Perform one Nadam update without bias correction. Update the moments:
mt=β1mt−1+(1−β1)gt vt=β2vt−1+(1−β2)gt2Form the Nesterov-adjusted first moment:
mt=β1mt+(1−β1)gtThen update the parameters:
wt=wt−1−ηvt+εmtHere, w contains parameters, g contains gradients, m and v are moment arrays, and η is lr. Return new_w, new_m, and new_v in a dictionary of NumPy arrays.
Input: w = [1.0, -1.0], m = [0.1, -0.1], v = [0.01, 0.01], grad = [0.2, -0.3], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.997624, -0.997251], "new_m": [0.11, -0.12], "new_v": [0.01003, 0.01008]}
Explanation: The updated first moment is combined with the current gradient before adaptive scaling.
Input: w = [1.0, 2.0], m = [0.1, 0.2], v = [0.01, 0.04], grad = [0.0, 0.0], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.998379, 1.998379], "new_m": [0.09, 0.18], "new_v": [0.00999, 0.03996]}
Input: w = [1.0, 2.0], m = [0.0, 0.0], v = [0.0, 0.0], grad = [0.1, 0.2], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.987983, 1.987983], "new_m": [0.01, 0.02], "new_v": [0.00001, 0.00004]}
Compute the ordinary first and second moments before nesterov_m.
Use beta1 * new_m + (1 - beta1) * grad in the numerator.
Accepts: array
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Perform one Nadam update without bias correction. Update the moments:
mt=β1mt−1+(1−β1)gt vt=β2vt−1+(1−β2)gt2Form the Nesterov-adjusted first moment:
mt=β1mt+(1−β1)gtThen update the parameters:
wt=wt−1−ηvt+εmtHere, w contains parameters, g contains gradients, m and v are moment arrays, and η is lr. Return new_w, new_m, and new_v in a dictionary of NumPy arrays.
Input: w = [1.0, -1.0], m = [0.1, -0.1], v = [0.01, 0.01], grad = [0.2, -0.3], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.997624, -0.997251], "new_m": [0.11, -0.12], "new_v": [0.01003, 0.01008]}
Explanation: The updated first moment is combined with the current gradient before adaptive scaling.
Input: w = [1.0, 2.0], m = [0.1, 0.2], v = [0.01, 0.04], grad = [0.0, 0.0], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.998379, 1.998379], "new_m": [0.09, 0.18], "new_v": [0.00999, 0.03996]}
Input: w = [1.0, 2.0], m = [0.0, 0.0], v = [0.0, 0.0], grad = [0.1, 0.2], lr = 0.002, beta1 = 0.9, beta2 = 0.999, eps = 1e-8
Output: {"new_w": [0.987983, 1.987983], "new_m": [0.01, 0.02], "new_v": [0.00001, 0.00004]}
Compute the ordinary first and second moments before nesterov_m.
Use beta1 * new_m + (1 - beta1) * grad in the numerator.
Accepts: array
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Accepts: number
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