---
_id: '7808'
abstract:
- lang: eng
text: Quantization converts neural networks into low-bit fixed-point computations
which can be carried out by efficient integer-only hardware, and is standard practice
for the deployment of neural networks on real-time embedded devices. However,
like their real-numbered counterpart, quantized networks are not immune to malicious
misclassification caused by adversarial attacks. We investigate how quantization
affects a network’s robustness to adversarial attacks, which is a formal verification
question. We show that neither robustness nor non-robustness are monotonic with
changing the number of bits for the representation and, also, neither are preserved
by quantization from a real-numbered network. For this reason, we introduce a
verification method for quantized neural networks which, using SMT solving over
bit-vectors, accounts for their exact, bit-precise semantics. We built a tool
and analyzed the effect of quantization on a classifier for the MNIST dataset.
We demonstrate that, compared to our method, existing methods for the analysis
of real-numbered networks often derive false conclusions about their quantizations,
both when determining robustness and when detecting attacks, and that existing
methods for quantized networks often miss attacks. Furthermore, we applied our
method beyond robustness, showing how the number of bits in quantization enlarges
the gender bias of a predictor for students’ grades.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Mirco
full_name: Giacobbe, Mirco
id: 3444EA5E-F248-11E8-B48F-1D18A9856A87
last_name: Giacobbe
orcid: 0000-0001-8180-0904
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000-0002-2985-7724
- first_name: Mathias
full_name: Lechner, Mathias
id: 3DC22916-F248-11E8-B48F-1D18A9856A87
last_name: Lechner
citation:
ama: 'Giacobbe M, Henzinger TA, Lechner M. How many bits does it take to quantize
your neural network? In: International Conference on Tools and Algorithms for
the Construction and Analysis of Systems. Vol 12079. Springer Nature; 2020:79-97.
doi:10.1007/978-3-030-45237-7_5'
apa: 'Giacobbe, M., Henzinger, T. A., & Lechner, M. (2020). How many bits does
it take to quantize your neural network? In International Conference on Tools
and Algorithms for the Construction and Analysis of Systems (Vol. 12079, pp.
79–97). Dublin, Ireland: Springer Nature. https://doi.org/10.1007/978-3-030-45237-7_5'
chicago: Giacobbe, Mirco, Thomas A Henzinger, and Mathias Lechner. “How Many Bits
Does It Take to Quantize Your Neural Network?” In International Conference
on Tools and Algorithms for the Construction and Analysis of Systems, 12079:79–97.
Springer Nature, 2020. https://doi.org/10.1007/978-3-030-45237-7_5.
ieee: M. Giacobbe, T. A. Henzinger, and M. Lechner, “How many bits does it take
to quantize your neural network?,” in International Conference on Tools and
Algorithms for the Construction and Analysis of Systems, Dublin, Ireland,
2020, vol. 12079, pp. 79–97.
ista: 'Giacobbe M, Henzinger TA, Lechner M. 2020. How many bits does it take to
quantize your neural network? International Conference on Tools and Algorithms
for the Construction and Analysis of Systems. TACAS: Tools and Algorithms for
the Construction and Analysis of Systems, LNCS, vol. 12079, 79–97.'
mla: Giacobbe, Mirco, et al. “How Many Bits Does It Take to Quantize Your Neural
Network?” International Conference on Tools and Algorithms for the Construction
and Analysis of Systems, vol. 12079, Springer Nature, 2020, pp. 79–97, doi:10.1007/978-3-030-45237-7_5.
short: M. Giacobbe, T.A. Henzinger, M. Lechner, in:, International Conference on
Tools and Algorithms for the Construction and Analysis of Systems, Springer Nature,
2020, pp. 79–97.
conference:
end_date: 2020-04-30
location: Dublin, Ireland
name: 'TACAS: Tools and Algorithms for the Construction and Analysis of Systems'
start_date: 2020-04-25
date_created: 2020-05-10T22:00:49Z
date_published: 2020-04-17T00:00:00Z
date_updated: 2023-06-23T07:01:11Z
day: '17'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-030-45237-7_5
file:
- access_level: open_access
checksum: f19905a42891fe5ce93d69143fa3f6fb
content_type: application/pdf
creator: dernst
date_created: 2020-05-26T12:48:15Z
date_updated: 2020-07-14T12:48:03Z
file_id: '7893'
file_name: 2020_TACAS_Giacobbe.pdf
file_size: 2744030
relation: main_file
file_date_updated: 2020-07-14T12:48:03Z
has_accepted_license: '1'
intvolume: ' 12079'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 79-97
project:
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
publication: International Conference on Tools and Algorithms for the Construction
and Analysis of Systems
publication_identifier:
eissn:
- '16113349'
isbn:
- '9783030452360'
issn:
- '03029743'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11362'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: How many bits does it take to quantize your neural network?
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12079
year: '2020'
...