* [Perf]Removed usless assign op in while_loop

* refine assign

* add 0d support for dist, trace, paddle.linalg.cond test=allcase

* add_0d_output_support_for_det

* test=allcase

* support_0d_output_for_linalg.norm

* support linalg.norm 0d output, test=allcase

* fix 0D test

* fix zero dim test, test=allcase

* fix 0D test

* fix tets,test=allcase

* fix error,test=allcase

* fix errors ,test=allcase

* add static backward , test=allcase

* add static backwward test, test=allcase

* fix pr-ci-build error;test=document_fix (#53060)

* [Cherry-Pick] Unique support float16&bfloat16 (#53023)

unique支持float16和bfloat16数据类型，并完善相关单测。

* slogdet_support_0D_output

* add new case

* fix tests, test=allcase

* fix p_norm related test, test=allcase

* fix some err, test=allcase

* test=allcase

* move out trace

* open some case, test=allcase

* fix norm all case, test=allcase

* fix some test error, test=allcase

* fix typro,test=allcase

* fix test err, test=allcase

* test=allcase

* test

* fix test error, test=allcase

* fix test error, test=allcase

* fallback norm, test=allcase

---------
Co-authored-by: Ntianshuo78520a <707759223@qq.com>
Co-authored-by: NZhang Zheng <32410583+ZzSean@users.noreply.github.com>

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* fix test cases, test=allcase

* fix test cases, test=allcase

* modify the test_squeeze to not use Tensor type axis, test=allcase

* add grad check for unbind and unstack, test=allcase

* check for squeeze axis tensor type, test=allcase

* fix bug, test=allcase

* 【Hackathon 4th No.12】为 Paddle 新增 Cauchy API

* [Change]修改初始化方法与类型检查

* [Change]将测试用例移动到新的目录下

* [Change]适配to_tensor的0D

To make it synchronized at the first recv operator.
If warping all send and recv operators with group start and end, the received tensor will be not complete.

* 'fmin'

* 'fix'

* 'fix'

* add mul doubel grad

* add sub_double_grad

* add add sub high test

* add mutiply test

* modify other unsqueeze

* delete api.yaml

* only for make ci run

* midify unsqueeze

* modify unsqueeze

* tmp

* modify operants gen

[Dy2St]Get grad names when call append backward to fix high order gradient (#53250)

* support fp16 for maxout op

* format code

* change api

* add test for static float16

* format code

* formatting code

* atol alignment

* experiment—1

* experiment-2

* experiment-3

* format code

* trans fused_feedward Compute function to phi

* add register info

* remove maxfunctor

* move fused feedward to phi

* remove sig file

* remove fliud include

* add include

* add include

* add sig file

* add output register info

* fix sig file

* Update fused_feedforward_sig.cc

* fix grad kernel

* update output register info

* fix

* open fused_feedforward static build

* add optional and fix code style

* fix output info for fused attention

* add optional param

* merge

* support OD level and skip dynamic loss scaling for bf16

* [Fix CppExtension Unittest] Change CUDAExtension to CppExtension if necessary

* Temporarily test cpp_extension under GPU

* Split mixed_extension unittest

* add jacobian and hessian in paddle.autograd

* disable unitest 'func_multi_input' for bug in high-order gradient of multiply

* add dimension checks

* add support for 0-D tensor

* change return type from Jacobian to Hessian in hessian function

* refine Jacobian _flatten function for single xs

* refine support for 0-D tensor

* 1. add 'func_multi_input' unitest for multiply_grad_kernel bug fixed
already.
2. support non-inplace math operation via magical method overwriting.

* add unitest for math operation and raise error when 0-D tensor is indexed

* add ndim check on ys and xs according to is_batched, and add one unitest

* refine docstring of jacobian and hessian

* move paddle.incubate.autograd.Jacobian/Hessian to paddle.incubate.autograd.functional.Jacobian/Hessian

* remove single_input unitest case because numerical differentiation is wrong

* remove 3 unitest for numerical result(reference result) is wrong

* 1. rename autodiff.py to autograd.py
2. increase TIMEOUT to 100

* cancel modification for functional Jacobian/Hessian

* 1. use tuple as return type instead of list
2. refine docstring

* add more unitest case to improve coverage

* remove 2 unitest of Hessian for numerical result is wrong

* remove 1 unitest of Hessian for numerical result is wrong

* remove 1 unitest of Hessian for numerical result is wrong

* change unit test to shape check

* correct doc and replace incubate API to stable API in _grad

* modify concat_grad add sum comp rule

* modify opcompat

* updata Adamw.py

out.backward()  -> loss.backward()

* Update adamw.py

* [XPU] remove scale_loss in parallel.py

* [XPU] throw Unimplemented when using Reducer

* add pad op

* add_some_code

* modify some code

* add some code

* add some code

* modify some code

* add some code

* modify some code

* Update composite_backward_api.h

* modify some code

* add some code

* add some code

* add some code

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* polish

* rm paddle_install_dir

* update test=document_fix

* update test=document_fix

* update

* add test

* update

* update

* update

* update

* update

* update

* update

* update

* update

* add todo commont

* add scatter_nd_add comp

* add scatter_nd_add prim

* fix

* fix

* add public_python_api in TestScatterNdAddSimpleOp setup function

* fix composite_backward_api.h

* fix composite_backward

* add test cases

* fix composite_backward_api.h, unittest

* add test cases, test=allcase

* fix test cases, test=allcase

* fix test cases, test=allcase

* assert_allclose, test=allcase

* 1e-5 to 1e-4, test=allcase

* change rtol from 1e-4 to 1e-3, test=allcase

* modify numel in lbfgs and add a new test case. test=develop

* change param 'lr' to 'learning_rate' in lbfgs and its test

* add opt LBFGS and change test