{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FYDRKS3C6XC7LDZZUJFDBEH2W7","short_pith_number":"pith:FYDRKS3C","canonical_record":{"source":{"id":"1810.09274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-22T13:39:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2cc3b9584a984b672585d049a5d2159319a4f813f714be2387b7a8840158eaad","abstract_canon_sha256":"28847d9ca4803a69ac83f078c0d70046d3abfe71eaf6e01b006bbe46441f3a1b"},"schema_version":"1.0"},"canonical_sha256":"2e07154b62f5c5f58f39a24a3090fab7cc7fa7f723dd0fd4c27cc185d8f2e7fa","source":{"kind":"arxiv","id":"1810.09274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09274","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09274v1","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09274","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"FYDRKS3C6XC7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FYDRKS3C6XC7LDZZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FYDRKS3C","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FYDRKS3C6XC7LDZZUJFDBEH2W7","target":"record","payload":{"canonical_record":{"source":{"id":"1810.09274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-22T13:39:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"2cc3b9584a984b672585d049a5d2159319a4f813f714be2387b7a8840158eaad","abstract_canon_sha256":"28847d9ca4803a69ac83f078c0d70046d3abfe71eaf6e01b006bbe46441f3a1b"},"schema_version":"1.0"},"canonical_sha256":"2e07154b62f5c5f58f39a24a3090fab7cc7fa7f723dd0fd4c27cc185d8f2e7fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:40.636734Z","signature_b64":"xwcj3Xk3Ob8EwmXyRerXbugUyfHmZNnHE51Vl8fT7yT4NkMt4vNSLhA1X8v1sJSxqMUsqXQfLyZSX1BwUHmDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e07154b62f5c5f58f39a24a3090fab7cc7fa7f723dd0fd4c27cc185d8f2e7fa","last_reissued_at":"2026-05-18T00:02:40.636134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:40.636134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.09274","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8uV/QPKzc4bRMelMJ22voZPIp8dTcE1Kh5E/VAWVJm3QwRh/AmKQzQzGEu5B6qhfd9JqIHLY/hEYOGgBr7PbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:30:07.462818Z"},"content_sha256":"711a5facf04200f2658fd311308ef04e65cf40841798a3feeb4dba0d570a57cc","schema_version":"1.0","event_id":"sha256:711a5facf04200f2658fd311308ef04e65cf40841798a3feeb4dba0d570a57cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FYDRKS3C6XC7LDZZUJFDBEH2W7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Hard to Soft: Understanding Deep Network Nonlinearities via Vector Quantization and Statistical Inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Randall Balestriero, Richard G. Baraniuk","submitted_at":"2018-10-22T13:39:44Z","abstract_excerpt":"Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the r\\^ole played by piecewise affine and convex nonlinearities like the ReLU and absolute value activation functions and max-pooling. In particular, DN layers constructed from these operations can be interpreted as {\\em max-affine spline operators} (MASOs) that have an elegant link to vector quantization (VQ) and $K$-means. While this is good theoretical progress, the ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09274","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JkhlgjfOjwnIZaWuhCQhMYRLtl1W7KcBZUcH72dytH2OHCdRkJdoyYOhzh0T4QzbOVEXKKSnu/uvLA/hg1Z7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:30:07.463268Z"},"content_sha256":"32ba8f0783ceda419aefaf9b7ad3fb0e8e44c0028dba37e9783e98e6aad424d0","schema_version":"1.0","event_id":"sha256:32ba8f0783ceda419aefaf9b7ad3fb0e8e44c0028dba37e9783e98e6aad424d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/bundle.json","state_url":"https://pith.science/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/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":"2026-05-31T15:30:07Z","links":{"resolver":"https://pith.science/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7","bundle":"https://pith.science/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/bundle.json","state":"https://pith.science/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FYDRKS3C6XC7LDZZUJFDBEH2W7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FYDRKS3C6XC7LDZZUJFDBEH2W7","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":"28847d9ca4803a69ac83f078c0d70046d3abfe71eaf6e01b006bbe46441f3a1b","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-22T13:39:44Z","title_canon_sha256":"2cc3b9584a984b672585d049a5d2159319a4f813f714be2387b7a8840158eaad"},"schema_version":"1.0","source":{"id":"1810.09274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09274","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09274v1","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09274","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"FYDRKS3C6XC7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FYDRKS3C6XC7LDZZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FYDRKS3C","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:32ba8f0783ceda419aefaf9b7ad3fb0e8e44c0028dba37e9783e98e6aad424d0","target":"graph","created_at":"2026-05-18T00:02:40Z","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"},"paper":{"abstract_excerpt":"Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the r\\^ole played by piecewise affine and convex nonlinearities like the ReLU and absolute value activation functions and max-pooling. In particular, DN layers constructed from these operations can be interpreted as {\\em max-affine spline operators} (MASOs) that have an elegant link to vector quantization (VQ) and $K$-means. While this is good theoretical progress, the ent","authors_text":"Randall Balestriero, Richard G. Baraniuk","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-22T13:39:44Z","title":"From Hard to Soft: Understanding Deep Network Nonlinearities via Vector Quantization and Statistical Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09274","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":"sha256:711a5facf04200f2658fd311308ef04e65cf40841798a3feeb4dba0d570a57cc","target":"record","created_at":"2026-05-18T00:02:40Z","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":"28847d9ca4803a69ac83f078c0d70046d3abfe71eaf6e01b006bbe46441f3a1b","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-22T13:39:44Z","title_canon_sha256":"2cc3b9584a984b672585d049a5d2159319a4f813f714be2387b7a8840158eaad"},"schema_version":"1.0","source":{"id":"1810.09274","kind":"arxiv","version":1}},"canonical_sha256":"2e07154b62f5c5f58f39a24a3090fab7cc7fa7f723dd0fd4c27cc185d8f2e7fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e07154b62f5c5f58f39a24a3090fab7cc7fa7f723dd0fd4c27cc185d8f2e7fa","first_computed_at":"2026-05-18T00:02:40.636134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:40.636134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xwcj3Xk3Ob8EwmXyRerXbugUyfHmZNnHE51Vl8fT7yT4NkMt4vNSLhA1X8v1sJSxqMUsqXQfLyZSX1BwUHmDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:40.636734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:711a5facf04200f2658fd311308ef04e65cf40841798a3feeb4dba0d570a57cc","sha256:32ba8f0783ceda419aefaf9b7ad3fb0e8e44c0028dba37e9783e98e6aad424d0"],"state_sha256":"60301f35bd79249fcb6bebb27ad8b624a7cc4c9325b31baa95aab89e2fb44001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ofmXvAg6rvZEK0Zte0WezLPcsxm7oXKGngEoqB1UzjXnYfAxa4wBBQkVIyW40NCw18q7wEa2x2D3JYpzkbUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:30:07.467493Z","bundle_sha256":"264b6d4af7c7075fd366486d6c8b33a5f74f401e6d5ff33a23aa17a1c393eaca"}}