diff --git a/mergekit/merge_methods/__init__.py b/mergekit/merge_methods/__init__.py
index 84d64476..9f218dd8 100644
--- a/mergekit/merge_methods/__init__.py
+++ b/mergekit/merge_methods/__init__.py
@@ -1,6 +1,7 @@
 # Copyright (C) 2025 Arcee AI
 # SPDX-License-Identifier: LGPL-3.0-only
 
+import mergekit.merge_methods.core_space
 import mergekit.merge_methods.multislerp
 import mergekit.merge_methods.nearswap
 import mergekit.merge_methods.sce
diff --git a/mergekit/merge_methods/core_space.py b/mergekit/merge_methods/core_space.py
new file mode 100644
index 00000000..826e0c43
--- /dev/null
+++ b/mergekit/merge_methods/core_space.py
@@ -0,0 +1,149 @@
+from typing import List
+
+import torch
+from torch import Tensor
+
+from mergekit.merge_methods.easy_define import merge_method
+
+
+def _lora_factor_from_delta(delta: Tensor, rank: int) -> tuple[Tensor, Tensor]:
+    """
+    Approximate a LoRA-style factorization ΔW ≈ B @ A
+    delta: [m, n]
+    returns: A: [r, n], B: [m, r] such that B@A ~ delta
+    """
+    # SVD in float32 for numerical stability
+    U, S, Vh = torch.linalg.svd(delta.to(torch.float32), full_matrices=False)
+    r_eff = min(rank, S.shape[0])
+    if r_eff == 0:
+        # No meaningful update at all
+        m, n = delta.shape
+        return delta.new_zeros((0, n)), delta.new_zeros((m, 0))
+
+    U_r = U[:, :r_eff]  # [m, r_eff]
+    S_r = S[:r_eff]  # [r_eff]
+    Vh_r = Vh[:r_eff, :]  # [r_eff, n]
+
+    # Δ ≈ (U * sqrt(S)) @ (sqrt(S) * Vh)
+    sqrt_S = S_r.sqrt()
+    B = U_r * sqrt_S.unsqueeze(0)  # scale columns of U
+    A = sqrt_S.unsqueeze(1) * Vh_r  # scale rows of Vh
+    return A, B
+
+
+def _core_space_ta_single(
+    tensors: List[Tensor],
+    base_tensor: Tensor,
+    rank: int,
+) -> Tensor:
+    """
+    Core Space Task Arithmetic for a single 2D weight matrix.
+    tensors: list of [m, n] (full weights for each model)
+    base_tensor: [m, n]
+    """
+    if not tensors:
+        return base_tensor
+
+    # Compute per-task deltas
+    deltas = [t.to(torch.float32) - base_tensor.to(torch.float32) for t in tensors]
+
+    # Factorize each delta as Δ ≈ B @ A
+    A_list: List[Tensor] = []
+    B_list: List[Tensor] = []
+    for delta in deltas:
+        if delta.abs().max() == 0:
+            # pure base, ignore
+            continue
+        A, B = _lora_factor_from_delta(delta, rank=rank)
+        if A.numel() == 0 or B.numel() == 0:
+            continue
+        A_list.append(A)  # [r, n]
+        B_list.append(B)  # [m, r]
+
+    if not A_list:
+        # no non‑zero updates
+        return base_tensor
+
+    m, n = base_tensor.shape
+    T = len(A_list)
+    # All A_i are [r, n], B_i are [m, r]
+    r = A_list[0].shape[0]
+
+    # Stack to build global reference bases (Core Space)
+    A_stack = torch.cat(A_list, dim=0)  # [T * r, n]
+    B_stack = torch.cat(B_list, dim=1)  # [m, T * r]
+
+    # SVDs to get reference bases
+    # A_stack: we want a "right" basis for columns -> Vh
+    _, _, Vh_A_ref = torch.linalg.svd(A_stack, full_matrices=False)  # [R_A, n]
+    # B_stack: we want a "left" basis for rows -> U
+    U_B_ref, _, _ = torch.linalg.svd(B_stack, full_matrices=False)  # [m, R_B]
+
+    # Make both bases the same core dimensionality R
+    R = min(U_B_ref.shape[1], Vh_A_ref.shape[0])
+    U_B_ref = U_B_ref[:, :R]  # [m, R]
+    Vh_A_ref = Vh_A_ref[:R, :]  # [R, n]
+
+    # Represent each task in Core Space:
+    # M_t = U_B_ref^T @ B_t @ A_t @ Vh_A_ref^T
+    M_list: List[Tensor] = []
+    for A, B in zip(A_list, B_list):
+        # shapes: [R, m] @ [m, r] @ [r, n] @ [n, R] -> [R, R]
+        M_aligned = U_B_ref.T @ B @ A @ Vh_A_ref.T
+        M_list.append(M_aligned)
+
+    # Task Arithmetic in Core Space: sum the core matrices
+    M_merged = torch.stack(M_list, dim=0).sum(dim=0)  # [R, R]
+
+    # Reconstruct merged delta in the original weight space:
+    # Δ_merged = U_B_ref @ M_merged @ Vh_A_ref
+    delta_merged = U_B_ref @ M_merged @ Vh_A_ref  # [m, n]
+    return (base_tensor.to(torch.float32) + delta_merged).to(base_tensor.dtype)
+
+
+@merge_method(
+    name="core_ta",
+    pretty_name="Task Arithmetic in Core Space",
+    reference_url="https://arxiv.org/abs/2509.17786",
+)
+def core_space_task_arithmetic(
+    tensors: List[Tensor],
+    base_tensor: Tensor,
+    rank: int = 16,
+) -> Tensor:
+    """
+    Merge method: 'core_ta'
+
+    - For 1D / scalar tensors: falls back to simple Task Arithmetic.
+    - For 2D tensors: run Core Space Task Arithmetic as in Panariello et al. (NeurIPS 2025).
+    - 'rank' controls the truncation rank when approximating LoRA-style factors.
+    """
+    if not tensors:
+        return base_tensor
+
+    # Non-matrix parameters: simple Task Arithmetic (sum of deltas)
+    if base_tensor.ndim < 2:
+        deltas = torch.stack(
+            [t.to(torch.float32) - base_tensor.to(torch.float32) for t in tensors],
+            dim=0,
+        )
+        merged = base_tensor.to(torch.float32) + deltas.sum(dim=0)
+        return merged.to(base_tensor.dtype)
+
+    # Treat last two dims as the matrix, keep any leading dims (e.g. heads)
+    *prefix, m, n = base_tensor.shape
+    if len(prefix) == 0:
+        # Simple [m, n] case
+        return _core_space_ta_single(tensors, base_tensor, rank=rank)
+
+    # Handle batched / multihead weights by looping over the prefix
+    base_2d = base_tensor.reshape(-1, m, n)
+    merged_2d = torch.empty_like(base_2d)
+    tensor_2d_list = [t.reshape(-1, m, n) for t in tensors]
+
+    for i in range(base_2d.shape[0]):
+        layer_base = base_2d[i]
+        layer_tensors = [t[i] for t in tensor_2d_list]
+        merged_2d[i] = _core_space_ta_single(layer_tensors, layer_base, rank=rank)
+
+    return merged_2d.reshape(base_tensor.shape)