torch.distributions.Uniform

class Uniform extends Distribution

new Uniform(low: number | Tensor, high: number | Tensor, options?: DistributionOptions)

readonlylow(Tensor): – Lower bound of the uniform distribution (inclusive).
readonlyhigh(Tensor): – Upper bound of the uniform distribution (exclusive).
readonlyarg_constraints(unknown)
readonlysupport(Constraint)
readonlyhas_rsample(unknown)
readonlymean(Tensor)
readonlymode(Tensor)
readonlyvariance(Tensor)

Uniform distribution: constant probability over an interval [low, high).

Parameterized by lower and upper bounds. Assigns equal probability to all values in the interval. Essential for:

Random initialization of model parameters (when bounds matter)
Prior distributions in Bayesian models (non-informative prior)
Data augmentation and sampling
Baseline comparisons (maximum entropy for bounded domain)
Scenario testing and robustness

The probability density function: f(x) = 1/(high - low) for x in [low, high), 0 otherwise

\begin{aligned} \text{PDF: } f(x) = \frac{1}{b - a} \quad x \in [a, b) \\ \text{CDF: } F(x) = \frac{x - a}{b - a} \quad x \in [a, b) \\ \text{Mean: } \mathbb{E}[X] = \frac{a + b}{2} \\ \text{Variance: } \text{Var}(X) = \frac{(b - a)^2}{12} \\ \text{Mode: } \text{undefined (constant)} \\ \text{Entropy: } H(X) = \ln(b - a) \end{aligned}

Interval notation: [low, high) is half-open (includes low, excludes high)
No maximum entropy: Subject to bounds, has maximum entropy
Constant density: All values in range have equal probability (not normalized to 1)
CDF simplicity: CDF is linear: F(x) = (x - low) / (high - low)
Reparameterizable: rsample() = low + (high - low) * U[0,1)
Bounded domain: Finite support unlike normal, crucial advantage for constraints

Bounds order: Must have low high, otherwise error
Floating-point bounds: high is excluded; careful with boundary conditions
Not smooth: PDF is discontinuous at boundaries

Examples

// Standard uniform on [0, 1)
const uniform = new torch.distributions.Uniform(0, 1);
const samples = uniform.sample([1000]);
const log_probs = uniform.log_prob(samples);

// Uniform on custom range [-1, 1)
const custom = new torch.distributions.Uniform(-1, 1);
const sample = custom.sample();  // value in [-1, 1)

// Batched uniform distributions
const lows = torch.tensor([0, -5, 10]);
const highs = torch.tensor([1, 5, 20]);
const dist = new torch.distributions.Uniform(lows, highs);
const batch_samples = dist.sample();  // [3] shaped samples

// Parameter initialization: uniform instead of normal
const layer_size = 512;
const input_size = 256;
const limit = Math.sqrt(6.0 / (input_size + layer_size));  // uniform bound
const init_dist = new torch.distributions.Uniform(-limit, limit);
const weights = init_dist.sample([layer_size, input_size]);

// Prior distribution: model uncertainty uniformly
const param_dist = new torch.distributions.Uniform(0, 1);  // no prior knowledge
const sample = param_dist.sample([10]);  // unbiased sample

// Probability of value in specific range: P(a < X < b)
const dist = new torch.distributions.Uniform(0, 10);
const p_1_to_3 = dist.cdf(3) - dist.cdf(1);  // P(1 < X < 3) = 0.2