D-Roberts opened a new pull request #18757: URL: https://github.com/apache/incubator-mxnet/pull/18757
As titled. This is a resubmit of [#18197](https://github.com/apache/incubator-mxnet/pull/18197) . In addition, tests were re-verified for robustness. ``` MXNET_TEST_COUNT=10000 pytest -v ~/workspace/incubator mxnet/tests/python/unittest/test_numpy_op.py::test_np_linalg_qr incubator-mxnet/tests/python/unittest/test_numpy_op.py::test_np_linalg_qr PASSED [100%] ``` The obtained gradient has the same values for a given input as with TensorFlow. The implemented method is similar to the method implemented in [tf](https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/linalg_grad.py) . Here are cross-checked examples: ``` import mxnet as mx import mxnet.numpy as np import numpy as _np _np.random.seed(42) data_np = _np.random.uniform(-1, 1, (3, 5)).astype(_np.float32) data = np.array(data_np, dtype='float32') data.attach_grad() with mx.autograd.record(): ret = np.linalg.qr(data) mx.autograd.backward(ret) print(data.grad) [[ 0.7569422 0.5140486 -0.48962986 -0.48962957 -0.48962957] [-2.414882 -1.2380642 -1.6602778 -1.6602782 -1.6602782 ] [ 0.2763981 -0.5044659 0.06115001 0.06115055 0.06115055]] import tensorflow as tf import numpy as _np _np.random.seed(42) data_np = _np.random.uniform(-1, 1, (3, 5)).astype(_np.float32) data = tf.convert_to_tensor(data_np) with tf.GradientTape() as g: g.watch(data) ret = tf.linalg.qr(data) print(g.gradient(ret, data)) tf.Tensor( [[ 0.75694233 0.51404876 -0.48962957 -0.48962957 -0.48962957] [-2.414882 -1.2380638 -1.6602784 -1.6602781 -1.6602781 ] [ 0.276398 -0.50446594 0.0611502 0.06115052 0.06115052]], shape=(3, 5), dtype=float32) ``` At high level the methodology is: partition/split the input A into 2 matrices X and Y and split matrix R (from A=QR decomposition) into 2 matrices U and V. Then X = QU and get X_grad by applying the gradient derivation from the square input case (m=n) with adjusted Q_grad. Also get Y_grad separately. Then A_grad is the concatenation of X_grad and Y_grad. ### Changes ### - [ ] qr backward wide input - [ ] tests ---------------------------------------------------------------- This is an automated message from the Apache Git Service. To respond to the message, please log on to GitHub and use the URL above to go to the specific comment. For queries about this service, please contact Infrastructure at: us...@infra.apache.org
