diff --git a/src/brevitas/graph/gpxq.py b/src/brevitas/graph/gpxq.py
index 5acd4d736..1bc520963 100644
--- a/src/brevitas/graph/gpxq.py
+++ b/src/brevitas/graph/gpxq.py
@@ -308,17 +308,44 @@ def get_quant_weights(self, i, i1, permutation_list):
         return q
 
 
-def random_projection(float_input: torch.Tensor, quantized_input: torch.Tensor, target_dim: int):
+def random_projection(
+        float_input: torch.Tensor,
+        quantized_input: torch.Tensor,
+        target_dim: int,
+        batch_size: int = 2048):
     # use random projection to reduce dimensionality
     n = quantized_input.size(1)
     dev = float_input.device
-    # create gaussian random matrix
-    R = torch.normal(mean=0.0, std=1. / math.sqrt(n), size=(target_dim, n), device=dev)
-    quantized_input = torch.transpose(quantized_input, 1, 2) @ R.T
-    float_input = torch.transpose(float_input, 1, 2) @ R.T
-    del R
+    # use batching if target_dim is greater than 8000 to avoid memory issues
+    if target_dim > 8000:
+        accumulated_batches = 0
+        first_batch = True
+        quantized_input = torch.transpose(quantized_input, 1, 2)
+        float_input = torch.transpose(float_input, 1, 2)
+        while accumulated_batches < target_dim:
+            # cur_target_dim makes sure to fully use batch_size unless we're too close to target_dim
+            cur_target_dim = min(batch_size, target_dim - accumulated_batches)
+            accumulated_batches += cur_target_dim
+            R = torch.normal(mean=0.0, std=1. / math.sqrt(n), size=(cur_target_dim, n), device=dev)
+            if first_batch:
+                quantized_input_proj = (quantized_input @ R.T).cpu()
+                float_input_proj = (float_input @ R.T).cpu()
+                first_batch = False
+            else:
+                # concatenate projected input along last dimension
+                quantized_input_proj = torch.cat(
+                    [quantized_input_proj, (quantized_input @ R.T).cpu()], dim=-1)
+                float_input_proj = torch.cat([float_input_proj, (float_input @ R.T).cpu()], dim=-1)
+    else:
+        # create gaussian random matrix
+        R = torch.normal(mean=0.0, std=1. / math.sqrt(n), size=(target_dim, n), device=dev)
+        quantized_input_proj = torch.transpose(quantized_input, 1, 2) @ R.T
+        float_input_proj = torch.transpose(float_input, 1, 2) @ R.T
+        del R
     # reshape back
-    quantized_input = torch.transpose(quantized_input, 1, 2)
-    float_input = torch.transpose(float_input, 1, 2)
+    quantized_input_proj = torch.transpose(quantized_input_proj, 1, 2)
+    float_input_proj = torch.transpose(float_input_proj, 1, 2)
+    del quantized_input
+    del float_input
 
-    return float_input, quantized_input
+    return float_input_proj, quantized_input_proj