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. 2025 Aug 25;15:31215. doi: 10.1038/s41598-025-14358-5

Table 2.

Summary of notations.

Notation Description
Inline graphic Final predicted output for the ith input sample
Inline graphic The ith input data sample
Inline graphic Predicted class label by the nth model or client for input Inline graphic
graphic file with name 41598_2025_14358_IEq1_HTML.gif Summation overall N models or clients
Inline graphic Averaging factor to compute the mean prediction from all contributors
Inline graphic Total number of models or clients
Inline graphic Statistical mode function that returns the most frequent class label
Inline graphic Total loss function with parameters Inline graphic
Inline graphic Total number of data samples
Inline graphic Loss between ground truth Inline graphic and predicted output Inline graphic
graphic file with name 41598_2025_14358_IEq2_HTML.gif Summation overall n training samples
graphic file with name 41598_2025_14358_IEq3_HTML.gif Summation over all K model components
Inline graphic Regularization term for the kth model component
Inline graphic Model parameters of the kth component
Inline graphic Overall set of model parameters
Inline graphic Bias or constant term related to iteration T
Inline graphic Regularization coefficient
Inline graphic Total number of training iterations or time steps
Inline graphic Model weight parameter at step j
Inline graphic Sum of squared weights
Inline graphic L2 regularization term
Inline graphic Output of the kth model when applied to input Inline graphic
Inline graphic Total number of models contributing to the aggregation
graphic file with name 41598_2025_14358_IEq4_HTML.gif Summation over all K models
Inline graphic An estimated value at index k
graphic file with name 41598_2025_14358_IEq5_HTML.gif Summation from j = 0 to j = n, so summing up n + 1 terms
Inline graphic Classifier
Inline graphic Weight assigned to jth classifier