TOPIQ: Statistical Error Propagation for Quantity-of-Interest Prediction under Lossy Compression

What the math gives to ML

The paper provides an operator-composable representation of compressed-data uncertainty, carrying not only the mean and variance of a signal but also compression bias, error variance, and signal-error coupling. Its key transferable asset is second-order propagation through nonlinear functions, which can turn cheap compression metadata into approximate prediction bias and uncertainty for an entire MLP or other differentiable computation graph. A practical neural-network adaptation is compression-aware inference: propagate a five-component moment tuple alongside activations, correct nonlinear means using curvature, and expose a calibrated output interval without Monte Carlo decompression or repeated forward passes. The same machinery can also select compression tolerances by constraining predicted QoI uncertainty.