{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PMLZWCCQ3UCIKIOPVPACUI7VNO","short_pith_number":"pith:PMLZWCCQ","schema_version":"1.0","canonical_sha256":"7b179b0850dd048521cfabc02a23f56ba17a010bce5e601667ce4d515cc5970e","source":{"kind":"arxiv","id":"2406.07049","version":3},"attestation_state":"computed","paper":{"title":"GridPE: A Grid Cell-Inspired Unified Position Embedding for Arbitrary-Dimensional Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.NE","authors_text":"Boyang Li, Nuoxian Huang, Wenjia Zhang, Yulin Wu","submitted_at":"2024-06-11T08:25:11Z","abstract_excerpt":"Understanding spatial relationships across all dimensions is fundamental for intelligent systems. However, existing positional embeddings, such as Rotary Positional Embedding (RoPE), lack theoretical guarantees for high-dimensional spatiotemporal tasks like video understanding and robotic navigation. Inspired by the hexagonal periodic coding of grid cells in mammalian spatial cognition, we propose GridPE -- a novel positional embedding framework that integrates computational neuroscience principles with harmonic analysis. Our approach builds upon Random Fourier Features and leverages principle"},"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":"2406.07049","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-06-11T08:25:11Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"17c2f40b3c69d4c4ff0858df1625953bdefb3472c2eff09f7d190904a433d115","abstract_canon_sha256":"5ec37d5d755121536dd43d80788d9abde2ae433db7fec93f0ece60a966906ac7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:14:24.285566Z","signature_b64":"RM9ARXyuWJ42CXotTcgMnXgQhIyU19/bBFN6M3A27nTLPmZ4+aTD6Y+TcSinUzRv/FLLahEg05Mp6VPhCib8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b179b0850dd048521cfabc02a23f56ba17a010bce5e601667ce4d515cc5970e","last_reissued_at":"2026-06-05T01:14:24.284708Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:14:24.284708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"GridPE: A Grid Cell-Inspired Unified Position Embedding for Arbitrary-Dimensional Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.NE","authors_text":"Boyang Li, Nuoxian Huang, Wenjia Zhang, Yulin Wu","submitted_at":"2024-06-11T08:25:11Z","abstract_excerpt":"Understanding spatial relationships across all dimensions is fundamental for intelligent systems. However, existing positional embeddings, such as Rotary Positional Embedding (RoPE), lack theoretical guarantees for high-dimensional spatiotemporal tasks like video understanding and robotic navigation. Inspired by the hexagonal periodic coding of grid cells in mammalian spatial cognition, we propose GridPE -- a novel positional embedding framework that integrates computational neuroscience principles with harmonic analysis. Our approach builds upon Random Fourier Features and leverages principle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07049","kind":"arxiv","version":3},"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/2406.07049/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":"2406.07049","created_at":"2026-06-05T01:14:24.284837+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07049v3","created_at":"2026-06-05T01:14:24.284837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07049","created_at":"2026-06-05T01:14:24.284837+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMLZWCCQ3UCI","created_at":"2026-06-05T01:14:24.284837+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMLZWCCQ3UCIKIOP","created_at":"2026-06-05T01:14:24.284837+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMLZWCCQ","created_at":"2026-06-05T01:14:24.284837+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO","json":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO.json","graph_json":"https://pith.science/api/pith-number/PMLZWCCQ3UCIKIOPVPACUI7VNO/graph.json","events_json":"https://pith.science/api/pith-number/PMLZWCCQ3UCIKIOPVPACUI7VNO/events.json","paper":"https://pith.science/paper/PMLZWCCQ"},"agent_actions":{"view_html":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO","download_json":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO.json","view_paper":"https://pith.science/paper/PMLZWCCQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07049&json=true","fetch_graph":"https://pith.science/api/pith-number/PMLZWCCQ3UCIKIOPVPACUI7VNO/graph.json","fetch_events":"https://pith.science/api/pith-number/PMLZWCCQ3UCIKIOPVPACUI7VNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO/action/storage_attestation","attest_author":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO/action/author_attestation","sign_citation":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO/action/citation_signature","submit_replication":"https://pith.science/pith/PMLZWCCQ3UCIKIOPVPACUI7VNO/action/replication_record"}},"created_at":"2026-06-05T01:14:24.284837+00:00","updated_at":"2026-06-05T01:14:24.284837+00:00"}