Harmonic Analysis And The Complexity Of Computing With Threshold (Neural) Elements
Bibliographic record
Abstract
The main purpose of this talk is to introduce a \nuseful tool for the analysis of discrete neural networks \nin which every node is a Boolean threshold \ngate. The difficulty in the analysis of neural \nnetworks arises from the fact that the basic \nprocessing elements (linear threshold gates) are \nnonlinear. The key idea in harmonic analysis \nof threshold functions is to represent the functions \nas polynomials over the field of real numbers. \nAnswering different questions regarding \nneural networks becomes equivalent to answering \nquestions related to the coefficients of these \npolynomials. We have applied these techniques \nand obtained many interesting and surprising results \n[1, 2, 3, 4]. The focus of this talk will \nbe on presenting a theorem that characterizes-using \nspetral norms-the complexity of computing \na Boolean function with threshold circuits \n[2, 3]. This result establishes the first known link \nbetween harmonic analysis and the complexity of \ncomputing with neural networks.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".