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The Rate-Distortion-Perception Trade-Off with Algorithmic Realism

Yassine Hamdi, Aaron B. Wagner, Deniz Gündüz

TL;DR

This paper rethinks realism constraints in lossy compression by replacing traditional divergence-based realism with a realization-based criterion evaluated by computable critics. It shows that the rate-distortion-perception (RDP) trade-off can be achieved without common randomness in the sub-exponential batch regime, while extremely large batches recover the distribution-matching regime where randomness becomes necessary. The authors introduce a formal one-shot and asymptotic framework anchored in algorithmic information theory, including a universal critic linked to Kolmogorov complexity, and they prove that deterministic codes suffice in practical regimes. Moreover, they connect the realization-based approach to the classical distribution-matching viewpoint, establishing equivalence at large batch sizes and clarifying when randomness is beneficial. Overall, the work explains why large common randomness has not been observed in practice and highlights the critical role of batch size in realism assessments for compression systems.

Abstract

Realism constraints (or constraints on perceptual quality) have received considerable recent attention within the context of lossy compression, particularly of images. Theoretical studies of lossy compression indicate that high-rate common randomness between the compressor and the decompressor is a valuable resource for achieving realism. On the other hand, the utility of significant amounts of common randomness has not been noted in practice. We offer an explanation for this discrepancy by considering a realism constraint that requires satisfying a universal critic that inspects realizations of individual compressed reconstructions, or batches thereof. We characterize the optimal rate-distortion trade-off under such a realism constraint, and show that it is asymptotically achievable without any common randomness, unless the batch size is impractically large.

The Rate-Distortion-Perception Trade-Off with Algorithmic Realism

TL;DR

This paper rethinks realism constraints in lossy compression by replacing traditional divergence-based realism with a realization-based criterion evaluated by computable critics. It shows that the rate-distortion-perception (RDP) trade-off can be achieved without common randomness in the sub-exponential batch regime, while extremely large batches recover the distribution-matching regime where randomness becomes necessary. The authors introduce a formal one-shot and asymptotic framework anchored in algorithmic information theory, including a universal critic linked to Kolmogorov complexity, and they prove that deterministic codes suffice in practical regimes. Moreover, they connect the realization-based approach to the classical distribution-matching viewpoint, establishing equivalence at large batch sizes and clarifying when randomness is beneficial. Overall, the work explains why large common randomness has not been observed in practice and highlights the critical role of batch size in realism assessments for compression systems.

Abstract

Realism constraints (or constraints on perceptual quality) have received considerable recent attention within the context of lossy compression, particularly of images. Theoretical studies of lossy compression indicate that high-rate common randomness between the compressor and the decompressor is a valuable resource for achieving realism. On the other hand, the utility of significant amounts of common randomness has not been noted in practice. We offer an explanation for this discrepancy by considering a realism constraint that requires satisfying a universal critic that inspects realizations of individual compressed reconstructions, or batches thereof. We characterize the optimal rate-distortion trade-off under such a realism constraint, and show that it is asymptotically achievable without any common randomness, unless the batch size is impractically large.

Paper Structure

This paper contains 43 sections, 14 theorems, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Notation
  4. Background on algorithmic information theory
  5. New model for the rate-distortion-perception trade-off
  6. The one-shot setting
  7. Asymptotic setting
  8. Results
  9. Low batch size regime
  10. One-shot achievable points
  11. Generalizing the distribution matching formalism
  12. Background
  13. Connection to our formalism
  14. Conclusion
  15. Further background on algorithmic information theory
  16. ...and 28 more sections

Key Result

Proposition 2

Consider a finite set $\mathcal{X}.$ Let $q$ be a distribution on $\mathcal{X}$ such that $\forall x \in \mathcal{X}, q(x)>0.$ Let $e_0$ be any symbol in $\mathcal{X} .$ For any $n\in\mathbb{N}$ and any $x_{1:n }\in \mathcal{X} ^n ,$ let $S(x_{1:n })$ denote the number of occurrences of $e_0$ in $x_ if $S(x_{1:n})\neq q(e_0)n,$ and $x_{1:n} \mapsto 0$ otherwise. Then, $\delta-2\log(\delta+ 3 )$ is

Figures (2)

  • Figure 1: The system model for the one-shot setting.
  • Figure 2: The system model for the asymptotic setting. Index $k$ ranges from $1$ to the batch size. The same encoder-decoder pair is used to process each source sample in the batch.

Theorems & Definitions (33)

  • Definition 1
  • Proposition 2
  • Proposition 3
  • Remark 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Theorem 10
  • ...and 23 more