# Energy-Based Relational Reasoning > Source: > Published: 2026-10-24 00:00:00+00:00 # Energy-Based Relational Reasoning ## Abstract Humans naturally reason about relations—between cause and effect, forces and motions, premises and conclusions. Such reasoning is inherently bidirectional (from cause to effect and from effect to cause) and compositional (combining simple inferences into novel structures). I introduce energy-based relational programming, a purely neural framework for bidirectional and compositional reasoning over discrete relations. My approach represents each relation with a smoothed energy function and composes them zero-shot at query time to solve reasoning problems. The method achieves 100% success on evaluated satisfiable algebra, digital circuit, and graph-coloring instances, alongside strong performance on Sudoku and arithmetic with handwritten digit images. The resulting models are fully bidirectional, recover satisfying assignments for algebraic properties such as commutativity and associativity, and generalize from single operations to expression trees of unseen depth. ## Bio Matthew Retchin is a third-year CS PhD student at Harvard and is co-advised by Nada Amin and Yilun Du. His research combines programming language theory and energy-based modeling. He is interested in finding new architectures with inductive biases that make language models more interpretable and better at reasoning.