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PreprintCC BY-NC 4.0HAL

Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks

  • Michel Barlaud
  • Jean-Paul Marmorat
  • Guillaume Perez
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Abstract

The ℓ1,∞ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, O nm log(nm) for a matrix in R n×m . In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the ℓ1,∞ norm is only O nm for a matrix in R n×m . Moreover, we provide a new ℓ1,∞ identity with mathematical proof and experimental validation. Experiments show that our bi-level ℓ1,∞ projection is O log(nm) times faster than the actual fastest algorithm. Our bi-level ℓ1,∞ projection outperforms the sparsity of the usual ℓ1,∞ projection while keeping the same or slightly better accuracy in classification applications.

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Cite

BibTeXRIS
BibTeX
@misc{barlaud2026lineartime,
  title = {{Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks}},
  author = {Michel Barlaud and Jean-Paul Marmorat and Guillaume Perez},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  url = {https://hal.science/hal-05303330v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - Linear-Time Bilevel Clipping operators for Structured Sparsity in Neural Networks
AU  - Michel Barlaud
AU  - Jean-Paul Marmorat
AU  - Guillaume Perez
PY  - 2026
DA  - 2026/08/04
PB  - HAL
UR  - https://hal.science/hal-05303330v1
AB  - The ℓ1,∞ norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, O nm log(nm) for a matrix in R n×m . In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the ℓ1,∞ norm is only O nm for a matrix in R n×m . Moreover, we provide a new ℓ1,∞ identity with mathematical proof and experimental validation. Experiments show that our bi-level ℓ1,∞ projection is O log(nm) times faster than the actual fastest algorithm. Our bi-level ℓ1,∞ projection outperforms the sparsity of the usual ℓ1,∞ projection while keeping the same or slightly better accuracy in classification applications.
ER  -