[BUG] Differences between training result using zero-2 and zero-3

Describe the bug
I fine-tune Mistral using deepspeed with the same config including seed except zero setting (one is zero-2 and the other is zero-3). The first 20 steps' training loss differences are huge. zero-2's loss is 1.5 but zero-3's loss is 1.8.

To Reproduce
Steps to reproduce the behavior:
fine-tuning mistral with huggingface trainer integrated with deepspeed

Expected behavior
similar training loss

ds_report output
[2024-02-25 06:04:23,954] [INFO] [real_accelerator.py:161:get_accelerator] Setting ds_accelerator to cuda (auto detect)

DeepSpeed C++/CUDA extension op report

NOTE: Ops not installed will be just-in-time (JIT) compiled at
runtime if needed. Op compatibility means that your system
meet the required dependencies to JIT install the op.

JIT compiled ops requires ninja
ninja .................. [OKAY]

op name ................ installed .. compatible

[WARNING] async_io requires the dev libaio .so object and headers but these were not found.
[WARNING] async_io: please install the libaio-dev package with apt
[WARNING] If libaio is already installed (perhaps from source), try setting the CFLAGS and LDFLAGS environment variables to where it can be found.
async_io ............... [NO] ....... [NO]
fused_adam ............. [NO] ....... [OKAY]
cpu_adam ............... [NO] ....... [OKAY]
cpu_adagrad ............ [NO] ....... [OKAY]
cpu_lion ............... [NO] ....... [OKAY]
[WARNING] Please specify the CUTLASS repo directory as environment variable $CUTLASS_PATH
evoformer_attn ......... [NO] ....... [NO]
fused_lamb ............. [NO] ....... [OKAY]
fused_lion ............. [NO] ....... [OKAY]
inference_core_ops ..... [NO] ....... [OKAY]
cutlass_ops ............ [NO] ....... [OKAY]
quantizer .............. [NO] ....... [OKAY]
ragged_device_ops ...... [NO] ....... [OKAY]
ragged_ops ............. [NO] ....... [OKAY]
random_ltd ............. [NO] ....... [OKAY]
[WARNING] sparse_attn requires a torch version >= 1.5 and < 2.0 but detected 2.1
[WARNING] using untested triton version (2.1.0), only 1.0.0 is known to be compatible
sparse_attn ............ [NO] ....... [NO]
spatial_inference ...... [NO] ....... [OKAY]
transformer ............ [NO] ....... [OKAY]
stochastic_transformer . [NO] ....... [OKAY]
transformer_inference .. [NO] ....... [OKAY]

DeepSpeed general environment info:
torch install path ............... ['/opt/conda/lib/python3.10/site-packages/torch']
torch version .................... 2.1.0
deepspeed install path ........... ['/opt/conda/lib/python3.10/site-packages/deepspeed']
deepspeed info ................... 0.12.5, unknown, unknown
torch cuda version ............... 11.8
torch hip version ................ None
nvcc version ..................... 11.8
deepspeed wheel compiled w. ...... torch 2.1, cuda 11.8
shared memory (/dev/shm) size .... 503.37 GB

System info (please complete the following information):

• GPU: 8XA100 in a single node
• Python 3.10
• transformers 4.36.2
• deepspeed 0.12.5

Launcher context
yes

Docker context
pytorch 2.1.0 with cuda 11.8

Start by reproducing the Mistral fine-tuning run with Hugging Face Trainer using the same seed and configuration, changing only DeepSpeed ZeRO-2 versus ZeRO-3 on the reported environment. Compare the first 20 training losses and investigate the differing ZeRO behavior; done means the cause is identified and the expected loss consistency is restored or documented.