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torch.logcumsumexp

function logcumsumexp(input: Tensor, dim: number): Tensor

Returns the logarithm of the cumulative summation of the exponentiation of elements.

Computes log(∑ exp(x)) along a dimension in a numerically stable way. This function is critical for numerical stability when working with probabilities and likelihoods, where direct computation would cause overflow. Uses the log-sum-exp trick internally.

Commonly used for:

Computing log-probabilities in probabilistic models
Softmax and cross-entropy loss calculations
Numerical stability in likelihood computations
Gaussian mixture models and sequence models

\log(\sum_{i=1}^{n} e^{x_i}) = \max(x) + \log(\sum_{i=1}^{n} e^{x_i - \max(x)})

Internally uses the numerically stable log-sum-exp trick: max(x) + log(sum(exp(x - max(x))))
Gradient computation is fully stable due to the implementation technique
Output values are typically large; they represent log(·) of cumulative sums

Parameters

inputTensor: The input tensor (typically log probabilities or large exponentials)
dimnumber: The dimension along which to compute (0 to rank-1)

Returns

Tensor– Tensor containing log(∑ exp(input)) along the dimension

Examples

// Basic usage - log cumulative sum of exponentials
const x = torch.tensor([1.0, 2.0, 3.0]);
torch.logcumsumexp(x, 0);  // [log(e^1), log(e^1 + e^2), log(e^1 + e^2 + e^3)]

// Numerical stability for large values (prevents overflow)
const large = torch.tensor([700.0, 710.0, 720.0]);
torch.logcumsumexp(large, 0);  // Works fine, direct exp() would overflow

// Computing log-probabilities in batches
const logits = torch.randn(32, 10);  // [batch, classes]
const log_probs = torch.logcumsumexp(logits, 1);  // [32] - per-sample normalization

// In log-domain computations
const log_a = torch.tensor([1.0, 2.0, 3.0]);
const log_b = torch.tensor([1.5, 2.5, 3.5]);
const log_sum = torch.logcumsumexp(torch.stack([log_a, log_b], 0), 0);  // [log(a+b), ...]

See Also

PyTorch torch.logcumsumexp()
cumsum - Regular cumulative sum without exponential
logsumexp - Reduces all elements instead of cumulative along dimension
log_softmax - Softmax in log domain for probabilities