Repository: pytorch
Issue: resutl of (torch.mm(a,b) does not match result of (a[:part,:], b)
Labels: module: numerical-stability,triaged,matrix multiplication

### 🐛 Describe the bug

I tried to use torch.mm compute block matrix multiplication  severally  instead of computing the result once , but I found the results of two computation are not close. For example,  when $a \in R^(m \times n)$, $a1 = a[:m/2, :]$,. $a2 = [m/2:,:]$ , $b \in R^{n \times kl}$,  torch.mm(a * b) should equal to torch.cat(torch.mm(a1, b), torch.mm(a2, b)), but actually they do not match. 

The following code presents this problem.  
```
import torch 

def test(m, n, k, dtype, rtol, atol):
    a = torch.randn(m, k, dtype=dtype).cuda() 
    b = torch.randn(k, n, dtype=dtype).cuda() 

    c = torch.mm(a, b) 
    for i in range(1,m+1):
        d = torch.mm(a[:i,:] , b)
        if not torch.allclose(d, c[:i, :], rtol, atol):
            print(f'Not match, m={i} {n=} {k=} {dtype=}')

dtypes = [(1.e-3, 1e-5, torch.float16),  (1.e-3, 1e-5, torch.bfloat16), (1e-5, 1e-8,torch.float32)]
for r, a, dtype in dtypes:
    for m in [4, 8, 16]:
        for n in [256, 512]:
            for k in [256, 512]:
                test(m, n, k, dtype, r, a)
```

### Versions

PyTorch version: 2.0.1+cu117
Is debug build: False
CUDA used to build PyTorch: 11.7
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.2 LTS (x86_64)
GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
Clang version: 14.0.0-1ubuntu1.1
CMake version: version 3.27.2
Libc version: glibc-2.35

Python version: 3.10.12 (main, Jun 11 2023, 05:26:28) [GCC 11.4.0] (64-bit runtime)
Python platform: Linux-5.10.16.3-microsoft-standard-WSL2-x86_64-with-glibc2.35
Is CUDA available: True
CUDA runtime version: Could not collect
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: NVIDIA GeForce RTX 3060 Ti
Nvidia driver version: 536.67
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
Address sizes:                   39 bits physical, 48 bits virtual
Byte Order:                      Little Endian
CPU(s):                          6
On-line CPU(s) list:             0-5
Vendor ID:                       GenuineIntel
Model name:                      12th Gen Intel(R) Core(TM) i5-12400
CPU family:                      6
Model:                           151
Thread(s) per core:              2
Core(s) per socket:              3
Socket(s):                       1
Stepping:                        5
BogoMIPS:                        4991.99
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 rep_good nopl xtopology tsc_reliable nonstop_tsc cpuid pni pclmulqdq vmx ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single ssbd ibrs ibpb stibp ibrs_enhanced tpr_shadow vnmi ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves umip waitpkg gfni vaes vpclmulqdq rdpid movdiri movdir64b fsrm serialize flush_l1d arch_capabilities
Virtualization:                  VT-x
Hypervisor vendor:               Microsoft
Virtualization type:             full
L1d cache:                       144 KiB (3 instances)
L1i cache:                       96 KiB (3 instances)
L2 cache:                        3.8 MiB (3 instances)
L3 cache:                        18 MiB (1 instance)
Vulnerability Itlb multihit:     Not affected
Vulnerability L1tf:              Not affected
Vulnerability Mds:               Not affected
Vulnerability Meltdown:          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
Vulnerability Srbds:             Not affected
Vulnerability Tsx async abort:   Not affected

Versions of relevant libraries:
[pip3] mypy-extensions==1.0.0
[pip3] numpy==1.25.2
[pip3] torch==2.0.1
[pip3] triton==2.0.0
[pip3] tritonclient==2.36.0
[conda] Could not collect