---
_id: '7639'
abstract:
- lang: eng
  text: Deep neural networks (DNNs) have become increasingly important due to their
    excellent empirical performance on a wide range of problems. However, regularization
    is generally achieved by indirect means, largely due to the complex set of functions
    defined by a network and the difficulty in measuring function complexity. There
    exists no method in the literature for additive regularization based on a norm
    of the function, as is classically considered in statistical learning theory.
    In this work, we study the tractability of function norms for deep neural networks
    with ReLU activations. We provide, to the best of our knowledge, the first proof
    in the literature of the NP-hardness of computing function norms of DNNs of 3
    or more layers. We also highlight a fundamental difference between shallow and
    deep networks. In the light on these results, we propose a new regularization
    strategy based on approximate function norms, and show its efficiency on a segmentation
    task with a DNN.
article_number: 748-752
article_processing_charge: No
author:
- first_name: Amal
  full_name: Rannen-Triki, Amal
  last_name: Rannen-Triki
- first_name: Maxim
  full_name: Berman, Maxim
  last_name: Berman
- first_name: Vladimir
  full_name: Kolmogorov, Vladimir
  id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
  last_name: Kolmogorov
- first_name: Matthew B.
  full_name: Blaschko, Matthew B.
  last_name: Blaschko
citation:
  ama: 'Rannen-Triki A, Berman M, Kolmogorov V, Blaschko MB. Function norms for neural
    networks. In: <i>Proceedings of the 2019 International Conference on Computer
    Vision Workshop</i>. IEEE; 2019. doi:<a href="https://doi.org/10.1109/ICCVW.2019.00097">10.1109/ICCVW.2019.00097</a>'
  apa: 'Rannen-Triki, A., Berman, M., Kolmogorov, V., &#38; Blaschko, M. B. (2019).
    Function norms for neural networks. In <i>Proceedings of the 2019 International
    Conference on Computer Vision Workshop</i>. Seoul, South Korea: IEEE. <a href="https://doi.org/10.1109/ICCVW.2019.00097">https://doi.org/10.1109/ICCVW.2019.00097</a>'
  chicago: Rannen-Triki, Amal, Maxim Berman, Vladimir Kolmogorov, and Matthew B. Blaschko.
    “Function Norms for Neural Networks.” In <i>Proceedings of the 2019 International
    Conference on Computer Vision Workshop</i>. IEEE, 2019. <a href="https://doi.org/10.1109/ICCVW.2019.00097">https://doi.org/10.1109/ICCVW.2019.00097</a>.
  ieee: A. Rannen-Triki, M. Berman, V. Kolmogorov, and M. B. Blaschko, “Function norms
    for neural networks,” in <i>Proceedings of the 2019 International Conference on
    Computer Vision Workshop</i>, Seoul, South Korea, 2019.
  ista: 'Rannen-Triki A, Berman M, Kolmogorov V, Blaschko MB. 2019. Function norms
    for neural networks. Proceedings of the 2019 International Conference on Computer
    Vision Workshop. ICCVW: International Conference on Computer Vision Workshop,
    748–752.'
  mla: Rannen-Triki, Amal, et al. “Function Norms for Neural Networks.” <i>Proceedings
    of the 2019 International Conference on Computer Vision Workshop</i>, 748–752,
    IEEE, 2019, doi:<a href="https://doi.org/10.1109/ICCVW.2019.00097">10.1109/ICCVW.2019.00097</a>.
  short: A. Rannen-Triki, M. Berman, V. Kolmogorov, M.B. Blaschko, in:, Proceedings
    of the 2019 International Conference on Computer Vision Workshop, IEEE, 2019.
conference:
  end_date: 2019-10-28
  location: Seoul, South Korea
  name: 'ICCVW: International Conference on Computer Vision Workshop'
  start_date: 2019-10-27
date_created: 2020-04-05T22:00:50Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-09-08T11:19:12Z
day: '01'
department:
- _id: VlKo
doi: 10.1109/ICCVW.2019.00097
external_id:
  isi:
  - '000554591600090'
isi: 1
language:
- iso: eng
month: '10'
oa_version: None
publication: Proceedings of the 2019 International Conference on Computer Vision Workshop
publication_identifier:
  isbn:
  - '9781728150239'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Function norms for neural networks
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...
---
_id: '7640'
abstract:
- lang: eng
  text: We propose a new model for detecting visual relationships, such as "person
    riding motorcycle" or "bottle on table". This task is an important step towards
    comprehensive structured mage understanding, going beyond detecting individual
    objects. Our main novelty is a Box Attention mechanism that allows to model pairwise
    interactions between objects using standard object detection pipelines. The resulting
    model is conceptually clean, expressive and relies on well-justified training
    and prediction procedures. Moreover, unlike previously proposed approaches, our
    model does not introduce any additional complex components or hyperparameters
    on top of those already required by the underlying detection model. We conduct
    an experimental evaluation on two datasets, V-COCO and Open Images, demonstrating
    strong quantitative and qualitative results.
article_number: 1749-1753
article_processing_charge: No
arxiv: 1
author:
- first_name: Alexander
  full_name: Kolesnikov, Alexander
  id: 2D157DB6-F248-11E8-B48F-1D18A9856A87
  last_name: Kolesnikov
- first_name: Alina
  full_name: Kuznetsova, Alina
  last_name: Kuznetsova
- first_name: Christoph
  full_name: Lampert, Christoph
  id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
  last_name: Lampert
  orcid: 0000-0001-8622-7887
- first_name: Vittorio
  full_name: Ferrari, Vittorio
  last_name: Ferrari
citation:
  ama: 'Kolesnikov A, Kuznetsova A, Lampert C, Ferrari V. Detecting visual relationships
    using box attention. In: <i>Proceedings of the 2019 International Conference on
    Computer Vision Workshop</i>. IEEE; 2019. doi:<a href="https://doi.org/10.1109/ICCVW.2019.00217">10.1109/ICCVW.2019.00217</a>'
  apa: 'Kolesnikov, A., Kuznetsova, A., Lampert, C., &#38; Ferrari, V. (2019). Detecting
    visual relationships using box attention. In <i>Proceedings of the 2019 International
    Conference on Computer Vision Workshop</i>. Seoul, South Korea: IEEE. <a href="https://doi.org/10.1109/ICCVW.2019.00217">https://doi.org/10.1109/ICCVW.2019.00217</a>'
  chicago: Kolesnikov, Alexander, Alina Kuznetsova, Christoph Lampert, and Vittorio
    Ferrari. “Detecting Visual Relationships Using Box Attention.” In <i>Proceedings
    of the 2019 International Conference on Computer Vision Workshop</i>. IEEE, 2019.
    <a href="https://doi.org/10.1109/ICCVW.2019.00217">https://doi.org/10.1109/ICCVW.2019.00217</a>.
  ieee: A. Kolesnikov, A. Kuznetsova, C. Lampert, and V. Ferrari, “Detecting visual
    relationships using box attention,” in <i>Proceedings of the 2019 International
    Conference on Computer Vision Workshop</i>, Seoul, South Korea, 2019.
  ista: 'Kolesnikov A, Kuznetsova A, Lampert C, Ferrari V. 2019. Detecting visual
    relationships using box attention. Proceedings of the 2019 International Conference
    on Computer Vision Workshop. ICCVW: International Conference on Computer Vision
    Workshop, 1749–1753.'
  mla: Kolesnikov, Alexander, et al. “Detecting Visual Relationships Using Box Attention.”
    <i>Proceedings of the 2019 International Conference on Computer Vision Workshop</i>,
    1749–1753, IEEE, 2019, doi:<a href="https://doi.org/10.1109/ICCVW.2019.00217">10.1109/ICCVW.2019.00217</a>.
  short: A. Kolesnikov, A. Kuznetsova, C. Lampert, V. Ferrari, in:, Proceedings of
    the 2019 International Conference on Computer Vision Workshop, IEEE, 2019.
conference:
  end_date: 2019-10-28
  location: Seoul, South Korea
  name: 'ICCVW: International Conference on Computer Vision Workshop'
  start_date: 2019-10-27
date_created: 2020-04-05T22:00:51Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-09-08T11:18:37Z
day: '01'
department:
- _id: ChLa
doi: 10.1109/ICCVW.2019.00217
ec_funded: 1
external_id:
  arxiv:
  - '1807.02136'
  isi:
  - '000554591601098'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1807.02136
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 2532554C-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '308036'
  name: Lifelong Learning of Visual Scene Understanding
publication: Proceedings of the 2019 International Conference on Computer Vision Workshop
publication_identifier:
  isbn:
  - '9781728150239'
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Detecting visual relationships using box attention
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...