diff --git a/trak/score_computers.py b/trak/score_computers.py
index 120e163..f82cf56 100644
--- a/trak/score_computers.py
+++ b/trak/score_computers.py
@@ -122,6 +122,7 @@ def __init__(
         device: torch.device,
         CUDA_MAX_DIM_SIZE: int = 20_000,
         logging_level=logging.INFO,
+        lambda_reg: float = 0.0,
     ) -> None:
         """
         Args:
@@ -132,11 +133,14 @@ def __init__(
                 Size of block for block-wise matmuls. Defaults to 100_000.
             logging_level (logging level, optional):
                 Logging level for the logger. Defaults to logging.info.
+            lambda_reg (int):
+                regularization term for l2 reg on xtx
         """
         super().__init__(dtype, device)
         self.CUDA_MAX_DIM_SIZE = CUDA_MAX_DIM_SIZE
         self.logger = logging.getLogger("ScoreComputer")
         self.logger.setLevel(logging_level)
+        self.lambda_reg = lambda_reg
 
     def get_xtx(self, grads: Tensor) -> Tensor:
         self.proj_dim = grads.shape[1]
@@ -152,7 +156,11 @@ def get_xtx(self, grads: Tensor) -> Tensor:
 
     def get_x_xtx_inv(self, grads: Tensor, xtx: Tensor) -> Tensor:
         blocks = ch.split(grads, split_size_or_sections=self.CUDA_MAX_DIM_SIZE, dim=0)
-        xtx_inv = ch.linalg.inv(xtx.to(ch.float32))
+
+        xtx_reg = xtx + self.lambda_reg * torch.eye(
+            xtx.size(dim=0), device=xtx.device, dtype=xtx.dtype
+        )
+        xtx_inv = ch.linalg.inv(xtx_reg.to(ch.float32))
 
         # center X^TX inverse a bit to avoid numerical issues when going to float16
         xtx_inv /= xtx_inv.abs().mean()
diff --git a/trak/traker.py b/trak/traker.py
index 21e30f1..907935e 100644
--- a/trak/traker.py
+++ b/trak/traker.py
@@ -64,6 +64,7 @@ def __init__(
         proj_max_batch_size: int = 32,
         projector_seed: int = 0,
         grad_wrt: Optional[Iterable[str]] = None,
+        lambda_reg: float = 0.0,
     ) -> None:
         """
 
@@ -127,7 +128,10 @@ def __init__(
                 as they appear in the model's state dictionary. If None,
                 gradients are taken with respect to all model parameters.
                 Defaults to None.
-
+            lambda_reg (float):
+                The :math:`\ell_2` (ridge) regularization penalty added to the
+                :math:`XTX` term in score computers when computing the matrix
+                inverse :math:`(XTX)^{-1}`. Defaults to 0.
         """
 
         self.model = model
@@ -136,6 +140,7 @@ def __init__(
         self.device = device
         self.dtype = ch.float16 if use_half_precision else ch.float32
         self.grad_wrt = grad_wrt
+        self.lambda_reg = lambda_reg
 
         logging.basicConfig()
         self.logger = logging.getLogger("TRAK")
@@ -181,7 +186,10 @@ def __init__(
         if score_computer is None:
             score_computer = BasicScoreComputer
         self.score_computer = score_computer(
-            dtype=self.dtype, device=self.device, logging_level=logging_level
+            dtype=self.dtype,
+            device=self.device,
+            logging_level=logging_level,
+            lambda_reg=self.lambda_reg,
         )
 
         metadata = {