{"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/stochastic-multiple-target-sampling-gradient","title":"Stochastic Multiple Target Sampling Gradient Descent","arxiv_id":"2206.01934","date":"2022-06-04","proceeding":null,"authors":["Hoang Phan","Ngoc Tran","Trung Le","Toan Tran","Nhat Ho","Dinh Phung"],"abstract":"Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of particles to approximate the distribution of interest. Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem. A natural question then arises: \"Can we derive a probabilistic version of the multi-objective optimization?\". To answer this question, we propose Stochastic Multiple Target Sampling Gradient Descent (MT-SGD), enabling us to sample from multiple unnormalized target distributions. Specifically, our MT-SGD conducts a flow of intermediate distributions gradually orienting to multiple target distributions, which allows the sampled particles to move to the joint high-likelihood region of the target distributions. Interestingly, the asymptotic analysis shows that our approach reduces exactly to the multiple-gradient descent algorithm for multi-objective optimization, as expected. Finally, we conduct comprehensive experiments to demonstrate the merit of our approach to multi-task learning.","url_abs":"https://arxiv.org/abs/2206.01934v4","url_pdf":"https://arxiv.org/pdf/2206.01934v4.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":"stochastic-multiple-target-sampling-gradient","repo_url":"https://github.com/VietHoang1512/MT-SGD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"multi-task-learning","task_name":"Multi-Task Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.01934","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.01934"}},"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/VietHoang1512/MT-SGD","reach":{"status":"ok"}},{"provenance":"deterministic:regex_extraction","url":"https://github.com/isl-org/MultiObjectiveOptimization","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_draft_wrong":3,"unverified":8},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1},"found_in_text":{"samples":10,"ran":2,"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":1,"samples":[{"code_sha256_prefix":"46e47135d4d407b3","entry":"expected_calibration_error","repo":"viethoang1512/mt-sgd","repo_kind":"official","path":"celeba/multi_task/train_mt_sgd.py","file_url":"https://github.com/viethoang1512/mt-sgd/blob/HEAD/celeba/multi_task/train_mt_sgd.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":2,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"46e47135d4d407b3"}},{"code_sha256_prefix":"dbcb53696bc43ef9","entry":"conv3x3","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/models/pspnet.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/models/pspnet.py","link_basis":"harvester_set","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":"dbcb53696bc43ef9"}},{"code_sha256_prefix":"fca7e85d958618dd","entry":"conv3x3_bn_relu","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/models/pspnet.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/models/pspnet.py","link_basis":"harvester_set","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":"fca7e85d958618dd"}},{"code_sha256_prefix":"90e50bc6f1220bdd","entry":"conv3x3","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/models/resnet_mit.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/models/resnet_mit.py","link_basis":"harvester_set","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":"90e50bc6f1220bdd"}},{"code_sha256_prefix":"36497fd5247322ab","entry":"cross_entropy2d","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/losses.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/losses.py","link_basis":"harvester_set","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":"36497fd5247322ab"}},{"code_sha256_prefix":"7adcc62e674f9a40","entry":"get_metrics","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/metrics.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/metrics.py","link_basis":"harvester_set","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":"7adcc62e674f9a40"}},{"code_sha256_prefix":"faa96c0ba935fc57","entry":"gradient_normalizers","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/min_norm_solvers.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/min_norm_solvers.py","link_basis":"harvester_set","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":"faa96c0ba935fc57"}},{"code_sha256_prefix":"e870ff8870d18569","entry":"l1_loss_depth","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/losses.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/losses.py","link_basis":"harvester_set","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":"e870ff8870d18569"}},{"code_sha256_prefix":"a90eec2e662e141f","entry":"nll","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/losses.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/losses.py","link_basis":"harvester_set","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":"a90eec2e662e141f"}},{"code_sha256_prefix":"deddf757c7ef17c5","entry":"resnet101","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/models/resnet_mit.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/models/resnet_mit.py","link_basis":"harvester_set","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":"deddf757c7ef17c5"}},{"code_sha256_prefix":"db1b66fff0c3985f","entry":"resnet50","repo":"isl-org/MultiObjectiveOptimization","repo_kind":"found_in_text","path":"multi_task/models/resnet_mit.py","file_url":"https://github.com/isl-org/MultiObjectiveOptimization/blob/HEAD/multi_task/models/resnet_mit.py","link_basis":"harvester_set","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":"db1b66fff0c3985f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}