Repository: pytorch
Issue: RWKV + Adam exp_avg_sq will change from positive to negative after loss.backward()
Labels: needs reproduction,module: optimizer,triaged

### 🐛 Describe the bug

when I run a task with RWKV(transformers RWKV, not directly from RWKV-LM repo) + Adam, I observe that in the second step, loss will become `NaN`. 
1. When I dive into that, I find out some values from `exp_avg_sqs`(state value in optimizer) are negative which will make https://github.com/pytorch/pytorch/blob/1b3dc05c3e703841e64e0277d473a0baf3296671/torch/optim/adam.py#L565 this line to give `NaN`(we are sqrt-ing on negative values). `exp_avg_sqs` is not supposed to be negative.
2. keep diving into this problem makes me find that when we call loss.backward() and we directly compare the `state['exp_avg_sqs']` value before https://github.com/pytorch/pytorch/blob/1b3dc05c3e703841e64e0277d473a0baf3296671/torch/autograd/__init__.py#L251 and after this line, some states' `exp_avg_sqs` will change from positive to negative which I think is not normal. 
3. looks like it is not a underflow, since some values with even lower number remain the same 
4. I am running under BFloat16 + autocast + GradScaler

How to fix this issue

Thanks in advance

### 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 20.04.5 LTS (x86_64)
GCC version: (Ubuntu 9.4.0-1ubuntu1~20.04.2) 9.4.0
Clang version: Could not collect
CMake version: version 3.26.4
Libc version: glibc-2.31

Python version: 3.10.12 (main, Jul  5 2023, 18:54:27) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-5.15.0-79-generic-x86_64-with-glibc2.31
Is CUDA available: True
CUDA runtime version: Could not collect
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: NVIDIA RTX A6000

Nvidia driver version: 530.30.02
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:                   43 bits physical, 48 bits virtual
CPU(s):                          64
On-line CPU(s) list:             0-63
Thread(s) per core:              2
Core(s) per socket:              16
Socket(s):                       2
NUMA node(s):                    2
Vendor ID:                       AuthenticAMD
CPU family:                      23
Model:                           49
Model name:                      AMD EPYC 7282 16-Core Processor
Stepping:                        0
Frequency boost:                 enabled
CPU MHz:                         1500.000
CPU max MHz:                     2800.0000
CPU min MHz:                     1500.0000
BogoMIPS:                        5599.92
Virtualization:                  AMD-V
L1d cache:                       1 MiB
L1i cache:                       1 MiB
L2 cache:                        16 MiB
L3 cache:                        128 MiB
NUMA node0 CPU(s):               0-15,32-47
NUMA node1 CPU(s):               16-31,48-63
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:          Mitigation; untrained return thunk; SMT enabled with STIBP protection
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; Retpolines, IBPB conditional, STIBP always-on, RSB filling, PBRSB-eIBRS Not affected
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 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip rdpid overflow_recov succor smca sme sev sev_es

Versions of relevant libraries:
[pip3] numpy==1.25.1
[pip3] pytorch-lightning==1.9.0
[pip3] torch==2.0.1
[pip3] torchaudio==2.0.2
[pip3] torchdata==0.6.1
[pip3] torchmetrics==1.0.3
[pip3] torchtext==0.15.2
[pip3] torchvision==0.15.2
[pip3] triton==2.0.0
[conda] numpy                     1.25.1                   pypi_0    pypi
[conda] pytorch-lightning         1.9.0                    pypi_0    pypi
[conda] torch                     2.0.1                    pypi_0    pypi
[conda] torchaudio                2.0.2                    pypi_0    pypi
[conda] torchdata                 0.6.1                    pypi_0    pypi
[conda] torchmetrics              1.0.3                    pypi_0    pypi
[conda] torchtext                 0.15.2                   pypi_0    pypi
[conda] torchvision               0.15.2                   pypi_0    pypi
[conda] triton                    2.0.0                    pypi_0    pypi

cc @vincentqb @jbschlosser @albanD @janeyx99 @crcrpar