression in Eq. (8) treats all cross-subcarrier interference as additional noise, and the achievable rate in Eq. (9) is the Shannon rate for independent Gaussian codebooks.
The paper assumes nearest-neighbor decoding for QPSK in experiments, but the reward uses the Shannon sum rate; the connection between the two is not established.
standard math Trajectory balance training (Eq. 16) converges to a policy that samples terminal states with probability proportional to the reward in Eq. (17).
This is the theoretical guarantee of GFlowNets cited from [24]; the paper relies on it to claim that high-reward configurations are sampled.
domain assumption The phase constraint |arg(V0)_u| <= xi_u is sufficient to preserve constellation integrity for M-PSK.
Used to define the feasible set in Eq. (11) and the reward in Eq. (17); no analysis of the effect of phase error on SER is given for finite xi.
domain assumption Multiple legitimate users receive independent data streams, so the sum rate in Eq. (10) is a meaningful multi-user objective.
The system model in Eq. (7) shows the same data symbols d(k) in all directions; no per-user data or precoding is described.
domain assumption The eavesdropper knows and can compensate for its channel, so the channel is omitted from the signal model.
Stated in Section II: 'we will assume the scenario in which the eavesdropper knows its channel and can compensate for it.'

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Cite this review

Pith. "Pith review of Secure Time-Modulated Intelligent Reflecting Surface via Generative Flow Networks." pith.science (2026). https://pith.science/paper/LHCXZYQX

@misc{pith2026250614992,
  author       = {Pith},
  title        = {Pith review of: Secure Time-Modulated Intelligent Reflecting Surface via Generative Flow Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LHCXZYQX}},
  note         = {Machine review of arXiv:2506.14992}
}

read the original abstract

We propose a novel directional modulation (DM) design for OFDM transmitters aided by a time-modulated intelligent reflecting surface (TM-IRS). The TM-IRS is configured to preserve the integrity of transmitted signals toward multiple legitimate users while scrambling the signal in all other directions. Existing TM-IRS design methods typically target a single user direction and follow predefined rule-based procedures, making them unsuitable for multi-user scenarios. Here, we propose a generative AI-based approach to design good sets of TM-IRS parameters out of a set of all possible quantized ranges of parameters. The design objective is to maximize the sum rate across the authorized directions. We model the TM-IRS parameter selection as a deterministic Markov decision process (MDP), where each terminal state corresponds to a specific configuration of TM-IRS parameters. GFlowNets are employed to learn a stochastic policy that samples TM-IRS parameter sets with probability proportional to their associated sum rate reward. Experimental results demonstrate that the proposed method effectively enhances the security of the TM-IRS-aided OFDM systems with multi-users. Also, despite the vast size of the TM-IRS configuration space, the GFlowNet is able to converge after training on fewer than 0.000001% of all possible configurations, demonstrating remarkable efficiency compared to exhaustive combinatorial search. Implementation code is available at https://github.com/ZhihaoTao/GFN4TM-RIS to facilitate reproducibility.

Figures

Figures reproduced from arXiv: 2506.14992 by the authors.

**Figure 2.** Comparison of SER over different spatial directions [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Enhancing security via TM parameter diversity: (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [18]

Time-modulated intelligent re ﬂecting surface for waveform security,

Z. Xu and A. Petropulu, “Time-modulated intelligent re ﬂecting surface for waveform security,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Seoul, Korea, 2024, pp. 8986–8990

work page 2024

[2] [1]

Communication theory of secrecy systems ,

C. E. Shannon, “Communication theory of secrecy systems ,” Bell Labs Tech. J., vol. 28, no. 4, pp. 656–715, Oct. 1949

work page 1949

[3] [2]

The wire-tap channel,

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J , vol. 54, no. 8, pp. 1355–1387, Aug. 1975

work page 1975

[4] [3]

Wireless physical layer se curity,

H. V . Poor and R. F. Schaefer, “Wireless physical layer se curity,” Proceedings of the National Academy of Sciences , vol. 114, no. 1, pp. 19–26, Jan. 2017

work page 2017

[5] [4]

Directional modulation te chnique for phased arrays,

M. P . Daly and J. T. Bernhard, “Directional modulation te chnique for phased arrays,” IEEE Tran. on Ante. and Prop. , vol. 57, no. 9, pp. 2633– 2640, Sep. 2009

work page 2009

[6] [5]

Decomposed and distribut ed direc- tional modulation for secure wireless communication,

B. Qiu, W. Cheng, and W. Zhang, “Decomposed and distribut ed direc- tional modulation for secure wireless communication,” IEEE Tran. on Wire. Commun., vol. 23, no. 5, pp. 5219–5231, May 2023

work page 2023

[7] [6]

How secure is the time-mo dulated array-enabled ofdm directional modulation?

Z. Tao, Z. Xu, and A. Petropulu, “How secure is the time-mo dulated array-enabled ofdm directional modulation?” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP) , Seoul, Korea, 2024

work page 2024

[8] [7]

Secrecy transmit beamforming for hetero- geneous networks,

T. Lv, H. Gao, and S. Y ang, “Secrecy transmit beamforming for hetero- geneous networks,” IEEE Journal on Selected Areas in Communications , vol. 33, no. 6, pp. 1154–1170, 2015

work page 2015