diff --git a/lmdeploy/pytorch/kernels/cuda/alibi_pagedattention.py b/lmdeploy/pytorch/kernels/cuda/alibi_pagedattention.py
index 1e54b5c13..66a844203 100644
--- a/lmdeploy/pytorch/kernels/cuda/alibi_pagedattention.py
+++ b/lmdeploy/pytorch/kernels/cuda/alibi_pagedattention.py
@@ -12,7 +12,7 @@
 
 assert triton.__version__ >= '2.1.0'
 
-LOG2 = math.log(2)
+LOG2: tl.constexpr = math.log(2)
 
 
 @triton.jit
diff --git a/lmdeploy/pytorch/kernels/cuda/pagedattention.py b/lmdeploy/pytorch/kernels/cuda/pagedattention.py
index d8e6ec501..7790a44b1 100644
--- a/lmdeploy/pytorch/kernels/cuda/pagedattention.py
+++ b/lmdeploy/pytorch/kernels/cuda/pagedattention.py
@@ -621,6 +621,7 @@ def convert_pv(p, v):
 
 
 _convert_pv = None
+_nv_cap = None
 
 
 # TODO: how to support inplace autotune?
@@ -1099,9 +1100,10 @@ def paged_attention_fwd(
         max_seqlen (int): The max input length.
         BLOCK (int): The kernel block size.
     """
-    global _convert_pv
+    global _convert_pv, _nv_cap
     if _convert_pv is None:
         nv_cap = torch.cuda.get_device_capability()
+        _nv_cap = nv_cap
         _convert_pv = _get_convert_pv(nv_cap)
 
     if kv_layout == 'bshd':
@@ -1150,7 +1152,10 @@ def _get_block_d(Lk):
     is_decoding = q.shape[-3] == q_seqlens.size(0)
     if not is_decoding:
         BLOCK_DMODEL, BLOCK_DMODEL1, BLOCK_DV = _get_block_d(Lq)
-        BLOCK_M = max(16, min(BLOCK, 16384 // BLOCK_DMODEL))
+        if _nv_cap[0] < 8:
+            BLOCK_M = max(16, min(BLOCK, 8192 // BLOCK_DMODEL))
+        else:
+            BLOCK_M = max(16, min(BLOCK, 16384 // BLOCK_DMODEL))
         num_warps = 4
         num_stages = 2
         kv_head = k.shape[h_dim]