[Update] Eliminate numpy usage and update learning rate application from EXAdam (#438)

Removed numpy dependency and adjusted step size calculation based on the latest update of the EXAdam paper https://arxiv.org/abs/2412.20302

Author: AhmedMostafa16

pytorch_optimizer/optimizer/exadam.py

@@ -1,4 +1,3 @@
-import numpy as np
 import torch
 
 from pytorch_optimizer.base.exception import NoSparseGradientError
@@ -38,8 +37,6 @@ def __init__(
 
         self.maximize = maximize
 
-        self.sq2: float = np.sqrt(2)
-
         defaults: DEFAULTS = {
             'lr': lr,
             'betas': betas,
@@ -88,8 +85,6 @@ def step(self, closure: CLOSURE = None) -> LOSS:
             bias_correction1: float = self.debias(beta1, group['step'])
             bias_correction2: float = self.debias(beta2, group['step'])
 
-            step_size: float = group['lr'] * np.log(np.sqrt(group['step'] + 1) * self.sq2)
-
             for p in group['params']:
                 if p.grad is None:
                     continue
@@ -128,6 +123,6 @@ def step(self, closure: CLOSURE = None) -> LOSS:
 
                 update = (m_tilde + g_tilde) / v_tilde.sqrt().add_(group['eps'])
 
-                p.add_(update, alpha=-step_size)
+                p.add_(update, alpha=-group['lr'])
 
         return loss