BDN: Blaschke Decomposition Networks
Bibliographic record
Abstract
We introduce the Blaschke Decomposition Network (BDN), a novel neural network architecture for analyzing continuous real-valued or complex-valued 1-D and 2-D signals-data types that existing architectures, such as transformers or recurrent networks, are not designed to model. These signals are common in medicine, biology, and other scientific domains, yet their analytic structure is often underutilized in machine learning. Our approach is based on the Blaschke decomposition, which "unwinds" a signal into a sequence of factors determined by its roots-the points in the complex unit disk where the analytic continuation of the signal vanishes. By iteratively peeling off these factors, the decomposition isolates oscillatory components of the signal and produces a compact representation. BDNs are trained to predict these roots directly, and we show that they provide powerful and interpretable representations for downstream tasks. We first design the architecture for 1-D signals and then extend it to 2-D using a wedge-based factorization, enabling the same framework to handle images and other spatially varying signals. Experiments on sensor-derived biomedical data, including electrocardiograms and phase holographic microscopy, show that BDNs achieve strong predictive performance while using fewer parameters than transformers, convolutional, or recurrent networks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".