{"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/asymptotics-of-network-embeddings-learned-via","title":"Asymptotics of Network Embeddings Learned via Subsampling","arxiv_id":"2107.02363","date":"2021-07-06","proceeding":null,"authors":["Andrew Davison","Morgane Austern"],"abstract":"Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which algorithms developed for vector-valued data are applied. For large networks, embeddings are learned using stochastic gradient methods where the sub-sampling scheme can be freely chosen. Despite the strong empirical performance of such methods, they are not well understood theoretically. Our work encapsulates representation methods using a subsampling approach, such as node2vec, into a single unifying framework. We prove, under the assumption that the graph is exchangeable, that the distribution of the learned embedding vectors asymptotically decouples. Moreover, we characterize the asymptotic distribution and provided rates of convergence, in terms of the latent parameters, which includes the choice of loss function and the embedding dimension. This provides a theoretical foundation to understand what the embedding vectors represent and how well these methods perform on downstream tasks. Notably, we observe that typically used loss functions may lead to shortcomings, such as a lack of Fisher consistency.","url_abs":"https://arxiv.org/abs/2107.02363v4","url_pdf":"https://arxiv.org/pdf/2107.02363v4.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":[{"paper_slug":"asymptotics-of-network-embeddings-learned-via","repo_url":"https://github.com/aday651/embed-asym-exeriments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"asymptotics-of-network-embeddings-learned-via","repo_url":"https://github.com/aday651/embed-asym-experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"node-classification","task_name":"Node Classification"},{"task_slug":"node-clustering","task_name":"Node Clustering"}],"methods":[{"method_slug":"node2vec","method_name":"node2vec"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2107.02363","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2107.02363"}},"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":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/aday651/embed-asym-exeriments","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/aday651/embed-asym-experiments","reach":null}],"summary":{"ran_violates":1,"ran_draft_wrong":2,"unverified":6},"by_repo_kind":{"official":{"samples":9,"ran":3,"repositories":2}},"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":"b8e95809ca2c17c9","entry":"sigmoid","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/gen_data.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/gen_data.py","link_basis":"plan_row","language":"python","status":"ran_violates","verification_level":2,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b8e95809ca2c17c9"}},{"code_sha256_prefix":"8d0a3c5e02c50236","entry":"gen_graphon_data","repo":"aday651/embed-asym-experiments","repo_kind":"official","path":"custom_scripts/gen_data.py","file_url":"https://github.com/aday651/embed-asym-experiments/blob/HEAD/custom_scripts/gen_data.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8d0a3c5e02c50236"}},{"code_sha256_prefix":"25492f639e03d229","entry":"parse_arguments","repo":"aday651/embed-asym-experiments","repo_kind":"official","path":"custom_scripts/gen_data.py","file_url":"https://github.com/aday651/embed-asym-experiments/blob/HEAD/custom_scripts/gen_data.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"25492f639e03d229"}},{"code_sha256_prefix":"25e12dd19a1cb4b7","entry":"colorbar","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/calc_minima.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/calc_minima.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":"25e12dd19a1cb4b7"}},{"code_sha256_prefix":"a18e1ebc5654c088","entry":"make_simple_skipgram_loss","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/skipgram_modified.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/skipgram_modified.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":"a18e1ebc5654c088"}},{"code_sha256_prefix":"c703de90c21e5f2a","entry":"make_weighted_loss","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/skipgram_modified.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/skipgram_modified.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":"c703de90c21e5f2a"}},{"code_sha256_prefix":"02f29b2b7763af89","entry":"pop_risk_constrained_optim","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/calc_minima.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/calc_minima.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":"02f29b2b7763af89"}},{"code_sha256_prefix":"8c68f103b0e5d903","entry":"pop_risk_optim","repo":"aday651/embed-asym-exeriments","repo_kind":"official","path":"custom_scripts/calc_minima.py","file_url":"https://github.com/aday651/embed-asym-exeriments/blob/HEAD/custom_scripts/calc_minima.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":"8c68f103b0e5d903"}},{"code_sha256_prefix":"c760bdad11675c47","entry":"sbm_eval","repo":"aday651/embed-asym-experiments","repo_kind":"official","path":"custom_scripts/learn_embed.py","file_url":"https://github.com/aday651/embed-asym-experiments/blob/HEAD/custom_scripts/learn_embed.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":"c760bdad11675c47"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}