Huge discrepancy between HuggingFace and Timm for ViT and other vision transformers
### Feature request

Differences between HugginFace and Timm implementation of Vision Transformers can be listed as below:
-Missing stochastic depth (https://arxiv.org/abs/2012.12877)
-Using m.weight.data.normal_(mean=0.0, std=0.02) instead of trunc_normal_()
-Missing trunc_normal_() init for the position embedding and cls_token

My DeiT started training properly once I started using the trunc_normal_() init and stochastic depth for my huggingface ViT model. Also, I remove the pruning head functionality and I no longer inherit the HuggingFace ViT model class from the "PretrainedModel" class, but I'm not actually sure if this actually caused my training to work properly.

### Motivation

These things could mean the difference between getting Nan or not during training for DeiT using the process from https://arxiv.org/abs/2012.12877

### Your contribution

Would love to share my code but I can't. I refer you to read the code (https://github.com/rwightman/pytorch-image-models/blob/master/timm/models/vision_transformer.py)
cc @NielsRogge @amyeroberts @alaradirik <|||||>@CharlesLeeeee thank you for bringing this up! We are aware of the discrepancy and aim to rectify it soon. We will fix the parameter initialization issue shortly and open a separate PR to add stochastic depth.

cc @LysandreJik @NielsRogge @amyeroberts <|||||>I believe setting eps in layernorm to 1e-6 rather than 1e-12 is also important.<|||||>FWIW there is an issue related to this on the timm side as well https://github.com/rwightman/pytorch-image-models/issues/1477

As per my comments, the init issue should be minor / non consequential as it would not result in a significant difference given that std == .02. I've trained from scratch with much more significantly different inits and the end results aren't too far off. 

The layer norm eps is likely an issue though, that was not mentioned on the timm side. For float16, 0 + 1e-12 = 0, not so for 1e-6 or 1e-5, which are defaults for all vision models I'm aware of that use LN. It looks like there are possibly other models that incorrectly use 1e-12 such as convnext? This could cause stability issues at reduced precision and will change the validation results for weights pretrained with 1e-5 or 1e-6. Generally 1e-12 should only be used as eps if you're sticking with float32 (or all uses of that eps are guaranteed to be upcast to float32).

<|||||>Kaiming initialization should be used for the nn.Conv2d rather than .normal_() initialization in the class ViTPreTrainedModel or any class that directly inherits from PretrainedModel. And the biases of the nn.Conv2d in ViT should be initialized the same way as PyTorch. (https://pytorch.org/docs/stable/_modules/torch/nn/modules/conv.html#Conv2d) @LysandreJik @NielsRogge @amyeroberts @alaradirik<|||||>This issue has been automatically marked as stale because it has not had recent activity. If you think this still needs to be addressed please comment on this thread.

Please note that issues that do not follow the [contributing guidelines](https://github.com/huggingface/transformers/blob/main/CONTRIBUTING.md) are likely to be ignored.<|||||>@CharlesLeeeee you are partially right, it seems that ViT uses PyTorch's default initialization scheme for `nn.conv2d`, at least in [timm](https://github.com/rwightman/pytorch-image-models/blob/7c4ed4d5a43f46084cc9b6f20a5edb8839bbeb14/timm/models/vision_transformer.py#L395). The JAX init however uses a LeCun normal as seen [here](https://github.com/rwightman/pytorch-image-models/blob/7c4ed4d5a43f46084cc9b6f20a5edb8839bbeb14/timm/models/vision_transformer.py#L415-L418). 

I'm working on this in #19449 