{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sparse-uncertainty-representation-in-deep-1","title":"Sparse Uncertainty Representation in Deep Learning with Inducing Weights","arxiv_id":"2105.14594","date":"2021-05-30","proceeding":"NeurIPS 2021 12","authors":["Hippolyt Ritter","Martin Kukla","Cheng Zhang","Yingzhen Li"],"abstract":"Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage several times higher than their deterministic counterparts. To address this, we augment the weight matrix of each layer with a small number of inducing weights, thereby projecting the uncertainty quantification into such low dimensional spaces. We further extend Matheron's conditional Gaussian sampling rule to enable fast weight sampling, which enables our inference method to maintain reasonable run-time as compared with ensembles. Importantly, our approach achieves competitive performance to the state-of-the-art in prediction and uncertainty estimation tasks with fully connected neural networks and ResNets, while reducing the parameter size to $\\leq 24.3\\%$ of that of a $single$ neural network.","url_abs":"https://arxiv.org/abs/2105.14594v2","url_pdf":"https://arxiv.org/pdf/2105.14594v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[{"method_slug":"deep-ensembles","method_name":"Deep Ensembles"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2105.14594","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2105.14594"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/microsoft/bayesianize","reach":null}],"summary":{"ran_draft_wrong":2,"ran_violates":1,"ran_fixture":1,"unverified":4},"by_repo_kind":{"found_in_text":{"samples":8,"ran":4,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"b7e49d4bd4a61d15","entry":"_jittered_cholesky","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b7e49d4bd4a61d15"}},{"code_sha256_prefix":"9a62afa5b91e4a9b","entry":"inverse_softplus","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9a62afa5b91e4a9b"}},{"code_sha256_prefix":"0f1e71e2afa65ee4","entry":"prod","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0f1e71e2afa65ee4"}},{"code_sha256_prefix":"658f0b11a92d4c5c","entry":"vec_to_chol","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"658f0b11a92d4c5c"}},{"code_sha256_prefix":"3763b3e1b90244a0","entry":"BayesianMixin","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3763b3e1b90244a0"}},{"code_sha256_prefix":"77c5e98b1f0161e7","entry":"InducingMixin","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"77c5e98b1f0161e7"}},{"code_sha256_prefix":"fb8eff98f8d123de","entry":"VariationalMixin","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fb8eff98f8d123de"}},{"code_sha256_prefix":"1e07f1a2a9eeabed","entry":"_InducingBase","repo":"microsoft/bayesianize","repo_kind":"found_in_text","path":"bnn/nn/mixins/variational/inducing.py","file_url":"https://github.com/microsoft/bayesianize/blob/HEAD/bnn/nn/mixins/variational/inducing.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1e07f1a2a9eeabed"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}