Описание промпта

Framework of M = 2 Co-teaching Training for Noisy Time Series Forecasting The framework follows a left-to-right pipeline with two parallel model branches and consists of four sequential stages: Input, Parallel Prediction, Sample Selection, and Cross Update. Input Module The input consists of sliding-window time series segments with window length 𝐿 L and prediction horizon 𝐻 H. Noise is injected only into the prediction targets, while the input sequences remain clean. The same input windows are fed simultaneously into two parallel models. Parallel Model Branches Two models, 𝑓 𝜃 1​ and 𝑓 𝜃 2 , are instantiated with identical architectures but independent parameters. Each model processes the same input windows in parallel and produces its own prediction.Prediction and Window-level Loss Each model outputs a prediction 𝑌 ^ ( 1 ) or 𝑌 ^ ( 2 ) A window-level loss is computed for each input window by aggregating the prediction errors over the forecasting horizon, using losses such as MSE or Huber.This window-level loss serves as a reliability indicator for noisy supervision. Small-loss Sample Selection For each model, samples are ranked according to their window-level loss.A subset of samples with the smallest losses (top 𝑟% r%) is selected, based on the assumption that lower-loss samples are more likely to be correctly supervised Cross Sample Exchange and Update Instead of updating each model using its own selected samples, the selected samples are exchanged between the two models Model 𝑓 𝜃 1 is updated using the small-loss samples selected by 𝑓 𝜃 2 and vice versa.This cross-update mechanism prevents self-confirmation on noisy samples and enables mutual error correction between the models. Iterative Training The prediction, selection, and cross-update process is repeated iteratively over training epochs.Through this iterative co-teaching procedure, the models progressively focus on reliable samples while suppressing the influence of noisy supervision