Repository: pytorch
Issue: With FSDP2, a small tensor on a 1-GPU world size has grad=0
Labels: oncall: distributed,triaged,module: fsdp

### 🐛 Describe the bug

I train a model normally, and one of the parameters remains at 0 throughout the run. Its grad is always zero, but it should be a large value.

Ablations:
If I use world_size 8, I don't see this. The parameter moves and the grad is 30000 rather than 0.
If I change the parameter from shape (1,) to shape (1, 1), the grad remains 0.
If I change the parameter from shape (1,) to shape (2,) and use `torch.mean(my_param)`, the grad remains 0.
If I change the parameter from shape (1,) to shape (10000000,) and use `torch.mean(my_param)`, the grad is non-zero and the parameter trains normally.
If I change the parameter from shape (1,) to shape (), I am told `ValueError: fully_shard doesn't support salar parameters. Change log_multiplier to a 1D tensor with numel equal to 1.` (This is a known limitation.)
I use 3 other instances of this class. Those instances do not have this problem and their gradient works normally. All the instances which have problems are in FSDP2 submodules, and all the instances without problems are in the root FSDP2 module. I do not know if this is connected. These other instances have numel 256, 768, and 1.
When I check `my_parameter.requires_grad`, it's `True`.

I unfortunately am too busy to produce a repro in the next week. Some brief attempts at creating one from scratch did not produce this error. For example, the following code works fine and does not exhibit the error (it's not a repro):

```
# torchrun --standalone --nnodes=1 --nproc-per-node=1 fsdp2_1nodes.py
import torch
from torch.distributed._tensor import DTensor, Shard, Replicate, distribute_tensor, distribute_module, init_device_mesh
import os
import torch.distributed as dist
import datetime
import torch.nn as nn
import torch.nn.functional as F
from torch.distributed._composable.fsdp import fully_shard, MixedPrecisionPolicy

world_size = int(os.getenv("WORLD_SIZE", None))
local_rank = int(os.getenv("LOCAL_RANK", None))
global_rank = int(os.getenv("RANK", None))
print(f"world_size: {world_size}, local_rank: {local_rank}, global_rank: {global_rank}")

dist.init_process_group(
    backend="cpu:gloo,cuda:nccl",
    init_method=None,
    world_size=world_size,
    rank=global_rank,
    device_id=torch.device(f"cuda:{local_rank}"),
    timeout=datetime.timedelta(seconds=120),
)
torch.cuda.set_device(local_rank)

device_mesh = init_device_mesh("cuda", (1,))
model = torch.nn.Linear(8, 8, device=f"cuda:{local_rank}")

class ExpMultiply(nn.Module):
    def __init__(self, shape=(1, 1), starting_value=0.0):
        super().__init__()
        # any init here would not survive FSDP1/FSDP2 sharding.
        # shape must be 1D instead of 0D to make FSDP1 happy. "ValueError: FSDP doesn't support salar parameters. Change resnets.0.resnet_blocks.0.skip_projection_multiplier to a 1D tensor with numel equal to 1."
        self.log_multiplier = torch.nn.Parameter(
            torch.empty(shape, dtype=torch.float32, device=f"cuda:{local_rank}")
        )
        self.starting_value = starting_value

    def init_weights(self, generator=None):
        # torch.nn.init.constant_(self.log_multiplier, self.starting_value)
        torch.nn.init.zeros_(self.log_multiplier)

    def forward(self, x):
        return torch.mul(x, torch.exp(self.log_multiplier + self.starting_value))

a = ExpMultiply((1,), 1.0)

fully_shard(model)
fully_shard(a)
nn.init.zeros_(model.weight)
a.init_weights()
print(model.weight)
a(model(torch.randn(8, 8, device=f"cuda:{local_rank}"))).sum().backward()
print(model.weight.grad)
print(a.log_multiplier.grad)
```

To exhibit the issue, `a.log_multiplier.grad` would have to be 0. It is not.

### Versions

```
Collecting environment information...
PyTorch version: 2.5.1
Is debug build: False
CUDA used to build PyTorch: 12.6
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.5 LTS (x86_64)
GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
Clang version: Could not collect
CMake version: version 3.31.1
Libc version: glibc-2.35

Python version: 3.10.12 (main, Nov  6 2024, 20:22:13) [GCC 11.4.0] (64-bit runtime)
Python platform: Linux-6.5.13-650-3434-22042-coreweave-1-x86_64-with-glibc2.35
Is CUDA available: True
CUDA runtime version: 12.6.85
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: NVIDIA H100 80GB HBM3
Nvidia driver version: 535.216.01
cuDNN version: Probably one of the following:
/usr/lib/x86_64-linux-gnu/libcudnn.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_adv.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_cnn.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_engines_precompiled.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_engines_runtime_compiled.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_graph.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_heuristic.so.9.5.1
/usr/lib/x86_64-linux-gnu/libcudnn_ops.so.9.5.1
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:                      46 bits physical, 57 bits virtual
Byte Order:                         Little Endian
CPU(s):                             128
On-line CPU(s) list:                0-127
Vendor ID:                          GenuineIntel
Model name:                         Intel(R) Xeon(R) Platinum 8462Y+
CPU family:                         6
Model:                              143
Thread(s) per core:                 2
Core(s) per socket:                 32
Socket(s):                          2
Stepping:                           8
CPU max MHz:                        4100.0000
CPU min MHz:                        800.0000
BogoMIPS:                           5600.00
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 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 cat_l2 cdp_l3 invpcid_single cdp_l2 ssbd mba ibrs ibpb stibp ibrs_enhanced tpr_shadow flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb intel_pt avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local split_lock_detect avx_vnni avx512_bf16 wbnoinvd dtherm ida arat pln pts hfi vnmi avx512vbmi umip pku ospke waitpkg avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg tme avx512_vpopcntdq la57 rdpid bus_lock_detect cldemote movdiri movdir64b enqcmd fsrm md_clear serialize tsxldtrk pconfig arch_lbr ibt amx_bf16 avx512_fp16 amx_tile amx_int8 flush_l1d arch_capabilities
Virtualization:                     VT-x
L1d cache:                          3 MiB (64 instances)
L1i cache:                          2 MiB (64 instances)
L2 cache:                           128 MiB (64 instances)
L3 cache:                           120 MiB (2 instances)
NUMA node(s):                       2
NUMA node0 CPU(s):                  0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126
NUMA node1 CPU(s):                  1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127
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 / Automatic IBRS; IBPB conditional; RSB filling; PBRSB-eIBRS SW sequence; BHI BHI_DIS_S
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Not affected

Versions of relevant libraries:
[pip3] clip-anytorch==2.6.0
[pip3] dctorch==0.1.2
[pip3] DISTS-pytorch==0.1
[pip3] gpytorch==1.13
[pip3] lovely-numpy==0.2.13
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.24.4
[pip3] torch==2.5.1
[pip3] torchaudio==2.5.0
[pip3] torchdiffeq==0.2.5
[pip3] torchsde==0.2.6
[pip3] torchvision==0.20.0
[pip3] triton==3.1.0
[pip3] welford-torch==0.2.4
[conda] Could not collect
```

cc @H-Huang @awgu @kwen2501 @wanchaol @fegin @fduwjj @wz337 @wconstab @d4l3k @c-p-i-o @zhaojuanmao @mrshenli @rohan-varma @chauhang