pytorch - 💡(How to fix) Fix `linalg.svd: algorithm failed to converge` on output of `torch.cumprod` over repeated embedding rows [1 comments, 2 participants]

pytorch2026-04-27 19:26:46

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pytorch/pytorch#181641•Fetched 2026-04-28 06:24:10

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jasminetrail

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jasminetrail

lezcano

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Error Message

torch._C._LinAlgError: linalg.svd: The algorithm failed to converge because the input matrix is ill-conditioned or has too many repeated singular values (error code: 12).

Root Cause

torch._C._LinAlgError: linalg.svd: The algorithm failed to converge because the
input matrix is ill-conditioned or has too many repeated singular values (error code: 12).

The failure is caused by a deterministic input construction that produces an extremely ill-conditioned matrix:

torch.zeros([16]) is used as input indices, so all 16 embedding lookups return the same row (index 0)
After rms_norm → LeakyReLU → GroupNorm → addcdiv, the 16 rows remain identical or nearly so
torch.cumprod(..., dim=0) over 16 identical rows produces exponentially scaled copies of the same vector (row k = row_0 ** (k+1) elementwise), creating a highly structured rank-1-like matrix with extreme value ranges
torch.linalg.svdvals calls LAPACK's divide-and-conquer SVD, which fails to converge on this numerically degenerate input (LAPACK error code 12)

Fix Action

Fix / Workaround

CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Address sizes: 52 bits physical, 57 bits virtual Byte Order: Little Endian CPU(s): 384 On-line CPU(s) list: 0-383 Vendor ID: AuthenticAMD Model name: AMD EPYC 9684X 96-Core Processor CPU family: 25 Model: 17 Thread(s) per core: 2 Core(s) per socket: 96 Socket(s): 2 Stepping: 2 BogoMIPS: 5099.98 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 amd_lbr_v2 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 perfmon_v2 ibrs ibpb stibp ibrs_enhanced vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local user_shstk avx512_bf16 clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin cppc amd_ibpb_ret arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif x2avic v_spec_ctrl vnmi avx512vbmi umip pku ospke avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq la57 rdpid overflow_recov succor smca fsrm flush_l1d debug_swap ibpb_exit_to_user Virtualization: AMD-V L1d cache: 6 MiB (192 instances) L1i cache: 6 MiB (192 instances) L2 cache: 192 MiB (192 instances) L3 cache: 2.3 GiB (24 instances) NUMA node(s): 2 NUMA node0 CPU(s): 0-95,192-287 NUMA node1 CPU(s): 96-191,288-383 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 Reg file data sampling: Not affected Vulnerability Retbleed: Not affected Vulnerability Spec rstack overflow: Mitigation; Safe RET 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; Enhanced / Automatic IBRS; IBPB conditional; STIBP always-on; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Not affected Vulnerability Vmscape: Mitigation; IBPB before exit to userspace

Code Example

torch._C._LinAlgError: linalg.svd: The algorithm failed to converge because the
input matrix is ill-conditioned or has too many repeated singular values (error code: 12).

---

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

m_emb  = nn.Embedding(15, 13)
m_relu = nn.LeakyReLU()
m_gn   = nn.GroupNorm(1, 13).eval()

torch.manual_seed(0)

def model():
    idx = (torch.abs(torch.zeros([16])) * 15).long().clamp(0, 14)  # all zeros -> index 0
    out = m_emb(idx)                                                # 16 identical rows [16, 13]
    out = F.rms_norm(out, [13])
    out = m_relu(out)
    out = m_gn(out)
    out = torch.addcdiv(m_emb(idx), out, torch.clamp(out, min=1e-6))
    out = torch.cumprod(out, dim=0)                                 # exponentially scaled identical rows
    out = torch.linalg.svdvals(out)                                 # ← LinAlgError
    return out

print(model())

RAW_BUFFERClick to expand / collapse

🐛 Describe the bug

torch.linalg.svdvals raises a LinAlgError in eager mode:

torch._C._LinAlgError: linalg.svd: The algorithm failed to converge because the
input matrix is ill-conditioned or has too many repeated singular values (error code: 12).

The failure is caused by a deterministic input construction that produces an extremely ill-conditioned matrix:

torch.zeros([16]) is used as input indices, so all 16 embedding lookups return the same row (index 0)
After rms_norm → LeakyReLU → GroupNorm → addcdiv, the 16 rows remain identical or nearly so
torch.cumprod(..., dim=0) over 16 identical rows produces exponentially scaled copies of the same vector (row k = row_0 ** (k+1) elementwise), creating a highly structured rank-1-like matrix with extreme value ranges
torch.linalg.svdvals calls LAPACK's divide-and-conquer SVD, which fails to converge on this numerically degenerate input (LAPACK error code 12)

Error logs

Minimal Reproducer

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

m_emb  = nn.Embedding(15, 13)
m_relu = nn.LeakyReLU()
m_gn   = nn.GroupNorm(1, 13).eval()

torch.manual_seed(0)

def model():
    idx = (torch.abs(torch.zeros([16])) * 15).long().clamp(0, 14)  # all zeros -> index 0
    out = m_emb(idx)                                                # 16 identical rows [16, 13]
    out = F.rms_norm(out, [13])
    out = m_relu(out)
    out = m_gn(out)
    out = torch.addcdiv(m_emb(idx), out, torch.clamp(out, min=1e-6))
    out = torch.cumprod(out, dim=0)                                 # exponentially scaled identical rows
    out = torch.linalg.svdvals(out)                                 # ← LinAlgError
    return out

print(model())

Versions

Collecting environment information... PyTorch version: 2.11.0+cu130 Is debug build: False CUDA used to build PyTorch: 13.0 ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.5 LTS (x86_64) GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04.3) 11.4.0 Clang version: 15.0.0 ([email protected]:llvm/llvm-project.git 4ba6a9c9f65bbc8bd06e3652cb20fd4dfc846137) CMake version: version 3.22.1 Libc version: glibc-2.35

Python version: 3.10.12 (main, Mar 3 2026, 11:56:32) [GCC 11.4.0] (64-bit runtime) Python platform: Linux-6.8.0-94-generic-x86_64-with-glibc2.35 Is CUDA available: False CUDA runtime version: No CUDA CUDA_MODULE_LOADING set to: N/A GPU models and configuration: No CUDA Nvidia driver version: No CUDA cuDNN version: No CUDA Is XPU available: False HIP runtime version: N/A MIOpen runtime version: N/A Is XNNPACK available: True Caching allocator config: N/A

Versions of relevant libraries: [pip3] numpy==2.2.6 [pip3] nvidia-cublas==13.1.0.3 [pip3] nvidia-cuda-cupti==13.0.85 [pip3] nvidia-cuda-nvrtc==13.0.88 [pip3] nvidia-cuda-runtime==13.0.96 [pip3] nvidia-cudnn-cu13==9.19.0.56 [pip3] nvidia-cufft==12.0.0.61 [pip3] nvidia-curand==10.4.0.35 [pip3] nvidia-cusolver==12.0.4.66 [pip3] nvidia-cusparse==12.6.3.3 [pip3] nvidia-cusparselt-cu13==0.8.0 [pip3] nvidia-nccl-cu13==2.28.9 [pip3] nvidia-nvjitlink==13.0.88 [pip3] nvidia-nvtx==13.0.85 [pip3] torch==2.11.0 [pip3] triton==3.6.0 [conda] Could not collect

cc @jianyuh @nikitaved @mruberry @walterddr @xwang233 @Lezcano @chauhang @penguinwu

extent analysis

TL;DR

The LinAlgError in torch.linalg.svdvals can be addressed by modifying the input matrix construction to avoid creating an ill-conditioned matrix.

Guidance

Verify that the input matrix is not ill-conditioned by checking its condition number before passing it to torch.linalg.svdvals.
Consider adding a small random noise to the input matrix to perturb it and avoid the degenerate case.
Use a different SVD algorithm that is more robust to ill-conditioned matrices, such as torch.svd with the full_matrices argument set to False.
Check the documentation of torch.linalg.svdvals for any specific requirements or recommendations for the input matrix.

Example

import torch

# Create a random matrix
matrix = torch.randn(16, 13)

# Add a small random noise to the matrix
matrix += 1e-6 * torch.randn(16, 13)

# Compute the SVD
svdvals = torch.linalg.svdvals(matrix)

Notes

The provided minimal reproducer creates a highly structured rank-1-like matrix with extreme value ranges, which causes the SVD algorithm to fail. Modifying the input matrix construction to avoid this degenerate case should resolve the issue.

Recommendation

Apply a workaround by adding a small random noise to the input matrix to perturb it and avoid the degenerate case, as shown in the example above. This should allow the SVD algorithm to converge and produce a valid result.

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pytorch - 💡(How to fix) Fix `linalg.svd: algorithm failed to converge` on output of `torch.cumprod` over repeated embedding rows [1 comments, 2 participants]

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pytorch - 💡(How to fix) Fix `linalg.svd: algorithm failed to converge` on output of `torch.cumprod` over repeated embedding rows [1 comments, 2 participants]

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