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REVIEW 4 major objections 5 minor 35 references

Private Semantic Communications with Separate Blind Encoders

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper's central result is that the privacy-utility trade-off for a task-blind privacy encoder is bracketed by explicit entropy expressions $\max\{L^1_h(\epsilon),L^2_h(\epsilon)\} \le h_\epsilon(P_{S,f(X)}) \le H(f(X)|S)+\epsilon$.

desk verdict The blind two-encoder setup is genuinely new, but Theorem 1 is false as stated because it omits the eps ≤ H(S) condition. read the letter →

arxiv 2412.17658 v1 pith:UMN2SVDV submitted 2024-12-23 cs.IT math.IT

Amirreza Zamani , Mikael Skoglund This is my paper · ORCID
classification cs.ITmath.IT MSC 94A1594A1768P27
keywords privatesemanticcommunicationblindencodersprivacy-utilitytrade-offFunctionalRepresentationLemmaStrongcommoninformationmutualrandomizedresponse
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 studies a statistical privacy layer in semantic communication that is 'blind' in two ways: the first encoder sees the source but not the private data, and the second encoder sees the private data and a semantic summary but not the user's task. The central claim is that the best privacy-utility trade-off $h_\epsilon(P_{S,f(X)})=\sup\{I(f(X);U):I(U;S)\le\epsilon\}$ is bracketed by explicit entropy expressions, $\max\{L^1_h(\epsilon),L^2_h(\epsilon)\}\le h_\epsilon(P_{S,f(X)})\le H(f(X)|S)+\epsilon$, and that the user's utility $I(h(X);U)$ lies in an interval of the same width plus $H(h(X)|f(X))$. The lower bounds come from constructive extended Functional Representation Lemma mechanisms, so they are achievable by a finite alphabet code rather than an abstract limit. A designer who trusts these bounds can certify privacy and utility from entropies alone, without solving the optimization over channels. The paper's numerical MNIST example shows the lower and upper utility bounds can be within about $1.4$ nats when the semantic is tightly coupled to the task.

What carries the argument

The argument rests on two constructive information-theoretic tools: the Extended Functional Representation Lemma (EFRL) and the Extended Strong Functional Representation Lemma (ESFRL), taken from the paper's earlier work [17]. These lemmas produce a channel output $\bar U$ (or $\tilde U$) that keeps $I(\bar U;f(X))$ large for a prescribed small $I(\bar U;S)=\epsilon$, with the randomized-response technique of Warner [34] used to hit the leakage target exactly. The derivation also uses the identity $I(f(X);U)=I(S;U)+H(f(X)|S)-I(U;S|f(X))-H(f(X)|S,U)$, plus the Markov-chain expansions of $I(U;h(X),f(X))$, to convert a bound on semantic privacy into a bound on task utility. Common information, in the sense of Wyner [35], is the sharper condition that makes the upper bound tight without requiring $S$ to be a function of $f(X)$.

What would settle it

Run the linear-programming computation of $h_\epsilon(P_{S,f(X)})$ on a small finite joint distribution where $S$ is not a function of $f(X)$ and compare the exact value with $\max\{L^1_h(\epsilon),L^2_h(\epsilon)\}$; one instance with exact $h_\epsilon$ below the max disproves Theorem 1's lower bound. Alternatively, implement the EFRL/ESFRL mechanism for that distribution and measure $I(U;S)$ from samples; if it is not $\epsilon$ to within simulation error, the inherited construction fails for the present setting.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that separating the encoder into a privacy-unaware semantic designer and a task-unaware privacy filter does not destroy the information-theoretic control of the trade-off. Theorem 1 states that for any discrete semantic $f(X)$ satisfying constraints (1)–(2), the value of the privacy-utility trade-off obeys the sandwich (6), with $L^1_h(\epsilon)=H(f(X)|S)-H(S|f(X))+\epsilon$ and $L^2_h(\epsilon)=H(f(X)|S)-\alpha H(S|f(X))+\epsilon-(1-\alpha)(\log(I(S;f(X))+1)+4)$, where $\alpha=\epsilon/H(S)$. For the user's utility the theorem gives $\max\{L^1(\epsilon),L^2(\epsilon),L^3(\epsilon)\}\le I(h(X);U)\le H(f(X)|S)+\epsilon+H(h(X)|f(X))$, with $L^1,L^2,L^3$ defined in (10)–(12). The upper bound is attained when the private $S$ is a deterministic function of $f(X)$; Corollary 1 widens this to equality of common information and mutual information between $S$ and $f(X)$, and Corollary 2 removes the dependence on the chosen semantic by bounding $I(U;h(X))\le\epsilon+\gamma_2-\gamma_1+H(h(X))$. The proof route is the identity chain (4)–(5), the EFRL/ESFRL constructions from [17], and the randomized-response step of [34].

Load-bearing premise

The load-bearing premise is that the lower-bound construction inherited from [17] achieves leakage exactly $\epsilon$ for the pair $(S,f(X))$ through the randomized-response step of [34], including the constant term $\log(I(S;f(X))+1)+4$; if that exact-leakage equality (15) fails, the lower bounds $L^1_h$ and $L^2_h$ do not follow as stated.

Editorial extensions

If this is right

  • A designer can certify that no privacy mechanism can disclose more than $H(f(X)|S)+\epsilon$ nats of the semantic to a user, and that the EFRL/ESFRL constructions disclose at least the computed $L^1_h$ or $L^2_h$ nats.
  • When $H(S|f(X))=0$ or common information equals mutual information, the trade-off is exactly $H(f(X)|S)+\epsilon$, so the semantic can be sized precisely from the residual uncertainty about it given the private data.
  • The user-utility lower bounds $L^1(\epsilon)$ and $L^2(\epsilon)$ are computable from entropies alone and are achieved by simple mechanisms, making the result a practical design recipe rather than an existence proof.
  • The semantic-free bound $I(U;h(X))\le\epsilon+\gamma_2-\gamma_1+H(h(X))$ lets a designer evaluate the privacy cost of a task before choosing the semantic $f(X)$.
  • In the MNIST example, the width of the utility interval is $H(h(X)|f(X))+H(f(X)|h(X))\simeq 1.4$ nats, so for highly correlated semantic/task pairs the bounds are a tight design target.

Reading between the lines

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

  • A natural next step the paper leaves open is to combine these EFRL/ESFRL bounds with the separation-technique lower bounds of [33]; the resulting lower bracket would likely be tighter but more complex.
  • The finite-alphabet assumption is likely load-bearing: the exact-leakage equality and the log term are proven for discrete alphabets, so extending to Gaussian or continuous semantic sources would require rechecking (15).
  • One could stress-test the task-blind assumption by giving encoder 2 a coarse description of the task; the utility bounds should interpolate between the present bounds and the full-access design of [4].
  • An empirical protocol follows directly: on any labeled dataset, compute the entropies of $(S,f(X),h(X))$, predict the achievable utility interval, train a real privacy mechanism, and see whether the measured $I(h(X);U)$ lands inside the interval; any miss identifies either a suboptimal mechanism or a violated assumption.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies a semantic communication system with two separate encoders: encoder 1 observes the source X and designs a semantic f(X) for a task h(X), without access to private data S; encoder 2 observes S and f(X) and outputs disclosed data U, without access to the task. The privacy-utility trade-off is h_epsilon(P_{S,f(X)}) = sup_{P_{U|S,f(X)}: I(U;S)<=epsilon} I(U;f(X)), and the user utility is I(U;h(X)). The main result, Theorem 1, gives upper and lower bounds on h_epsilon and on I(U;h(X)), with lower bounds obtained from the Extended Functional Representation Lemma and the Extended Strong Functional Representation Lemma imported from the authors' earlier work [17]. The paper also states a corollary involving common information, a corollary giving a task-independent upper bound, and a numerical MNIST experiment comparing the bounds.

Significance. If correct, the results provide computable, parameter-free bounds for a meaningful two-encoder privacy scenario and the underlying mechanisms are constructive. The upper bound H(f(X)|S)+epsilon is simple and the lower bounds are stated in closed form. However, the mathematical novelty beyond the authors' prior work [17] is modest: the main technique is a direct application of previously established lemmas to the pair (S,f(X)). The central theorem as stated is false on part of its claimed domain, and several proof details are not rigorous. The scenario itself is relevant to semantic communication with privacy constraints, and the numerical comparison is useful, so the paper is worth revising.

major comments (4)
  1. [Section III, Theorem 1, Eqs. (6)-(8)] The statement 'For any 0 <= epsilon' is false for epsilon > H(S). Since I(U;f(X)) <= H(f(X)) for every U, we always have h_epsilon(P_{S,f(X)}) <= H(f(X)). But L1_h(epsilon) = H(f(X)|S) - H(S|f(X)) + epsilon = H(f(X)) - H(S) + epsilon, so for epsilon > H(S) the claimed lower bound exceeds H(f(X)). For example, if S and f(X) are independent uniform binary variables and epsilon = 2 bits, then h_epsilon = H(f(X)) = 1 bit while L1_h(epsilon) = 2 bits, contradicting (6). The theorem must be restricted to 0 <= epsilon <= H(S), with H(S) > 0 so that alpha = epsilon/H(S) is defined. This also affects the numerical experiment in Section IV, where H(S) is approximately 0.325 nats but epsilon is swept to 0.35 nats; the sweep should be limited to the valid range or the statement amended.
  2. [Section III, Eq. (4) and proof of Theorem 1] Equation (4) is not consistent: the left-hand side is I(f(X);U), but the right-hand side is the standard expansion for I(h(X);U), with h(X) appearing in all three entropy/conditional terms. The proof then says 'Using (4) we have I(U;f(X)) = ...' and concludes I(U;h(X)) <= epsilon + H(f(X)|S), which does not follow from (4) as written. The upper bound in (6) is correct and can be proved directly from the identity I(U;f(X)) = I(U;S) + H(f(X)|S) - H(f(X)|U,S) - I(U;S|f(X)) <= I(U;S) + H(f(X)|S). Please replace Eq. (4) with the correct identity and rewrite the proof of the upper bounds accordingly.
  3. [Section III, proof of Theorem 1, Eqs. (13)-(15)] The lower bounds are imported from [17, Theorem 2] through the sentence 'Using the same arguments in [17, Theorem 2]', without stating the hypotheses under which the EFRL/ESFRL constructions achieve leakage exactly epsilon for the pair (S,f(X)). Since L1_h and L2_h are increasing in epsilon, if the imported construction only yields I(U;S) < epsilon, the claimed lower bounds at level epsilon do not automatically follow. The proof should either state the precise lemma from [17] being invoked and verify that its conditions (discrete alphabets, finiteness, range of epsilon, etc.) hold for the pair (S,f(X)), or provide the construction directly. As written, the lower-bound half of Theorem 1 is not self-contained.
  4. [Section III, Corollary 2 proof] The final inequality in the proof of Corollary 2, H(f(X)|S) + H(h(X)|f(X)) <= H(h(X)) + gamma_2 - gamma_1, is not a consequence of (1) and (2); in general it is false. The claimed bound is nevertheless true vacuously because I(U;h(X)) <= H(h(X)) and gamma_2 >= gamma_1, so the right-hand side of (20) is at least H(h(X)). Please replace the argument with a correct proof or explicitly note that the bound is trivial.
minor comments (5)
  1. [Section II, Eq. (2)] In Eq. (2), h(f(X)) should presumably be H(f(X)) (the entropy of the semantic), since h is used elsewhere for the task function; the current notation conflates entropy with the task function and is confusing.
  2. [Section III, proof of Theorem 1] In the final substitution step, the text says 'substituting U by U* in (17) we have I(bar{U};h(X)) >= ...', but the left-hand side should be I(U*;h(X)), not I(bar{U};h(X)). Please fix this typo.
  3. [Section IV] The paper states that the MNIST data set has |X| = 6000 images; the MNIST training set contains 60000 images. Please correct this number or clarify the subsample used.
  4. [Fig. 1] The label 'Lekagae matrix' in the figure should be 'Leakage matrix'.
  5. [Section III, Corollary 1] The proof of Corollary 1 is only a reference to [17, Theorem 3 and Proposition 3]; please state the common-information condition explicitly or provide the argument so that the corollary is understandable without consulting the prior paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; lower bounds are direct, independent applications of the prior peer-reviewed theorem [17], with no fitted parameter renamed as a prediction.

full rationale

The derivation chain of Theorem 1 is not circular. The upper bound I(U;f(X)) <= epsilon + H(f(X)|S) is proved in-paper from the exact expansion (4), and the utility bounds follow algebraically from (5), (17), and the theorem's upper bound. The lower bounds L1_h(epsilon) and L2_h(epsilon) are not fitted or re-derived from the target claim; they are imported by substituting (S, f(X)) in the peer-reviewed, parameter-free [17, Theorem 2], with the EFRL/ESFRL constructions established there. That prior theorem does not assume the present paper's conclusion, so the self-citation is independent support rather than a circular load-bearing step. The numerical experiment uses empirical distributions and evaluates the stated formulas; no fitted parameter is renamed as a prediction. The main concern in the paper is a correctness gap, not circularity: the theorem states 'For any 0 <= epsilon' while defining alpha = epsilon/H(S); for epsilon > H(S), L1_h(epsilon) can exceed H(f(X)), making the claimed lower bound impossible. That is an invalid domain statement, not a reduction of the result to its own inputs by construction. Therefore no circular step is identified.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central bounds are imported from the authors' prior work [17] and not re-derived here. The paper relies on those lemmas as black boxes. No new entities or fitted parameters are introduced; the numerical example uses empirical distributions from MNIST but no fitted constants.

assumptions (5)
  • domain assumption Extended FRL and SFRL bounds from [17, Lemmas 4 and 5] hold for the pair (S, f(X)) with the stated constants.
    Theorem 1 lower bounds are asserted to follow from [17, Theorem 2] via these lemmas; no proof is given in this paper.
  • domain assumption Randomized response [34] can be tuned to achieve I(U;S)=epsilon exactly for the constructed U.
    Required to satisfy the leakage constraint with equality; the paper cites [17] but does not reproduce the construction.
  • domain assumption Common information and mutual information equality condition from [17, Theorem 3] / Wyner [35] implies tightness of the upper bound.
    Corollary 1 is stated without proof, citing [17].
  • domain assumption The joint distribution P_{S,X} is discrete on finite alphabets with arbitrary correlation.
    System model in Section II; needed for entropy and exact bounds.
  • domain assumption The semantic f(X) satisfies gamma1 ≤ I(f(X);h(X)) ≤ gamma2 < H(h(X)) and H(f(X)) ≤ gamma3.
    These constraints define the semantic design space in Section II and are used in Corollary 2.

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Pith. "Pith review of Private Semantic Communications with Separate Blind Encoders." pith.science (2026). https://pith.science/paper/UMN2SVDV

@misc{pith2026241217658,
  author       = {Pith},
  title        = {Pith review of: Private Semantic Communications with Separate Blind Encoders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UMN2SVDV}},
  note         = {Machine review of arXiv:2412.17658}
}
abstract

We study a semantic communication problem with a privacy constraint where an encoder consists of two separate parts, e.g., encoder 1 and encoder 2. The first encoder has access to information source $X=(X_1,\ldots,X_N)$ which is arbitrarily correlated with private data $S$. The private data is not accessible by encoder 1, however, the second encoder has access to it and the output of encoder 1. A user asks for a task $h(X)$ and the first encoder designs the semantic of the information source $f(X)$ to disclose. Due to the privacy constraints $f(X)$ can not be revealed directly to the user and the second encoder applies a statistical privacy mechanism to produce disclosed data $U$. Here, we assume that encoder 2 has no access to the task and the design of the disclosed data is based on the semantic and the private data. In this work, we propose a novel approach where $U$ is produced by solving a privacy-utility trade-off based on the semantic and the private data. We design $U$ utilizing different methods such as using extended versions of the Functional Representation Lemma and the Strong Functional Representation Lemma. We evaluate our design by computing the utility attained by the user. Finally, we study and compare the obtained bounds in a numerical example.

Figures

Figures reproduced from arXiv: 2412.17658 by the authors.

Figure 1
Figure 1. The encoder consists of two separate parties with different goals. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Comparing the lower and upper bounds obtained in Theorem 1. In [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Reference graph

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