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A Rate-Distortion Framework for Summarization

Enes Arda, Aylin Yener

TL;DR

This work addresses the fundamental question of limits in text summarization by introducing the summarizer rate-distortion function $R_S(D)$ and proving that any summarizer achieving distortion $D$ must operate at rate $R \ge R_S(D)$. It provides a Blahut–Arimoto–style algorithm to compute $R_S(D)$ and a practical, data-efficient approach using Gaussian embeddings and reverse water-filling to approximate $R_S(D)$ from real datasets. Empirically, the approximated $R_S(D)$ on CNN/DailyMail aligns as a plausible lower bound for popular summarizers (e.g., BART-Large-CNN, PEGASUS), validating the framework’s relevance for benchmarking and understanding rate–distortion trade-offs in summarization. Overall, the paper offers a principled, information-theoretic view on summarization that can guide evaluation and development of summarizers toward fundamental performance limits.

Abstract

This paper introduces an information-theoretic framework for text summarization. We define the summarizer rate-distortion function and show that it provides a fundamental lower bound on summarizer performance. We describe an iterative procedure, similar to Blahut-Arimoto algorithm, for computing this function. To handle real-world text datasets, we also propose a practical method that can calculate the summarizer rate-distortion function with limited data. Finally, we empirically confirm our theoretical results by comparing the summarizer rate-distortion function with the performances of different summarizers used in practice.

A Rate-Distortion Framework for Summarization

TL;DR

This work addresses the fundamental question of limits in text summarization by introducing the summarizer rate-distortion function and proving that any summarizer achieving distortion must operate at rate . It provides a Blahut–Arimoto–style algorithm to compute and a practical, data-efficient approach using Gaussian embeddings and reverse water-filling to approximate from real datasets. Empirically, the approximated on CNN/DailyMail aligns as a plausible lower bound for popular summarizers (e.g., BART-Large-CNN, PEGASUS), validating the framework’s relevance for benchmarking and understanding rate–distortion trade-offs in summarization. Overall, the paper offers a principled, information-theoretic view on summarization that can guide evaluation and development of summarizers toward fundamental performance limits.

Abstract

This paper introduces an information-theoretic framework for text summarization. We define the summarizer rate-distortion function and show that it provides a fundamental lower bound on summarizer performance. We describe an iterative procedure, similar to Blahut-Arimoto algorithm, for computing this function. To handle real-world text datasets, we also propose a practical method that can calculate the summarizer rate-distortion function with limited data. Finally, we empirically confirm our theoretical results by comparing the summarizer rate-distortion function with the performances of different summarizers used in practice.
Paper Structure (16 sections, 8 theorems, 44 equations, 5 figures, 2 algorithms)

This paper contains 16 sections, 8 theorems, 44 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Fundamental Limits of Summarizers
  4. Computing $R_S(D)$
  5. Approximating $R_S(D)$ From A Dataset
  6. Conclusion
  7. Appendix: Proof of Theorem \ref{['thm:sum_bound1']}
  8. Appendix: Proof of Theorem \ref{['thm:gaussian-sum-rd']}
  9. Appendix: Experiment Details
  10. Tokenization
  11. The Embedding Model
  12. The Pooling Method
  13. Creating The Length Grid
  14. Eigenvalues of Covariance Matrices
  15. Running Summarizers At Specific Rates
  16. ...and 1 more sections

Key Result

Lemma 1

For a fixed $p_T$, $I\left(T;S \mid \ell\left(T\right)\right)$ is a convex function of $p_{S|T}$.

Figures (5)

  • Figure 1: The summarizer rate-distortion curve, computed via Algorithm \ref{['alg:ba']} for the setup of Example \ref{['ex:one-shot']}, and the performance of one-shot summarizers.
  • Figure 2: The summarizer rate-distortion curve, computed via Algorithm \ref{['alg:approx-rs-d']} for CNN/DailyMail dataset, and the performance of different summarizers.
  • Figure 3: The distribution of text lengths in the CNN/DailyMail test split, tokenized with BGE-M3 tokenizer
  • Figure 4: Comparison of the sample covariance eigenvalues for each interval.
  • Figure 5: Comparison of summarizer rate-distortion curves computed with Algorithm \ref{['alg:approx-rs-d']} using different number of length intervals.

Theorems & Definitions (16)

  • Definition 1
  • Definition 2
  • Example 1
  • Definition 3
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Definition 4
  • Lemma 3
  • Remark 1
  • ...and 6 more