BendMlAutograd.linear_bwd: def of bend-ml-autograd@0.1.1.0
Import: import bend-ml-autograd@0.1.1.0/main.bend as BendMlAutograd
Lines 215-221 of bend-ml-autograd@0.1.1.0/main.bend: https://jend.leeeet.dev/read.txt?path=bend-ml-autograd@0.1.1.0/main.bend&start_line=215&end_line=221

import Base
import bend-ml-tensor@0.1.0.0/main.bend as T

# Given the gradient dy arriving at y, returns (dx, (dW, db)):
#   dx = dy · Wᵀ   (n x o)·(o x i) = n x i
#   dW = xᵀ · dy   (i x n)·(n x o) = i x o
#   db = sum of the rows of dy
# If any of these products had the wrong dimensions, the program would not compile.
def linear_bwd(+n: Nat, +i: Nat, +o: Nat, x: T.Mat<n, i>, w: T.Mat<i, o>, +dy: T.Mat<n, o>) -> T.Mat<n, i> & (T.Mat<i, o> & T.Vec<o>):
  (T.Mat.matmul(n, o, i, dy, T.Mat.transpose(i, o, w)), (T.Mat.matmul(i, n, o, T.Mat.transpose(n, i, x), dy), T.Mat.col_sums(n, o, dy)))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor@0.1.2.0/main.bend&name=Mat
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor@0.1.2.0/main.bend&name=Mat.col_sums
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor@0.1.2.0/main.bend&name=Mat.matmul
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor@0.1.2.0/main.bend&name=Mat.transpose
  https://jend.leeeet.dev/definition.txt?path=bend-ml-tensor@0.1.2.0/main.bend&name=Vec