Virtual Point

In distributed scenarios, each participant only needs to generate dummy points as agreed and have them participate in aggregation together with the real data, without requiring additional secure channels or complex protocol modifications.

The injection of dummy points yields subsampling-style privacy amplification for the count release, so that the expected number of required dummy points can be asymptotically smaller than what is needed to directly privatize the batch size with non-negative noise (sensitivity 1).

The number of dummy points varies with the privacy parameters and the batch upper bound, and deployment requires a concrete trade-off between privacy budget and computational overhead.

A recent study proposes masking the true batch size by injecting a random number of dummy points into the batch, thereby preserving privacy amplification under conditions where the batch size is observable and a truncation limit exists.

Dummy points participate in the forward and backward computations, but their gradient contributions are discarded or cancelled out, so they do not affect the model update.

The probability of noisy virtual constraint events under the equality posterior measure can serve as a diagnostic indicator for measuring, prior to updating, how well the solution conforms to the specified boundaries.

The physics-informed posterior itself serves as a valid prior for inequality updates; one can first perform PDE equality conditioning and then apply inequality constraint updates at virtual points, without modifying the original pipeline in either step.