update lbfgs to avoid the randomness caused by paddle.dot() temporari…

…ly (#60591)

* update lbfgs to avoid the randomness caused by paddle.dot() temporarily

* add note

python/paddle/optimizer/lbfgs.py

@@ -23,6 +23,14 @@
 __all__ = []
 
 
+def dot(x, y):
+    r"""
+    NOTE: This is a temporary workaround for unstable result computed by `paddle.dot`,
+    which will be reverted when the problem is fixed."
+    """
+    return (x * y).sum(axis=-1)
+
+
 def _cubic_interpolate(x1, f1, g1, x2, f2, g2, bounds=None):
     r"""Cubic interpolation between (x1, f1, g1) and (x2, f2, g2).
         Use two points and their gradient to determine a cubic function and get the minimum point
@@ -152,7 +160,7 @@ def _strong_wolfe(
     # evaluate objective and gradient using initial step
     loss_new, grad_new = obj_func(xk, alpha, d)
     ls_func_evals = 1
-    gtd_new = paddle.dot(grad_new, d)
+    gtd_new = dot(grad_new, d)
 
     # bracket an interval containing a point satisfying the Wolfe criteria
     t_prev, f_prev, g_prev, gtd_prev = (0, loss, grad, gtd)
@@ -205,7 +213,7 @@ def _strong_wolfe(
 
         loss_new, grad_new = obj_func(xk, alpha, d)
         ls_func_evals += 1
-        gtd_new = grad_new.dot(d)
+        gtd_new = dot(grad_new, d)
         ls_iter += 1
 
     # reached max number of iterations?
@@ -265,7 +273,7 @@ def _strong_wolfe(
         # Evaluate new point
         loss_new, grad_new = obj_func(xk, alpha, d)
         ls_func_evals += 1
-        gtd_new = grad_new.dot(d)
+        gtd_new = dot(grad_new, d)
         ls_iter += 1
 
         if (
@@ -644,7 +652,7 @@ def step(self, closure):
                     # do lbfgs update (update memory)
                     y = flat_grad.subtract(prev_flat_grad)
                     s = d.multiply(paddle.to_tensor(alpha, dtype=d.dtype))
-                    ys = y.dot(s)
+                    ys = dot(y, s)
                     if ys > 1e-10:
                         # updating memory
                         if len(old_yk) == history_size:
@@ -659,7 +667,7 @@ def step(self, closure):
                         ro.append(1.0 / ys)
 
                         # update scale of initial Hessian approximation
-                        H_diag = ys / y.dot(y)  # (y*y)
+                        H_diag = ys / dot(y, y)  # (y*y)
 
                     # compute the approximate (L-BFGS) inverse Hessian
                     # multiplied by the gradient
@@ -672,14 +680,14 @@ def step(self, closure):
                     # iteration in L-BFGS loop collapsed to use just one buffer
                     q = flat_grad.neg()
                     for i in range(num_old - 1, -1, -1):
-                        al[i] = old_sk[i].dot(q) * ro[i]
+                        al[i] = dot(old_sk[i], q) * ro[i]
                         paddle.assign(q.add(old_yk[i] * (-al[i])), q)
 
                     # multiply by initial Hessian
                     # r/d is the final direction
                     d = r = paddle.multiply(q, H_diag)
                     for i in range(num_old):
-                        be_i = old_yk[i].dot(r) * ro[i]
+                        be_i = dot(old_yk[i], r) * ro[i]
                         paddle.assign(r.add(old_sk[i] * (al[i] - be_i)), r)
 
                 if prev_flat_grad is None:
@@ -700,7 +708,7 @@ def step(self, closure):
                     alpha = learning_rate
 
                 # directional derivative
-                gtd = flat_grad.dot(d)
+                gtd = dot(flat_grad, d)
 
                 # directional derivative is below tolerance
                 if gtd > -tolerance_change: