Repository: pytorch
Issue: Spectral Normalization can not be applied to Conv{1,2,3}d
Labels: module: nn,module: convolution,triaged,needs research,module: norms and normalization

### 🐛 Describe the bug

I would like to raise a concern about the spectral_norm parameterization. 

I strongly believe that Spectral-Normalization Parameterization introduced several versions ago does not work for Conv{1,2,3}d layers.

The reason is that reshaping the weight into a 2D is not enough. 
An easy fix could be obtained by rescaling through a scale factor of 1/(k1*k2)**0.5  the parameterized weights, where k1, k2 are the dimensions of the kernel filters. However, note that only should solve the problem for the case stride=1.

By running the following code
```
  import torch
  from torch.nn.utils.parametrizations import spectral_norm

  original_conv = torch.nn.Conv2d(200, 200, 7, padding=7//2, bias=False)
  lip_conv = spectral_norm(original_conv, n_power_iterations=40)

  with torch.no_grad():
      # Initializing original_conv weight to higher values
      for p in original_conv.parameters():
          p += 10*torch.rand(200, 200, 7, 7)

  # Estimating the Lipschitz constant on several inputs
  lip_cons = 0.
  for _ in range(100):
      dim = torch.randint(7, 100, [1]).item()
      x = 100*torch.rand(1, 200, dim, dim)
      lip_cons = max(lip_cons, lip_conv(x).norm(2)/x.norm(2))

  print(f'Lipschitz constant of lip_conv is greater than 1: {lip_cons}')
  
  # Power method applied to the weights of the lip_conv
  w = lip_conv.weight
  x = torch.randn(1, 200, 250, 250)
  for _ in range(40):
      x = torch.nn.functional.conv2d(x, w, padding=7//2,)
      sigma = x.norm(2)
      x /= sigma
  print(f'Estimated Lipschitz constant of lip_conv: {sigma} ~ 7')
  print()
```
you should obtain something like

```
Lipschitz constant of lip_conv is greater than 1: 5.880033016204834
Esitmated Lipschitz constant of lip_conv: 6.902995586395264 ~ 7
```

There is something I am doing wrong? If this is not the case, I would like to ask the developers, to properly notify in the Documentation that this feature is not valid for convolutional layers. This could avoid misuse of this implementation.

Thanks for your time,
Fabio

### Versions

Collecting environment information...
PyTorch version: 2.0.0
Is debug build: False
CUDA used to build PyTorch: 11.7
ROCM used to build PyTorch: N/A

OS: Ubuntu 18.04.4 LTS (x86_64)
GCC version: (Ubuntu 7.5.0-3ubuntu1~18.04) 7.5.0
Clang version: Could not collect
CMake version: version 3.10.2
Libc version: glibc-2.27

Python version: 3.10.10 (main, Mar 21 2023, 18:45:11) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-4.15.0-76-generic-x86_64-with-glibc2.27
Is CUDA available: True
CUDA runtime version: 10.1.243
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: Tesla V100-DGXS-32GB
GPU 1: Tesla V100-DGXS-32GB
GPU 2: Tesla V100-DGXS-32GB
GPU 3: Tesla V100-DGXS-32GB

Nvidia driver version: 515.65.01
cuDNN version: /usr/lib/x86_64-linux-gnu/libcudnn.so.7.6.5
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):              40
On-line CPU(s) list: 0-39
Thread(s) per core:  2
Core(s) per socket:  20
Socket(s):           1
NUMA node(s):        1
Vendor ID:           GenuineIntel
CPU family:          6
Model:               79
Model name:          Intel(R) Xeon(R) CPU E5-2698 v4 @ 2.20GHz
Stepping:            1
CPU MHz:             1485.012
CPU max MHz:         3600,0000
CPU min MHz:         1200,0000
BogoMIPS:            4397.23
Virtualization:      VT-x
L1d cache:           32K
L1i cache:           32K
L2 cache:            256K
L3 cache:            51200K
NUMA node0 CPU(s):   0-39
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 arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm rdt_a rdseed adx smap intel_pt xsaveopt cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts md_clear flush_l1d

Versions of relevant libraries:
[pip3] numpy==1.23.5
[pip3] torch==2.0.0
[pip3] torchvision==0.15.0
[pip3] triton==2.0.0
[conda] blas                      1.0                         mkl  
[conda] ffmpeg                    4.3                  hf484d3e_0    pytorch
[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] pytorch                   2.0.0           py3.10_cuda11.7_cudnn8.5.0_0    pytorch
[conda] pytorch-cuda              11.7                 h778d358_3    pytorch
[conda] pytorch-mutex             1.0                        cuda    pytorch
[conda] torchtriton               2.0.0                     py310    pytorch
[conda] torchvision               0.15.0              py310_cu117    pytorch


cc @albanD @mruberry @jbschlosser @walterddr @mikaylagawarecki