{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CUIZS75PZDTRY5MIONRK74364V","short_pith_number":"pith:CUIZS75P","schema_version":"1.0","canonical_sha256":"1511997fafc8e71c75887362aff37ee546f880416159d1945d428ed7d54ebb0b","source":{"kind":"arxiv","id":"2203.09168","version":2},"attestation_state":"computed","paper":{"title":"On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Arash Tavakoli, Dimitrije Antic, Georg Martius, Maximilian Seitzer","submitted_at":"2022-03-17T08:46:17Z","abstract_excerpt":"Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2203.09168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T08:46:17Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"588db8d9ff1005e28206432a296edcf6351471a8035e0fb33012e8417bd85410","abstract_canon_sha256":"ad440f753facea4a0ddbe37dc49237d6d53279b1db942289769d8e5a4da90cdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:10:40.178913Z","signature_b64":"jqPxd6L6fWQqCdpqoQvRAojdHrDI06u/I83aNafbaB95vOiA+zwiRK1pedviDQQCE2Fn+FXeaVT5u2vIfP6/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1511997fafc8e71c75887362aff37ee546f880416159d1945d428ed7d54ebb0b","last_reissued_at":"2026-07-05T04:10:40.178330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:10:40.178330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Arash Tavakoli, Dimitrije Antic, Georg Martius, Maximilian Seitzer","submitted_at":"2022-03-17T08:46:17Z","abstract_excerpt":"Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09168","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.09168/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2203.09168","created_at":"2026-07-05T04:10:40.178384+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.09168v2","created_at":"2026-07-05T04:10:40.178384+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.09168","created_at":"2026-07-05T04:10:40.178384+00:00"},{"alias_kind":"pith_short_12","alias_value":"CUIZS75PZDTR","created_at":"2026-07-05T04:10:40.178384+00:00"},{"alias_kind":"pith_short_16","alias_value":"CUIZS75PZDTRY5MI","created_at":"2026-07-05T04:10:40.178384+00:00"},{"alias_kind":"pith_short_8","alias_value":"CUIZS75P","created_at":"2026-07-05T04:10:40.178384+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21728","citing_title":"Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2606.09037","citing_title":"A Multi-Agent System for Motor Design Optimization via an FEA-AI Hybrid Approach","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2606.06631","citing_title":"From Pixels to Newtons: Predicting In Vivo Joint Contact Forces from Monocular Video","ref_index":47,"is_internal_anchor":false},{"citing_arxiv_id":"2606.28287","citing_title":"Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks","ref_index":67,"is_internal_anchor":false},{"citing_arxiv_id":"2606.16578","citing_title":"Walking on Heat Stars for Parabolic Heat Equations with Neumann Boundary Conditions","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"2509.00155","citing_title":"Amplitude Uncertainties Everywhere All at Once","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2602.15353","citing_title":"NeuroSymActive: Differentiable Neural-Symbolic Reasoning with Active Exploration for Knowledge Graph Question Answering","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11865","citing_title":"Variance-aware Reward Modeling with Anchor Guidance","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21717","citing_title":"Monte Carlo PDE Solvers for Nonlinear Radiative Boundary Conditions","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07819","citing_title":"Probabilistic denoising for reliable signal extraction in spectroscopy","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V","json":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V.json","graph_json":"https://pith.science/api/pith-number/CUIZS75PZDTRY5MIONRK74364V/graph.json","events_json":"https://pith.science/api/pith-number/CUIZS75PZDTRY5MIONRK74364V/events.json","paper":"https://pith.science/paper/CUIZS75P"},"agent_actions":{"view_html":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V","download_json":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V.json","view_paper":"https://pith.science/paper/CUIZS75P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.09168&json=true","fetch_graph":"https://pith.science/api/pith-number/CUIZS75PZDTRY5MIONRK74364V/graph.json","fetch_events":"https://pith.science/api/pith-number/CUIZS75PZDTRY5MIONRK74364V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V/action/storage_attestation","attest_author":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V/action/author_attestation","sign_citation":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V/action/citation_signature","submit_replication":"https://pith.science/pith/CUIZS75PZDTRY5MIONRK74364V/action/replication_record"}},"created_at":"2026-07-05T04:10:40.178384+00:00","updated_at":"2026-07-05T04:10:40.178384+00:00"}