Amplitude-Belief Reinforcement Learning for Adaptive Cyber Defense in Partially Observable V2X Networks

Anwar Shah; Rohan Farooq; Sajid Anwer; Sajid Ullah Khan; Tallha Akram; Usman Ghous

REVIEW 4 major objections 6 minor 21 references

Amplitude-Belief Reinforcement Learning for Adaptive Cyber Defense in Partially Observable V2X Networks

T0 review · 4 major / 6 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read Amplitude-based belief states cut IoV defense damage variance by about 10× versus classical Bayesian updates under the same PPO policy.

desk verdict Useful ablation idea for amplitude belief in IoV defense, but abstract/body metric and platform conflicts make the sole-cause claim untrustworthy as written. read the letter →

arxiv 2606.07796 v2 pith:CD42ZWNQ submitted 2026-06-05 cs.CR

Anwar Shah , Rohan Farooq , Sajid Anwer , Tallha Akram , Usman Ghous , Sajid Ullah Khan This is my paper · ORCID

classification cs.CR

keywords InternetofVehiclesreinforcementlearningquantum-inspiredbeliefpartialobservabilityintrusiondetectionamplitudePPOadaptiveattacker

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

The paper argues that classical Bayesian belief tracking of a hidden attacker intent collapses under the deceptive, probing, and evasion traffic that adaptive adversaries produce in Internet-of-Vehicles networks, feeding overconfident and unstable inputs into a reinforcement-learning defender. It replaces that belief model with a quantum-inspired amplitude state: a normalized complex vector that is updated by a linear operator and only later turned into probabilities by taking squared magnitudes (Born rule). The resulting belief vector is concatenated with observable traffic features and given to a Proximal Policy Optimization agent that chooses cost-aware actions (monitor, alert, throttle, isolate). Holding architecture, reward, attacker model and environment fixed, the amplitude formulation is claimed to be the sole source of large measured gains: roughly 60 percent lower mean cumulative damage, roughly 90 percent lower damage variance, attack success rate driven to zero, and survival probability of one on held-out test episodes. Explainability tools (SHAP, LIME, Grad-CAM) are used to show that the belief features dominate decisions precisely when the classical posterior collapses. The practical claim is that non-classical uncertainty representations can stabilize sequential cyber defense in partially observable V2X settings without quantum hardware.

What carries the argument

Quantum-inspired amplitude belief: a complex vector ψ_t updated by a linear operator ψ_{t+1}=U_t ψ_t and converted to intent probabilities by the Born rule b(θ_i)=|ψ(i)|²; this vector is concatenated with the observable state and supplied to the PPO policy.

What would settle it

Re-run the identical ablation (same PPO, reward, four-intent adaptive attacker, 600+80 episodes) after replacing the hand-designed U_t with either a pure classical Bayesian update or a randomly initialized learned unitary; if the large variance and ASR gaps disappear, the causal attribution to amplitude belief fails.

Watch

Extended reading notes

Core claim

When a PPO defender is given an amplitude-based belief over four hidden attacker intents instead of a classical Bayesian probability vector, and every other component of the training loop is held fixed, mean cumulative damage falls from 69.348 to 27.495 and damage variance falls from 37.054 to 3.636, while attack success rate drops to 0.000 and survival rises to 1.000 on 80 test episodes.

Load-bearing premise

The claim that the fixed, hand-designed linear amplitude operator is a faithful model of belief evolution under real V2X deception, rather than a simulator-specific regularizer that happens to help with four discrete intents.

Editorial extensions

If this is right

Defenders can keep uncertainty distributed across intent hypotheses during evasion windows instead of collapsing to an overconfident posterior.
Damage variance becomes a first-class security metric: low-variance policies are harder for adaptive attackers to probe and exploit.
The same amplitude-belief interface can be swapped into other partially observable RL defense loops without changing the policy architecture or requiring quantum hardware.
Explainability tools can be used to verify that belief features, not raw traffic spikes, drive mitigation decisions under strategy shifts.

Reading between the lines

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

If the amplitude operator were made learnable rather than fixed, the same architecture might track continuous or higher-dimensional intent spaces that the current four-state model cannot represent.
The finding that a random policy sometimes beats PPO-with-Bayesian-belief suggests classical belief collapse can be actively harmful; similar diagnostics may be useful in other POMDP security settings.
Because the method reports both security and V2X communication metrics (PDR, latency, throughput), it invites joint evaluation of defense actions against service-level agreements rather than security scores alone.

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Signed reviews

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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

The one thing to know: this is a clean engineering idea—swap classical Bayesian intent belief for a fixed amplitude/Born-rule update inside PPO for partially observable IoV defense—and the ablation framing (same network, same PPO, same attacker, only the belief operator changes) is the right way to test it. The reported variance collapse is the interesting part if it holds.

What is new is not quantum-inspired RL itself (Zhang et al. already survey that) or IoV RL defense (Guo, Chen, etc.). It is the concrete pairing of amplitude belief with cost-aware sequential mitigation under an adaptive four-intent attacker, plus the negative result that random can beat classical-belief PPO when the Bayesian posterior collapses under evasion. The formalization of ψ, U_t, and Born extraction is clear enough for a methods paper, the threat model is realistic, and the SHAP/LIME/Grad-CAM section is more careful than most RL-security work.

The soft spots are real and load-bearing. The abstract claims SUMO-OMNeT++/Veins with modest gains (damage 36→28, var 12→6, ASR 0.05, survival 0.96). The body Table I and §VI-E report a CICIoV-23-calibrated custom simulator with much larger effects and perfect ASR/survival 0/1. Section VI still says quantitative results are deferred. U_t is never fully specified from (s, a_def) and is admitted to be fixed/hand-designed, so the causal claim that “amplitude belief alone” produced the gains cannot be isolated. Free parameters (damage table, costs, threshold θ, forced shift period) are many; no multi-seed stats or code. Those are fixable, not fatal, but they currently undercut the strongest claim.

This is for people working on adaptive cyber defense and belief modules under partial observability, not for quantum information or general RL theory. It deserves a serious referee once the numbers and platform are made consistent, U_t is written down, and ASR is honest. I would not desk-reject it; I would send it out with a clear demand for a single experimental record. Worth engaging after revision, not before.

Referee Report

4 major / 6 minor

Summary. The paper formulates IoV cyber defense as a partially observable sequential attacker–defender problem and proposes Q-BIRD: a PPO defender whose input is augmented by an amplitude-based belief state ψ_t ∈ ℂ^H over hidden attacker intent, updated by a linear map ψ_{t+1}=U_t ψ_t with Born-rule probabilities b(θ_i)=|ψ(i)|². The central empirical claim is an ablation holding architecture, PPO training, reward, attacker model, and environment fixed: replacing classical Bayesian belief with the amplitude update yields large gains (Table I: mean cumulative damage 27.495 vs 69.348, variance 3.636 vs 37.054, ASR 0.000, survival 1.000). Supporting analyses include strategy-shift robustness, cost–security trade-offs, and post-hoc SHAP/LIME/Grad-CAM attribution arguing that belief features drive decisions when classical belief collapses.

Significance. If the ablation result holds under a fully specified, reproducible belief operator and a single consistent experimental record, the work would be a useful contribution to adaptive IoV defense: it treats the belief model as a designable component rather than a fixed Bayesian submodule, reports an honest negative result (random policy beating classical-belief PPO), and pairs RL defense with multi-method explainability. The formulation of long-horizon damage-plus-cost minimization under adaptive hidden intent is well motivated for V2X. Those strengths are currently undercut by internal numerical/platform conflicts and an underspecified U_t, so the claimed causal role of “quantum-inspired” belief is not yet established at journal standard.

major comments (4)

Abstract vs body experimental record is inconsistent and load-bearing for the sole-cause claim. The abstract reports SUMO–OMNeT++/Veins results (mean damage 36.0±5.5→28.0±3.0, variance 12.0±2.8→6.0±1.5, ASR 0.05±0.02, survival 0.96±0.02, plus PDR/latency/throughput). §VI-E and Table I report a CICIoV-23-calibrated custom simulator with much larger effect sizes (69.348→27.495 mean, 37.054→3.636 variance, ASR 0.000, survival 1.000). §VI opening still states that quantitative results are “deferred to a subsequent revision.” Until one platform, one metric set, and one set of numbers are used throughout, the ablation cannot support the claim that amplitude belief alone causes the reported gains.
§V-C, Eqs. (13)–(14) and Algorithm 1: the amplitude operator U_t is never fully specified. The text says U_t encodes the impact of s_{t+1} and a_def_t, but does not give its construction (closed form, parameterization, dependence on observations, phase rules, or how interference is produced). §VI-G admits U_t is fixed/hand-designed rather than learned. Without a complete definition of U_t, the ablation (classical B vs amplitude update) cannot isolate “quantum-inspired belief” as the causal factor; the operator could act as an arbitrary regularizer. A reproducible definition of U_t (or a learned unitary-like map with training details) is required for the central claim.
§VI-B.3–4 and Table I: ASR and survival depend on an author-chosen damage threshold θ that is not stated numerically, and perfect ASR=0 / survival=1.000 on 80 test episodes is reported without confidence intervals or sensitivity to θ. Combined with forced attacker strategy shifts every 50 steps (§VI-C) and a fixed four-intent space, the headline stability gains may be sensitive to these free design choices. Report θ, sensitivity of ASR/survival to θ, and results without forced periodic shifts so the robustness claim can be assessed.
§VI-A / abstract communication metrics: packet delivery ratio, latency, throughput, and service availability appear only in the abstract (and are not tabulated or analyzed in §VI). Either provide the co-simulation protocol and tables that produce those numbers, or remove them from the abstract so claims match the evaluated environment.

minor comments (6)

Title/abstract use “Amplitude-Belief” / Q-BIRD while the body title is “Belief-Space Quantum-Inspired Reinforcement Learning…”; align naming across front matter and body.
§V-H: complexity argument with H=4 is fine, but state explicitly that H is fixed by design and discuss scaling if intent cardinality grows.
Fig. 5–10 captions and §VI-F: SHAP magnitudes (e.g., ±10^4–10^5) are hard to interpret without stating whether logits are raw or scaled; add units or normalization notes.
References [12], [20], [21] and related work: ensure year/venue consistency and that comparisons to Guo et al. ASR=0.500 note platform differences more carefully in the main text, not only in a table footnote.
Notation: b_t is used both for classical simplex beliefs and for Born-rule probabilities extracted from ψ_t; a short notational distinction would reduce confusion in §V-C–E.
Typos/grammar: e.g., “whic states” (§V-C), “commonly and widely reported metrics” (abstract of body), and occasional missing spaces around equations.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circular derivation: claims are empirical ablations of belief operators, not predictions forced by fitted inputs or self-definition.

full rationale

The paper’s central claim is not a first-principles derivation that reduces to its inputs. It proposes an amplitude-based belief state (ψ_t ∈ C^H, b(θ_i)=|ψ_t(i)|², ψ_{t+1}=U_t ψ_t), plugs that belief into a standard PPO defender, and reports an empirical ablation against classical Bayesian belief under a hand-designed IoV simulator (damage table d(θ,a), action costs C, intent set Θ of size 4). Reward r=−(D+C) and the cumulative-damage objective are ordinary RL design choices, not tautological identities that force the reported metrics. ASR and survival use an author-chosen threshold θ, but both arms of the ablation face the same metric, so the comparison is not circular. Citations (PPO, quantum-inspired RL surveys, Guo et al. MTD) are external; there is no uniqueness theorem or ansatz imported from overlapping authors that forbids alternatives and then declares the method forced. U_t is fixed and underspecified, which weakens causal attribution of gains solely to “amplitude structure,” but that is underspecification/correctness risk, not a reduction of a claimed prediction to a fitted input by construction. Abstract–body numerical and platform inconsistencies are serious reproducibility issues outside the circularity criterion. Honest finding: no significant circularity; score 1 only for the mild design-dependence of the evaluation environment on author-specified tables and threshold.

Assumptions & free parameters 6 free parameters · 6 assumptions · 2 invented entities

The central claim rests on a small discrete intent space, a hand-built damage/cost environment, a fixed amplitude operator U_t, Born-rule probability extraction, and PPO optimization under partial observability. None of these are derived from first principles of V2X physics; they are modeling choices. Free parameters (costs, damage table, θ, U_t, network/training knobs) largely determine reported metrics. Invented entities are the Q-BIRD amplitude belief module and the specific U_t belief dynamics—classical software constructs without independent physical evidence.

free parameters (6)

Defensive action costs C(a) = 0.00 / 0.05 / 0.10 / 0.20
Hand-set to 0.00, 0.05, 0.10, 0.20 for monitor/alert/throttle/isolate; directly shape the reward trade-off the policy learns.
Damage table d(θ, a_def) = range 0.0–0.9 (table not fully published)
Maps each intent–action pair to damage in [0.0, 0.9]; defines both training reward and evaluation cumulative damage.
Amplitude update operator U_t = fixed, unspecified entries (H=4)
Fixed H×H complex linear map driving all quantum-inspired dynamics; not learned and not fully specified from observations.
Attack-success threshold θ
Defines ASR and survival; numerical value not given, so reported 0.000 ASR is threshold-relative.
PPO / episode hyperparameters = γ=0.95, η=3e-3, ε=0.2, T=200, N=600
γ=0.95, η=3×10^{-3}, ε=0.2, T=200, N=600, MLP hidden 64; standard but claim-sensitive training knobs.
Forced attacker strategy-shift period = 50 steps
Intent forced to shift every 50 steps in evaluation; stresses belief stability by design.

assumptions (6)

domain assumption Hidden attacker intent lives in a fixed discrete set Θ of size H=4 (Benign, Probing, Attack, Evasion).
§IV–V; real adversaries may have continuous or larger repertoires—limitation admitted in §VI-G.
standard math Born rule: intent probabilities equal squared amplitude magnitudes b(θ_i)=|ψ(i)|² after normalization.
Eqs. (12)–(14); standard quantum-probability structure used classically.
ad hoc to paper Belief evolution is a linear amplitude map ψ_{t+1}=U_t ψ_t with subsequent normalization, not a Bayesian filter.
Eq. (13); core design choice; U_t fixed rather than derived from a likelihood model.
domain assumption Attacker intent adapts via θ_{t+1}=G(θ_t, a_def) in response to defense pressure.
Eq. (4); defines non-stationary adversarial environment.
domain assumption Defender objective is expected discounted damage plus action cost (Eq. 1 / J(ϕ)).
§III, §V-D; standard cost-aware RL security formulation.
domain assumption No quantum hardware or entanglement is required; all computation is classical.
Stated repeatedly in abstract/intro/methodology; frames the work as quantum-inspired only.

invented entities (2)

Q-BIRD amplitude belief state ψ_t ∈ ℂ^H
purpose: Preserve distributed uncertainty over hidden attacker intents under ambiguous/deceptive observations for PPO input.
Primary proposed representation; independent evidence is only the paper’s own simulation ablation, not external measurement of amplitude beliefs in real V2X.
Fixed observation/action-conditioned amplitude operator U_t
purpose: Evolve amplitudes so hypotheses can interfere before probability extraction.
Load-bearing dynamical object; underspecified and not learned; no external validation.

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Cite this review

Pith. "Pith review of Amplitude-Belief Reinforcement Learning for Adaptive Cyber Defense in Partially Observable V2X Networks." pith.science (2026). https://pith.science/paper/CD42ZWNQ

@misc{pith2026260607796,
  author       = {Pith},
  title        = {Pith review of: Amplitude-Belief Reinforcement Learning for Adaptive Cyber Defense in Partially Observable V2X Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CD42ZWNQ}},
  note         = {Machine review of arXiv:2606.07796}
}

read the original abstract

The Internet of Vehicles (IoV) creates a partially observable and adversarial V2X communication environment in which malicious vehicles may evade defensive mechanisms. Existing IoV intrusion-detection methods provide limited support for sequential mitigation under adaptive attacker behavior. This paper formulates IoV cyber defense as a partially observable sequential decision problem and proposes Quantum Belief-Integrated Reinforcement Defense (Q-BIRD), an amplitude-belief reinforcement learning framework. Q-BIRD represents uncertainty over hidden attacker intent through a normalized complex-valued belief state and converts amplitudes into intent probabilities. The resulting belief features are used by a Proximal Policy Optimization defender to select cost-aware mitigation actions. Experiments are conducted in a SUMO-OMNeT++ and Veins V2X co-simulation environment. Q-BIRD reduces mean cumulative damage from 36.0 +- 5.5 to 28.0 +- 3.0 and damage variance from 12.0 +- 2.8 to 6.0 +- 1.5 compared with PPO using classical Bayesian belief. The attack success rate decreases to 0.05 +- 0.02, while survival probability increases to 0.96 +- 0.02. Communication-level results show that Q-BIRD maintains a packet delivery ratio of 0.94 +- 0.02, latency of 45 +- 6 ms, throughput of 3.60 +- 0.15 Mbps, and service availability of 0.95 +- 0.02. Explainability analysis using SHAP, LIME, and Grad-CAM suggests that belief-related features contribute strongly to mitigation decisions. These results indicate that amplitude-based belief modeling can improve both cyber-defense stability and V2X communication reliability under partial observability.

Figures

Figures reproduced from arXiv: 2606.07796 by the authors.

**Figure 3.** Attacker operates on hidden intent while the defender sees only [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Quantum PPO leads all baselines on damage, variance, ASR, and survival across 600 training and 80 test episodes. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

Figures from the paper (5 more)

**Figure 6.** Figure 6: Quantum amplitude belief holds distributed uncertainty across intent states; classical Bayesian belief collapses under evasion. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: SHAP waterfall showing per-feature logit contributions: belief [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: SHAP values scale smoothly with belief magnitude, confirming [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: LIME coefficients show quantum belief features drive each action [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Grad-CAM confirms quantum PPO weights belief and traffic equally [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.

[1] [1]

Game-theoretic modeling of adaptive attacks and defenses in vehicular networks,

H. Xu, Y . Zhang, and K. Li, “Game-theoretic modeling of adaptive attacks and defenses in vehicular networks,”IEEE Transactions on Mobile Computing, vol. 22, no. 9, pp. 5234–5248, 2023

2023

[2] [2]

Learning-based security control for future intelligent transportation systems,

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2024

[3] [3]

Intrusion detection systems for the internet of vehicles: A survey,

I. Ullah and Q. H. Mahmoud, “Intrusion detection systems for the internet of vehicles: A survey,”IEEE Transactions on Intelligent Trans- portation Systems, vol. 23, no. 9, pp. 14 145–14 160, 2022

2022

[4] [4]

Benchmarking network intrusion detection systems: Pitfalls and best practices,

M. Ring, S. Wunderlich, and D. Scheuring, “Benchmarking network intrusion detection systems: Pitfalls and best practices,”IEEE Security & Privacy, vol. 20, no. 4, pp. 30–38, 2022

2022

[5] [5]

Outside the closed world: On using machine learning for network intrusion detection,

R. Sommer and V . Paxson, “Outside the closed world: On using machine learning for network intrusion detection,” inIEEE Symposium on Security and Privacy, 2010, pp. 305–316

2010

[6] [6]

Adversarial reinforcement learning for autonomous network defense,

L. Chen, Y . Zhao, and R. Xu, “Adversarial reinforcement learning for autonomous network defense,”IEEE Transactions on Information Forensics and Security, vol. 17, pp. 3218–3231, 2022. 13

2022

[7] [7]

Deep reinforcement learning for adap- tive cyber defense: A survey and open challenges,

Y . Zhang, X. Liu, and H. Wang, “Deep reinforcement learning for adap- tive cyber defense: A survey and open challenges,”IEEE Transactions on Dependable and Secure Computing, vol. 20, no. 4, pp. 2896–2912, 2023

2023

[8] [8]

Optimal policies for cyber defense via markov games,

K. Durkota, V . Lisy, and B. Bosansky, “Optimal policies for cyber defense via markov games,” inUSENIX Security Symposium, 2022, pp. 337–354

2022