diff --git a/nanochat/engine.py b/nanochat/engine.py
index d13e2b8..dc43faf 100644
--- a/nanochat/engine.py
+++ b/nanochat/engine.py
@@ -107,17 +107,23 @@ class KVCache:
         # 1) validate the shapes
         assert self.kv_cache is None, "Cannot prefill a non-empty KV cache"
         assert other.kv_cache is not None, "Cannot prefill with a None KV cache"
-        for ix, (dim1, dim2) in enumerate(zip(self.kv_shape, other.kv_shape)):
-            # ix 0: num_layers, 1: k/v, 2: batch_size, 3: num_heads, 4: seq_len, 5: head_dim
-            if ix in [0, 1, 3, 5]:
-                # num_layers, k/v, num_heads, head_dim must match
-                assert dim1 == dim2, f"Dim {ix} mismatch: {dim1} != {dim2}"
-            elif ix == 2:
-                # batch_size can be expanded
-                assert dim1 == dim2 or dim2 == 1, f"Batch dim mismatch: {dim1} != {dim2}"
-            elif ix == 4:
-                # seq_len: self must be longer than other
-                assert dim1 >= dim2, f"Seq len mismatch: {dim1} < {dim2}"
+        
+        # Extract dimensions explicitly
+        self_layers, self_kv, self_batch, self_heads, self_seq, self_head_dim = self.kv_shape
+        other_layers, other_kv, other_batch, other_heads, other_seq, other_head_dim = other.kv_shape
+        
+        # Validate dimensions
+        assert self_layers == other_layers, f"Layer count mismatch: {self_layers} != {other_layers}"
+        assert self_kv == other_kv, f"K/V dimension mismatch: {self_kv} != {other_kv}"
+        assert self_heads == other_heads, f"Head count mismatch: {self_heads} != {other_heads}"
+        assert self_head_dim == other_head_dim, f"Head dim mismatch: {self_head_dim} != {other_head_dim}"
+        
+        # Batch size can be expanded (other can be 1, self can be larger)
+        assert self_batch == other_batch or other_batch == 1, f"Batch size mismatch: {self_batch} vs {other_batch} (other must be 1 or equal)"
+        
+        # Sequence length: self must be longer than other
+        assert self_seq >= other_seq, f"Sequence length mismatch: {self_seq} < {other_seq}"
+        
         # 2) initialize the cache
         dtype, device = other.kv_cache.dtype, other.kv_cache.device
         self.kv_cache = torch.empty(self.kv_shape, dtype=dtype, device=device)