torch.combinations exhibits excessive memory usage and hangs for moderate n and r due to n^r #153337
Description
🐛 Describe the bug
The torch.combinations function becomes practically unusable for moderate n (number of elements in the input tensor) and r (combination size) due to excessive memory allocation and computation time, causing it to hang or result in an Out-of-Memory error. On my machine, a moderate n and r will use 200G RAM. This issue occurs because the underlying C++ implementation materializes intermediate tensors of size with_replacement flag and even when the final number of combinations (
Case
import torch
tensor = torch.tensor([-1.7267e-23+5.2018e-31j, -2.3499e+36-1.3891e-03j,
-5.1408e-37-2.9564e+04j, 1.9863e-35-2.4211e+23j,
-6.4697e+17+3.1194e+21j, 3.6179e+11-2.0433e+20j,
2.2603e+24-9.4820e+33j, -5.3270e-36-3.4165e-32j,
6.8278e+34+1.7954e-29j, -3.7343e-03-6.3649e+25j,
-1.2775e+17-5.5035e-17j])
torch.combinations(tensor, 10, with_replacement=True)Current behavior: Consumes huge memory and never finishes.
Root Cause
The implementation ( in aten/src/ATen/native/Itertools.cpp ) uses at::meshgrid to create r grid tensors.
If self has n elements and r is the combination size, meshgrid generates r output tensors. Each of these output tensors is expanded to r dimensions, with each dimension having size n. This results in each grid tensor having
The algorithm generate full Cartesian product then filter. However, that will generate huge tensors in the middle, The result is at size
I may expect that the memory and time complexity should ideally be more closely related to the number of output combinations rather than
Colab: https://colab.research.google.com/drive/1pzpf8PUKVkuRQ70_0Q8wFHvUkdtDMCFq?usp=sharing
// aten/src/ATen/native/Itertools.cpp:60
Tensor combinations(const Tensor& self, int64_t r, bool with_replacement) {
TORCH_CHECK(self.dim() == 1, "Expect a 1D vector, but got shape ", self.sizes());
TORCH_CHECK(r >= 0, "Expect a non-negative number, but got ", r);
if (r == 0) {
return at::empty({0}, self.options());
}
int64_t num_elements = self.numel();
std::vector<Tensor> grids = at::meshgrid(std::vector<Tensor>(r, self), "ij");
Tensor mask = _triu_mask(num_elements, r, with_replacement, self.options());
for(Tensor &t : grids) {
t = t.masked_select(mask);
}
return at::stack(grids, 1);
}Versions
Collecting environment information...
PyTorch version: 2.7.0+cu126
Is debug build: False
CUDA used to build PyTorch: 12.6
ROCM used to build PyTorch: N/A
OS: Ubuntu 24.04.1 LTS (x86_64)
GCC version: (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0
Clang version: 18.1.8 (++20240731025043+3b5b5c1ec4a3-1~exp1~20240731145144.92)
CMake version: version 4.0.2
Libc version: glibc-2.39
Python version: 3.12.3 (main, Feb 4 2025, 14:48:35) [GCC 13.3.0] (64-bit runtime)
Python platform: Linux-6.8.0-58-generic-x86_64-with-glibc2.39
Is CUDA available: False
CUDA runtime version: 12.8.93
CUDA_MODULE_LOADING set to: N/A
GPU models and configuration: Could not collect
Nvidia driver version: Could not collect
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: 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
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
Versions of relevant libraries:
[pip3] numpy==2.2.5
[pip3] nvidia-cublas-cu12==12.6.4.1
[pip3] nvidia-cuda-cupti-cu12==12.6.80
[pip3] nvidia-cuda-nvrtc-cu12==12.6.77
[pip3] nvidia-cuda-runtime-cu12==12.6.77
[pip3] nvidia-cudnn-cu12==9.5.1.17
[pip3] nvidia-cufft-cu12==11.3.0.4
[pip3] nvidia-curand-cu12==10.3.7.77
[pip3] nvidia-cusolver-cu12==11.7.1.2
[pip3] nvidia-cusparse-cu12==12.5.4.2
[pip3] nvidia-cusparselt-cu12==0.6.3
[pip3] nvidia-nccl-cu12==2.26.2
[pip3] nvidia-nvjitlink-cu12==12.6.85
[pip3] nvidia-nvtx-cu12==12.6.77
[pip3] optree==0.15.0
[pip3] torch==2.7.0
[pip3] triton==3.3.0
[conda] Could not collect