For each element $x_i$, draw an independent $m_i \sim \mathrm{Bernoulli}(1 - p)$ and apply

Backward uses the same saved mask, so gradients also propagate only through surviving positions. For correlated activations (sequence / image channels) prefer dropout1d / dropout2d / dropout3d, which drop whole feature maps and give stronger regularisation.

Compile path routing. When called inside a lucid.compile._tracing context with training=True and p > 0, this wrapper allocates a Philox state buffer and routes through the sibling engine op _C_engine.nn.dropout_stateful. The captured trace then carries the 2-input/2-output schema the compile path needs to plumb MPSGraph's stateful Philox RNG — giving genuinely-per-dispatch varying masks where the stateless seed path produces dispatch-deterministic ones. Eager-only callers (no active tracer) keep using the standard nn.dropout.

.. [1] Srivastava et al., Dropout: A Simple Way to Prevent Neural Networks from Overfitting, JMLR 2014.