🐛 Describe the bug

torch.compile(backend='inductor') crashes with TypeError: list indices must be integers or slices, not NoneType when compiling torch.cumsum over a tensor that includes a broadcast addition with a bias vector, and the scan dimension size is >= 129.

The crash is in Inductor's SplitScan codegen path. When the scan dimension is <= 128, Inductor uses a single-block scan (works fine). When >= 129, it switches to SplitScan (multi-block), which crashes because TritonSplitScanKernel.initialize_range_tree sets tensor_dim=None for pointwise range trees, but the codegen later indexes a list with this None value when loading broadcast variables.

The same crash affects torch.cumprod, torch.logcumsumexp, and torch._higher_order_ops.associative_scan.

Reproducer

import torch

x = torch.randn(1, 129, 64, device='cuda')
b = torch.randn(64, device='cuda')

# Works
print(torch.cumsum(x + b, dim=1).shape)

# Crashes
print(torch.compile(lambda x, b: torch.cumsum(x + b, dim=1))(x, b).shape)

Error:

torch._inductor.exc.InductorError: TypeError: list indices must be integers or slices, not NoneType

Trigger conditions

The crash requires both:

1. A scan op (cumsum/cumprod/logcumsumexp) with scan dim size >= 129
2. A broadcast variable in the fused input (e.g., adding a bias vector)

Without broadcast (standalone cumsum(x)): compiles fine at any size. With broadcast but scan dim <= 128: compiles fine (uses single-block scan, not SplitScan).

Versions

• PyTorch 2.11.0+cu126: CRASH
• PyTorch 2.12.0.dev20260410+cu126 (nightly): CRASH
• GPU: NVIDIA Tesla T4 (sm_75), but not GPU-specific (codegen crash before kernel launch)

cc @chauhang @penguinwu @voznesenskym @EikanWang @jgong5 @Guobing-Chen @XiaobingSuper @zhuhaozhe @blzheng @wenzhe-nrv @jiayisunx @ipiszy @kadeng @muchulee8 @amjames @aakhundov @coconutruben @jataylo