diff --git a/include/cutlass/arch/barrier.h b/include/cutlass/arch/barrier.h
index db2777e24..0e1f344f2 100644
--- a/include/cutlass/arch/barrier.h
+++ b/include/cutlass/arch/barrier.h
@@ -37,7 +37,7 @@
 #include <cutlass/arch/memory_sm75.h>
 #include <cute/arch/cluster_sm90.hpp>
 
-#if defined SYCL_INTEL_TARGET
+#if defined(SYCL_INTEL_TARGET)
 SYCL_EXTERNAL __attribute__((convergent)) void __spirv_ControlBarrierWaitINTEL(int execution_scope, int memory_scope, int memory_semantics);
 SYCL_EXTERNAL __attribute__((convergent)) void __spirv_ControlBarrierArriveINTEL(int execution_scope, int memory_scope, int memory_semantics);
 
@@ -160,10 +160,10 @@ class NamedBarrier {
  private:
   CUTLASS_DEVICE
   static void arrive_and_wait_internal(uint32_t num_threads, uint32_t barrier_id) {
-#if defined SYCL_INTEL_TARGET
+#if defined(SYCL_INTEL_TARGET)
     __spirv_ControlBarrierArriveINTEL(EXECUTION_SCOPE_WORK_GROUP, MEMORY_SCOPE_WORK_GROUP, MEMORY_SEMANTICS_RELAXED);
     __spirv_ControlBarrierWaitINTEL(EXECUTION_SCOPE_WORK_GROUP, MEMORY_SCOPE_WORK_GROUP, MEMORY_SEMANTICS_RELAXED);
-#elif defined CUDA_BARRIER_ENABLED
+#elif CUDA_BARRIER_ENABLED
     asm volatile("bar.sync %0, %1;" : : "r"(barrier_id), "r"(num_threads));
 #elif defined(__CUDA_ARCH__)
     asm volatile ("brkpt;\n" ::);
@@ -172,7 +172,7 @@ class NamedBarrier {
 
   CUTLASS_DEVICE
   static void arrive_internal(uint32_t num_threads, uint32_t barrier_id) {
-#if defined SYCL_INTEL_TARGET
+#if defined(SYCL_INTEL_TARGET)
     __spirv_ControlBarrierArriveINTEL(EXECUTION_SCOPE_WORK_GROUP, MEMORY_SCOPE_WORK_GROUP, MEMORY_SEMANTICS_RELAXED);
 #elif CUDA_BARRIER_ENABLED
     asm volatile("bar.arrive %0, %1;" : : "r"(barrier_id), "r"(num_threads));
diff --git a/include/cutlass/gemm/kernel/xe_persistent_tile_scheduler_params_streamk.hpp b/include/cutlass/gemm/kernel/xe_persistent_tile_scheduler_params_streamk.hpp
index 443e2cf10..b98613b54 100644
--- a/include/cutlass/gemm/kernel/xe_persistent_tile_scheduler_params_streamk.hpp
+++ b/include/cutlass/gemm/kernel/xe_persistent_tile_scheduler_params_streamk.hpp
@@ -244,8 +244,6 @@ struct PersistentTileSchedulerXeStreamKParams {
 
     // Calculate the number of work units covering the data-parallel and stream-K tiles.
     // A "work unit" is a single index in the linearized ID space used by the scheduler.
-    // We distinguish it from a "block," which is typically tied to a hardware unit
-    // (e.g., the callers into this scheduler will be persistent thread blocks).
     // A work unit can encompass multiple output tiles worth of work (as will be the
     // case for stream-K blocks).
     // Since splitting is not required for data-parallel tiles, only one data-parallel unit
@@ -438,12 +436,12 @@ struct PersistentTileSchedulerXeStreamKParams {
   static uint64_t
   get_num_sk_units(uint64_t wgs_per_sk_wave, uint32_t sk_tiles, uint32_t k_tiles_per_output_tile) {
     // If there are stream-K tiles to compute and a sufficiently large number of k iterations
-    // across them, they will be covered by a single wave of persistent threadblocks. Thus, there
-    // will be as many work units as there are threadblocks in a single wave.
+    // across them, they will be covered by a single wave of persistent work_groups. Thus, there
+    // will be as many work units as there are work_groups in a single wave.
     //
     // When the total k iterations across stream-K tiles is too small to justify distributing
-    // across an entire wave of blocks, we instead distribute the iterations over a smaller
-    // set of blocks.
+    // across an entire wave of work_groups, we instead distribute the iterations over a smaller
+    // set of work_groups.
 
     // Calculate the number of stream-K units that would be needed if each stream-K unit
     // computed the minimum allowable k iterations.
diff --git a/include/cutlass/gemm/kernel/xe_tile_scheduler_streamk.hpp b/include/cutlass/gemm/kernel/xe_tile_scheduler_streamk.hpp
index 1caf2cba0..4b405b39c 100644
--- a/include/cutlass/gemm/kernel/xe_tile_scheduler_streamk.hpp
+++ b/include/cutlass/gemm/kernel/xe_tile_scheduler_streamk.hpp
@@ -245,8 +245,7 @@ class PersistentTileSchedulerXeStreamK {
     current_work_linear_idx_ += uint64_t(GridDimX()) * uint64_t(GridDimY()) * uint64_t(GridDimZ()) * uint64_t(advance_count);
   }
 
-  // Given the inputs, computes the total number of output blocks this problem will compute over
-  // Note that this is only the logical size of our grid, not the physical grid we will actually launch.
+  // Given the inputs, computes the total number of output work-groups this problem will compute over.
   template <class ProblemShape>
   CUTLASS_HOST_DEVICE static
   dim3
@@ -254,7 +253,7 @@ class PersistentTileSchedulerXeStreamK {
     return Params::get_tiled_wg_shape_mnl(to_gemm_coord(problem_shape_mnkl), to_gemm_coord(cta_shape));
   }
 
-  // Given the cluster shape, computes the physical grid we should launch.
+  // Computes the physical grid we should launch.
   template <class ProblemShape>
   CUTLASS_HOST_DEVICE static
   dim3