Repository: pytorch
Issue: Inconsistency between CPU and GPU for `Linear()` layer with input size 0
Labels: module: nn,triaged,actionable,module: edge cases

### 🐛 Describe the bug

On a CPU, the following code:

```python
import torch

layer = torch.nn.Linear(0, 2)
x = torch.randn(3, 0)
print(x.shape)
y = layer(x)
print(y.shape)
print(y)
```

gives the following output:

```
/home/tgebhard/.virtualenvs/venv/lib/python3.10/site-packages/torch/nn/init.py:405: UserWarning: Initializing zero-element tensors is a no-op
  warnings.warn("Initializing zero-element tensors is a no-op")
torch.Size([3, 0])
torch.Size([3, 2])
tensor([[0., 0.],
        [0., 0.],
        [0., 0.]], grad_fn=<AddmmBackward0>)
```

Meanwhile, on a GPU, the equivalent code:
```python
import torch

layer = torch.nn.Linear(0, 2).to("cuda")
x = torch.randn(2, 0, device="cuda")
print(x.shape)
y = layer(x)
print(y.shape)
print(y)
```

produces:

```
torch.Size([3, 0])
/home/tgebhard/.virtualenvs/venv/lib/python3.10/site-packages/torch/nn/modules/linear.py:114: UserWarning: An output with one or more elements was resized since it had shape [3, 2], which does not match the required output shape [2]. This behavior is deprecated, and in a future PyTorch release outputs will not be resized unless they have zero elements. You can explicitly reuse an out tensor t by resizing it, inplace, to zero elements with t.resize_(0). (Triggered internally at ../aten/src/ATen/native/Resize.cpp:26.)
  return F.linear(input, self.weight, self.bias)
torch.Size([2])
tensor([0., 0.], device='cuda:0', grad_fn=<AddmmBackward0>)
```

I will admit that a linear layer with zero input features is a somewhat questionable use case, but as long as PyTorch supports such layers, I feel they should behave consistently?

### Versions

```
PyTorch version: 2.0.1+cu117
Is debug build: False
CUDA used to build PyTorch: 11.7
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.1 LTS (x86_64)
GCC version: (Ubuntu 11.3.0-1ubuntu1~22.04) 11.3.0
Clang version: Could not collect
CMake version: version 3.26.4
Libc version: glibc-2.35

Python version: 3.10.6 (main, Nov 14 2022, 16:10:14) [GCC 11.3.0] (64-bit runtime)
Python platform: Linux-5.15.0-58-generic-x86_64-with-glibc2.35
Is CUDA available: True
CUDA runtime version: Could not collect
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: NVIDIA A100-SXM4-40GB
Nvidia driver version: 530.30.02
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:                   43 bits physical, 48 bits virtual
Byte Order:                      Little Endian
CPU(s):                          256
On-line CPU(s) list:             4-7
Off-line CPU(s) list:            0-3,8-255
Vendor ID:                       AuthenticAMD
Model name:                      AMD EPYC 7662 64-Core Processor
CPU family:                      23
Model:                           49
Thread(s) per core:              2
Core(s) per socket:              64
Socket(s):                       2
Stepping:                        0
Frequency boost:                 enabled
CPU max MHz:                     2154.2959
CPU min MHz:                     1500.0000
BogoMIPS:                        4000.00
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 rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 x2apic 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 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 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 rdpru wbnoinvd amd_ppin arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip rdpid overflow_recov succor smca sme sev sev_es
Virtualization:                  AMD-V
L1d cache:                       4 MiB (128 instances)
L1i cache:                       4 MiB (128 instances)
L2 cache:                        64 MiB (128 instances)
L3 cache:                        512 MiB (32 instances)
NUMA node(s):                    2
NUMA node0 CPU(s):               0-63,128-191
NUMA node1 CPU(s):               64-127,192-255
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:          Mitigation; untrained return thunk; SMT enabled with STIBP protection
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl and seccomp
Vulnerability Spectre v1:        Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:        Mitigation; Retpolines, IBPB conditional, STIBP always-on, RSB filling, PBRSB-eIBRS Not affected
Vulnerability Srbds:             Not affected
Vulnerability Tsx async abort:   Not affected

Versions of relevant libraries:
[pip3] mypy==1.4.1
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.24.4
[pip3] torch==2.0.1
[pip3] torchdiffeq==0.2.3
[pip3] torchvision==0.15.2
[pip3] triton==2.0.0
[conda] blas                      1.0                         mkl
[conda] mkl                       2021.4.0           h06a4308_640
[conda] mkl-service               2.4.0           py310h7f8727e_0
[conda] mkl_fft                   1.3.1           py310hd6ae3a3_0
[conda] mkl_random                1.2.2           py310h00e6091_0
[conda] numpy                     1.23.5          py310hd5efca6_0
[conda] numpy-base                1.23.5          py310h8e6c178_0
[conda] numpydoc                  1.5.0           py310h06a4308_0
[conda] pytorch                   1.12.1          cpu_py310hb1f1ab4_1
```

cc @albanD @mruberry @jbschlosser @walterddr @mikaylagawarecki