Inconsistent results between F.linear and manual computation

[eliahuhorwitz]

🐛 Describe the bug

I am observing an inconsistency between the results of F.linear and the manual computation of xW^T+b.

Below is a snipped that reproduces this (I ran it on a CPU, and on float16, float32, and float64):

import torch
from torch import nn
from torch.nn import functional as F


lin_layer = nn.Linear(200, 300)
input = torch.randn(1, 400, 200)
out_lin_layer = lin_layer(input)
out_lin = F.linear(input, lin_layer.weight.data, lin_layer.bias.data)
out_manual = input @ lin_layer.weight.data.t() + lin_layer.bias.data

print(f"torch.allclose(out_lin_layer, out_lin): {torch.allclose(out_lin_layer, out_lin)}") # prints True
print(f"torch.allclose(out_lin_layer, out_manual): {torch.allclose(out_lin_layer, out_manual)}")  # prints False

When looking at the out_manual tensor, some values have an error of 1e-7 to 1e-9. It's small, but in some cases may be enough to change the results.

This seems to be somehow related to the bias, when running the snipped below the manual calculation works as expected:

import torch
from torch import nn
from torch.nn import functional as F


lin_layer = nn.Linear(200, 300, bias=False)
input = torch.randn(1, 400, 200)
out_lin_layer = lin_layer(input)
out_lin = F.linear(input, lin_layer.weight.data)
out_manual = input @ lin_layer.weight.data.t()

print(f"torch.allclose(out_lin_layer, out_lin): {torch.allclose(out_lin_layer, out_lin)}") # prints True
print(f"torch.allclose(out_lin_layer, out_manual): {torch.allclose(out_lin_layer, out_manual)}")  # prints True

Versions

Collecting environment information...
PyTorch version: 2.5.1+cu124
Is debug build: False
CUDA used to build PyTorch: 12.4
ROCM used to build PyTorch: N/A

OS: CS HUJI Debian GNU/Linux 12 (bookworm) 5785 (x86_64)
GCC version: (Debian 12.2.0-14) 12.2.0
Clang version: 14.0.6
CMake version: version 3.25.1
Libc version: glibc-2.36

Python version: 3.10.15 (main, Oct 3 2024, 07:27:34) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-6.6.20-aufs-1-x86_64-with-glibc2.36
Is CUDA available: True
CUDA runtime version: Could not collect
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: GPU 0: NVIDIA RTX A5000
Nvidia driver version: 550.90.07
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: 48 bits physical, 48 bits virtual
Byte Order: Little Endian
CPU(s): 48
On-line CPU(s) list: 0-47
Vendor ID: AuthenticAMD
Model name: AMD EPYC 7443 24-Core Processor
CPU family: 25
Model: 1
Thread(s) per core: 1
Core(s) per socket: 24
Socket(s): 2
Stepping: 1
Frequency boost: enabled
CPU(s) scaling MHz: 65%
CPU max MHz: 4035.6440
CPU min MHz: 1500.0000
BogoMIPS: 5699.59
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 pcid sse4_1 sse4_2 x2apic 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 erms invpcid cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin brs arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold v_vmsave_vmload vgif v_spec_ctrl umip pku ospke vaes vpclmulqdq rdpid overflow_recov succor smca fsrm debug_swap
Virtualization: AMD-V
L1d cache: 1.5 MiB (48 instances)
L1i cache: 1.5 MiB (48 instances)
L2 cache: 24 MiB (48 instances)
L3 cache: 256 MiB (8 instances)
NUMA node(s): 8
NUMA node0 CPU(s): 0-5
NUMA node1 CPU(s): 6-11
NUMA node2 CPU(s): 12-17
NUMA node3 CPU(s): 18-23
NUMA node4 CPU(s): 24-29
NUMA node5 CPU(s): 30-35
NUMA node6 CPU(s): 36-41
NUMA node7 CPU(s): 42-47
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: Vulnerable: Safe RET, no microcode
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; Retpolines, IBPB conditional, IBRS_FW, STIBP disabled, RSB filling, PBRSB-eIBRS Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Not affected

Versions of relevant libraries:
[pip3] numpy==2.2.0
[pip3] nvidia-cublas-cu12==12.4.5.8
[pip3] nvidia-cuda-cupti-cu12==12.4.127
[pip3] nvidia-cuda-nvrtc-cu12==12.4.127
[pip3] nvidia-cuda-runtime-cu12==12.4.127
[pip3] nvidia-cudnn-cu12==9.1.0.70
[pip3] nvidia-cufft-cu12==11.2.1.3
[pip3] nvidia-curand-cu12==10.3.5.147
[pip3] nvidia-cusolver-cu12==11.6.1.9
[pip3] nvidia-cusparse-cu12==12.3.1.170
[pip3] nvidia-nccl-cu12==2.21.5
[pip3] nvidia-nvjitlink-cu12==12.4.127
[pip3] nvidia-nvtx-cu12==12.4.127
[pip3] torch==2.5.1
[pip3] torchaudio==2.5.1
[pip3] torchvision==0.20.1
[pip3] triton==3.1.0
[conda] numpy 2.2.0 pypi_0 pypi
[conda] nvidia-cublas-cu12 12.4.5.8 pypi_0 pypi
[conda] nvidia-cuda-cupti-cu12 12.4.127 pypi_0 pypi
[conda] nvidia-cuda-nvrtc-cu12 12.4.127 pypi_0 pypi
[conda] nvidia-cuda-runtime-cu12 12.4.127 pypi_0 pypi
[conda] nvidia-cudnn-cu12 9.1.0.70 pypi_0 pypi
[conda] nvidia-cufft-cu12 11.2.1.3 pypi_0 pypi
[conda] nvidia-curand-cu12 10.3.5.147 pypi_0 pypi
[conda] nvidia-cusolver-cu12 11.6.1.9 pypi_0 pypi
[conda] nvidia-cusparse-cu12 12.3.1.170 pypi_0 pypi
[conda] nvidia-nccl-cu12 2.21.5 pypi_0 pypi
[conda] nvidia-nvjitlink-cu12 12.4.127 pypi_0 pypi
[conda] nvidia-nvtx-cu12 12.4.127 pypi_0 pypi
[conda] torch 2.5.1 pypi_0 pypi
[conda] torchaudio 2.5.1 pypi_0 pypi
[conda] torchvision 0.20.1 pypi_0 pypi
[conda] triton 3.1.0 pypi_0 pypi

cc @albanD @mruberry @jbschlosser @walterddr @mikaylagawarecki

[malfet]

This feels like a classical example of https://pytorch.org/docs/main/notes/numerical_accuracy.html

I suspect you get the same discrepancy using https://pytorch.org/docs/stable/generated/torch.addmm.html vs the manual calculation. When matmul and bias operations are fused, results are usually more "accurate", but slightly different that results of unfused operation