DS-OPT: Optimization-Native Reasoning via Dynamical System Machines

Many structured reasoning tasks, such as logic puzzles and constraint satisfaction, require solving combinatorial optimization problems over many interacting discrete variables. Neural networks are built from primitives such as matrix multiplication, which excel at representation learning but are not native mechanisms for combinatorial search, so neural models must grow in size or computation to emulate reasoning over global constraints. We propose DS-OPT, a neural reasoning framework that adds a Dynamical System Machine (DSM) as a layer of the network. The neural layers learn to construct, for each input, a multi-state energy whose low-energy states answer the task, and the DSM minimizes this energy through its native discrete dynamics, using noisy winner-take-all units that reduce to an Ising machine in the two-state case. A differentiable relaxation makes the layer trainable end to end, while inference always runs the discrete DSM. On Zebra puzzles, visual Sudoku and binary image completion, DS-OPT is more accurate than neural baselines of comparable size. On Zebra it solves up to 98.4% of the puzzles, against 82.6% for a Transformer with five times more parameters, at half its inference time and energy, with DSM costs estimated by circuit-level simulation. These results suggest that DSM hardware can complement neural networks as an efficient substrate for combinatorial reasoning.