diff --git a/mlx/backend/cuda/CMakeLists.txt b/mlx/backend/cuda/CMakeLists.txt
index 59db14535..084e449b0 100644
--- a/mlx/backend/cuda/CMakeLists.txt
+++ b/mlx/backend/cuda/CMakeLists.txt
@@ -53,10 +53,10 @@ target_sources(
 
 if(CMAKE_CUDA_COMPILER_VERSION VERSION_GREATER_EQUAL 12.9.0)
   target_sources(
-    mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/cublas_batched_gemm_12_9.cu)
+    mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/cublas_gemm_batched_12_9.cu)
 else()
   target_sources(
-    mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/cublas_batched_gemm_12_0.cpp)
+    mlx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/gemms/cublas_gemm_batched_12_0.cpp)
 endif()
 
 target_compile_definitions(mlx PRIVATE MLX_USE_CUDA)
diff --git a/mlx/backend/cuda/gemms/cublas_gemm.cpp b/mlx/backend/cuda/gemms/cublas_gemm.cpp
index 61f12ba1d..1aeeefa38 100644
--- a/mlx/backend/cuda/gemms/cublas_gemm.cpp
+++ b/mlx/backend/cuda/gemms/cublas_gemm.cpp
@@ -7,10 +7,12 @@
 
 #include <fmt/format.h>
 
-namespace mlx::core::cu {
+namespace mlx::core {
+
+namespace {
 
 struct CublasPreference {
-  CublasPreference(Device& device) {
+  CublasPreference(cu::Device& device) {
     // The recommended cublas workspace size is 4 MiB for pre-Hopper and 32 MiB
     // for Hopper+:
     // https://docs.nvidia.com/cuda/cublas/#cublassetworkspace
@@ -33,7 +35,7 @@ struct CublasPreference {
   cublasLtMatmulPreference_t pref_{nullptr};
 };
 
-cublasLtMatmulPreference_t cublas_preference(Device& device) {
+cublasLtMatmulPreference_t cublas_preference(cu::Device& device) {
   static CublasPreference pref(device);
   return pref.pref_;
 }
@@ -52,7 +54,7 @@ cublasComputeType_t dtype_to_compute_type(Dtype dtype) {
       return CUBLAS_COMPUTE_64F;
     default:
       throw std::runtime_error(fmt::format(
-          "Unsupported dtype in Matmul: {}.", dtype_to_string(dtype)));
+          "Unsupported dtype in CublasGemm: {}.", dtype_to_string(dtype)));
   }
 }
 
@@ -70,7 +72,7 @@ cudaDataType_t dtype_to_cublas_type(Dtype dtype) {
       return CUDA_C_32F;
     default:
       throw std::runtime_error(fmt::format(
-          "Unsupported dtype in Matmul: {}.", dtype_to_string(dtype)));
+          "Unsupported dtype in CublasGemm: {}.", dtype_to_string(dtype)));
   }
 }
 
@@ -102,8 +104,10 @@ cublasLtMatrixLayout_t create_matrix_layout(
   return desc;
 }
 
-Matmul::Matmul(
-    Device& device,
+} // namespace
+
+CublasGemm::CublasGemm(
+    cu::Device& device,
     Dtype dtype,
     bool a_transposed,
     uint64_t a_rows,
@@ -155,8 +159,8 @@ Matmul::Matmul(
       type, a_rows, b_cols, false, b_cols, batch_count, a_rows * b_cols);
 }
 
-Matmul::Matmul(
-    Device& device,
+CublasGemm::CublasGemm(
+    cu::Device& device,
     Dtype dtype,
     bool a_transposed,
     uint64_t a_rows,
@@ -171,7 +175,7 @@ Matmul::Matmul(
     int64_t a_batch_stride,
     int64_t b_batch_stride,
     int64_t c_batch_stride)
-    : Matmul(
+    : CublasGemm(
           device,
           dtype,
           a_transposed,
@@ -190,7 +194,7 @@ Matmul::Matmul(
       type, a_rows, b_cols, false, ldc, batch_count, c_batch_stride);
 }
 
-Matmul::~Matmul() {
+CublasGemm::~CublasGemm() {
   CHECK_CUBLAS_ERROR(cublasLtMatrixLayoutDestroy(a_desc_));
   CHECK_CUBLAS_ERROR(cublasLtMatrixLayoutDestroy(b_desc_));
   CHECK_CUBLAS_ERROR(cublasLtMatrixLayoutDestroy(c_desc_));
@@ -198,7 +202,73 @@ Matmul::~Matmul() {
   CHECK_CUBLAS_ERROR(cublasLtMatmulDescDestroy(matmul_desc_));
 }
 
-void Matmul::run_impl(
+void CublasGemm::run(
+    cu::CommandEncoder& encoder,
+    array& out,
+    const array& a,
+    const array& b,
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides) {
+  int batch_count = out.size() / (M_ * N_);
+  if (batch_count / batch_shape.back() > 1) {
+    run_batched(
+        encoder, out, a, b, batch_shape, a_batch_strides, b_batch_strides);
+    return;
+  }
+
+  encoder.set_input_array(a);
+  encoder.set_input_array(b);
+  encoder.set_output_array(out);
+
+  execute(encoder, out.data<void>(), a.data<void>(), b.data<void>(), nullptr);
+}
+
+void CublasGemm::run(
+    cu::CommandEncoder& encoder,
+    array& out,
+    const array& a,
+    const array& b,
+    const array& c,
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides,
+    const Strides& c_batch_strides,
+    float alpha,
+    float beta) {
+  int batch_count = out.size() / (M_ * N_);
+  if (batch_count / batch_shape.back() > 1) {
+    run_batched(
+        encoder,
+        out,
+        a,
+        b,
+        c,
+        batch_shape,
+        a_batch_strides,
+        b_batch_strides,
+        c_batch_strides,
+        alpha,
+        beta);
+    return;
+  }
+
+  encoder.set_input_array(a);
+  encoder.set_input_array(b);
+  encoder.set_input_array(c);
+  encoder.set_output_array(out);
+
+  execute(
+      encoder,
+      out.data<void>(),
+      a.data<void>(),
+      b.data<void>(),
+      c.data<void>(),
+      alpha,
+      beta);
+}
+
+void CublasGemm::execute(
     cu::CommandEncoder& encoder,
     void* out,
     const void* a,
@@ -256,29 +326,4 @@ void Matmul::run_impl(
       encoder.stream()));
 }
 
-void Matmul::run(
-    cu::CommandEncoder& encoder,
-    array& out,
-    const array& a,
-    const array& b,
-    const std::optional<array>& c /* = std::nullopt */,
-    float alpha /* = 1 */,
-    float beta /* = 0 */) {
-  encoder.set_input_array(a);
-  encoder.set_input_array(b);
-  if (c) {
-    encoder.set_input_array(*c);
-  }
-  encoder.set_output_array(out);
-
-  run_impl(
-      encoder,
-      out.data<void>(),
-      a.data<void>(),
-      b.data<void>(),
-      c ? c->data<void>() : nullptr,
-      alpha,
-      beta);
-}
-
-} // namespace mlx::core::cu
+} // namespace mlx::core
diff --git a/mlx/backend/cuda/gemms/cublas_gemm.h b/mlx/backend/cuda/gemms/cublas_gemm.h
index eccee8580..e093351b6 100644
--- a/mlx/backend/cuda/gemms/cublas_gemm.h
+++ b/mlx/backend/cuda/gemms/cublas_gemm.h
@@ -5,13 +5,13 @@
 #include "mlx/backend/cuda/device.h"
 
 #include <cublasLt.h>
-#include <optional>
 
-namespace mlx::core::cu {
-class Matmul {
+namespace mlx::core {
+
+class CublasGemm {
  public:
-  Matmul(
-      Device& device,
+  CublasGemm(
+      cu::Device& device,
       Dtype dtype,
       bool a_transposed,
       uint64_t a_rows,
@@ -25,8 +25,8 @@ class Matmul {
       int64_t a_batch_stride,
       int64_t b_batch_stride);
 
-  Matmul(
-      Device& device,
+  CublasGemm(
+      cu::Device& device,
       Dtype dtype,
       bool a_transposed,
       uint64_t a_rows,
@@ -42,25 +42,39 @@ class Matmul {
       int64_t b_batch_stride,
       int64_t c_batch_stride);
 
-  ~Matmul();
+  ~CublasGemm();
 
   void run(
       cu::CommandEncoder& encoder,
       array& out,
       const array& a,
       const array& b,
-      const std::optional<array>& c = std::nullopt,
-      float alpha = 1,
-      float beta = 0);
+      const Shape& batch_shape,
+      const Strides& a_batch_strides,
+      const Strides& b_batch_strides);
 
+  void run(
+      cu::CommandEncoder& encoder,
+      array& out,
+      const array& a,
+      const array& b,
+      const array& c,
+      const Shape& batch_shape,
+      const Strides& a_batch_strides,
+      const Strides& b_batch_strides,
+      const Strides& c_batch_strides,
+      float alpha,
+      float beta);
+
+ private:
   void run_batched(
       cu::CommandEncoder& encoder,
       array& out,
       const array& a,
       const array& b,
-      const mlx::core::Shape& batch_shape,
-      const mlx::core::Strides& a_batch_strides,
-      const mlx::core::Strides& b_batch_strides);
+      const Shape& batch_shape,
+      const Strides& a_batch_strides,
+      const Strides& b_batch_strides);
 
   void run_batched(
       cu::CommandEncoder& encoder,
@@ -68,15 +82,14 @@ class Matmul {
       const array& a,
       const array& b,
       const array& c,
-      const mlx::core::Shape& batch_shape,
-      const mlx::core::Strides& a_batch_strides,
-      const mlx::core::Strides& b_batch_strides,
-      const mlx::core::Strides& c_batch_strides,
+      const Shape& batch_shape,
+      const Strides& a_batch_strides,
+      const Strides& b_batch_strides,
+      const Strides& c_batch_strides,
       float alpha,
       float beta);
 
- private:
-  void run_impl(
+  void execute(
       cu::CommandEncoder& encoder,
       void* out,
       const void* a,
@@ -97,4 +110,4 @@ class Matmul {
   cublasLtMatmulHeuristicResult_t heuristic_;
 };
 
-} // namespace mlx::core::cu
+} // namespace mlx::core
diff --git a/mlx/backend/cuda/gemms/cublas_batched_gemm_12_0.cpp b/mlx/backend/cuda/gemms/cublas_gemm_batched_12_0.cpp
similarity index 80%
rename from mlx/backend/cuda/gemms/cublas_batched_gemm_12_0.cpp
rename to mlx/backend/cuda/gemms/cublas_gemm_batched_12_0.cpp
index 39a8a5ddd..56c731587 100644
--- a/mlx/backend/cuda/gemms/cublas_batched_gemm_12_0.cpp
+++ b/mlx/backend/cuda/gemms/cublas_gemm_batched_12_0.cpp
@@ -4,16 +4,16 @@
 #include "mlx/backend/cuda/device.h"
 #include "mlx/backend/cuda/gemms/cublas_gemm.h"
 
-namespace mlx::core::cu {
+namespace mlx::core {
 
-void Matmul::run_batched(
+void CublasGemm::run_batched(
     cu::CommandEncoder& encoder,
     array& out,
     const array& a,
     const array& b,
-    const mlx::core::Shape& batch_shape,
-    const mlx::core::Strides& a_batch_strides,
-    const mlx::core::Strides& b_batch_strides) {
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides) {
   encoder.set_input_array(a);
   encoder.set_input_array(b);
   encoder.set_output_array(out);
@@ -22,7 +22,7 @@ void Matmul::run_batched(
   ContiguousIterator b_it(batch_shape, b_batch_strides, batch_shape.size() - 1);
   auto concurrent = encoder.concurrent_context();
   for (size_t i = 0; i < nbatch; ++i) {
-    run_impl(
+    execute(
         encoder,
         out.data<int8_t>() + out.itemsize() * i * batch_shape.back() * M_ * N_,
         a.data<int8_t>() + a.itemsize() * a_it.loc,
@@ -33,16 +33,16 @@ void Matmul::run_batched(
   }
 }
 
-void Matmul::run_batched(
+void CublasGemm::run_batched(
     cu::CommandEncoder& encoder,
     array& out,
     const array& a,
     const array& b,
     const array& c,
-    const mlx::core::Shape& batch_shape,
-    const mlx::core::Strides& a_batch_strides,
-    const mlx::core::Strides& b_batch_strides,
-    const mlx::core::Strides& c_batch_strides,
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides,
+    const Strides& c_batch_strides,
     float alpha,
     float beta) {
   encoder.set_input_array(a);
@@ -56,7 +56,7 @@ void Matmul::run_batched(
   ContiguousIterator c_it(batch_shape, c_batch_strides, batch_shape.size() - 1);
   auto concurrent = encoder.concurrent_context();
   for (size_t i = 0; i < nbatch; ++i) {
-    run_impl(
+    execute(
         encoder,
         out.data<int8_t>() + out.itemsize() * i * batch_shape.back() * M_ * N_,
         a.data<int8_t>() + a.itemsize() * a_it.loc,
@@ -70,4 +70,4 @@ void Matmul::run_batched(
   }
 }
 
-} // namespace mlx::core::cu
+} // namespace mlx::core
diff --git a/mlx/backend/cuda/gemms/cublas_batched_gemm_12_9.cu b/mlx/backend/cuda/gemms/cublas_gemm_batched_12_9.cu
similarity index 95%
rename from mlx/backend/cuda/gemms/cublas_batched_gemm_12_9.cu
rename to mlx/backend/cuda/gemms/cublas_gemm_batched_12_9.cu
index da7163b42..570b79463 100644
--- a/mlx/backend/cuda/gemms/cublas_batched_gemm_12_9.cu
+++ b/mlx/backend/cuda/gemms/cublas_gemm_batched_12_9.cu
@@ -6,7 +6,9 @@
 
 #include <cooperative_groups.h>
 
-namespace mlx::core::cu {
+namespace mlx::core {
+
+namespace cu {
 
 namespace cg = cooperative_groups;
 
@@ -128,6 +130,10 @@ __global__ void set_addmm_device_pointers_g(
       out_start + item_size * index * batch_stride;
 }
 
+} // namespace cu
+
+namespace {
+
 void set_pointer_mode(cublasLtMatrixLayout_t desc, int batch_count) {
   auto batch_mode = CUBLASLT_BATCH_MODE_POINTER_ARRAY;
   CHECK_CUBLAS_ERROR(cublasLtMatrixLayoutSetAttribute(
@@ -139,14 +145,16 @@ void set_pointer_mode(cublasLtMatrixLayout_t desc, int batch_count) {
       desc, CUBLASLT_MATRIX_LAYOUT_BATCH_COUNT, &batch_count, sizeof(int32_t)));
 }
 
-void Matmul::run_batched(
+} // namespace
+
+void CublasGemm::run_batched(
     cu::CommandEncoder& encoder,
     array& out,
     const array& a,
     const array& b,
-    const mlx::core::Shape& batch_shape,
-    const mlx::core::Strides& a_batch_strides,
-    const mlx::core::Strides& b_batch_strides) {
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides) {
   int batch_count = out.size() / (M_ * N_);
   set_pointer_mode(a_desc_, batch_count);
   set_pointer_mode(b_desc_, batch_count);
@@ -213,7 +221,7 @@ void Matmul::run_batched(
   auto a_pointers = pointers.data<int8_t*>();
   auto b_pointers = a_pointers + batch_count;
   auto out_pointers = b_pointers + batch_count;
-  run_impl(
+  execute(
       encoder,
       reinterpret_cast<void*>(out_pointers),
       reinterpret_cast<void*>(a_pointers),
@@ -221,16 +229,16 @@ void Matmul::run_batched(
       nullptr);
 }
 
-void Matmul::run_batched(
+void CublasGemm::run_batched(
     cu::CommandEncoder& encoder,
     array& out,
     const array& a,
     const array& b,
     const array& c,
-    const mlx::core::Shape& batch_shape,
-    const mlx::core::Strides& a_batch_strides,
-    const mlx::core::Strides& b_batch_strides,
-    const mlx::core::Strides& c_batch_strides,
+    const Shape& batch_shape,
+    const Strides& a_batch_strides,
+    const Strides& b_batch_strides,
+    const Strides& c_batch_strides,
     float alpha,
     float beta) {
   int batch_count = out.size() / (M_ * N_);
@@ -306,7 +314,7 @@ void Matmul::run_batched(
   auto b_pointers = a_pointers + batch_count;
   auto c_pointers = b_pointers + batch_count;
   auto out_pointers = c_pointers + batch_count;
-  run_impl(
+  execute(
       encoder,
       reinterpret_cast<void*>(out_pointers),
       reinterpret_cast<void*>(a_pointers),
@@ -316,4 +324,4 @@ void Matmul::run_batched(
       beta);
 }
 
-} // namespace mlx::core::cu
+} // namespace mlx::core
diff --git a/mlx/backend/cuda/matmul.cpp b/mlx/backend/cuda/matmul.cpp
index 283aaaf2e..b11fae538 100644
--- a/mlx/backend/cuda/matmul.cpp
+++ b/mlx/backend/cuda/matmul.cpp
@@ -97,7 +97,7 @@ void Matmul::eval_gpu(const std::vector<array>& inputs, array& out) {
 
   /////////////////////////////////////////////////////////////////////////////
   // Invoke cublasLt
-  cu::Matmul matmul(
+  CublasGemm gemm(
       cu::device(s.device),
       a.dtype(),
       a_transposed,
@@ -111,14 +111,7 @@ void Matmul::eval_gpu(const std::vector<array>& inputs, array& out) {
       batch_shape.back(),
       a_batch_strides.back(),
       b_batch_strides.back());
-
-  if ((batch_count / batch_shape.back()) == 1) {
-    matmul.run(encoder, out, a, b);
-    return;
-  }
-
-  matmul.run_batched(
-      encoder, out, a, b, batch_shape, a_batch_strides, b_batch_strides);
+  gemm.run(encoder, out, a, b, batch_shape, a_batch_strides, b_batch_strides);
 }
 
 void AddMM::eval_gpu(const std::vector<array>& inputs, array& out) {
@@ -186,7 +179,7 @@ void AddMM::eval_gpu(const std::vector<array>& inputs, array& out) {
   /////////////////////////////////////////////////////////////////////////////
   // Invoke cublasLt
 
-  cu::Matmul matmul(
+  CublasGemm gemm(
       cu::device(s.device),
       a.dtype(),
       a_transposed,
@@ -202,12 +195,7 @@ void AddMM::eval_gpu(const std::vector<array>& inputs, array& out) {
       a_batch_strides.back(),
       b_batch_strides.back(),
       c_batch_strides.back());
-
-  if ((batch_count / batch_shape.back()) == 1) {
-    matmul.run(encoder, out, a, b, c, alpha_, beta_);
-    return;
-  }
-  matmul.run_batched(
+  gemm.run(
       encoder,
       out,
       a,