Split Group Knockoffs: Controlling False Discovery Rate in Transformational Group Sparsity

Siqi Chen, Yachen Gao, Yanwei Fu, Xinwei Sun
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:14279-14298, 2026.

Abstract

Controlling the false discovery rate (FDR) under complex sparsity structures remains a fundamental challenge in large language model (LLM) analysis. Motivated by multiple comparison problems in LLMs, we consider a setting in which sparsity arises at the group level after a linear transformation of model parameters. We propose Split Group Knockoffs (SGKs), a general framework for group-wise variable selection under grouped transformational sparsity that extends the Split Knockoff procedure to grouped transformed variables. We establish theoretical guarantees for group-level FDR control and support recovery consistency, addressing challenges induced by group-wise penalties in transformed spaces. Applying SGK to LLM behavior auditing experiment reveals that model disagreement is not uniform across subjects, but instead concentrates in domains with greater semantic and reasoning complexity, where SGK effectively distinguishes genuine behavioral deviations from surface-level performance variation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26af, title = {Split Group Knockoffs: Controlling False Discovery Rate in Transformational Group Sparsity}, author = {Chen, Siqi and Gao, Yachen and Fu, Yanwei and Sun, Xinwei}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {14279--14298}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26af/chen26af.pdf}, url = {https://proceedings.mlr.press/v306/chen26af.html}, abstract = {Controlling the false discovery rate (FDR) under complex sparsity structures remains a fundamental challenge in large language model (LLM) analysis. Motivated by multiple comparison problems in LLMs, we consider a setting in which sparsity arises at the group level after a linear transformation of model parameters. We propose Split Group Knockoffs (SGKs), a general framework for group-wise variable selection under grouped transformational sparsity that extends the Split Knockoff procedure to grouped transformed variables. We establish theoretical guarantees for group-level FDR control and support recovery consistency, addressing challenges induced by group-wise penalties in transformed spaces. Applying SGK to LLM behavior auditing experiment reveals that model disagreement is not uniform across subjects, but instead concentrates in domains with greater semantic and reasoning complexity, where SGK effectively distinguishes genuine behavioral deviations from surface-level performance variation.} }
Endnote
%0 Conference Paper %T Split Group Knockoffs: Controlling False Discovery Rate in Transformational Group Sparsity %A Siqi Chen %A Yachen Gao %A Yanwei Fu %A Xinwei Sun %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26af %I PMLR %P 14279--14298 %U https://proceedings.mlr.press/v306/chen26af.html %V 306 %X Controlling the false discovery rate (FDR) under complex sparsity structures remains a fundamental challenge in large language model (LLM) analysis. Motivated by multiple comparison problems in LLMs, we consider a setting in which sparsity arises at the group level after a linear transformation of model parameters. We propose Split Group Knockoffs (SGKs), a general framework for group-wise variable selection under grouped transformational sparsity that extends the Split Knockoff procedure to grouped transformed variables. We establish theoretical guarantees for group-level FDR control and support recovery consistency, addressing challenges induced by group-wise penalties in transformed spaces. Applying SGK to LLM behavior auditing experiment reveals that model disagreement is not uniform across subjects, but instead concentrates in domains with greater semantic and reasoning complexity, where SGK effectively distinguishes genuine behavioral deviations from surface-level performance variation.
APA
Chen, S., Gao, Y., Fu, Y. & Sun, X.. (2026). Split Group Knockoffs: Controlling False Discovery Rate in Transformational Group Sparsity. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:14279-14298 Available from https://proceedings.mlr.press/v306/chen26af.html.

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