{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7OL5UVXNNSCS6324H2UJ3VG2ON","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e1707bbe5ed656cf731ae44bab3d76f0f4ec3cacfb8e7400084a6fef8fc94d90","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-18T15:24:47Z","title_canon_sha256":"a8d3f939a4f0cf92251bf7e763f6eac16441bb87e2e43ddaedff1bc4452e17ab"},"schema_version":"1.0","source":{"id":"2403.11871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.11871","created_at":"2026-07-05T07:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"2403.11871v1","created_at":"2026-07-05T07:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.11871","created_at":"2026-07-05T07:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"7OL5UVXNNSCS","created_at":"2026-07-05T07:57:33Z"},{"alias_kind":"pith_short_16","alias_value":"7OL5UVXNNSCS6324","created_at":"2026-07-05T07:57:33Z"},{"alias_kind":"pith_short_8","alias_value":"7OL5UVXN","created_at":"2026-07-05T07:57:33Z"}],"graph_snapshots":[{"event_id":"sha256:6ea53d81f9721613accfe215eb2c9535229ab7e021d192e323e83412c0be3982","target":"graph","created_at":"2026-07-05T07:57:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.11871/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReLU neural networks is contained as a semialgebraic set inside the parameter space of tropical rational functions. We initiate the study of two different subdivisions of this parameter space: a subdivision into semialgebraic sets, on which the combinatorial type of the decision boundary is fixed, and a subdivision into a polyhedral fan, capturing the combinatorics of the partitions of the dataset. The sublevel sets of ","authors_text":"Georg Loho, Guido Mont\\'ufar, Marie-Charlotte Brandenburg","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-18T15:24:47Z","title":"The Real Tropical Geometry of Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11871","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:982b4048be84c7e222edaab6d6e15df4ab63469d01bc2bd7f22c3a11bdf43514","target":"record","created_at":"2026-07-05T07:57:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e1707bbe5ed656cf731ae44bab3d76f0f4ec3cacfb8e7400084a6fef8fc94d90","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-03-18T15:24:47Z","title_canon_sha256":"a8d3f939a4f0cf92251bf7e763f6eac16441bb87e2e43ddaedff1bc4452e17ab"},"schema_version":"1.0","source":{"id":"2403.11871","kind":"arxiv","version":1}},"canonical_sha256":"fb97da56ed6c852f6f5c3ea89dd4da736c5d67c47ebaffab7db858cf9cf0fd7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb97da56ed6c852f6f5c3ea89dd4da736c5d67c47ebaffab7db858cf9cf0fd7a","first_computed_at":"2026-07-05T07:57:33.019808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:57:33.019808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFacZPK79PpcE5K+SOyq7hPo62UtUrFd6dyNqUiHUDtpzF0BwZ5KPkHS/q7OqfhE5GqTbzgyevjwkADCF+sgCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:57:33.020307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.11871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:982b4048be84c7e222edaab6d6e15df4ab63469d01bc2bd7f22c3a11bdf43514","sha256:6ea53d81f9721613accfe215eb2c9535229ab7e021d192e323e83412c0be3982"],"state_sha256":"ac0ebd0cded93985b47a740a80a071796774ec0111f195810f0851bf32dfd737"}