Exact Dual Geometry of SOC-ICNN Value Functions
A recent study published on arXiv (2605.04722) examines the precise first-order and local second-order geometry of Second-Order Cone Input Convex Neural Networks (SOC-ICNNs) through a dual perspective. These SOC-ICNNs enhance ReLU-based ICNNs by incorporating quadratic and conic components and can be accurately expressed as value functions of second-order cone programs (SOCPs). The researchers demonstrate that optimal dual variables can be used to directly obtain supporting slopes, subdifferentials, directional derivatives, and local Hessians, facilitating white-box inference instead of relying solely on black-box automatic differentiation. Additionally, numerical tests confirm the accuracy of the local Hessian computation and multiplier readout.
Key facts
- arXiv paper 2605.04722
- SOC-ICNNs are Input Convex Neural Networks with quadratic and conic modules
- SOC-ICNNs admit exact representation as value functions of SOCPs
- Study of exact first-order and local second-order geometry from dual viewpoint
- Supporting slopes, subdifferentials, directional derivatives, local Hessians recovered from optimal dual variables
- Enables white-box SOC-ICNN inference
- Numerical experiments validate exact multiplier readout and local Hessian
Entities
Institutions
- arXiv