Repository: pytorch
Issue: Precision Differences in Using `dropout` and `linear`
Labels: module: numerical-stability,triaged

### 🐛 Describe the bug

**Description:**

I have encountered some precision differences when using the `dropout` and `linear` in the following way.

**Code to Reproduce:**

```python
import torch.nn.functional as f
import torch

# Precision error is calculated based on the Chebyshev distance.

args = torch.load('dropout.pt')

output = f.dropout(args['parameter:0'], args['parameter:1'], args['parameter:2'], args['parameter:3'])

args = torch.load('linear.pt')

output = f.linear(output, args['parameter:1'], args['parameter:2'])
```

**Precision Differences:**

- `dropout`: 
  - CPU: -397.17065
  - GPU: -397.17065
  - Precision Differences: 0.
- `linear`: 
  - CPU: -43764688.
  - GPU: -43764812.
  - Precision Differences: 124.

**System Info:**
- PyTorch Version: 2.3.1+cu121
- OS: Ubuntu 20.04.3 LTS
- Python version: Python 3.8.0
- CUDA version: 12.1

**Expected Behavior:**
The calculation results of every API are consistent across CPU and GPU, with precision differences less than 1e-3.

**Actual Behavior:**
The CPU and GPU results of the second API `linear` show differences greater than the accepted threshold 1e-3.

**Additional Context:**
[2200 pt files](https://drive.google.com/drive/folders/17CIzezLLKD86a4XBTntrzAi2GRg7GU-i?usp=sharing)

Thank you for your attention to this matter. Please let me know if any further information is required.

### Versions

PyTorch version: 2.3.1+cu121
Is debug build: False
CUDA used to build PyTorch: 12.1
ROCM used to build PyTorch: N/A

OS: Ubuntu 20.04.3 LTS (x86_64)
GCC version: (Ubuntu 9.3.0-17ubuntu1~20.04) 9.3.0
Clang version: Could not collect
CMake version: Could not collect
Libc version: glibc-2.31

Python version: 3.8.0 (default, Nov  6 2019, 21:49:08)  [GCC 7.3.0] (64-bit runtime)
Python platform: Linux-5.15.0-100-generic-x86_64-with-glibc2.10
Is CUDA available: True
CUDA runtime version: 10.1.243
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: NVIDIA GeForce RTX 2080 Ti
GPU 1: NVIDIA GeForce RTX 2080 Ti
GPU 2: NVIDIA GeForce RTX 2080 Ti

Nvidia driver version: 550.54.14
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
Byte Order:                         Little Endian
Address sizes:                      45 bits physical, 48 bits virtual
CPU(s):                             80
On-line CPU(s) list:                40,58,63,66
Off-line CPU(s) list:               0-39,41-57,59-62,64,65,67-79
Thread(s) per core:                 0
Core(s) per socket:                 40
Socket(s):                          2
NUMA node(s):                       2
Vendor ID:                          GenuineIntel
CPU family:                         6
Model:                              106
Model name:                         Intel(R) Xeon(R) Gold 5320 CPU @ 2.20GHz
Stepping:                           6
CPU MHz:                            2199.999
BogoMIPS:                           4399.99
L1d cache:                          3.8 MiB
L1i cache:                          2.5 MiB
L2 cache:                           100 MiB
L3 cache:                           78 MiB
NUMA node0 CPU(s):                  0-39
NUMA node1 CPU(s):                  40-79
Vulnerability Gather data sampling: Vulnerable: No microcode
Vulnerability Itlb multihit:        KVM: Mitigation: VMX unsupported
Vulnerability L1tf:                 Not affected
Vulnerability Mds:                  Not affected
Vulnerability Meltdown:             Not affected
Vulnerability Mmio stale data:      Vulnerable: Clear CPU buffers attempted, no microcode; SMT disabled
Vulnerability Retbleed:             Not affected
Vulnerability Spec rstack overflow: Not affected
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; Enhanced IBRS, IBPB conditional, RSB filling, PBRSB-eIBRS SW sequence
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Not affected
Flags:                              fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc arch_perfmon rep_good nopl xtopology tsc_reliable nonstop_tsc cpuid tsc_known_freq pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch invpcid_single ssbd ibrs ibpb stibp ibrs_enhanced fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves wbnoinvd arat avx512vbmi umip pku ospke avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq rdpid fsrm md_clear flush_l1d arch_capabilities

Versions of relevant libraries:
[pip3] numpy==1.24.4
[pip3] torch==2.3.1
[pip3] torchaudio==2.3.1
[pip3] torchvision==0.18.1
[pip3] triton==2.3.1
[conda] numpy                     1.24.4                   pypi_0    pypi
[conda] torch                     2.3.1                    pypi_0    pypi
[conda] torchaudio                2.3.1                    pypi_0    pypi
[conda] torchvision               0.18.1                   pypi_0    pypi
[conda] triton                    2.3.1                    pypi_0    pypi