The DOI matches its Crossref record.
Almost optimal lower bounds for small depth circuits
Abstract
Article Almost optimal lower bounds for small depth circuits Share on Author: J Hastad Applied Mathematics department and Laboratory of Computer Science, MIT Applied Mathematics department and Laboratory of Computer Science, MITView Profile Authors Info & Claims STOC '86: Proceedings of the eighteenth annual ACM symposium on Theory of computingNovember 1986 Pages 6–20https://doi.org/10.1145/12130.12132Online:01 November 1986Publication History 257citation973DownloadsMetricsTotal Citations257Total Downloads973Last 12 Months50Last 6 weeks6 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Representation Learning: A Review and New Perspectives
Bengio, Y., Courville, A., & Vincent, P. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.50 · Cited by 13,001
Learning Deep Architectures for AI
Bengio, Y. (2009) · now publishers, Inc. eBooks · doi:10.1561/9781601982957 · Cited by 4,941
Practical Recommendations for Gradient-Based Training of Deep Architectures
Bengio, Y. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-35289-8_26 · Cited by 2,259
Multimodal Neuroimaging Feature Learning for Multiclass Diagnosis of Alzheimer's Disease
Liu, S., Liu, S., Cai, W., Che, H., Pujol, S., Kikinis, R., Feng, D., Fulham, M. J., & ADNI (2015) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2014.2372011 · Cited by 637
(2016) · Conference on Learning Theory · Cited by 443
Metadata
- Authors
- Hastad, J.
- Venue
- Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86
- Publisher
- ACM Press
- Published
- 1986
- Pages
- 6-20
- OpenAlex
- W2165293955
- Cited by
- 620
- References
- 0
- FWCI
- 14.83
- Type
- conference paper
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Almost optimal lower bounds for small depth circuits. https://app.cochat.ai/papers/10.1145/12130.12132
- The paper
- Hastad, J. (1986). Almost optimal lower bounds for small depth circuits. Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86. https://doi.org/10.1145/12130.12132
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
