pytorch - 💡(How to fix) Fix Distribution.icdf performs no argument validation even with validate_args=True, unlike cdf/log_prob

🐛 Describe the bug

With argument validation enabled (the default), cdf and log_prob reject out-of-support input — but icdf accepts any quantile and silently evaluates its formula:

import torch
td = torch.distributions

td.Uniform(0., 1.).cdf(torch.tensor(2.0))    # ValueError — validation works
td.Uniform(0., 1.).icdf(torch.tensor(2.0))   # tensor(2.) — silent linear extrapolation
td.Cauchy(0., 1.).icdf(torch.tensor(-1.0))   # tensor(83858288.)
td.Exponential(1.).icdf(torch.tensor(-2.0))  # tensor(-1.0986) — negative "quantile"

Quantiles are undefined outside [0, 1] (scipy returns nan for all of the above).

Root cause: the base Distribution.icdf is a bare raise NotImplementedError with no validation contract, and no subclass icdf implementation (Uniform, Cauchy, Exponential, Laplace, ...) checks the unit interval — while the cdf/log_prob siblings all call self._validate_sample when self._validate_args is set. There is no _validate_sample equivalent for quantile arguments.

Suggested fix: validate q ∈ [0,1] in icdf when _validate_args is set — a unit-interval check in the base class (or a shared helper used by subclasses) would cover all distributions. Alternatively, document that icdf performs no validation.

Related: #186824 (even valid boundary quantiles q=0/1 produce wrong finite values for Cauchy/Gumbel).

Versions

torch 2.12.0, CPU (arm64, macOS); behavior unchanged on current main.

cc @fritzo @neerajprad @alicanb @nikitaved @malfet