diff --git a/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py b/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
index 4146ec4b4..83ce90a92 100644
--- a/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
+++ b/egs/librispeech/ASR/pruned_transducer_stateless7/optim.py
@@ -166,7 +166,7 @@ param_rms_smooth1: Smoothing proportion for parameter matrix, if assumed rank of
             lr=3e-02,
             betas=(0.9, 0.98),
             size_lr_scale=0.1,
-            cov_min=(0.025, 0.0025, 0.02, 0.0001, 0.1),
+            cov_min=(0.025, 0.0025, 0.02, 0.0001, 0.025),
             cov_max=(10.0, 80.0, 5.0, 400.0, 100.0),
             cov_pow=(1.0, 1.0, 1.0, 1.0),
             param_rms_smooth0=0.4,
@@ -969,30 +969,24 @@ param_rms_smooth1: Smoothing proportion for parameter matrix, if assumed rank of
                 _check_similar(G_prime, G_prime_check, "G_prime")
 
 
-            Z_prime_inv_diag = _diag(Z_prime_inv)  # aliased with Z_prime_inv
+            Z_inv = torch.matmul(U_g, torch.matmul(Z_prime_inv, U_g.transpose(2, 3)))
+            Z_inv = 0.5 * (Z_inv + Z_inv.transpose(2, 3))  # make sure exactly symmetric
+
+            Z_inv_diag = _diag(Z_inv)  # aliased with Z_inv
             # this is smoothing Z relative to its own diagonal.  This is z_inv,
             # so by applying a minimum here, we are applying a maximum of the
             # eigs of Z after normalizing so the diagonal is 1.
-            Z_prime_inv_diag *= (1. + group["cov_min"][4])
+            Z_inv_diag *= (1. + group["cov_min"][4])
 
             # We really want the SVD on Z, which will be used for the learning-rate matrix
             # Q, but Z_prime is better, numerically, to work on because it's closer to
             # being diagonalized.
-            U_z_prime, S_z_prime_inv, _ = _svd(Z_prime_inv)
+            U_z, S_z_inv, _ = _svd(Z_inv)
 
 
-            U_z = torch.matmul(U_g, U_z_prime)
-            # We could obtain Z in two possible ways.
-            # Commenting the check below.
-            # Z_a = torch.matmul(U_z * S.unsqueeze(-2), U_z.transpose(2, 3))
-            # Z_b = torch.matmul(U_g, torch.matmul(Z_prime, U_g.transpose(2, 3)))
-            # _check_similar(Z_a, Z_b, "Z")
-            ## OK, Z is the SPD transform that maps G to P, as in Z G Z = P.
-            ## We just need the basis U_z that diagonalizes this.
-            ## U_z, S, _ = _svd(Z)
             if True:
                 skip = 10 if S.shape[-1] > 40 else 1
-                logging.info(f"dim={dim}, G_prime is {G_prime[0,0,::skip]}, Eigs of Z_inv are: {S_z_prime_inv[0,0,::skip]}")
+                logging.info(f"dim={dim}, G_prime is {G_prime[0,0,::skip]}, Eigs of Z_inv are: {S_z_inv[0,0,::skip]}")
 
             # state[f"Q_{dim}"] is indexed: [batch_idx, block_idx, diagonalized_coordinate, canonical_coordinate].
             # so we need to transpose U_z as U_z is indexed