{"paper":{"title":"Communication Dynamics Neural Networks: FFT-Diagonalized Layers for Improved Hessian Conditioning at Reduced Parameter Count","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Block-circulant layers with FFT diagonalization make the population Hessian exactly the identity under pre-whitening while using one-Bth the parameters of a dense layer.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Lurong Pan","submitted_at":"2026-05-04T23:43:09Z","abstract_excerpt":"Communication Dynamics Neural Networks (CDNNs) apply the circulant-spectral machinery of the Communication Dynamics framework to neural-network layer design. We introduce CDLinear, a block-circulant linear layer with block size B = 2l + 1 that uses 1/B the parameters of a dense layer with the same input and output dimensions. The construction gives an explicit Fourier-domain diagnostic for optimization: for mean-squared loss, the weight Hessian is diagonalized by the discrete Fourier transform, with eigenvalues determined directly by the Fourier spectrum of the input blocks. Under input pre-wh"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under input pre-whitening, the population Hessian condition number satisfies kappa = 1 exactly, with the empirical condition number bounded by 1+O(sqrt(B/N)) on N samples (Theorem 2). A CDLinear MLP at B = 4 achieves 97.50% +/- 0.23% test accuracy with 2,380 parameters versus 98.15% +/- 0.47% for a parameter-matched dense MLP at 8,970 parameters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the block-circulant restriction with block size B = 2l+1 preserves sufficient expressivity for the target task and that input pre-whitening can be performed without destroying the data distribution or introducing new instabilities.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CDLinear layers achieve population Hessian condition number exactly 1 under pre-whitening, deliver 3.8x parameter reduction versus dense layers at 0.65% accuracy cost, and show 310x better empirical conditioning on an MLP.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Block-circulant layers with FFT diagonalization make the population Hessian exactly the identity under pre-whitening while using one-Bth the parameters of a dense layer.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f48bf37ce82d213879d2d85f7076cd8a7ae478e601f66dfffbad7048c51ac426"},"source":{"id":"2605.08171","kind":"arxiv","version":2},"verdict":{"id":"8d6dafeb-35ab-455a-babc-bcf2481d61ad","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T01:26:28.750361Z","strongest_claim":"Under input pre-whitening, the population Hessian condition number satisfies kappa = 1 exactly, with the empirical condition number bounded by 1+O(sqrt(B/N)) on N samples (Theorem 2). A CDLinear MLP at B = 4 achieves 97.50% +/- 0.23% test accuracy with 2,380 parameters versus 98.15% +/- 0.47% for a parameter-matched dense MLP at 8,970 parameters.","one_line_summary":"CDLinear layers achieve population Hessian condition number exactly 1 under pre-whitening, deliver 3.8x parameter reduction versus dense layers at 0.65% accuracy cost, and show 310x better empirical conditioning on an MLP.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the block-circulant restriction with block size B = 2l+1 preserves sufficient expressivity for the target task and that input pre-whitening can be performed without destroying the data distribution or introducing new instabilities.","pith_extraction_headline":"Block-circulant layers with FFT diagonalization make the population Hessian exactly the identity under pre-whitening while using one-Bth the parameters of a dense layer."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.08171/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T14:35:20.618513Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T01:31:21.799294Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:34:04.388591Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"dfb2928701ec0810a0b468560b6ad56dbd2344904a922df402e1a6926cf2822e"},"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"}