Distributions

All distribution functions accept a positional *size argument and an optional generator= for deterministic streams. When generator is omitted, the module-level default generator is used.

uniform(*size, low=0.0, high=1.0, dtype=torch.float32, generator=None)

Uniform distribution on [low, high).

normal(*size, mean=0.0, std=1.0, dtype=torch.float32, generator=None)

Normal (Gaussian) distribution N(μ, σ²).

standard_normal(*size, dtype=torch.float32, generator=None)

Shorthand for normal(*size, mean=0.0, std=1.0, ...).

exponential(*size, rate=1.0, dtype=torch.float32, generator=None)

Exponential distribution with rate λ (mean 1/λ). Samples via -log(U) / λ with clamping to avoid log(0).

bernoulli(*size, p=0.5, dtype=torch.float32, generator=None)

Bernoulli distribution: 1 with probability p, 0 otherwise.

randint(*size, low=0, high=1, dtype=torch.long, generator=None)

Random integers from [low, high).

randperm(n, dtype=torch.long, generator=None)

Random permutation of 0..n-1.

truncated_normal(*size, mean=0.0, std=1.0, low=-2.0, high=2.0, dtype=torch.float32, generator=None)

Truncated normal clipped to [mean + low·std, mean + high·std] via rejection sampling. Useful for bounded weight initialization.

gamma(*size, shape, scale=1.0, dtype=torch.float32, generator=None)

Gamma distribution with shape k and scale θ. Mean k·θ, variance k·θ². Samples via Marsaglia-Tsang rejection for shape ≥ 1; falls back to the boost identity (Gamma(k) = Gamma(k+1) · U^(1/k)) for shape < 1.

chi_squared(*size, df, dtype=torch.float32, generator=None)

Chi-squared distribution with df degrees of freedom. Mean df, variance 2·df. Equivalent to Gamma(df/2, scale=2).

beta(*size, alpha, beta, dtype=torch.float32, generator=None)

Beta distribution on (0, 1) with shape parameters α, β > 0. Mean α/(α+β), variance αβ / ((α+β)²(α+β+1)). Sampled via the gamma-ratio identity X / (X + Y) where X ~ Gamma(α, 1), Y ~ Gamma(β, 1).

poisson(*size, lam=1.0, dtype=torch.float32, generator=None)

Poisson distribution with rate λ ≥ 0. Mean and variance both λ. Wraps torch.poisson with a generator-bound rates tensor for reproducibility.