Shared Symbolic Backbones for Physically Consistent Multi-Output Symbolic Regression

What the math gives to ML

The paper introduces a reusable symbolic latent layer for multi-output regression: transformed input features are passed through a small bank of symbolic units, and each output selects a sparse additive or multiplicative combination of the same units. The transferable asset is explicit mechanism sharing, where multiple outputs reuse identical intermediate factors rather than merely sharing an unconstrained neural trunk. This is especially useful when outputs share weakly identifiable denominators, rate laws, or physical correction factors. A practical neural-network adaptation is a differentiable symbolic bottleneck before multiple prediction heads, followed by operator and gate hardening for interpretable deployment.