diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
index 8b79fbf726495..e671c5e323a09 100644
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
@@ -200,7 +200,7 @@ def SparseTensorEncodingAttr : SparseTensor_Attr<"SparseTensorEncoding",
 
     // Sorted Coordinate Scheme.
     #SortedCOO = #sparse_tensor.encoding<{
-      lvlTypes = [ "compressed_nu", "singleton" ]
+      map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
     }>
     ... tensor<?x?xf64, #SortedCOO> ...
 
@@ -214,8 +214,12 @@ def SparseTensorEncodingAttr : SparseTensor_Attr<"SparseTensorEncoding",
 
     // Block sparse row storage (2x3 blocks).
     #BCSR = #sparse_tensor.encoding<{
-      lvlTypes = [ "compressed", "compressed", "dense", "dense" ],
-      dimToLvl = affine_map<(i, j) -> (i floordiv 2, j floordiv 3, i mod 2, j mod 3)>
+      map = ( i, j ) ->
+      ( i floordiv 2 : compressed,
+        j floordiv 3 : compressed,
+        i mod 2      : dense,
+        j mod 3      : dense
+      )
     }>
     ... tensor<20x30xf32, #BCSR> ...
 
diff --git a/mlir/test/Dialect/SparseTensor/GPU/gpu_matvec_lib.mlir b/mlir/test/Dialect/SparseTensor/GPU/gpu_matvec_lib.mlir
index 4f25322df2c90..50ff81cb6ecd0 100644
--- a/mlir/test/Dialect/SparseTensor/GPU/gpu_matvec_lib.mlir
+++ b/mlir/test/Dialect/SparseTensor/GPU/gpu_matvec_lib.mlir
@@ -2,7 +2,7 @@
 // RUN:             --sparsification="enable-gpu-libgen" | FileCheck %s
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 module {
diff --git a/mlir/test/Dialect/SparseTensor/codegen.mlir b/mlir/test/Dialect/SparseTensor/codegen.mlir
index c5061c40eb0b1..f1317f23d6568 100644
--- a/mlir/test/Dialect/SparseTensor/codegen.mlir
+++ b/mlir/test/Dialect/SparseTensor/codegen.mlir
@@ -27,7 +27,7 @@
 }>
 
 #UCSR = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed_no" ]
+  map = (d0, d1) -> (d0 : dense, d1 : compressed(nonordered))
 }>
 
 #CSC = #sparse_tensor.encoding<{
@@ -41,21 +41,19 @@
 }>
 
 #Dense3D = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "dense" ],
-  dimToLvl = affine_map<(i, j, k) -> (k, i, j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : dense, d1 : dense)
 }>
 
 #Coo = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CooPNo = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton_no" ],
-  dimToLvl = affine_map<(i, j) -> (j, i)>
+  map = (d0, d1) -> (d1 : compressed(nonunique), d0 : singleton(nonordered))
 }>
 
 #ccoo = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed(nonunique), d2 : singleton)
 }>
 
 // CHECK-LABEL: func @sparse_nop(
diff --git a/mlir/test/Dialect/SparseTensor/codegen_sparse_alloc.mlir b/mlir/test/Dialect/SparseTensor/codegen_sparse_alloc.mlir
index 479642e5db4ed..50ad4a0a1ea24 100644
--- a/mlir/test/Dialect/SparseTensor/codegen_sparse_alloc.mlir
+++ b/mlir/test/Dialect/SparseTensor/codegen_sparse_alloc.mlir
@@ -1,7 +1,7 @@
 // RUN: mlir-opt %s --sparse-tensor-codegen --canonicalize --cse | FileCheck %s
 
 #CSR = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : dense, d1 : compressed)}>
-#COO = #sparse_tensor.encoding<{ lvlTypes = ["compressed_nu", "singleton"]}>
+#COO = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
 
 // CHECK-LABEL:   func.func @sparse_alloc_copy_CSR(
 // CHECK-SAME:      %[[VAL_0:.*0]]: memref<?xindex>,
diff --git a/mlir/test/Dialect/SparseTensor/conversion.mlir b/mlir/test/Dialect/SparseTensor/conversion.mlir
index f8e30872a0756..64f66c5cb65eb 100644
--- a/mlir/test/Dialect/SparseTensor/conversion.mlir
+++ b/mlir/test/Dialect/SparseTensor/conversion.mlir
@@ -25,8 +25,7 @@
 }>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["dense", "compressed", "compressed"],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : compressed, d1 : compressed)
 }>
 
 // CHECK-LABEL: func @sparse_nop(
diff --git a/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir b/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir
index 4707b199222ad..9fb1946d56263 100644
--- a/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir
+++ b/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir
@@ -15,8 +15,7 @@
 }>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["dense", "compressed", "compressed"],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : compressed, d1 : compressed)
 }>
 
 // CHECK-LABEL: func @sparse_convert_1d(
diff --git a/mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir b/mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir
index 363a63eb8ed1e..621235182c9a8 100644
--- a/mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir
+++ b/mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir
@@ -12,8 +12,7 @@
 }>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["dense", "compressed", "compressed"],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : compressed, d1 : compressed)
 }>
 
 // CHECK-LABEL: func @sparse_convert_1d(
diff --git a/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir b/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
index 296e1bf9030c6..b3eb50f1755da 100644
--- a/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
+++ b/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
@@ -26,17 +26,16 @@
 }>
 
 #SortedCOO2D = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ],
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton),
 }>
 
 #SortedCOO3D = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : compressed(nonunique), d1 : singleton(nonunique), d2 : singleton)
 
 }>
 
 #TsssPermuted = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : compressed, d0 : compressed, d1 : compressed)
 }>
 
 #COOSlice = #sparse_tensor.encoding<{
@@ -115,13 +114,13 @@ func.func @sparse_convert(%arg0: tensor<?xf32, #SparseVector64>) -> tensor<?xf32
 }
 
 #SparseSingleton64 = #sparse_tensor.encoding<{
-  lvlTypes = ["singleton"],
+  map = (d0) -> (d0 : singleton),
   posWidth = 64,
   crdWidth = 64
 }>
 
 #SparseSingleton32 = #sparse_tensor.encoding<{
-  lvlTypes = ["singleton"],
+  map = (d0) -> (d0 : singleton),
   posWidth = 32,
   crdWidth = 32
 }>
diff --git a/mlir/test/Dialect/SparseTensor/invalid.mlir b/mlir/test/Dialect/SparseTensor/invalid.mlir
index 8e25cf06bcb62..71e6eebb30261 100644
--- a/mlir/test/Dialect/SparseTensor/invalid.mlir
+++ b/mlir/test/Dialect/SparseTensor/invalid.mlir
@@ -32,7 +32,7 @@ func.func @invalid_pack_type(%values: tensor<6xf64>, %pos: tensor<2xi32>, %coord
 
 // -----
 
-#SparseVector = #sparse_tensor.encoding<{lvlTypes = ["compressed_nu", "singleton"], posWidth=32, crdWidth=32}>
+#SparseVector = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton), posWidth=32, crdWidth=32}>
 
 func.func @invalid_pack_type(%values: tensor<6xf64>, %pos: tensor<2xi32>, %coordinates: tensor<6x3xi32>)
                             -> tensor<100x2xf64, #SparseVector> {
@@ -68,7 +68,7 @@ func.func @invalid_unpack_type(%sp: tensor<100xf32, #SparseVector>, %values: ten
 
 // -----
 
-#SparseVector = #sparse_tensor.encoding<{lvlTypes = ["compressed_nu", "singleton"], posWidth=32, crdWidth=32}>
+#SparseVector = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton), posWidth=32, crdWidth=32}>
 
 func.func @invalid_unpack_type(%sp: tensor<100x2xf64, #SparseVector>, %values: tensor<6xf64>, %pos: tensor<2xi32>, %coordinates: tensor<6x3xi32>) {
   // expected-error@+1 {{input/output trailing COO level-ranks don't match}}
@@ -270,7 +270,7 @@ func.func @sparse_get_md(%arg0: !sparse_tensor.storage_specifier<#SparseVector>)
 
 // -----
 
-#COO = #sparse_tensor.encoding<{lvlTypes = ["compressed_nu", "singleton"]}>
+#COO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
 
 func.func @sparse_get_md(%arg0: !sparse_tensor.storage_specifier<#COO>) -> index {
   // expected-error@+1 {{requested position memory size on a singleton level}}
@@ -658,7 +658,7 @@ func.func @invalid_concat_dim(%arg0: tensor<2x4xf64, #DC>,
 
 #C = #sparse_tensor.encoding<{map = (d0) -> (d0 : compressed)}>
 #DC = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : dense, d1 : compressed)}>
-#DCC = #sparse_tensor.encoding<{lvlTypes = ["dense", "compressed", "compressed"]}>
+#DCC = #sparse_tensor.encoding<{map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : compressed)}>
 func.func @invalid_concat_rank_mismatch(%arg0: tensor<2xf64, #C>,
                                         %arg1: tensor<3x4xf64, #DC>,
                                         %arg2: tensor<4x4x4xf64, #DCC>) -> tensor<9x4xf64, #DC> {
diff --git a/mlir/test/Dialect/SparseTensor/pre_rewriting.mlir b/mlir/test/Dialect/SparseTensor/pre_rewriting.mlir
index 1245cb0eeed3c..5aa4acaf86393 100644
--- a/mlir/test/Dialect/SparseTensor/pre_rewriting.mlir
+++ b/mlir/test/Dialect/SparseTensor/pre_rewriting.mlir
@@ -5,7 +5,7 @@
 }>
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #DCSR = #sparse_tensor.encoding<{
diff --git a/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir b/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
index 0312758722bea..913059e2197f1 100644
--- a/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
+++ b/mlir/test/Dialect/SparseTensor/rewriting_for_codegen.mlir
@@ -10,7 +10,7 @@
 }>
 
 #COO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 // CHECK-LABEL:   func.func @sparse_new(
diff --git a/mlir/test/Dialect/SparseTensor/roundtrip.mlir b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
index d3f07fd298d72..d1262cb7aea02 100644
--- a/mlir/test/Dialect/SparseTensor/roundtrip.mlir
+++ b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
@@ -77,7 +77,7 @@ func.func @sparse_convert_1d_to_sparse(%arg0: tensor<64xf32>) -> tensor<64xf32,
 
 // -----
 
-#SparseTensor = #sparse_tensor.encoding<{ lvlTypes = [ "dense", "dense", "compressed" ] }>
+#SparseTensor = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : compressed) }>
 
 // CHECK-LABEL: func @sparse_convert_3d_from_sparse(
 // CHECK-SAME: %[[A:.*]]: tensor<8x8x8xf64, #{{.*}}>)
@@ -103,7 +103,7 @@ func.func @sparse_positions(%arg0: tensor<128xf64, #SparseVector>) -> memref<?xi
 
 // -----
 
-#COO = #sparse_tensor.encoding<{lvlTypes = ["compressed_nu", "singleton"]}>
+#COO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
 
 // CHECK-LABEL: func @sparse_indices_buffer(
 //  CHECK-SAME: %[[A:.*]]: tensor<?x?xf64, #{{.*}}>)
diff --git a/mlir/test/Dialect/SparseTensor/roundtrip_encoding.mlir b/mlir/test/Dialect/SparseTensor/roundtrip_encoding.mlir
index 1cc5c0e3f6152..60367b43a6ee0 100644
--- a/mlir/test/Dialect/SparseTensor/roundtrip_encoding.mlir
+++ b/mlir/test/Dialect/SparseTensor/roundtrip_encoding.mlir
@@ -85,8 +85,12 @@ func.func private @sparse_sorted_coo(tensor<10x10xf64, #SortedCOO>)
 // -----
 
 #BCSR = #sparse_tensor.encoding<{
-   lvlTypes = [ "compressed", "compressed", "dense", "dense" ],
-   dimToLvl  = affine_map<(i, j) -> (i floordiv 2, j floordiv 3, i mod 2, j mod 3)>
+   map = ( i, j ) ->
+      ( i floordiv 2 : compressed,
+        j floordiv 3 : compressed,
+        i mod 2      : dense,
+        j mod 3      : dense
+      )
 }>
 
 // CHECK-LABEL: func private @sparse_bcsr(
diff --git a/mlir/test/Dialect/SparseTensor/sorted_coo.mlir b/mlir/test/Dialect/SparseTensor/sorted_coo.mlir
index e4bc55fcdb062..95c410a08b0e4 100644
--- a/mlir/test/Dialect/SparseTensor/sorted_coo.mlir
+++ b/mlir/test/Dialect/SparseTensor/sorted_coo.mlir
@@ -1,7 +1,7 @@
 // RUN: mlir-opt %s -sparsification --canonicalize | FileCheck %s
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #trait_scale = {
diff --git a/mlir/test/Dialect/SparseTensor/sparse_2d.mlir b/mlir/test/Dialect/SparseTensor/sparse_2d.mlir
index 44c731e930274..00bf4ea440628 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_2d.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_2d.mlir
@@ -1050,7 +1050,7 @@ func.func @cmp_ss_ss(%arga: tensor<32x16xf32, #Tss>, %argb: tensor<32x16xf32, #T
 }
 
 #BatchedVector = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed_hi" ],
+  map = (d0, d1) -> (d0 : dense, d1 : compressed(high))
 }>
 // CHECK-LABEL:   func.func @sub_ss_batched(
 // CHECK-SAME:      %[[VAL_0:.*]]: tensor<2x3xf64, #{{.*}}>>,
diff --git a/mlir/test/Dialect/SparseTensor/sparse_3d.mlir b/mlir/test/Dialect/SparseTensor/sparse_3d.mlir
index 9019b9984d8f6..3513bc48ffc0e 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_3d.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_3d.mlir
@@ -3,14 +3,14 @@
 
 #Td = #sparse_tensor.encoding<{ map = (d0) -> (d0 : dense) }>
 
-#Tddd = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "dense",      "dense"      ] }>
-#Tdds = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "dense",      "compressed" ] }>
-#Tdsd = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "compressed", "dense"      ] }>
-#Tdss = #sparse_tensor.encoding<{ lvlTypes = [ "dense",      "compressed", "compressed" ] }>
-#Tsdd = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense",      "dense"      ] }>
-#Tsds = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "dense",      "compressed" ] }>
-#Tssd = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "dense"      ] }>
-#Tsss = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "compressed" ] }>
+#Tddd = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : dense) }>
+#Tdds = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : compressed) }>
+#Tdsd = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : dense) }>
+#Tdss = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : compressed) }>
+#Tsdd = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : dense, d2 : dense) }>
+#Tsds = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : dense, d2 : compressed) }>
+#Tssd = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : dense) }>
+#Tsss = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed) }>
 
 #trait3 = {
   indexing_maps = [
diff --git a/mlir/test/Dialect/SparseTensor/sparse_broadcast.mlir b/mlir/test/Dialect/SparseTensor/sparse_broadcast.mlir
index 3af4614dfe93e..ae5b941259f65 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_broadcast.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_broadcast.mlir
@@ -1,7 +1,7 @@
 // RUN: mlir-opt %s --sparsification --canonicalize --cse | FileCheck %s
 
 #DCSR = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed, d1 : compressed) }>
-#SparseTensor = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "compressed" ] }>
+#SparseTensor = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed) }>
 
 #trait = {
   indexing_maps = [
diff --git a/mlir/test/Dialect/SparseTensor/sparse_foreach.mlir b/mlir/test/Dialect/SparseTensor/sparse_foreach.mlir
index baa30c9457d2d..822cfb0148f24 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_foreach.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_foreach.mlir
@@ -141,7 +141,7 @@ func.func @foreach_print_slice(%A: tensor<4x4xf64, #CSR_SLICE>) {
 }
 
 #BCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed_hi_nu", "singleton" ],
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed(nonunique, high), d2 : singleton)
 }>
 
 // CHECK-LABEL:   func.func @foreach_bcoo(
diff --git a/mlir/test/Dialect/SparseTensor/sparse_nd.mlir b/mlir/test/Dialect/SparseTensor/sparse_nd.mlir
index 742d42be3f8c5..d05cebd55ce31 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_nd.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_nd.mlir
@@ -5,8 +5,10 @@
 // but an acyclic iteration graph using sparse constraints only.
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "dense", "compressed",
-                   "compressed", "dense", "dense", "dense" ]
+  map = (d0, d1, d2, d3,
+         d4, d5, d6, d7) -> (d0 : dense, d1 : dense, d2 : dense,
+                             d3 : compressed, d4 : compressed, d5 : dense,
+                             d6 : dense, d7 : dense)
 }>
 
 #trait_mul = {
diff --git a/mlir/test/Dialect/SparseTensor/sparse_out.mlir b/mlir/test/Dialect/SparseTensor/sparse_out.mlir
index 128c290e966b9..97d8da213423d 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_out.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_out.mlir
@@ -9,7 +9,7 @@
 }>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #trait_scale_inpl = {
diff --git a/mlir/test/Dialect/SparseTensor/sparse_pack.mlir b/mlir/test/Dialect/SparseTensor/sparse_pack.mlir
index 45906f4983567..8caf756362777 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_pack.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_pack.mlir
@@ -1,7 +1,7 @@
 // RUN: mlir-opt %s --canonicalize --post-sparsification-rewrite="enable-runtime-library=false" --sparse-tensor-codegen -cse --canonicalize | FileCheck %s
 
 #COO = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed_nu", "singleton"],
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton),
   crdWidth=32
 }>
 
diff --git a/mlir/test/Dialect/SparseTensor/sparse_perm.mlir b/mlir/test/Dialect/SparseTensor/sparse_perm.mlir
index 438f2c496d891..26712f2c7b001 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_perm.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_perm.mlir
@@ -2,8 +2,7 @@
 // RUN: mlir-opt %s -sparsification | FileCheck %s
 
 #X = #sparse_tensor.encoding<{
- lvlTypes = [ "dense", "dense", "dense" ],
- dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : dense, d1 : dense)
 }>
 
 #trait = {
diff --git a/mlir/test/Dialect/SparseTensor/sparse_perm_lower.mlir b/mlir/test/Dialect/SparseTensor/sparse_perm_lower.mlir
index 2e3d723889cdd..fd8aaf28697e4 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_perm_lower.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_perm_lower.mlir
@@ -4,8 +4,7 @@
 // RUN: FileCheck %s --check-prefix=CHECK-MIR
 
 #X = #sparse_tensor.encoding<{
- lvlTypes = [ "dense", "dense", "dense" ],
- dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : dense, d1 : dense)
 }>
 
 #trait = {
diff --git a/mlir/test/Dialect/SparseTensor/sparse_reshape_dot.mlir b/mlir/test/Dialect/SparseTensor/sparse_reshape_dot.mlir
index 43cf36fc0ac72..395a915f32806 100644
--- a/mlir/test/Dialect/SparseTensor/sparse_reshape_dot.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_reshape_dot.mlir
@@ -4,8 +4,8 @@
 //
 // RUN: mlir-opt %s --linalg-generalize-named-ops --sparsification --cse --canonicalize | FileCheck %s
 
-#COO_2D = #sparse_tensor.encoding<{ lvlTypes = [ "compressed_nu", "singleton" ], posWidth = 32, crdWidth = 32 }>
-#COO_3D = #sparse_tensor.encoding<{ lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ], posWidth = 32, crdWidth = 32 }>
+#COO_2D = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton), posWidth = 32, crdWidth = 32 }>
+#COO_3D = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed(nonunique), d1 : singleton(nonunique), d2 : singleton), posWidth = 32, crdWidth = 32 }>
 
 
 // CHECK-LABEL:   func.func @sparse_reshape_fused(
diff --git a/mlir/test/Dialect/SparseTensor/unsparsifiable_dense_op.mlir b/mlir/test/Dialect/SparseTensor/unsparsifiable_dense_op.mlir
index 2cef1afad2b89..7112d7dc8ca90 100644
--- a/mlir/test/Dialect/SparseTensor/unsparsifiable_dense_op.mlir
+++ b/mlir/test/Dialect/SparseTensor/unsparsifiable_dense_op.mlir
@@ -15,8 +15,8 @@
 }
 
 #VEC = #sparse_tensor.encoding<{ map = (d0) -> (d0 : compressed), posWidth = 32, crdWidth = 32 }>
-#COO = #sparse_tensor.encoding<{ lvlTypes = [ "compressed_nu", "singleton" ], posWidth = 32, crdWidth = 32 }>
-#CCC = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "compressed" ], posWidth = 32, crdWidth = 32 }>
+#COO = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton), posWidth = 32, crdWidth = 32 }>
+#CCC = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed), posWidth = 32, crdWidth = 32 }>
 
 //
 // This kernel can be sparsified as all unsparsifiable operations'
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/reshape_dot.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/reshape_dot.mlir
index a530f61959c20..27c2793a7688d 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/reshape_dot.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/reshape_dot.mlir
@@ -33,8 +33,8 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{env} %{run_sve} | FileCheck %s %}
 
 
-#COO_2D = #sparse_tensor.encoding<{ lvlTypes = [ "compressed_nu", "singleton" ], posWidth = 32, crdWidth = 32 }>
-#COO_3D = #sparse_tensor.encoding<{ lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ], posWidth = 32, crdWidth = 32 }>
+#COO_2D = #sparse_tensor.encoding<{ map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton), posWidth = 32, crdWidth = 32 }>
+#COO_3D = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed(nonunique), d1 : singleton(nonunique), d2 : singleton), posWidth = 32, crdWidth = 32 }>
 
 module {
   func.func private @printMemref3dF32(%ptr : tensor<?x?x?xf32>) attributes { llvm.emit_c_interface }
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_codegen_foreach.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_codegen_foreach.mlir
index af2c296459d5e..801c041eef1e3 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_codegen_foreach.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_codegen_foreach.mlir
@@ -43,17 +43,15 @@
 }>
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #SortedCOOPerm = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ],
-  dimToLvl = affine_map<(i,j) -> (j,i)>
+  map = (d0, d1) -> (d1 : compressed(nonunique), d0 : singleton)
 }>
 
 #CCCPerm = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed"],
-  dimToLvl = affine_map<(d0, d1, d2) -> (d1, d2, d0)>
+  map = (d0, d1, d2) -> (d1 : compressed, d2 : compressed, d0 : compressed)
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_collapse_shape.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_collapse_shape.mlir
index cbb4a81694602..bb0b69286d2b6 100755
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_collapse_shape.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_collapse_shape.mlir
@@ -39,11 +39,11 @@
 }>
 
 #Sparse3dTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed", "compressed", "compressed"]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #Sparse4dTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed", "compressed", "compressed", "compressed"]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed)
 }>
 
 //
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_1d_nwc_wcf.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_1d_nwc_wcf.mlir
index a2eafb8cc134c..8ed81cef82802 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_1d_nwc_wcf.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_1d_nwc_wcf.mlir
@@ -31,10 +31,11 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #CCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ] }>
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed) }>
 
 #CDC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : dense, d2 : compressed)
+
   // FIXME: Still inadmissible might need investigation
   // dimToLvl = affine_map<(i,j,k) -> (j,k,i)>
 }>
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nchw_fchw.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nchw_fchw.mlir
index 0d2e2582bd371..18a32ab8b503a 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nchw_fchw.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nchw_fchw.mlir
@@ -35,12 +35,12 @@
 
 
 #CDCD = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed", "dense" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : dense, d2 : compressed, d3 : dense)
 }>
 
 
 #CCCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed)
 }>
 
 // Creates and returns 4-D buffer of size (%s1, %s2, %s3, %s4) filled with the value %f
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nhwc_hwcf.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nhwc_hwcf.mlir
index c5ce85593d845..3f9db4e144e14 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nhwc_hwcf.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_2d_nhwc_hwcf.mlir
@@ -31,15 +31,15 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #CCCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed)
 }>
 
 #CDCD = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed", "dense" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : dense, d2 : compressed, d3 : dense)
 }>
 
 #DCCD = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "compressed", "dense" ]
+  map = (d0, d1, d2, d3) -> (d0 : dense, d1 : compressed, d2 : compressed, d3 : dense)
 }>
 
 // Creates and returns 4-D buffer of size (%s1, %s2, %s3, %s4) filled with the value %f
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d.mlir
index 3695bf3ffa3d6..cde0d4a750cdc 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d.mlir
@@ -31,15 +31,15 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #CCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #CDC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : dense, d2 : compressed)
 }>
 
 #DDC = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : compressed)
 }>
 
 // Creates and returns 3-D buffer of size (%s1, %s2, %s3) filled with the value %f
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d_ndhwc_dhwcf.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d_ndhwc_dhwcf.mlir
index 97b73175dc5f5..aa153f98339ba 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d_ndhwc_dhwcf.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conv_3d_ndhwc_dhwcf.mlir
@@ -31,11 +31,11 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #CCCCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2, d3, d4) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed, d4 : compressed)
 }>
 
 #CDCDC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed", "dense", "compressed"]
+  map = (d0, d1, d2, d3, d4) -> (d0 : compressed, d1 : dense, d2 : compressed, d3 : dense, d4 : compressed)
 }>
 
 // Creates and returns 5-D buffer of size (%s1, %s2, %s3, %s4, %s5) filled with the value %f
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion.mlir
index 783117954bc68..fe237588fff22 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion.mlir
@@ -31,18 +31,15 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #Tensor1  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (i,j,k)>
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #Tensor2  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (j,k,i)>
+  map = (d0, d1, d2) -> (d1 : compressed, d2 : compressed, d0 : compressed)
 }>
 
 #Tensor3  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : compressed, d0 : compressed, d1 : compressed)
 }>
 
 //
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_element.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_element.mlir
index 2ba3e57940bef..16eaca7663aaf 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_element.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_element.mlir
@@ -29,16 +29,15 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #Tensor1 = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : compressed(nonunique), d1 : singleton(nonunique), d2 : singleton)
 }>
 
 #Tensor2 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "dense" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : dense)
 }>
 
 #Tensor3 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (i,k,j)>
+  map = (d0, d1, d2) -> (d0 : dense, d2 : dense, d1 : compressed)
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2dense.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2dense.mlir
index 0e5de2e5ec9e8..04299101e40e4 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2dense.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2dense.mlir
@@ -31,33 +31,27 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #Tensor1  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (i,j,k)>
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #Tensor2  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (j,k,i)>
+  map = (d0, d1, d2) -> (d1 : compressed, d2 : compressed, d0 : compressed),
 }>
 
 #Tensor3  = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : compressed, d0 : compressed, d1 : compressed),
 }>
 
 #Tensor4  = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (i,j,k)>
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : compressed)
 }>
 
 #Tensor5  = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (j,k,i)>
+  map = (d0, d1, d2) -> (d1 : dense, d2 : compressed, d0 : compressed)
 }>
 
 #Tensor6  = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : dense, d0 : compressed, d1 : compressed)
 }>
 
 //
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2sparse.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2sparse.mlir
index 0f953a3c4e3c0..1c74b6827d980 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2sparse.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_sparse2sparse.mlir
@@ -32,32 +32,37 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #Tensor1 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : compressed)
+
 }>
 
 // NOTE: dense after compressed is not currently supported for the target
 // of direct-sparse2sparse conversion.  (It's fine for the source though.)
 #Tensor2 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "dense" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : dense)
+
 }>
 
 #Tensor3 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "compressed" ],
-  dimToLvl = affine_map<(i,j,k) -> (i,k,j)>
+  map = (d0, d1, d2) -> (d0 : dense, d2 : dense, d1 : compressed)
+
 }>
 
 #SingletonTensor1 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed, d2 : singleton)
+
 }>
 
 // This also checks the compressed->dense conversion (when there are zeros).
 #SingletonTensor2 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : singleton)
+
 }>
 
 // This also checks the singleton->compressed conversion.
 #SingletonTensor3 = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "dense", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : dense, d2 : compressed)
+
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_coo_test.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_coo_test.mlir
index fdbe84b9d332c..a1d8ab53fcba1 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_coo_test.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_coo_test.mlir
@@ -31,7 +31,7 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CSR = #sparse_tensor.encoding<{
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_expand_shape.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_expand_shape.mlir
index ae93f71e99a4a..c642f537411f4 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_expand_shape.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_expand_shape.mlir
@@ -39,11 +39,11 @@
 }>
 
 #Sparse3dTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed", "compressed", "compressed"]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #Sparse4dTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed", "compressed", "compressed", "compressed"]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed)
 }>
 
 //
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_flatten.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_flatten.mlir
index 56a26ec08b610..60f2e22ab4a82 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_flatten.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_flatten.mlir
@@ -34,12 +34,14 @@
 !Filename = !llvm.ptr<i8>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed", "compressed",
-                   "compressed", "compressed", "compressed", "compressed" ],
   // Note that any dimToLvl permutation should give the same results
   // since, even though it impacts the sparse storage scheme layout,
   // it should not change the semantics.
-  dimToLvl = affine_map<(i,j,k,l,m,n,o,p) -> (p,o,j,k,i,l,m,n)>
+  map = (d0, d1, d2, d3,
+         d4, d5, d6, d7) -> (d7 : compressed, d6 : compressed,
+                             d1 : compressed, d2 : compressed,
+                             d0 : compressed, d3 : compressed,
+                             d4 : compressed, d5 : compressed)
 }>
 
 #trait_flatten = {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_foreach_slices.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_foreach_slices.mlir
index cc472fc2ed848..d10ae8aee8141 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_foreach_slices.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_foreach_slices.mlir
@@ -38,7 +38,7 @@
 }>
 
 #COO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #COO_SLICE = #sparse_tensor.encoding<{
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_2d.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_2d.mlir
index 656fae6b7084d..a96e1a93cc56b 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_2d.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_2d.mlir
@@ -32,7 +32,7 @@
 }>
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CSR = #sparse_tensor.encoding<{
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_3d.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_3d.mlir
index 6c39796ac6648..d71ebf98cc943 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_3d.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_insert_3d.mlir
@@ -28,19 +28,19 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #TensorCSR = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : dense, d2 : compressed)
 }>
 
 #TensorRow = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "dense" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : dense)
 }>
 
 #CCoo = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed(nonunique), d2 : singleton)
 }>
 
 #DCoo = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed(nonunique), d2 : singleton)
 }>
 
 
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_matmul_slice.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_matmul_slice.mlir
index ac2a9c58220c9..6be70c3e41856 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_matmul_slice.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_matmul_slice.mlir
@@ -41,7 +41,7 @@
 }>
 
 #COO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CSR_SLICE_1 = #sparse_tensor.encoding<{
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_mttkrp.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_mttkrp.mlir
index e91fa97586b8c..306b88149e736 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_mttkrp.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_mttkrp.mlir
@@ -35,7 +35,7 @@
 !Filename = !llvm.ptr<i8>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #mttkrp = {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_out_reduction.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_out_reduction.mlir
index 7749f2845e115..f58094c8303e8 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_out_reduction.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_out_reduction.mlir
@@ -35,7 +35,7 @@
 }>
 
 #SparseTensor = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 #redsum = {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack.mlir
index 171c4afb3ea70..c464d01bf2ab3 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack.mlir
@@ -27,11 +27,11 @@
 // TODO: support sparse_tensor.unpack on libgen path.
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #SortedCOOI32 = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ],
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton),
   posWidth = 32,
   crdWidth = 32
 }>
@@ -43,7 +43,7 @@
 }>
 
 #BCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "dense", "compressed_hi_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : dense, d1 : compressed(nonunique, high), d2 : singleton)
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack_libgen.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack_libgen.mlir
index 9a48e7d466f92..b24dd8304b883 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack_libgen.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pack_libgen.mlir
@@ -27,11 +27,11 @@
 // after sparse_tensor.unpack is supported on libgen path.
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #SortedCOOI32 = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ],
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton),
   posWidth = 32,
   crdWidth = 32
 }>
@@ -44,7 +44,7 @@
 
 // TODO: "compressed_hi" is not supported by libgen path.
 // #BCOO = #sparse_tensor.encoding<{
-//   lvlTypes = [ "dense", "compressed_hi_nu", "singleton" ]
+//   map = (d0, d1, d2) -> (d0 : dense, d1 : compressed(nonunique, high), d2 : singleton)
 //}>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pooling_nhwc.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pooling_nhwc.mlir
index fb1f766495529..adea21aa8bdd0 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pooling_nhwc.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_pooling_nhwc.mlir
@@ -24,7 +24,7 @@
 // REDEFINE: %{sparse_compiler_opts} = enable-runtime-library=false enable-buffer-initialization=true enable-index-reduction=true
 // RUN: %{compile} | %{run} | FileCheck %s
 
-#CCCC = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "compressed", "compressed" ], posWidth = 32, crdWidth = 32 }>
+#CCCC = #sparse_tensor.encoding<{  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed), posWidth = 32, crdWidth = 32 }>
 
 func.func @pooling_nhwc_sum_CCCC(%input: tensor<1x4x4x1xf32, #CCCC>, %filter: tensor<2x2xf32>) -> tensor<1x3x3x1xf32, #CCCC> {
   %init = bufferization.alloc_tensor() : tensor<1x3x3x1xf32, #CCCC>
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_reshape.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_reshape.mlir
index 74803ec0e5584..cf6cee2f3b733 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_reshape.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_reshape.mlir
@@ -39,7 +39,7 @@
 }>
 
 #Sparse3dTensor = #sparse_tensor.encoding<{
-  lvlTypes = ["compressed", "compressed", "compressed"]
+  map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_scf_nested.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_scf_nested.mlir
index f451ae43cdef8..615c1d7bc4798 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_scf_nested.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_scf_nested.mlir
@@ -31,7 +31,7 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #map = affine_map<(d0, d1, d2) -> (d0, d1, d2)>
-#SparseMatrix = #sparse_tensor.encoding<{ lvlTypes = [ "compressed", "compressed", "compressed" ] }>
+#SparseMatrix = #sparse_tensor.encoding<{ map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed) }>
 
 module @func_sparse.2 {
   // Do elementwise x+1 when true, x-1 when false
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sorted_coo.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sorted_coo.mlir
index 177272e45a10c..b789450b4f88b 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sorted_coo.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_sorted_coo.mlir
@@ -35,21 +35,20 @@
 !Filename = !llvm.ptr<i8>
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #SortedCOOPermuted = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ],
-  dimToLvl = affine_map<(i,j) -> (j,i)>
+  map = (d0, d1) -> (d1 : compressed(nonunique), d0 : singleton),
 }>
 
 #SortedCOO3D = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ]
+  map = (d0, d1, d2) -> (d0 : compressed(nonunique), d1 : singleton(nonunique), d2 : singleton)
 }>
 
 #SortedCOO3DPermuted = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton_nu", "singleton" ],
-  dimToLvl = affine_map<(i,j,k) -> (k,i,j)>
+  map = (d0, d1, d2) -> (d2 : compressed(nonunique), d0 : singleton(nonunique), d1 : singleton)
+
 }>
 
 #trait_scale = {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_strided_conv_2d_nhwc_hwcf.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_strided_conv_2d_nhwc_hwcf.mlir
index 748b740d99abd..4c2af8cfa4327 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_strided_conv_2d_nhwc_hwcf.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_strided_conv_2d_nhwc_hwcf.mlir
@@ -31,11 +31,11 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #CCCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "compressed", "compressed", "compressed" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : compressed, d2 : compressed, d3 : compressed)
 }>
 
 #CDCC = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed", "dense", "compressed", "compressed" ]
+  map = (d0, d1, d2, d3) -> (d0 : compressed, d1 : dense, d2 : compressed, d3 : compressed)
 }>
 
 // Creates and returns 4-D buffer of size (%s1, %s2, %s3, %s4) filled with the value %f
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_mul.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_mul.mlir
index 9da1405163cb0..b37dc9e3d6316 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_mul.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_mul.mlir
@@ -30,7 +30,7 @@
 // Do the same run, but now with  VLA vectorization.
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
-#ST = #sparse_tensor.encoding<{lvlTypes = ["compressed", "compressed", "compressed"]}>
+#ST = #sparse_tensor.encoding<{map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)}>
 
 //
 // Trait for 3-d tensor element wise multiplication.
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_ops.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_ops.mlir
index b0a3691adae34..4d4ae1f19f963 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_ops.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_tensor_ops.mlir
@@ -30,8 +30,8 @@
 // Do the same run, but now with  VLA vectorization.
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
-#ST1 = #sparse_tensor.encoding<{lvlTypes = ["compressed", "compressed", "compressed"]}>
-#ST2 = #sparse_tensor.encoding<{lvlTypes = ["compressed", "compressed", "dense"]}>
+#ST1 = #sparse_tensor.encoding<{map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : compressed)}>
+#ST2 = #sparse_tensor.encoding<{map = (d0, d1, d2) -> (d0 : compressed, d1 : compressed, d2 : dense)}>
 
 //
 // Trait for 3-d tensor operation.
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_transpose_coo.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_transpose_coo.mlir
index 5cb3e5e6cd45d..e2e474a5492ed 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_transpose_coo.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_transpose_coo.mlir
@@ -32,7 +32,7 @@
 // RUN: %if mlir_arm_sve_tests %{ %{compile_sve} | %{run_sve} | FileCheck %s %}
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 module {
diff --git a/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matmul-lib.mlir b/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matmul-lib.mlir
index bb7efc8c3c2ae..6782f2d0e2014 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matmul-lib.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matmul-lib.mlir
@@ -25,7 +25,7 @@
 // RUNNOT: %{compile} enable-runtime-library=false gpu-data-transfer-strategy=zero-copy" | %{run}
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CSR = #sparse_tensor.encoding<{
diff --git a/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matvec-lib.mlir b/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matvec-lib.mlir
index 409eb96972971..eadc408fcc441 100644
--- a/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matvec-lib.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/GPU/CUDA/sparse-matvec-lib.mlir
@@ -25,7 +25,7 @@
 //
 
 #SortedCOO = #sparse_tensor.encoding<{
-  lvlTypes = [ "compressed_nu", "singleton" ]
+  map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)
 }>
 
 #CSR = #sparse_tensor.encoding<{