[WIP][SYSTEMDS-3259] Shampoo optimizer

scripts/nn/optim/shampoo.dml

@@ -0,0 +1,44 @@
+#-------------------------------------------------------------
+#
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+#-------------------------------------------------------------
+
+/*
+ * Shampoo optimizer.
+ */
+
+update = function(matrix[double] X, matrix[double] dX, matrix[double] L, matrix[double] R, double lr)
+    return (matrix[double] X) {
+  /*
+   * Performs a vanilla SGD update.
+   *
+   * Inputs:
+   *  - X: Parameters to update, of shape (any, any).
+   *  - dX: Gradient wrt `X` of a loss function being optimized, of same shape as `X`.
+   *  - L: Left second-moment information of the accumulated gradients.
+   *  - R: Right second-moment information of the accumulated gradients.
+   *  - lr: Learning rate.
+   *
+   * Outputs:
+   *  - X: Updated parameters `X`, of same shape as input `X`.
+   */
+  L = L + dX %*% t(dX)
+  R = R + t(dX) %*% dX
+  X = X – lr * pow(L, -1/4) %*% dX %*% pow(R, -1/4))
+}