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torch.nn.functional.log_softmax

function log_softmax<S extends Shape, D extends DType = DType, Dev extends DeviceType = DeviceType>(input: Tensor<S, D, Dev>, options?: SoftmaxOptions): Tensor<S, D, Dev>

function log_softmax<S extends Shape, D extends DType = DType, Dev extends DeviceType = DeviceType>(input: Tensor<S, D, Dev>, dim: number, options?: SoftmaxOptions): Tensor<S, D, Dev>

Log-Softmax activation function: numerically stable log(softmax(x)).

Applies log(softmax(x)) = x - log(Σ exp(x)) efficiently and numerically stably. More efficient and numerically stable than computing softmax then log separately, especially important for:

Classification loss functions (combined with negative log likelihood)
Probability calculations requiring log-space (important for numerical stability)
Deep networks where numerical precision is critical

When to use Log-Softmax:

With NLLLoss (Negative Log Likelihood Loss)
When you need log-probabilities instead of probabilities
For numerical stability in probability calculations
In likelihood-based models and Bayesian inference

Important: For simple classification with targets, use CrossEntropyLoss directly, which is more convenient and handles the softmax + log + loss combination automatically. Log-Softmax is useful when you need explicit log-probabilities for custom loss functions.

\text{log\_softmax}(x_i) = \log\left(\frac{e^{x_i}}{\sum_j e^{x_j}}\right) = x_i - \log\left(\sum_j e^{x_j}\right)

Numerical stability: More stable than softmax + log for extreme values
Log-space calculations: Output in log-space, not interpretable as probabilities
Use with NLLLoss: Designed to work with Negative Log Likelihood Loss
Simpler alternative: CrossEntropyLoss combines softmax + log + loss for classification

Parameters

inputTensor<S, D, Dev>: Input tensor of any shape (typically logits [batch, num_classes])
optionsSoftmaxOptionsoptional: Optional settings: - dtype: Output data type

Returns

Tensor<S, D, Dev>– Tensor with log_softmax applied, same shape as input

Examples

// Classification with explicit log-probabilities
const logits = torch.randn([batch_size, num_classes]);
const log_probs = torch.nn.functional.log_softmax(logits, { dim: -1 });  // Log-probabilities

// Use with NLLLoss
const nll_loss = new torch.nn.NLLLoss();
const targets = torch.tensor([0, 2, 1, 0]);  // Class indices
const loss = nll_loss.forward(log_probs, targets);

// Custom loss requiring log-probabilities
const logits = torch.randn([batch_size, num_classes]);
const log_probs = torch.nn.functional.log_softmax(logits, { dim: -1 });
const target_log_probs = torch.log(target_dist);  // Target distribution
const kl_div = (target_log_probs - log_probs).mean();

See Also

PyTorch torch.nn.functional.log_softmax
softmax - Regular softmax for probability outputs
cross_entropy - One-step function for classification
nll_loss - Used with log_softmax outputs

LocalResponseNormFunctionalOptions