{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FTHYL7WAQJW6IZ5DMVGS34Z3XJ","short_pith_number":"pith:FTHYL7WA","canonical_record":{"source":{"id":"2404.04549","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-04-06T08:17:07Z","cross_cats_sorted":["cs.LG","math.FA","stat.ML"],"title_canon_sha256":"66d2a21387f562e508a863eac7420926cfdc9a1ae325c55098902e24f002024a","abstract_canon_sha256":"9b3179c1ac6c2e6fdd17996c55db94eaf16d747a7d738ff6c478a5b1230d148b"},"schema_version":"1.0"},"canonical_sha256":"2ccf85fec0826de467a3654d2df33bba4c8dcc6f915859708d19396cbfa9171f","source":{"kind":"arxiv","id":"2404.04549","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04549","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04549v3","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04549","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"FTHYL7WAQJW6","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_16","alias_value":"FTHYL7WAQJW6IZ5D","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_8","alias_value":"FTHYL7WA","created_at":"2026-07-05T11:24:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FTHYL7WAQJW6IZ5DMVGS34Z3XJ","target":"record","payload":{"canonical_record":{"source":{"id":"2404.04549","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-04-06T08:17:07Z","cross_cats_sorted":["cs.LG","math.FA","stat.ML"],"title_canon_sha256":"66d2a21387f562e508a863eac7420926cfdc9a1ae325c55098902e24f002024a","abstract_canon_sha256":"9b3179c1ac6c2e6fdd17996c55db94eaf16d747a7d738ff6c478a5b1230d148b"},"schema_version":"1.0"},"canonical_sha256":"2ccf85fec0826de467a3654d2df33bba4c8dcc6f915859708d19396cbfa9171f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:24:03.315384Z","signature_b64":"t/bGCAGVRkZRlwuCqJ/l/NmXWCK4JbFpB9sAAf3rBXjCachWcN97bCkOYGcPKzyB2Tb1wXmnBKeVE7Xbeon8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ccf85fec0826de467a3654d2df33bba4c8dcc6f915859708d19396cbfa9171f","last_reissued_at":"2026-07-05T11:24:03.314925Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:24:03.314925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.04549","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ok3+/aOdSQqzZCtjqssFORUM4sy3fo5jOxqN5Y1sIWnDphtS9d2F2gFftiQIYrcBaNsjB8jbq/Q7vmZvgGnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T21:14:17.500697Z"},"content_sha256":"634fff71fef1e08182d29e215e6e55dee4c9c07fb3cf16c311d64ba1ea68fe8d","schema_version":"1.0","event_id":"sha256:634fff71fef1e08182d29e215e6e55dee4c9c07fb3cf16c311d64ba1ea68fe8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FTHYL7WAQJW6IZ5DMVGS34Z3XJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.FA","stat.ML"],"primary_cat":"cs.NE","authors_text":"A. Martina Neuman, Dominik Dold, Philipp Christian Petersen","submitted_at":"2024-04-06T08:17:07Z","abstract_excerpt":"We study the learning problem associated with spiking neural networks. Specifically, we focus on spiking neural networks composed of simple spiking neurons having only positive synaptic weights, equipped with an affine encoder and decoder; we refer to these as affine spiking neural networks. These neural networks are shown to depend continuously on their parameters, which facilitates classical covering number-based generalization statements and supports stable gradient-based training. We demonstrate that the positivity of the weights enables a wide range of expressivity results, including rate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04549","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/2404.04549/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"laXNqaNwIFi5zzg/UEM8+sbytfC7XQPnExZEqqFeBhyC2k7lBIS9S0K211Tx6jZOVgBJdLSQVB1uzf/3suqAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T21:14:17.501642Z"},"content_sha256":"c9cee76fc1f55575f8e9e4c00230a8e581f346226402c52c5af3682d44071461","schema_version":"1.0","event_id":"sha256:c9cee76fc1f55575f8e9e4c00230a8e581f346226402c52c5af3682d44071461"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/bundle.json","state_url":"https://pith.science/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T21:14:17Z","links":{"resolver":"https://pith.science/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ","bundle":"https://pith.science/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/bundle.json","state":"https://pith.science/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FTHYL7WAQJW6IZ5DMVGS34Z3XJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FTHYL7WAQJW6IZ5DMVGS34Z3XJ","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":"9b3179c1ac6c2e6fdd17996c55db94eaf16d747a7d738ff6c478a5b1230d148b","cross_cats_sorted":["cs.LG","math.FA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-04-06T08:17:07Z","title_canon_sha256":"66d2a21387f562e508a863eac7420926cfdc9a1ae325c55098902e24f002024a"},"schema_version":"1.0","source":{"id":"2404.04549","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.04549","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"2404.04549v3","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04549","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"FTHYL7WAQJW6","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_16","alias_value":"FTHYL7WAQJW6IZ5D","created_at":"2026-07-05T11:24:03Z"},{"alias_kind":"pith_short_8","alias_value":"FTHYL7WA","created_at":"2026-07-05T11:24:03Z"}],"graph_snapshots":[{"event_id":"sha256:c9cee76fc1f55575f8e9e4c00230a8e581f346226402c52c5af3682d44071461","target":"graph","created_at":"2026-07-05T11:24:03Z","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/2404.04549/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the learning problem associated with spiking neural networks. Specifically, we focus on spiking neural networks composed of simple spiking neurons having only positive synaptic weights, equipped with an affine encoder and decoder; we refer to these as affine spiking neural networks. These neural networks are shown to depend continuously on their parameters, which facilitates classical covering number-based generalization statements and supports stable gradient-based training. We demonstrate that the positivity of the weights enables a wide range of expressivity results, including rate","authors_text":"A. Martina Neuman, Dominik Dold, Philipp Christian Petersen","cross_cats":["cs.LG","math.FA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-04-06T08:17:07Z","title":"Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04549","kind":"arxiv","version":3},"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":"sha256:634fff71fef1e08182d29e215e6e55dee4c9c07fb3cf16c311d64ba1ea68fe8d","target":"record","created_at":"2026-07-05T11:24:03Z","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":"9b3179c1ac6c2e6fdd17996c55db94eaf16d747a7d738ff6c478a5b1230d148b","cross_cats_sorted":["cs.LG","math.FA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2024-04-06T08:17:07Z","title_canon_sha256":"66d2a21387f562e508a863eac7420926cfdc9a1ae325c55098902e24f002024a"},"schema_version":"1.0","source":{"id":"2404.04549","kind":"arxiv","version":3}},"canonical_sha256":"2ccf85fec0826de467a3654d2df33bba4c8dcc6f915859708d19396cbfa9171f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ccf85fec0826de467a3654d2df33bba4c8dcc6f915859708d19396cbfa9171f","first_computed_at":"2026-07-05T11:24:03.314925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:03.314925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t/bGCAGVRkZRlwuCqJ/l/NmXWCK4JbFpB9sAAf3rBXjCachWcN97bCkOYGcPKzyB2Tb1wXmnBKeVE7Xbeon8Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:03.315384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.04549","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:634fff71fef1e08182d29e215e6e55dee4c9c07fb3cf16c311d64ba1ea68fe8d","sha256:c9cee76fc1f55575f8e9e4c00230a8e581f346226402c52c5af3682d44071461"],"state_sha256":"649d505bfe578109f3afc1c40b63e24038fd126a1b328924abeb27011cdc474f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xylCBYcdBo4udrksgRAanRQTmHnS+DM7yvKOjD5KNDi0Os5/FW7J94+E1k3vntEZYGGNrwHGq/tVV0yT9FQrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T21:14:17.559276Z","bundle_sha256":"cd1b8ffde2008f318a168507828742838430c6ca3649bd1b5a4d34bac6f02726"}}