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torch.cumprod

function cumprod(input: unknown, dim: unknown, options: unknown): Tensor

Returns the cumulative product along a dimension.

Computes running products, where each element is the product of all previous elements along the specified dimension. Useful for multiplicative processes and probability chains.

Commonly used for:

Computing joint probabilities (product of independent probabilities)
Factorial and combinatorial computations
Multiplicative growth/decay processes (interest, population)
Computing path weights in importance sampling
Sequential model computations

\text{output}[i_0, \ldots, i_{d}, \ldots, i_n] = \prod_{j=0}^{i_d} \text{input}[i_0, \ldots, j, \ldots, i_n]

Shape is preserved - output has the same shape as input
Multiplication can underflow (result → 0) or overflow (result → ∞) with many elements
For numerical stability with many elements, consider computing in log-domain with cumsum(log(x))
Unlike cumsum, products depend on all previous values - very sensitive to zeros

Parameters

inputunknown: The input tensor (any shape)
dimunknown: The dimension along which to compute cumulative product (0 to rank-1)
optionsunknown: Optional settings:

Returns

Tensor– Tensor with same shape as input, containing cumulative products

Examples

// Basic 1D cumulative product
const x = torch.tensor([1, 2, 3, 4, 5]);
torch.cumprod(x, 0);  // [1, 2, 6, 24, 120] (factorials)

// 2D cumulative product along different dimensions
const x = torch.tensor([[1, 2, 3], [4, 5, 6]]);
torch.cumprod(x, 0);  // [[1, 2, 3], [4, 10, 18]] - product along rows
torch.cumprod(x, 1);  // [[1, 2, 6], [4, 20, 120]] - product along columns

// Joint probability computation
const probs = torch.tensor([0.9, 0.8, 0.7]);  // Independent event probabilities
const joint = torch.cumprod(probs, 0);  // [0.9, 0.72, 0.504]

// Discount factors (e.g., compound interest)
const rate = 1.05;  // 5% growth
const years = torch.tensor([1, 2, 3, 4, 5], { dtype: 'float32' });
const factors = torch.fill(torch.empty([5]), rate);
const compound = torch.cumprod(factors, 0);  // [1.05, 1.1025, 1.157625, ...]

See Also

PyTorch torch.cumprod()
cumsum - Cumulative sum instead of product
cumprod_ - In-place cumulative product
logcumsumexp - Stable log computation for avoiding underflow
prod - Total product (non-cumulative reduction)