Quadratic quantum speedup for perceptron training
Bibliographic record
Abstract
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size $N$ and margin $\ensuremath{\gamma}$ (how well the given data are separated), the query complexity of the best-known quantum training algorithm scales as either $(\sqrt{N}/{\ensuremath{\gamma}}^{2})log(1/{\ensuremath{\gamma}}^{2})$ or $N/\sqrt{\ensuremath{\gamma}}$, which is achieved by a hybrid of classical and quantum search. In this paper, we improve the version space quantum training method for perceptrons such that the query complexity of our algorithm scales as $\sqrt{N/\ensuremath{\gamma}}$. This is achieved by constructing an oracle for the perceptrons using quantum counting of the number of data elements that are correctly classified. Once such an oracle is constructed, bounded-error quantum search can be used to search over the hyperplane instances. The optimality of our algorithm is proven by reducing the evaluation of a two-level and-or tree (for which the query complexity lower bound is known) to a multicriterion search. Our quantum training algorithm can be generalized to train more complex machine learning models such as neural networks, which are built on a large number of perceptrons.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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".