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pytorch - 💡(How to fix) Fix GPU gives wrong answer for rank-deficient lstsq [1 comments, 2 participants]

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pytorch/pytorch#180157•Fetched 2026-04-12 13:23:33
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beanduan22beanduan22
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beanduan22beanduan22lezcanolezcano
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Code Example

import torch
import numpy as np

A = torch.tensor([
    [1., 2., 3.],
    [4., 5., 6.],
    [7., 8., 9.],
], dtype=torch.float32)
B = A.clone()

# Reference: NumPy uses LAPACK gelsd (handles rank deficiency correctly)
ref = np.linalg.lstsq(A.numpy(), B.numpy(), rcond=None)[0]

cpu = torch.linalg.lstsq(A, B).solution
gpu = torch.linalg.lstsq(A.cuda(), B.cuda()).solution.cpu()

cpu_l2 = np.linalg.norm(ref - cpu.numpy())
gpu_l2 = np.linalg.norm(ref - gpu.numpy())

print("NumPy (reference):", ref[0])
print("CPU:              ", cpu[0].numpy())
print("GPU:              ", gpu[0].numpy())
print(f"CPU vs NumPy L2: {cpu_l2:.4e}")
print(f"GPU vs NumPy L2: {gpu_l2:.4e} ")
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🐛 Describe the bug

import torch
import numpy as np

A = torch.tensor([
    [1., 2., 3.],
    [4., 5., 6.],
    [7., 8., 9.],
], dtype=torch.float32)
B = A.clone()

# Reference: NumPy uses LAPACK gelsd (handles rank deficiency correctly)
ref = np.linalg.lstsq(A.numpy(), B.numpy(), rcond=None)[0]

cpu = torch.linalg.lstsq(A, B).solution
gpu = torch.linalg.lstsq(A.cuda(), B.cuda()).solution.cpu()

cpu_l2 = np.linalg.norm(ref - cpu.numpy())
gpu_l2 = np.linalg.norm(ref - gpu.numpy())

print("NumPy (reference):", ref[0])
print("CPU:              ", cpu[0].numpy())
print("GPU:              ", gpu[0].numpy())
print(f"CPU vs NumPy L2: {cpu_l2:.4e}")
print(f"GPU vs NumPy L2: {gpu_l2:.4e} ")

Versions

NumPy (reference): [ 0.8333333 0.33333334 -0.16666667] CPU: [ 0.83333385 0.3333333 -0.1666666 ] GPU: [ 0.58141476 0.7630715 -0. ] CPU vs NumPy L2: 7.5424e-07 GPU vs NumPy L2: 1.2867e+00

cc @ptrblck @msaroufim @eqy @jerryzh168 @tinglvv @nWEIdia @jianyuh @nikitaved @mruberry @walterddr @xwang233 @Lezcano

extent analysis

TL;DR

The issue can be mitigated by ensuring consistent numerical stability and potentially using a different solver or configuration for GPU computations in torch.linalg.lstsq.

Guidance

  • The discrepancy between CPU and GPU results suggests a numerical stability or precision issue, potentially due to differences in how torch.linalg.lstsq is implemented on CPU versus GPU.
  • Verify that the GPU has sufficient precision and that the input matrices A and B are correctly transferred to the GPU, as indicated by the .cuda() method.
  • Consider using a different solver or configuration for GPU computations, such as specifying a different algorithm or increasing the numerical precision, if possible.
  • To further diagnose the issue, compare the results of torch.linalg.lstsq on the CPU and GPU with a simpler or more robust solver, if available.

Example

No specific code example is provided due to the lack of detailed implementation specifics in the issue description.

Notes

The issue may be related to the inherent differences in floating-point precision between CPU and GPU architectures or the specific implementation of torch.linalg.lstsq on each platform. Further investigation into the solver's configuration and numerical stability is necessary.

Recommendation

Apply a workaround by using the CPU version of torch.linalg.lstsq for critical computations or exploring alternative solvers that can provide more consistent results across different hardware platforms.

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