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pytorch - 💡(How to fix) Fix torch.xlogy(0, 0) returns NaN, while in many numerical computing libraries (e.g., SciPy) and common machine learning practice, it is defined as 0.

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Root Cause

Minimal 3-line version:

print("\nMinimal: xlogy at x=0") v = torch.tensor([0.0, 0.5, 1.0, 2.0]) print(f"xlogy(v, v) = {torch.xlogy(v, v)}")

Expected: [nan, -0.3466, 0.0, 1.3863]

NaN because xlogy(0, 0) = 0 * log(0) = 0 * -inf = NaN

Code Example

import torch
import torch.nn as nn

torch.manual_seed(0)

fc1 = nn.Linear(8, 8)
fc2 = nn.Linear(8, 8)
bn  = nn.BatchNorm1d(8)

x = torch.randn(4, 8)

with torch.enable_grad():
    x = x.requires_grad_(True)
    x_ = fc1(x)
    x_ = torch.nn.functional.hardswish(x_)   # can output exactly 0
    x_ = bn(x_)
    x_ = fc2(x_)
    x_ = torch.log1p(x_)
    out = torch.xlogy(x_, x_)                 # xlogy(0, 0) = NaN if any element = 0

print(f"hardswish zeros: {(torch.nn.functional.hardswish(fc1(x).detach()) == 0).sum().item()}")
print(f"xlogy output: nan={torch.isnan(out).any().item()}")

# Minimal 3-line version:
print("\nMinimal: xlogy at x=0")
v = torch.tensor([0.0, 0.5, 1.0, 2.0])
print(f"xlogy(v, v) = {torch.xlogy(v, v)}")
# Expected: [nan, -0.3466, 0.0, 1.3863]
# NaN because xlogy(0, 0) = 0 * log(0) = 0 * -inf = NaN

# The mathematically correct value:
print(f"lim_{{x→0}} x*log(x) = 0, but torch gives: {torch.xlogy(torch.tensor(0.0), torch.tensor(0.0))}")
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🐛 Describe the bug

import torch
import torch.nn as nn

torch.manual_seed(0)

fc1 = nn.Linear(8, 8)
fc2 = nn.Linear(8, 8)
bn  = nn.BatchNorm1d(8)

x = torch.randn(4, 8)

with torch.enable_grad():
    x = x.requires_grad_(True)
    x_ = fc1(x)
    x_ = torch.nn.functional.hardswish(x_)   # can output exactly 0
    x_ = bn(x_)
    x_ = fc2(x_)
    x_ = torch.log1p(x_)
    out = torch.xlogy(x_, x_)                 # xlogy(0, 0) = NaN if any element = 0

print(f"hardswish zeros: {(torch.nn.functional.hardswish(fc1(x).detach()) == 0).sum().item()}")
print(f"xlogy output: nan={torch.isnan(out).any().item()}")

# Minimal 3-line version:
print("\nMinimal: xlogy at x=0")
v = torch.tensor([0.0, 0.5, 1.0, 2.0])
print(f"xlogy(v, v) = {torch.xlogy(v, v)}")
# Expected: [nan, -0.3466, 0.0, 1.3863]
# NaN because xlogy(0, 0) = 0 * log(0) = 0 * -inf = NaN

# The mathematically correct value:
print(f"lim_{{x→0}} x*log(x) = 0, but torch gives: {torch.xlogy(torch.tensor(0.0), torch.tensor(0.0))}")

Versions

2.9.1+cu128 (PyTorch 2.9.1, CUDA 12.8)

torch.xlogy(0, 0) returns NaN, while in many numerical computing libraries (e.g., SciPy) and common machine learning practice, it is defined as 0.

cc @mruberry @kshitij12345

extent analysis

TL;DR

The issue can be fixed by handling the special case where the input to torch.xlogy is zero, as the function currently returns NaN in this case, whereas the expected result is 0.

Guidance

  • Identify where torch.xlogy is used in the code and add a check for zero input values to handle this special case.
  • Consider using a small epsilon value to avoid division by zero and log of zero issues.
  • Review the documentation of torch.xlogy to see if there are any plans to change its behavior for zero inputs.
  • If possible, use a different function or library that handles this case correctly, such as SciPy.

Example

import torch

def safe_xlogy(x, y):
    return torch.where(x == 0, torch.zeros_like(x), torch.xlogy(x, y))

v = torch.tensor([0.0, 0.5, 1.0, 2.0])
print(f"safe_xlogy(v, v) = {safe_xlogy(v, v)}")

Notes

This fix assumes that the desired behavior for torch.xlogy(0, 0) is to return 0, as is common in many numerical computing libraries.

Recommendation

Apply workaround: use a custom function like safe_xlogy to handle the special case where the input to torch.xlogy is zero.

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