Reliable convergence of WARP-LUT training with four-input LUTs

Determine whether gradient-based training of Walsh-Assisted Relaxation for Probabilistic Look-Up Tables (WARP-LUTs) using four-input look-up tables, parameterized via 16 Walsh–Hadamard coefficients per node, converges reliably on standard benchmarks.

Background

The paper introduces WARP-LUTs, a differentiable, Walsh–Hadamard–based parameterization of weightless neural networks that scales exponentially with the number of LUT inputs, in contrast to Differentiable Logic Gate Networks (DLGNs), which scale doubly exponentially. This improved scaling suggests feasibility of training higher-input logic blocks, such as four-input LUTs, with only 16 trainable parameters per node.

Despite promising two-input results, the authors explicitly note uncertainty about whether WARP-LUT training remains reliable when extended to higher-input LUTs on standard benchmarks. Establishing reliable convergence for such models is crucial for leveraging modern FPGA primitives (e.g., LUT-6) and achieving practical deployment in resource-constrained environments.