Repository: pytorch
Issue: Composition of torch.compile and torch.func.grad silently produces a wrong result. 
Labels: high priority,triaged,oncall: pt2,module: inductor

### 🐛 Describe the bug

The following code sample shows the case when the composition of ```torch.compile``` and ```torch.func.grad``` of a function silently produces a wrong result. 

The output of the JIT-compiled version of the function itself is the same as the output of the uncompiled version of the function.

Curiously, if one comments out the last line before the return statement in the test function ```test_func```, namely ```processed_vars = (processed_vars.unsqueeze(-2) @ dependency_matrix).squeeze(dim=-2)```, the results of the compiled and uncompiled gradients are the same. 

```python
import torch

fixed_values = torch.tensor([[    0.0000,     0.0000,     0.0000,     0.0000,     0.0000,     0.0000],
                             [    0.0000,     0.0000,     0.0000,     0.0000,     0.0000,     0.0000],
                             [    0.0000,     0.0000,     0.0000,     0.0000,     0.0000,     0.0000],
                             [-1068.6385,     0.0000,    65.0000,     0.0000, -torch.inf,     0.0000]],
                            dtype=torch.float64)

free_vars_mask = torch.tensor([[ True,  True, False,  True,  True,  True],
                               [ True, False,  True,  True,  True,  True],
                               [ True,  True,  True,  True,  True,  True],
                               [False, False, False, False, False,  True]])

dependency_matrix = torch.tensor([[[1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 1.0000, 2.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.5000, 1.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000]],
                        
                                  [[1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000]],
                          
                                  [[1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000]],
                          
                                  [[1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000],
                                   [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000]]],
                                 dtype=torch.float64)

free_vars_linear_indices = torch.where(free_vars_mask.ravel())[0]
free_vars_indices = tuple(map(lambda x: x.detach().clone(),\
                              torch.unravel_index(free_vars_linear_indices,\
                                                  free_vars_mask.shape)))

test_input = torch.tensor([-218.5399,    3.1056,   21.8333,    4.1535,    0.2   ,  144.8986,
                             49.6429,   60.1429,    3.9028,    0.59  ,  126.218 ,   -6.0392,
                             98.5   ,   35.5714,    4.8792,    0.2   ,    0.01  ],
                          dtype=torch.float64)

def to_constrained_params(vars):
    
    two_over_pi = torch.tensor(2.0 / torch.pi, dtype=vars.dtype)
    one = torch.tensor(1.0, dtype=vars.dtype)
    hundred = torch.tensor(100.0, dtype=vars.dtype)
    fifty = torch.tensor(50.0, dtype=vars.dtype)
    
    processed_vars = torch.zeros_like(vars)

    processed_vars[:, 0] += (two_over_pi * torch.arctan(vars[:, 0] / hundred) + one)*fifty
    processed_vars[:, 2] += torch.abs(vars[:, 2])
    processed_vars[:, 3] += torch.abs(vars[:, 3])
    processed_vars[:, 4] += torch.exp(vars[:, 4])

    processed_vars[:, 1] += torch.abs(vars[:, 1])
    processed_vars[[2], 1] *= -1
    
    weights = torch.abs(vars[:, 5])
    weights = weights / torch.sum(weights)
    processed_vars[:, 5] += weights

    return processed_vars
    
def test_func(free_vars):

    # Prepare free variable by placing them at the right indices of the All Variables Matrix
    free_vars_same_shape = torch.zeros_like(fixed_values, dtype=free_vars.dtype)
    free_vars_same_shape[free_vars_indices] += free_vars

    # Create All Variables Matrix by merging free variable and fixed variables
    # and performing Unconstrained-To-Constrained transformation
    processed_vars = to_constrained_params(fixed_values + free_vars_same_shape)

    processed_vars = (processed_vars.unsqueeze(-2) @ dependency_matrix).squeeze(dim=-2)
    
    return processed_vars.sum()

# the Test Function without JIT compilation
print(test_func(test_input))
# tensor(760.4707, dtype=torch.float64)

# the Test Function with JIT compilation - Same Output
print(torch.compile(test_func, fullgraph=True)(test_input))
# tensor(760.4707, dtype=torch.float64)


# The gradient of the test function without JIT
print(torch.func.grad(test_func, argnums=0)(test_input))
# tensor([5.5109e-02, 1.0000e+00, 1.5000e+00, 6.3656e+01, 0.0000e+00, 1.0270e-01,
#         1.0000e+00, 1.0000e+00, 4.9541e+01, 0.0000e+00, 1.2275e-01, 1.0000e+00,
#         1.0000e+00, 1.0000e+00, 1.3153e+02, 0.0000e+00, 0.0000e+00],
#        dtype=torch.float64)

# The gradient of the test function with JIT
print(torch.compile(torch.func.grad(test_func, argnums=0), fullgraph=True)(test_input))
# tensor([0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
#        dtype=torch.float64)
```

### Error logs

_No response_

### Minified repro

_No response_

### Versions

Collecting environment information...
PyTorch version: 2.4.1
Is debug build: False
CUDA used to build PyTorch: None
ROCM used to build PyTorch: N/A

OS: Ubuntu 24.04.1 LTS (x86_64)
GCC version: (Ubuntu 13.2.0-23ubuntu4) 13.2.0
Clang version: Could not collect
CMake version: version 3.28.3
Libc version: glibc-2.39

Python version: 3.12.2 | packaged by conda-forge | (main, Feb 16 2024, 20:50:58) [GCC 12.3.0] (64-bit runtime)
Python platform: Linux-6.11.0-1-t2-noble-x86_64-with-glibc2.39
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
Address sizes:                        39 bits physical, 48 bits virtual
Byte Order:                           Little Endian
CPU(s):                               16
On-line CPU(s) list:                  0-15
Vendor ID:                            GenuineIntel
Model name:                           Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
CPU family:                           6
Model:                                158
Thread(s) per core:                   2
Core(s) per socket:                   8
Socket(s):                            1
Stepping:                             13
CPU(s) scaling MHz:                   74%
CPU max MHz:                          5000.0000
CPU min MHz:                          800.0000
BogoMIPS:                             4800.00
Flags:                                fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb ssbd ibrs ibpb stibp ibrs_enhanced tpr_shadow flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid mpx rdseed adx smap clflushopt intel_pt xsaveopt xsavec xgetbv1 xsaves dtherm ida arat pln pts hwp hwp_act_window hwp_epp vnmi md_clear flush_l1d arch_capabilities
Virtualization:                       VT-x
L1d cache:                            256 KiB (8 instances)
L1i cache:                            256 KiB (8 instances)
L2 cache:                             2 MiB (8 instances)
L3 cache:                             16 MiB (1 instance)
NUMA node(s):                         1
NUMA node0 CPU(s):                    0-15
Vulnerability Gather data sampling:   Mitigation; Microcode
Vulnerability Itlb multihit:          KVM: Mitigation: VMX disabled
Vulnerability L1tf:                   Not affected
Vulnerability Mds:                    Not affected
Vulnerability Meltdown:               Not affected
Vulnerability Mmio stale data:        Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed:               Mitigation; Enhanced IBRS
Vulnerability Spec rstack overflow:   Not affected
Vulnerability Spec store bypass:      Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1:             Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:             Mitigation; Enhanced / Automatic IBRS; IBPB conditional; RSB filling; PBRSB-eIBRS SW sequence; BHI SW loop, KVM SW loop
Vulnerability Srbds:                  Mitigation; Microcode
Vulnerability Tsx async abort:        Mitigation; TSX disabled

Versions of relevant libraries:
[pip3] flake8==7.0.0
[pip3] mypy==1.10.0
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.26.4
[pip3] numpydoc==1.7.0
[pip3] optree==0.12.1
[pip3] torch==2.4.1
[pip3] torchaudio==2.4.1
[pip3] torchopt==0.7.3
[pip3] torchvision==0.19.1
[conda] _anaconda_depends         2024.06             py312_mkl_2  
[conda] blas                      1.0                         mkl  
[conda] cpuonly                   2.0                           0    pytorch
[conda] ffmpeg                    4.3                  hf484d3e_0    pytorch
[conda] libjpeg-turbo             2.0.0                h9bf148f_0    pytorch
[conda] mkl                       2023.1.0         h213fc3f_46344  
[conda] mkl-service               2.4.0           py312h5eee18b_1  
[conda] mkl_fft                   1.3.10          py312h5eee18b_0  
[conda] mkl_random                1.2.7           py312h526ad5a_0  
[conda] numpy                     1.26.4          py312hc5e2394_0  
[conda] numpy-base                1.26.4          py312h0da6c21_0  
[conda] numpydoc                  1.7.0           py312h06a4308_0  
[conda] optree                    0.12.1                   pypi_0    pypi
[conda] pytorch                   2.4.1              py3.12_cpu_0    pytorch
[conda] pytorch-mutex             1.0                         cpu    pytorch
[conda] torchaudio                2.4.1                 py312_cpu    pytorch
[conda] torchopt                  0.7.3                    pypi_0    pypi
[conda] torchvision               0.19.1                py312_cpu    pytorch

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