diff --git a/.github/workflows/array-api-tests-numpy-1-21.yml b/.github/workflows/array-api-tests-numpy-1-21.yml
index 5c64f16a..2d81c3cd 100644
--- a/.github/workflows/array-api-tests-numpy-1-21.yml
+++ b/.github/workflows/array-api-tests-numpy-1-21.yml
@@ -3,7 +3,7 @@ name: Array API Tests (NumPy 1.21)
 on: [push, pull_request]
 
 jobs:
-  array-api-tests-numpy:
+  array-api-tests-numpy-1-21:
     uses: ./.github/workflows/array-api-tests.yml
     with:
       package-name: numpy
diff --git a/.github/workflows/array-api-tests-numpy.yml b/.github/workflows/array-api-tests-numpy.yml
index b97786df..36984345 100644
--- a/.github/workflows/array-api-tests-numpy.yml
+++ b/.github/workflows/array-api-tests-numpy.yml
@@ -3,7 +3,7 @@ name: Array API Tests (NumPy Latest)
 on: [push, pull_request]
 
 jobs:
-  array-api-tests-numpy-1-21:
+  array-api-tests-numpy-latest:
     uses: ./.github/workflows/array-api-tests.yml
     with:
       package-name: numpy
diff --git a/array_api_compat/torch/linalg.py b/array_api_compat/torch/linalg.py
index c803228a..afef7504 100644
--- a/array_api_compat/torch/linalg.py
+++ b/array_api_compat/torch/linalg.py
@@ -22,6 +22,34 @@ def cross(x1: array, x2: array, /, *, axis: int = -1) -> array:
     x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
     return torch_linalg.cross(x1, x2, dim=axis)
 
-__all__ = linalg_all + ['outer', 'trace', 'matrix_transpose', 'tensordot']
+def vecdot(x1: array, x2: array, /, *, axis: int = -1, **kwargs) -> array:
+    from ._aliases import isdtype
+
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+
+    # torch.linalg.vecdot doesn't support integer dtypes
+    if isdtype(x1.dtype, 'integral') or isdtype(x2.dtype, 'integral'):
+        if kwargs:
+            raise RuntimeError("vecdot kwargs not supported for integral dtypes")
+        ndim = max(x1.ndim, x2.ndim)
+        x1_shape = (1,)*(ndim - x1.ndim) + tuple(x1.shape)
+        x2_shape = (1,)*(ndim - x2.ndim) + tuple(x2.shape)
+        if x1_shape[axis] != x2_shape[axis]:
+            raise ValueError("x1 and x2 must have the same size along the given axis")
+
+        x1_, x2_ = torch.broadcast_tensors(x1, x2)
+        x1_ = torch.moveaxis(x1_, axis, -1)
+        x2_ = torch.moveaxis(x2_, axis, -1)
+
+        res = x1_[..., None, :] @ x2_[..., None]
+        return res[..., 0, 0]
+    return torch.linalg.vecdot(x1, x2, dim=axis, **kwargs)
+
+def solve(x1: array, x2: array, /, **kwargs) -> array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    return torch.linalg.solve(x1, x2, **kwargs)
+
+__all__ = linalg_all + ['outer', 'trace', 'matrix_transpose', 'tensordot',
+                        'vecdot', 'solve']
 
 del linalg_all
diff --git a/numpy-1-21-xfails.txt b/numpy-1-21-xfails.txt
index d9b76859..505cf7d2 100644
--- a/numpy-1-21-xfails.txt
+++ b/numpy-1-21-xfails.txt
@@ -118,6 +118,7 @@ array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[_
 array_api_tests/test_operators_and_elementwise_functions.py::test_floor_divide[floor_divide(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_greater[greater(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_less[__lt__(x1, x2)]
+array_api_tests/test_operators_and_elementwise_functions.py::test_less_equal[less_equal(x1, x2)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_logaddexp
 array_api_tests/test_operators_and_elementwise_functions.py::test_multiply[__imul__(x, s)]
 array_api_tests/test_operators_and_elementwise_functions.py::test_multiply[__mul__(x, s)]
diff --git a/torch-xfails.txt b/torch-xfails.txt
index d6cf1670..ad5d25bc 100644
--- a/torch-xfails.txt
+++ b/torch-xfails.txt
@@ -57,8 +57,8 @@ array_api_tests/test_operators_and_elementwise_functions.py::test_remainder[__im
 array_api_tests/test_operators_and_elementwise_functions.py::test_subtract[__sub__(x1, x2)]
 
 
-# Mac-only bug (overflow near float max)
-# array_api_tests/test_operators_and_elementwise_functions.py::test_log1p
+# overflow near float max
+array_api_tests/test_operators_and_elementwise_functions.py::test_log1p
 
 # torch doesn't handle shifting by more than the bit size correctly
 # https://github.com/pytorch/pytorch/issues/70904