{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/349393"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/349393","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Random Features for Efficient Attention Approximation","abstract":"Transformers are, perhaps, the most widespread architectures in today's landscape of deep learning. They, however, do not scale well with long sequences, resulting in O(L^2) computational complexity for the sequence length L. In this thesis, we propose a holistic approach for reducing this complexity to linear O(L) via an unbiased approximation of the softmax kernel appearing in self-attention, the main component in the Transformer backbone. The obtained efficient Transformer architecture is referred to as Performer. Compared to other developments in the area of efficient Transformers, Performer is theory-grounded and the problem of long-sequence processing can be reduced to a theoretical derivation of random features with certain properties minimizing the variance of the approximation. This thesis describes an evolution of mechanisms for random-feature approximation: from the so-called FAVOR, to FAVOR+ and, finally, to FAVOR++. The FAVOR++ mechanism has the tightest concentration properties and the best performance in practice. On the way to FAVOR++, we also discuss several extensions of the proposed efficient self-attention mechanism, among which are masked self-attention, sub-linear memory Performers, generalized attention, and more. For each proposed method, this thesis contains empirical evaluations in real-life large-scale learning setups and thorough theoretical analyses with proofs.","abstract_html":"Transformers are, perhaps, the most widespread architectures in today&#x27;s landscape of deep learning. They, however, do not scale well with long sequences, resulting in O(L^2) computational complexity for the sequence length L. In this thesis, we propose a holistic approach for reducing this complexity to linear O(L) via an unbiased approximation of the softmax kernel appearing in self-attention, the main component in the Transformer backbone. The obtained efficient Transformer architecture is referred to as Performer. Compared to other developments in the area of efficient Transformers, Performer is theory-grounded and the problem of long-sequence processing can be reduced to a theoretical derivation of random features with certain properties minimizing the variance of the approximation. This thesis describes an evolution of mechanisms for random-feature approximation: from the so-called FAVOR, to FAVOR+ and, finally, to FAVOR++. The FAVOR++ mechanism has the tightest concentration properties and the best performance in practice. On the way to FAVOR++, we also discuss several extensions of the proposed efficient self-attention mechanism, among which are masked self-attention, sub-linear memory Performers, generalized attention, and more. For each proposed method, this thesis contains empirical evaluations in real-life large-scale learning setups and thorough theoretical analyses with proofs.","abstract_has_math":false,"creators":["Likhosherstov, Valerii"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Weller, Adrian"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12-01","date_published":"2022-12-01","updated_at":"2026-07-22T22:24:17Z","subjects":["deep learning","self-attention","Transformer networks"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6aae78a5-080c-4b06-aca4-0db634b88daf/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.96501","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Weller, Adrian"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["Cambridge University Department of Engineering and Cambridge Trust"]},{"key":"dc:creator","label":"Author","values":["Likhosherstov, Valerii"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2022-12-01"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/349393"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["deep learning","self-attention","Transformer networks"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6aae78a5-080c-4b06-aca4-0db634b88daf/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.96501"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7a2e8fbd-a502-47c3-9ce5-20d7d9640bcc/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Transformers are, perhaps, the most widespread architectures in today's landscape of deep learning. They, however, do not scale well with long sequences, resulting in O(L^2) computational complexity for the sequence length L. In this thesis, we propose a holistic approach for reducing this complexity to linear O(L) via an unbiased approximation of the softmax kernel appearing in self-attention, the main component in the Transformer backbone. The obtained efficient Transformer architecture is referred to as Performer. Compared to other developments in the area of efficient Transformers, Performer is theory-grounded and the problem of long-sequence processing can be reduced to a theoretical derivation of random features with certain properties minimizing the variance of the approximation. This thesis describes an evolution of mechanisms for random-feature approximation: from the so-called FAVOR, to FAVOR+ and, finally, to FAVOR++. The FAVOR++ mechanism has the tightest concentration properties and the best performance in practice. On the way to FAVOR++, we also discuss several extensions of the proposed efficient self-attention mechanism, among which are masked self-attention, sub-linear memory Performers, generalized attention, and more. For each proposed method, this thesis contains empirical evaluations in real-life large-scale learning setups and thorough theoretical analyses with proofs."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["671700c6e9ad52eaab165ce4c28451ce","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["Random Features for Efficient Attention Approximation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Weller, Adrian"],"dc:contributor.sponsor":["Cambridge University Department of Engineering and Cambridge Trust"],"dc:creator":["Likhosherstov, Valerii"],"dc:date.issued":["2022-12-01"],"dc:description.abstract":["Transformers are, perhaps, the most widespread architectures in today's landscape of deep learning. They, however, do not scale well with long sequences, resulting in O(L^2) computational complexity for the sequence length L. In this thesis, we propose a holistic approach for reducing this complexity to linear O(L) via an unbiased approximation of the softmax kernel appearing in self-attention, the main component in the Transformer backbone. The obtained efficient Transformer architecture is referred to as Performer. Compared to other developments in the area of efficient Transformers, Performer is theory-grounded and the problem of long-sequence processing can be reduced to a theoretical derivation of random features with certain properties minimizing the variance of the approximation. This thesis describes an evolution of mechanisms for random-feature approximation: from the so-called FAVOR, to FAVOR+ and, finally, to FAVOR++. The FAVOR++ mechanism has the tightest concentration properties and the best performance in practice. On the way to FAVOR++, we also discuss several extensions of the proposed efficient self-attention mechanism, among which are masked self-attention, sub-linear memory Performers, generalized attention, and more. For each proposed method, this thesis contains empirical evaluations in real-life large-scale learning setups and thorough theoretical analyses with proofs."],"dc:format.checksum.md5":["671700c6e9ad52eaab165ce4c28451ce","87eda9de84448d1f82354d60eee3eb5f"],"dc:identifier.doi":["https://doi.org/10.17863/CAM.96501"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7a2e8fbd-a502-47c3-9ce5-20d7d9640bcc/download"],"dc:language":["eng"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/349393"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/6aae78a5-080c-4b06-aca4-0db634b88daf/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["deep learning","self-attention","Transformer networks"],"dc:title":["Random Features for Efficient Attention Approximation"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-22T22:24:17Z"}