Repository: pytorch
Issue: `autograd.Function` leads to `pylint` warnings in valid user code
Labels: module: autograd,module: typing,triaged,needs design

### 🐛 Describe the bug

Consider the following piece of code:

```python
# pylint: disable=missing-docstring

from torch import autograd


class Exp(autograd.Function):
    @staticmethod
    def forward(ctx, i):
        result = i.exp()
        ctx.save_for_backward(result)
        return result

    @staticmethod
    def backward(ctx, grad_output):
        (result,) = ctx.saved_tensors
        return grad_output * result


def usage():
    # Use it by calling the apply method:
    _ = Exp.apply(input)
```

This is a perfectly valid usage of `autograd.Function` (taken straight from the documentation). However, running `pylint` on this code results in the following warnings:

```python
************* Module example
example.py:6:0: W0223: Method 'jvp' is abstract in class '_SingleLevelFunction' but is not overridden in child class 'Exp' (abstract-method)
example.py:6:0: W0223: Method 'setup_context' is abstract in class '_SingleLevelFunction' but is not overridden in child class 'Exp' (abstract-method)
example.py:6:0: W0223: Method 'vjp' is abstract in class '_SingleLevelFunction' but is not overridden in child class 'Exp' (abstract-method)
example.py:6:0: W0223: Method 'vmap' is abstract in class 'Function' but is not overridden in child class 'Exp' (abstract-method)
example.py:8:4: W0221: Number of parameters was 3 in '_SingleLevelFunction.forward' and is now 2 in overriding 'Exp.forward' method (arguments-differ)
example.py:8:4: W0221: Variadics removed in overriding 'Exp.forward' method (arguments-differ)
example.py:14:4: W0221: Number of parameters was 2 in '_SingleLevelFunction.backward' and is now 2 in overriding 'Exp.backward' method (arguments-differ)
example.py:14:4: W0221: Variadics removed in overriding 'Exp.backward' method (arguments-differ)
```

The `abstract-method` warnings are triggered because the default implementation of the `forward`, `backward`, `jvp`, `vjp`, `vmap` and `setup_context` static methods raises `NotImplementedError`.

According to the [official python docs](https://docs.python.org/3/library/exceptions.html#NotImplementedError):

> *exception* `NotImplementedError`
> > This exception is derived from `RuntimeError`. In user defined base classes, abstract methods should raise this exception when they require derived classes to override the method, or while the class is being developed to indicate that the real implementation still needs to be added.

So all these methods are marked as abstract and `pylint` starts complaining that the user is not overriding them (even though overriding them is supposed to be optional). I think that this issue can be pretty trivially fixed by simply raising a different exception type.

---

Regarding the `arguments-differ` warnings, I think that they are happening because
```python
def forward(ctx, i): ...
def backward(ctx, grad_output): ...
```
technically, have narrower signatures than
```python
def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any: ...
def backward(ctx: Any, *grad_outputs: Any) -> Any: ...
```
and therefore break the Liskov substitution principle. I am honestly not sure, how to fix.

I guess, the "correct" way to fix this would be to make `_SingleLevelFunction` inherit from `Generic[P]` where `P` is a [`ParamSpec`](https://typing.readthedocs.io/en/latest/spec/generics.html#paramspec) and then annotate `apply` and all the other methods using `P.args` and `P.kwargs` instead of `Any`.

Edit: I wasn't able to make the `ParamSpec` version work, so I opened issue https://github.com/pylint-dev/pylint/issues/9424 asking about how this should be implemented.

### Versions

<details>

```
Collecting environment information...
PyTorch version: 2.1.2
Is debug build: False
CUDA used to build PyTorch: 12.2
ROCM used to build PyTorch: N/A

OS: NixOS 24.05 (Uakari) (x86_64)
GCC version: Could not collect
Clang version: Could not collect
CMake version: Could not collect
Libc version: glibc-2.38

Python version: 3.11.7 (main, Dec  4 2023, 18:10:11) [GCC 13.2.0] (64-bit runtime)
Python platform: Linux-6.1.74-x86_64-with-glibc2.38
Is CUDA available: True
CUDA runtime version: 12.2.140
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: NVIDIA GeForce RTX 3070 Ti Laptop GPU
Nvidia driver version: 545.29.06
cuDNN version: Could not collect
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):                             20
On-line CPU(s) list:                0-19
Vendor ID:                          GenuineIntel
Model name:                         12th Gen Intel(R) Core(TM) i9-12900HK
CPU family:                         6
Model:                              154
Thread(s) per core:                 2
Core(s) per socket:                 14
Socket(s):                          1
Stepping:                           3
CPU(s) scaling MHz:                 13%
CPU max MHz:                        5000.0000
CPU min MHz:                        400.0000
BogoMIPS:                           5836.80
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 tsc_known_freq pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm 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 vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid rdseed adx smap clflushopt clwb intel_pt sha_ni xsaveopt xsavec xgetbv1 xsaves split_lock_detect avx_vnni dtherm ida arat pln pts hwp hwp_notify hwp_act_window hwp_epp hwp_pkg_req hfi umip pku ospke waitpkg gfni vaes vpclmulqdq rdpid movdiri movdir64b fsrm md_clear serialize arch_lbr ibt flush_l1d arch_capabilities
Virtualization:                     VT-x
L1d cache:                          544 KiB (14 instances)
L1i cache:                          704 KiB (14 instances)
L2 cache:                           11.5 MiB (8 instances)
L3 cache:                           24 MiB (1 instance)
NUMA node(s):                       1
NUMA node0 CPU(s):                  0-19
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit:        Not affected
Vulnerability L1tf:                 Not affected
Vulnerability Mds:                  Not affected
Vulnerability Meltdown:             Not affected
Vulnerability Mmio stale data:      Not affected
Vulnerability Retbleed:             Not affected
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 IBRS, IBPB conditional, RSB filling, PBRSB-eIBRS SW sequence
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Not affected

Versions of relevant libraries:
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.26.2
[pip3] onnx==1.15.0
[pip3] pytorch-lightning==2.1.3
[pip3] torch==2.1.2
[pip3] torchaudio==2.1.2
[pip3] torchmetrics==1.3.0.post0
[pip3] torchvision==0.16.2
[pip3] triton==2.1.0
[conda] Could not collect
```

</details>

cc @ezyang @albanD @zou3519 @gqchen @pearu @nikitaved @soulitzer @Lezcano @Varal7 @malfet @xuzhao9 @gramster