Repository: pytorch
Issue: grad_fn function disobeys broadcast rules
Labels: module: autograd,triaged

### grad_fn function disobeys broadcast rules

In the following code, `z.grad_fn` is `MulBackward0`. It should be the inverse of multiplication. However, the shapes of `x` and `x_` differ.
```
import torch

x = torch.randn(2, 1, requires_grad=True)
y = torch.randn(2, 3, requires_grad=True)
z = x * y
x_, y_ = z.grad_fn(z)
print(x_.shape, y_.shape) # Output: torch.Size([2, 3]) torch.Size([2, 3])
```

### Versions

Collecting environment information...
PyTorch version: 2.5.1+cu124
Is debug build: False
CUDA used to build PyTorch: 12.4
ROCM used to build PyTorch: N/A

OS: Rocky Linux release 8.10 (Green Obsidian) (x86_64)
GCC version: (GCC) 8.5.0 20210514 (Red Hat 8.5.0-22)
Clang version: Could not collect
CMake version: version 3.26.5
Libc version: glibc-2.28

Python version: 3.11.10 (main, Nov  5 2024, 07:57:54) [GCC 8.5.0 20210514 (Red Hat 8.5.0-22)] (64-bit runtime)
Python platform: Linux-4.18.0-553.27.1.el8_10.x86_64-x86_64-with-glibc2.28
Is CUDA available: False
CUDA runtime version: No CUDA
CUDA_MODULE_LOADING set to: N/A
GPU models and configuration: No CUDA
Nvidia driver version: No CUDA
cuDNN version: No CUDA
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: True

CPU:
Architecture:        x86_64
CPU op-mode(s):      32-bit, 64-bit
Byte Order:          Little Endian
CPU(s):              128
On-line CPU(s) list: 0-127
Thread(s) per core:  1
Core(s) per socket:  64
Socket(s):           2
NUMA node(s):        8
Vendor ID:           AuthenticAMD
CPU family:          25
Model:               1
Model name:          AMD EPYC 7763 64-Core Processor
Stepping:            1
CPU MHz:             3243.397
BogoMIPS:            4890.99
Virtualization:      AMD-V
L1d cache:           32K
L1i cache:           32K
L2 cache:            512K
L3 cache:            32768K
NUMA node0 CPU(s):   0-15
NUMA node1 CPU(s):   16-31
NUMA node2 CPU(s):   32-47
NUMA node3 CPU(s):   48-63
NUMA node4 CPU(s):   64-79
NUMA node5 CPU(s):   80-95
NUMA node6 CPU(s):   96-111
NUMA node7 CPU(s):   112-127
Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid aperfmperf pni pclmulqdq monitor ssse3 fma cx16 pcid sse4_1 sse4_2 movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 invpcid_single hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr wbnoinvd amd_ppin brs arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold v_vmsave_vmload vgif v_spec_ctrl umip pku ospke vaes vpclmulqdq rdpid overflow_recov succor smca fsrm

Versions of relevant libraries:
[pip3] numpy==2.1.3
[pip3] nvidia-cublas-cu12==12.4.5.8
[pip3] nvidia-cuda-cupti-cu12==12.4.127
[pip3] nvidia-cuda-nvrtc-cu12==12.4.127
[pip3] nvidia-cuda-runtime-cu12==12.4.127
[pip3] nvidia-cudnn-cu12==9.1.0.70
[pip3] nvidia-cufft-cu12==11.2.1.3
[pip3] nvidia-curand-cu12==10.3.5.147
[pip3] nvidia-cusolver-cu12==11.6.1.9
[pip3] nvidia-cusparse-cu12==12.3.1.170
[pip3] nvidia-nccl-cu12==2.21.5
[pip3] nvidia-nvjitlink-cu12==12.4.127
[pip3] nvidia-nvtx-cu12==12.4.127
[pip3] onnx==1.17.0
[pip3] torch==2.5.1
[pip3] torchvision==0.20.1
[pip3] triton==3.1.0
[conda] No relevant packages

cc @ezyang @albanD @gqchen @pearu @nikitaved @soulitzer @Varal7 @xmfan