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arxiv: 2605.14940 · v1 · pith:IFTH7YTSnew · submitted 2026-05-14 · 💻 cs.LG · cs.AI· eess.SP

Not All Symbols Are Equal: Importance-Aware Constellation Design for Semantic Communication

Albert Shaju , Christo Kurisummoottil Thomas , Mayukh Roy Chowdhury This is my paper

Pith reviewed 2026-06-30 20:51 UTC · model grok-4.3

classification 💻 cs.LG cs.AIeess.SP
keywords semantic communicationconstellation designM-QAMsemantic criticality indicatorsemantic protection probabilityVQ-VAEdeep reinforcement learningsemantic symbol vulnerability
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The pith

A learned semantic-aware constellation protects task-critical symbols far better than standard Gray-coded M-QAM by placing them according to importance and co-occurrence statistics.

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

Semantic communication systems must protect task-relevant information at the physical layer, not just through source coding. The paper shows that conventional uniform Gray-coded constellations treat every symbol the same and are therefore strictly suboptimal when semantic importance is non-uniform. By extracting discrete latents with a VQ-VAE, scoring each with a semantic criticality indicator, and learning symbol positions that reflect joint co-occurrence and those scores, the design concentrates protection on what matters most. A reinforcement-learning agent further chooses which symbols to send under current channel conditions. The result is near-complete protection for critical symbols even at high-order modulations while still delivering high compression and semantic fidelity across image and audio datasets.

Core claim

Any Gray-coded constellation is strictly suboptimal in SCI-Weighted SSV whenever the source exhibits non-uniform semantic importance and co-occurrence statistics. The proposed semantic-aware M-QAM constellation, learned jointly with the VQ-VAE and SCI scores, achieves near 100% semantic protection probability from 4-QAM to 1024-QAM versus roughly 50% for standard constellations at high spectral efficiency, while supporting a 21:1 compression ratio with semantic quality above 0.9 and generalizing across MNIST, Fashion-MNIST, and FSDD without modification.

What carries the argument

The semantic-aware M-QAM constellation that assigns symbol positions according to joint co-occurrence statistics and SCI scores.

If this is right

  • The learned constellation maintains near-100% SPP across modulation orders from 4-QAM to 1024-QAM.
  • Standard Gray-coded constellations reach only about 50% SPP at high spectral efficiency under the same conditions.
  • The framework delivers a 21:1 compression ratio while keeping semantic quality above 0.9.
  • The design generalizes without modification to MNIST, Fashion-MNIST, and FSDD.
  • A deep reinforcement learning agent selects the transmission subset according to instantaneous channel conditions.

Where Pith is reading between the lines

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

  • The same non-uniform protection logic could be applied to other modulation families or to forward error correction codes that allow unequal error protection.
  • End-to-end training that jointly optimizes the VQ-VAE, SCI, constellation, and DRL policy might produce additional gains beyond the staged approach described.
  • In deployed systems the constellation would need periodic re-learning whenever the downstream task or data distribution shifts.
  • The SPP and SSV metrics could serve as evaluation tools for any semantic communication system that maps discrete concepts to physical symbols.

Load-bearing premise

The semantic criticality indicator derived from the VQ-VAE latents accurately reflects true task relevance and the learned co-occurrence statistics generalize beyond the training datasets.

What would settle it

An experiment in which a standard Gray-coded constellation achieves equal or higher SCI-Weighted SSV than the learned design on a source with demonstrably non-uniform semantic importance and co-occurrence statistics would falsify the suboptimality claim.

Figures

Figures reproduced from arXiv: 2605.14940 by Albert Shaju, Christo Kurisummoottil Thomas, Mayukh Roy Chowdhury.

Figure 1
Figure 1. Figure 1: Overall Architecture of the proposed SC system. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of semantic 256-QAM constellation. preventing the agent from collapsing to a degenerate policy that ignores channel conditions. Two conditional bonuses guide exploration. Bcomp = α ln(N/K) if Qtask > Q0 and zero otherwise, rewarding compression only when semantic quality is preserved, and Ba incentivizes fewer concepts at high SNR and more at low SNR to enforce channel-adaptive behavior. The DQN … view at source ↗
Figure 3
Figure 3. Figure 3: Semantic Quality across distinct M-QAMs for MNIST. codebook size constrained to |C| = M in each configura￾tion. All numeric hyperparameters are listed in Table I. The standard M-QAM baseline retains the SC pipeline but uses a fixed rectangular grid instead of a learned constellation. The composite semantic quality score is defined as: Qsem = 0.6 Qtask + 0.25 Pc + 0.15 exp(−DKL(p∥pˆ)), where Qtask is strict… view at source ↗
Figure 5
Figure 5. Figure 5: Symbols transmitted vs. SNR. 10 5 0 5 10 15 Signal-to-Noise Ratio (dB) 0.0 0.2 0.4 0.6 0.8 1.0 Semantic Quality Score Sem. 4-QAM Std. 4-QAM Sem. 16-QAM Std. 16-QAM Sem. 64-QAM Std. 64-QAM Sem. 256-QAM Std. 256-QAM Sem. 1024-QAM Std. 1024-QAM (a) 10 5 0 5 10 15 Signal-to-Noise Ratio (dB) 0.0 0.2 0.4 0.6 0.8 1.0 Semantic Quality Score Sem. 4-QAM Std. 4-QAM Sem. 16-QAM Std. 16-QAM Sem. 64-QAM Std. 64-QAM Sem.… view at source ↗
Figure 6
Figure 6. Figure 6: Semantic Quality vs. SNR (dB) for FSDD audio (a) and Fashion-MNIST visual (b) datasets. semantic compression and PHY protection improves Qsem while reducing symbol count across all SNRs. C. Cross-Domain Generalization The system’s cross-domain applicability is validated on the Fashion-MNIST visual dataset [15] and the audio-based FSDD dataset, where semantics are extracted from audio spectrograms [PITH_FU… view at source ↗
read the original abstract

Semantic communication systems for goal-oriented transmission must protect task-relevant information not only through source compression but also via physical layer mapping. Existing approaches decouple constellation design and semantic encoding, exposing critical symbols to channel errors at the same rate as irrelevant ones. Contrary to this, in this paper, a joint semantic-physical layer framework is proposed, which is composed of a vector quantized-variational autoencoder that extracts discrete latent concepts, a semantic criticality indicator (SCI) that scores each concept by task relevance, and a deep reinforcement learning agent that dynamically selects the transmission subset based on instantaneous channel conditions. At the physical layer, a learned semantic-aware M -QAM constellation assigns symbol positions according to joint co-occurrence statistics and SCI scores, departing from the uniform spacing and Gray coding of standard M -QAM which minimizes average BER without regard for semantic content. We introduce a novel semantic symbol vulnerability (SSV) metric and a semantic protection probability (SPP) to quantify the exposure of task-critical symbols to decoding errors, and prove that any Gray-coded constellation is strictly suboptimal in SCI-Weighted SSV whenever the source exhibits non-uniform semantic importance and co-occurrence statistics. Simulation results demonstrate that the proposed constellation achieves near 100% SPP across modulation orders from 4-QAM to 1024-QAM versus 50% for standard constellations at high spectral efficiency, a 21:1 compression ratio with semantic quality above 0.9, generalizing across MNIST, Fashion-MNIST, and FSDD without modification.

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

3 major / 2 minor

Summary. The paper proposes a joint semantic-physical layer framework for goal-oriented communication consisting of a VQ-VAE to extract discrete latent concepts, a semantic criticality indicator (SCI) scoring concepts by task relevance, a DRL agent for dynamic transmission subset selection, and a learned semantic-aware M-QAM constellation whose positions are assigned according to joint co-occurrence statistics and SCI scores. It introduces SSV and SPP metrics, claims a proof that any Gray-coded constellation is strictly suboptimal in SCI-Weighted SSV for sources with non-uniform semantic importance, and reports near-100% SPP (versus ~50% for standard constellations) across 4-QAM to 1024-QAM together with 21:1 compression and semantic quality >0.9, generalizing without modification across MNIST, Fashion-MNIST, and FSDD.

Significance. If the suboptimality proof is valid and the SCI metric demonstrably aligns with end-to-end task degradation, the work would provide a concrete mechanism for protecting task-critical symbols at the physical layer, which could improve spectral efficiency in semantic communication systems. The attempt to derive a strict suboptimality result and the multi-dataset simulation results are positive elements that, if substantiated, would strengthen the contribution.

major comments (3)
  1. [Abstract] Abstract: the claim of a strict suboptimality proof that 'any Gray-coded constellation is strictly suboptimal in SCI-Weighted SSV' is not accompanied by the proof steps, the precise definitions of SSV and SPP, or the mathematical formulation of the SCI-Weighted SSV metric, rendering the central theoretical claim unverifiable from the supplied manuscript.
  2. [Abstract] Abstract / simulation results: the reported near-100% SPP gains versus 50% for standard constellations lack error bars, the exact training procedure for constellation point locations and the DRL policy, and any demonstration that co-occurrence statistics and SCI scores were computed on held-out data; without these the numerical results cannot be assessed for overfitting or circularity.
  3. [Abstract] Abstract: the SCI is asserted to 'score each concept by task relevance,' yet no derivation or validation is supplied showing that these scores correlate with actual task performance degradation (e.g., classification error under symbol errors) rather than a latent-norm or reconstruction proxy; if misaligned, both the suboptimality proof and the SPP metric become specific to the proxy rather than to semantic communication performance.
minor comments (2)
  1. The joint co-occurrence statistics used for constellation placement are referenced but not given an explicit equation or algorithmic description, which would aid reproducibility.
  2. Notation for the modulation order M and the transition from VQ-VAE latents to SCI scores could be introduced earlier with a compact table or diagram.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will incorporate revisions to enhance verifiability of the theoretical claims and experimental details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of a strict suboptimality proof that 'any Gray-coded constellation is strictly suboptimal in SCI-Weighted SSV' is not accompanied by the proof steps, the precise definitions of SSV and SPP, or the mathematical formulation of the SCI-Weighted SSV metric, rendering the central theoretical claim unverifiable from the supplied manuscript.

    Authors: The precise definitions of SSV, SPP, and the SCI-Weighted SSV metric appear in Section 3, while the full proof of strict suboptimality (including all steps and assumptions) is given in Section 4. The abstract summarizes the result for brevity. We will revise the abstract to include concise definitions of SSV/SPP and a high-level outline of the key proof steps so the central claim is verifiable without consulting the body of the paper. revision: yes

  2. Referee: [Abstract] Abstract / simulation results: the reported near-100% SPP gains versus 50% for standard constellations lack error bars, the exact training procedure for constellation point locations and the DRL policy, and any demonstration that co-occurrence statistics and SCI scores were computed on held-out data; without these the numerical results cannot be assessed for overfitting or circularity.

    Authors: We will add error bars to all reported SPP and semantic-quality figures. The training procedures for constellation-point optimization and the DRL policy are described in Sections 5.1 and 5.2; we will expand these descriptions with hyper-parameter tables and pseudocode. We will also add an explicit statement that co-occurrence statistics are computed exclusively on the training split while SCI scores are computed and cross-validated on held-out validation data, together with the exact train/validation/test ratios used for each dataset. revision: yes

  3. Referee: [Abstract] Abstract: the SCI is asserted to 'score each concept by task relevance,' yet no derivation or validation is supplied showing that these scores correlate with actual task performance degradation (e.g., classification error under symbol errors) rather than a latent-norm or reconstruction proxy; if misaligned, both the suboptimality proof and the SPP metric become specific to the proxy rather than to semantic communication performance.

    Authors: The SCI is obtained from the gradient of the downstream task loss with respect to each latent concept inside the VQ-VAE encoder; this construction directly measures impact on task error rather than reconstruction or latent-norm proxies. We will insert the full derivation in Section 3.2 and add an ablation study (new Figure) that plots SCI-ranked concepts against measured classification error under controlled symbol-error patterns, confirming alignment with end-task degradation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; proof and learning steps remain independent of fitted inputs

full rationale

The paper defines a new SCI-Weighted SSV metric from VQ-VAE latents and co-occurrence statistics, then provides a mathematical proof that Gray-coded constellations are strictly suboptimal under non-uniform importance (abstract and claimed derivation). This proof is a general argument about weighted error minimization and does not reduce to the specific fitted values or data used for learning the constellation positions. The DRL policy and constellation optimization are presented as downstream applications of the metric rather than inputs that define the suboptimality claim. No self-citation chain, ansatz smuggling, or renaming of known results is exhibited in the provided text that would force the central result by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 3 invented entities

The framework rests on data-driven components whose parameters are fitted to task performance and co-occurrence counts; several new metrics and the constellation geometry are introduced without external validation benchmarks.

free parameters (3)
  • SCI scores
    Task-relevance scores assigned to each latent concept; values are produced by the model and used to shape the constellation.
  • Constellation point locations
    Positions in the M-QAM plane are learned from co-occurrence statistics and SCI scores rather than fixed by standard spacing.
  • DRL policy parameters
    The reinforcement-learning agent that selects transmission subsets is trained on instantaneous channel and task reward.
axioms (1)
  • domain assumption The source exhibits non-uniform semantic importance and co-occurrence statistics.
    Explicitly required for the claimed strict suboptimality of any Gray-coded constellation.
invented entities (3)
  • Semantic Criticality Indicator (SCI) no independent evidence
    purpose: Scores each discrete latent concept by its relevance to the downstream task
    New scoring mechanism introduced to drive both subset selection and constellation geometry.
  • Semantic Symbol Vulnerability (SSV) no independent evidence
    purpose: Quantifies exposure of task-critical symbols to decoding errors
    Novel metric defined to evaluate the design.
  • Semantic Protection Probability (SPP) no independent evidence
    purpose: Measures the probability that task-critical symbols are correctly decoded
    Novel metric used to report near-100% performance.

pith-pipeline@v0.9.1-grok · 5818 in / 1656 out tokens · 33127 ms · 2026-06-30T20:51:00.725258+00:00 · methodology

discussion (0)

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Reference graph

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