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arxiv: 2605.15743 · v1 · pith:XQBF5JPXnew · submitted 2026-05-15 · 📡 eess.SY · cs.MA· cs.SY

Preserving Topology Privacy of Network Systems by Feedback: Conditions and Distributed Design

Yushan Li , Jiabao He , Julien M. Hendrickx , Dimos V. Dimarogonas This is my paper

Pith reviewed 2026-05-20 17:13 UTC · model grok-4.3

classification 📡 eess.SY cs.MAcs.SY
keywords topology privacyconsensus protocolsfeedback designnetwork identifiabilitydistributed algorithmsprivacy preservationmulti-agent systems
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The pith

Feedback can be designed to violate topology identifiability and preserve privacy in consensus networks while retaining convergence.

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

This paper develops conditions under which feedback makes the network topology unrecoverable from observation data in consensus systems. For partial observations, it characterizes when the topology is unsolvable. For full observations, it constructs solution spaces that force inaccuracy in any recovered topology. A distributed design then modifies the topology under privacy budget limits, guaranteeing a tradeoff where more privacy means controlled increase in consensus deviation. This allows networks to protect their connection structure without sacrificing the overall consensus goal.

Core claim

The authors establish feedback conditions that ensure topology unsolvability from partial observation data and construct the solution space enforcing topology inaccuracy from full data. They then introduce a distributed topology modification method that operates under limited privacy budgets and provides guarantees on the balance between consensus deviation and achieved privacy level, along with a heuristic for optimal preservation on existing edges.

What carries the argument

Feedback conditions characterizing topology unsolvability from data and the distributed topology modification design that enforces inaccuracy under privacy budgets.

If this is right

  • Observers cannot uniquely determine the network topology even with access to full system trajectories.
  • The consensus protocol still reaches agreement, but with a deviation that scales with the chosen privacy level.
  • The modification can be executed using only local neighbor communications at each node.
  • The low-complexity heuristic finds near-optimal privacy gains specifically on the existing edges.

Where Pith is reading between the lines

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

  • Similar identifiability-violation techniques could apply to privacy in other multi-agent coordination tasks such as formation control.
  • The explicit tradeoff bounds make it possible to tune the method for networks with strict convergence-time requirements.
  • The distributed nature suggests the approach remains feasible when the network size grows and central coordination is unavailable.

Load-bearing premise

Local node communications are sufficient to carry out the distributed topology changes while still ensuring global consensus convergence and respecting the privacy budget limits.

What would settle it

Apply the proposed feedback design to a network, collect the resulting state trajectories, and test whether an observer can reconstruct the exact original topology; successful unique reconstruction would show the privacy method has failed.

Figures

Figures reproduced from arXiv: 2605.15743 by Dimos V. Dimarogonas, Jiabao He, Julien M. Hendrickx, Yushan Li.

Figure 1
Figure 1. Figure 1: The roadmap illustration of this work. tackle the core challenge of preserving topology privacy in a distributed manner while simultaneously maintaining the original consensus behavior. Along this line, we introduce a controllable tradeoff between privacy and convergence per￾formance, and provide distributed design of the required feedback. The roadmap of this work is illustrated in [PITH_FULL_IMAGE:figur… view at source ↗
Figure 2
Figure 2. Figure 2: The original topology and the modified topologies given different [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Inference performance under different τ and comparisons with centralized and Laplacian-based methods. (a) State deviation. (b) Inference error Er1 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparisons with noise-adding based methods. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

This paper develops a feedback-based method to preserve the topology privacy of consensus protocols in network systems. The key idea is to intentionally violate topology identifiability conditions, thereby preventing unique or accurate recovery of the true topology from available observations, while preserving the intended consensus behavior. This problem is challenging because the feedback magnitude directly reflects the privacy level of edges, while it is strongly coupled with the consensus convergence and constrained by local communications at each node. To begin with, we derive the feedback conditions of both partial and full observation cases, where the topology unsolvability from observation data is characterized in the former, and the solution space that enforces topology inaccuracy from data is constructed in the latter. Then, we propose a novel distributed topology modification design under limited privacy budgets, and establish the performance guarantees through a controllable tradeoff between the consensus deviation and the topology privacy. Finally, we develop a low-complexity heuristic algorithm to achieve optimal privacy preservation on existing edges. Comparative simulations validate the effectiveness and outperformance of the proposed preservation design.

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.

Referee Report

2 major / 2 minor

Summary. The paper develops a feedback-based method to preserve topology privacy of consensus protocols in network systems by intentionally violating topology identifiability conditions. It derives feedback conditions for both partial-observation (characterizing unsolvability) and full-observation (constructing a solution space for inaccuracy) cases, proposes a distributed topology modification design under limited per-node privacy budgets, establishes performance guarantees via a controllable tradeoff between consensus deviation and privacy level, and presents a low-complexity heuristic for optimal privacy on existing edges, with comparative simulations.

Significance. If the distributed design rigorously enforces the global algebraic conditions derived for privacy while respecting local communications and convergence, the work would provide a concrete, implementable approach to topology privacy in multi-agent consensus systems, with explicit conditions and a quantifiable performance-privacy tradeoff that could inform secure networked control applications.

major comments (2)
  1. [§4.2] §4.2 (Distributed Topology Modification): The claim that local neighbor exchanges suffice to place the closed-loop effective adjacency matrix inside the solution space of §3.2 (full-observation inaccuracy) or satisfy the unsolvability conditions of §3.1 (partial observation) is load-bearing for the central privacy guarantee, yet the manuscript provides no explicit algebraic argument or convergence proof showing that the per-node updates collectively achieve the required global matrix properties without a central coordinator.
  2. [§4.3] §4.3 (Performance Guarantees): The tradeoff bound between consensus deviation and topology privacy is stated to hold under the distributed design, but it appears to rely on the assumption that the local feedback rules implicitly satisfy the global identifiability-violation conditions; if this coordination does not occur, the bound reduces to a local privacy metric without global guarantee, undermining the performance claim.
minor comments (2)
  1. [Abstract] The abstract refers to 'comparative simulations' but does not name the baseline methods or privacy metrics used for comparison.
  2. [§3] Notation for the effective adjacency matrix after feedback should be introduced earlier and used consistently in the conditions of §3.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. The concerns raised about the distributed implementation in §4.2 and the validity of the performance guarantees in §4.3 are important for ensuring the rigor of the privacy claims. We address each major comment below, providing clarifications based on the manuscript's constructions and indicating revisions to make the algebraic links and proofs more explicit.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (Distributed Topology Modification): The claim that local neighbor exchanges suffice to place the closed-loop effective adjacency matrix inside the solution space of §3.2 (full-observation inaccuracy) or satisfy the unsolvability conditions of §3.1 (partial observation) is load-bearing for the central privacy guarantee, yet the manuscript provides no explicit algebraic argument or convergence proof showing that the per-node updates collectively achieve the required global matrix properties without a central coordinator.

    Authors: We agree that the manuscript would benefit from a more explicit algebraic argument connecting the local updates to the global matrix properties. The distributed design in §4.2 constructs per-node feedback adjustments using only local neighbor exchanges and privacy budgets, with each node modifying its outgoing weights to satisfy row-specific constraints derived from the conditions in §3.1 and §3.2. These local modifications are structured so that, collectively, they enforce the required global properties of the effective adjacency matrix due to the row-wise nature of the identifiability conditions and the consensus dynamics. To address the gap, we will add a new lemma in the revised §4.2 that formally proves convergence of the iterative local updates to the desired global solution space (or unsolvability set) without a central coordinator, leveraging invariance of certain matrix invariants under distributed neighbor communication. revision: yes

  2. Referee: [§4.3] §4.3 (Performance Guarantees): The tradeoff bound between consensus deviation and topology privacy is stated to hold under the distributed design, but it appears to rely on the assumption that the local feedback rules implicitly satisfy the global identifiability-violation conditions; if this coordination does not occur, the bound reduces to a local privacy metric without global guarantee, undermining the performance claim.

    Authors: The tradeoff bound in §4.3 is derived under the premise that the distributed design from §4.2 achieves the global conditions of §3. We will revise the section to explicitly invoke the new convergence lemma (to be added in §4.2) to establish that the local rules do produce the required global coordination through iterative neighbor exchanges. This ensures the bound applies to the global privacy level rather than reducing to local metrics. We will also add a brief discussion of the convergence rate under limited communication and clarify the theorem assumptions to prevent misinterpretation if coordination is imperfect. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in standard identifiability and consensus analysis

full rationale

The paper derives feedback conditions that violate topology identifiability for partial and full observation cases, then constructs a distributed modification design under privacy budgets with explicit performance tradeoffs between consensus deviation and privacy. No equations or steps reduce by construction to fitted parameters, self-defined quantities, or load-bearing self-citations. The central claims rest on algebraic conditions for unsolvability/inaccuracy and local-to-global coordination arguments that are presented as derived results rather than tautologies. The approach builds on external concepts from network identifiability and consensus theory without renaming known results or smuggling ansatzes via prior self-work in a circular manner. This is the expected self-contained case for a control-theoretic privacy paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard consensus convergence assumptions from control theory and the premise that feedback can be locally chosen to break identifiability without destroying global behavior; no new entities are introduced and privacy budgets appear as design constraints rather than fitted constants.

free parameters (1)
  • privacy budget
    Limits the allowable feedback magnitude at each node; exact values are chosen per instance but not derived from first principles.
axioms (1)
  • domain assumption Local feedback signals can be designed to violate topology identifiability conditions while preserving the intended consensus dynamics.
    Invoked when stating that the feedback magnitude reflects privacy level yet remains compatible with convergence.

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