CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization

Shudi Guo; Bin Liu; Shihai Wang; Tengfei Shi; Yu Liu; Haoran Li

CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization

Shudi Guo, Bin Liu, Shihai Wang, Tengfei Shi, Yu Liu, Haoran Li

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Abstract

Randomized smoothing provides certified robustness guarantees, but its direct application to text remains challenging due to the discrete, sparse, and semantically structured nature of textual inputs. We propose CRICO, an input-dependent covariance optimization framework for certified robustness in the text embedding space. CRICO estimates token-level decision influence in a black-box manner, making it readily extensible to LLMs. By adapting the certified ellipsoid to local decision structure, CRICO significantly enhances certified robustness. Experiments on multiple tasks demonstrate its effectiveness and broad applicability.

Anthology ID:: 2026.emnlp-main.2369
Volume:: Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
Month:: October
Year:: 2026
Address:: Budapest, Hungary
Editors:: Hung-Yi Lee, Sunipa Dev, Jessy Li, Desmond Elliott
Venue:: EMNLP
SIG:: SIGDAT
Publisher:: Association for Computational Linguistics
Note:
Pages:: 53768–53784
Language:
URL:: https://aclanthology.org/2026.emnlp-main.2369/
DOI:
Bibkey:
Cite (ACL):: Shudi Guo, Bin Liu, Shihai Wang, Tengfei Shi, Yu Liu, and Haoran Li. 2026. CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 53768–53784, Budapest, Hungary. Association for Computational Linguistics.
Cite (Informal):: CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization (Guo et al., EMNLP 2026)
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PDF:: https://aclanthology.org/2026.emnlp-main.2369.pdf

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@inproceedings{guo-etal-2026-crico,
    title = "{CRICO}: A Certified Robustness Framework via Input-Dependent Covariance Optimization",
    author = "Guo, Shudi  and
      Liu, Bin  and
      Wang, Shihai  and
      Shi, Tengfei  and
      Liu, Yu  and
      Li, Haoran",
    editor = "Lee, Hung-Yi  and
      Dev, Sunipa  and
      Li, Jessy  and
      Elliott, Desmond",
    booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
    month = oct,
    year = "2026",
    address = "Budapest, Hungary",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2026.emnlp-main.2369/",
    pages = "53768--53784",
    ISBN = "979-8-89176-459-0",
    abstract = "Randomized smoothing provides certified robustness guarantees, but its direct application to text remains challenging due to the discrete, sparse, and semantically structured nature of textual inputs. We propose CRICO, an input-dependent covariance optimization framework for certified robustness in the text embedding space. CRICO estimates token-level decision influence in a black-box manner, making it readily extensible to LLMs. By adapting the certified ellipsoid to local decision structure, CRICO significantly enhances certified robustness. Experiments on multiple tasks demonstrate its effectiveness and broad applicability."
}

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%0 Conference Proceedings
%T CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization
%A Guo, Shudi
%A Liu, Bin
%A Wang, Shihai
%A Shi, Tengfei
%A Liu, Yu
%A Li, Haoran
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F guo-etal-2026-crico
%X Randomized smoothing provides certified robustness guarantees, but its direct application to text remains challenging due to the discrete, sparse, and semantically structured nature of textual inputs. We propose CRICO, an input-dependent covariance optimization framework for certified robustness in the text embedding space. CRICO estimates token-level decision influence in a black-box manner, making it readily extensible to LLMs. By adapting the certified ellipsoid to local decision structure, CRICO significantly enhances certified robustness. Experiments on multiple tasks demonstrate its effectiveness and broad applicability.
%U https://aclanthology.org/2026.emnlp-main.2369/
%P 53768-53784

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Markdown (Informal)

[CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization](https://aclanthology.org/2026.emnlp-main.2369/) (Guo et al., EMNLP 2026)

CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization (Guo et al., EMNLP 2026)

ACL

Shudi Guo, Bin Liu, Shihai Wang, Tengfei Shi, Yu Liu, and Haoran Li. 2026. CRICO: A Certified Robustness Framework via Input-Dependent Covariance Optimization. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 53768–53784, Budapest, Hungary. Association for Computational Linguistics.