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arxiv: 2605.09833 · v1 · submitted 2026-05-11 · 💻 cs.IT · cs.LG· math.IT

Recognition: no theorem link

Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling

An Vuong, Bella Bose, Hassan Tavakoli, Nam Nguyen, Thinh Nguyen

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:23 UTC · model grok-4.3

classification 💻 cs.IT cs.LGmath.IT
keywords cross-domain compressionminimum entropy couplingrate-constrained MECcommon randomnessdeterministic couplingBernoulli sourcesneural compression frameworkclassification regularization
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The pith

Common randomness makes intermediate representations unnecessary for optimal cross-domain lossy compression via minimum entropy coupling.

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

The paper sets out to show that cross-domain lossy compression, where the encoder sees only a degraded source and the decoder must generate samples from a target distribution while supporting a downstream classification task, can be handled by maximizing coupling strength between source and reconstruction under rate limits. Motivated by logarithmic loss rather than sample-wise distortion, it formulates a rate-constrained minimum entropy coupling problem and proves that common randomness allows the intermediate representation to be dropped without hurting optimality, reducing the problem to a direct deterministic coupling. Closed-form solutions are given for Bernoulli sources both with and without classification constraints, and a neural implementation using quantization and distribution matching is shown to improve classification accuracy and reconstruction quality as rate increases on image tasks.

Core claim

Under common randomness, the rate-constrained minimum entropy coupling problem (MEC-B) is equivalent to a deterministic coupling formulation, allowing the intermediate representation to be removed without loss of optimality. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. A neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization demonstrates the approach, with experiments on MNIST super-resolution and SVHN denoising showing that higher rates improve classification accuracy and yield more informative reconstructions.

What carries the argument

Rate-constrained minimum entropy coupling (MEC-B) under common randomness, which equates the problem to an equivalent deterministic coupling between the degraded source and the target distribution.

If this is right

  • Closed-form expressions give the exact optimal coupling for Bernoulli sources both with and without classification constraints.
  • In the neural implementation, higher available rate directly improves classification accuracy on the target task.
  • The same framework produces reconstructions that better match the target domain statistics in super-resolution and denoising settings.

Where Pith is reading between the lines

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

  • The removal of the intermediate representation could simplify training in other cross-domain settings if the common-randomness condition can be approximated by shared noise.
  • Testing the same deterministic-coupling reduction on non-Bernoulli discrete sources or quantized continuous sources would show how far the closed-form insight generalizes.
  • The classification-regularized coupling might be useful for privacy-preserving compression where the decoder must avoid leaking source-domain details.

Load-bearing premise

That maximizing coupling strength under a logarithmic-loss-style objective is the right way to measure performance in cross-domain reconstruction tasks.

What would settle it

A source-target pair and rate where the deterministic coupling formulation produces strictly lower mutual information or lower classification accuracy than a method that retains an explicit intermediate representation.

Figures

Figures reproduced from arXiv: 2605.09833 by An Vuong, Bella Bose, Hassan Tavakoli, Nam Nguyen, Thinh Nguyen.

Figure 1
Figure 1. Figure 1: System model: a noisy input X ∼ pX is restored as Y ∼ pY . 𝑋 𝑝𝑍|𝑋,𝑈 𝑍 𝑝𝑌|𝑍,𝑈 𝑌 𝑈 𝐼(𝑋, 𝑌) 𝑋 𝑝𝑌|𝑋,𝑈 𝑌 𝑈 𝐼(𝑋, 𝑌) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: System architecture corresponding to Theorem 1. The encoder maps [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: System model: a noisy input X ∼ pX is restored as Y ∼ pY , while supporting classification with label S. Classification constraint. In addition to reconstruction quality, we impose an explicit constraint on task-relevant information. Specifically, the reconstruction must satisfy H(S|Y ) ≤ C for some C > 0. This constraint bounds the residual uncertainty of S given Y , thereby ensuring a prescribed level of… view at source ↗
Figure 5
Figure 5. Figure 5: I (B) MEC−B−R−C (qX, qY , R, C) versus R for qX = 0.3, qY = 0.4, qS1 = 0.01, and C = 0.4. or low-resolution) and generates reconstructions following a target distribution Y ∼ pY (e.g., clean or high-resolution). The objective is to compress X while preserving task-relevant in￾formation for a downstream label S. The experimental scheme is shown in [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Experimental architecture: a stochastic autoencoder with classifier, reconstructor, and WGAN discriminator, conditioned on shared randomness [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Experimental results of 4× super-resolution on MNIST dataset and image denoising on the SVHN dataset corrupted by Gaussian noise, N (0, σ) with σ = 25. Increasing the rate improves classification performance. semantic and visual structure, while low-rate reconstructions lose fine details. Some denoised SVHN images exhibit mild color inconsistencies relative to the clean targets. This behavior is consistent… view at source ↗
read the original abstract

This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is required to generate outputs following a prescribed target distribution and to preserve information relevant to a downstream classification task. Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction, rather than minimizing a sample-wise distortion. Under common randomness, we formulate a rate-constrained MEC problem (MEC-B) and show that the intermediate representation can be removed without loss of optimality, yielding an equivalent deterministic coupling formulation. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. In addition, we implement a neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization. Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.

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 / 3 minor

Summary. The paper claims to advance cross-domain lossy compression by formulating it as a constrained minimum entropy coupling (MEC) problem. Under common randomness, it introduces a rate-constrained MEC-B formulation and shows that the intermediate representation can be removed without loss of optimality to yield an equivalent deterministic coupling. Closed-form expressions are derived for Bernoulli sources with and without classification constraints. A neural implementation using quantization, entropy modeling, distribution matching, and classification regularization is presented, with experiments on MNIST super-resolution and SVHN denoising demonstrating that higher rates improve classification accuracy and reconstruction informativeness.

Significance. If the equivalence result and Bernoulli closed-forms hold, this provides a theoretically grounded information-theoretic approach to cross-domain compression that jointly handles rate constraints, target marginal matching, and preservation of classification-relevant mutual information. The closed-forms offer concrete, verifiable benchmarks for simple sources, while the neural framework suggests extensibility to images. This could influence task-oriented and domain-adaptive compression research, though empirical significance would increase with stronger baseline comparisons.

major comments (2)
  1. [§3.2] §3.2 (equivalence of MEC-B to deterministic coupling): The argument that the intermediate representation can be removed without loss of optimality must explicitly confirm that the rate bound, the target marginal, and the classification mutual information I(Y;Z) are all preserved. The current reasoning appears to rely on properties of the common randomness that may fail when its support is finite or when the joint entropy terms interact with the classification constraint, which would invalidate the subsequent simplifications used for the Bernoulli cases.
  2. [§4] §4 (Bernoulli closed-forms): The derivations of the coupling probabilities (with and without classification constraints) need to show how the rate constraint is enforced in the optimization; if the expressions optimize only the coupling strength objective, they may violate the rate bound for some parameter values, undermining the claim that they solve the full MEC-B problem.
minor comments (3)
  1. [Abstract] The abstract states the main results but omits any equation or reference to the closed-form expressions, which would allow readers to immediately gauge the contribution.
  2. [§5] Experimental details in §5 (network architecture, quantization levels, entropy model specifics, and training hyperparameters) are insufficient for reproducibility; adding these would strengthen the empirical claims.
  3. [Preliminaries] Notation for the common randomness variable and the distinction between source and target domains should be introduced with a clear table or diagram in the preliminaries to avoid later confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each major comment point by point below, providing clarifications and committing to revisions where the concerns identify gaps in explicitness or detail.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (equivalence of MEC-B to deterministic coupling): The argument that the intermediate representation can be removed without loss of optimality must explicitly confirm that the rate bound, the target marginal, and the classification mutual information I(Y;Z) are all preserved. The current reasoning appears to rely on properties of the common randomness that may fail when its support is finite or when the joint entropy terms interact with the classification constraint, which would invalidate the subsequent simplifications used for the Bernoulli cases.

    Authors: We appreciate this observation, which correctly identifies that our current write-up in §3.2 could be more explicit. The equivalence proof relies on the fact that, under the common-randomness model, the deterministic coupling preserves the joint distribution properties needed for the MEC-B objective; specifically, the rate I(X;Z) is unchanged by the data-processing inequality, the target marginal is enforced by construction in the coupling, and I(Y;Z) is preserved because the classification constraint is applied to the same marginal on Z. Nevertheless, to address potential issues with finite-support common randomness and interactions with the classification term, we will revise §3.2 to include an explicit lemma verifying preservation of all three quantities (rate bound, target marginal, and I(Y;Z)) and add a short remark on the support condition. This will also strengthen the foundation for the Bernoulli derivations. revision: yes

  2. Referee: [§4] §4 (Bernoulli closed-forms): The derivations of the coupling probabilities (with and without classification constraints) need to show how the rate constraint is enforced in the optimization; if the expressions optimize only the coupling strength objective, they may violate the rate bound for some parameter values, undermining the claim that they solve the full MEC-B problem.

    Authors: We agree that the current presentation of the closed-forms in §4 could more clearly demonstrate enforcement of the rate constraint. The derivations solve the Lagrangian of the MEC-B problem, where the multiplier associated with the rate bound is chosen so that the resulting coupling probabilities satisfy I(X;Z) ≤ R for the admissible range of parameters; boundary cases where the constraint is active are handled by clipping the coupling strength. To eliminate any ambiguity, we will expand the derivations in the revised manuscript to include the explicit Lagrangian, the KKT conditions used to obtain the closed forms, and a short verification (via substitution) that the rate bound holds for the reported parameter values. This will confirm that the expressions solve the full constrained problem rather than an unconstrained relaxation. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation chain self-contained with independent closed-form results

full rationale

The paper formulates the rate-constrained MEC-B problem under common randomness and claims to prove that the intermediate representation can be removed without loss of optimality to obtain an equivalent deterministic coupling. It then derives closed-form expressions for Bernoulli sources both with and without classification constraints. No equations, fitted parameters, or self-citations are exhibited in the abstract or description that would reduce any claimed result to a tautology by construction, a renamed fit, or a load-bearing self-reference. The Bernoulli expressions are presented as derived rather than statistically forced, and the central equivalence is asserted as a mathematical step rather than a definitional identity. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the main domain assumption visible is the availability of common randomness.

axioms (1)
  • domain assumption Common randomness is shared between encoder and decoder
    Invoked to formulate the rate-constrained MEC-B problem and to remove the intermediate representation.

pith-pipeline@v0.9.0 · 5476 in / 1179 out tokens · 38936 ms · 2026-05-12T04:23:49.450352+00:00 · methodology

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Reference graph

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