A New Timing Error Cost Function for Binary Time Series Prediction
Bibliographic record
Abstract
The ability to make predictions is central to the artificial intelligence problem. While machine learning algorithms have difficulty in learning to predict events with hundreds of time-step dependencies, animals can learn event timing within tens of trials across a broad spectrum of time scales. This suggests strongly a need for new perspectives on the forecasting problem. This paper focuses on binary time series that can be predicted within some temporal precision. We demonstrate that the sum of squared errors (SSE) calculated at every time step is not appropriate for this problem. Next, we look at the advantages and shortcomings of using a dynamic time warping (DTW) cost function. Then, we propose the squared timing error (STE) that uses DTW on the event space and applies SSE on the timing error instead of at each time step. We evaluate all three cost functions on different types of timing errors, such as phase shift, warping, and missing events, on synthetic and real-world binary time series (heartbeats, finance, and music). The results show that STE provides more information about timing error, is differentiable, and can be computed online efficiently. Finally, we devise a gradient descent algorithm for STE on a simplified recurrent neural network. We then compare the performance of the STE-based algorithm to SSE- and logit-based gradient descent algorithms on the same network architecture. The results in real-world binary time series show that the STE algorithm generally outperforms all the other cost functions considered.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".