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  5. RelaxedBernoulli

torch.distributions.RelaxedBernoulli

class RelaxedBernoulli extends Distribution
new RelaxedBernoulli(temperature: number | Tensor, options: { probs?: number | number[] | Tensor; logits?: number | number[] | Tensor; } & DistributionOptions)
readonlytemperature(Tensor)
– Temperature parameter controlling the relaxation. Lower temperature = more discrete-like.
readonlyarg_constraints(unknown)
readonlysupport(unknown)
readonlyhas_rsample(unknown)
readonlyprobs(Tensor)
– Get probability of success.
readonlylogits(Tensor)
– Get log-odds.
readonlymean(Tensor)
readonlymode(Tensor)
readonlyvariance(Tensor)

Relaxed Bernoulli distribution: continuous relaxation of Bernoulli via Concrete/Gumbel-Softmax.

The RelaxedBernoulli is a continuous relaxation of the Bernoulli distribution using the Gumbel-Softmax (Concrete) trick. Essential for:

  • Reparameterized gradients through discrete-like samples
  • Differentiable discrete sampling
  • Variational inference with discrete variables
  • Annealing from continuous to discrete (temperature scheduling)
  • Neural network architecture search

As temperature → 0, the distribution approaches a Bernoulli. At temperature = 1, the distribution is more uniform.

Sampling: X=σ(log⁡(p)−log⁡(1−p)+log⁡(U)−log⁡(1−U)T)where U∼Uniform(0,1),T is temperature,σ is sigmoidSupport: (0,1) (continuous relaxation of {0,1})Limit: lim⁡T→0+X→Bernoulli(p)Entropy: H(X) increases with temperature T\begin{aligned} \text{Sampling: } X = \sigma\left(\frac{\log(p) - \log(1-p) + \log(U) - \log(1-U)}{T}\right) \\ \text{where } U \sim \text{Uniform}(0,1), T \text{ is temperature}, \sigma \text{ is sigmoid} \\ \text{Support: } (0, 1) \text{ (continuous relaxation of } \{0, 1\}) \\ \text{Limit: } \lim_{T \to 0^+} X \to \text{Bernoulli}(p) \\ \text{Entropy: } H(X) \text{ increases with temperature } T \end{aligned}Sampling: X=σ(Tlog(p)−log(1−p)+log(U)−log(1−U)​)where U∼Uniform(0,1),T is temperature,σ is sigmoidSupport: (0,1) (continuous relaxation of {0,1})Limit: T→0+lim​X→Bernoulli(p)Entropy: H(X) increases with temperature T​

Examples

const m = new RelaxedBernoulli(0.5, { probs: torch.tensor([0.7]) });
m.sample();  // relaxed sample in (0, 1)
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