[2603.28248] Reasoning as Energy Minimization over Structured Latent Trajectories

Computer Science > Artificial Intelligence arXiv:2603.28248 (cs) [Submitted on 30 Mar 2026] Title:Reasoning as Energy Minimization over Structured Latent Trajectories Authors:David K. Johansson View a PDF of the paper titled Reasoning as Energy Minimization over Structured Latent Trajectories, by David K. Johansson View PDF HTML (experimental) Abstract:Single-shot neural decoders commit to answers without iterative refinement, while chain-of-thought methods introduce discrete intermediate steps but lack a scalar measure of reasoning progress. We propose Energy-Based Reasoning via Structured Latent Planning (EBRM), which models reasoning as gradient-based optimization of a multi-step latent trajectory $z_{1:T}$ under a learned energy function $E(h_x, z)$. The energy decomposes into per-step compatibility, transition consistency, and trajectory smoothness terms. Training combines supervised encoder-decoder learning with contrastive energy shaping using hard negatives, while inference performs gradient descent or Langevin dynamics over $z$ and decodes from $z_T$. We identify a critical failure mode: on CNF logic satisfaction, latent planning reduces accuracy from $\approx 95\%$ to $\approx 56\%$. This degradation arises from a distribution mismatch, where the decoder is trained on encoder outputs $h_x$ but evaluated on planner outputs $z_T$ that drift into unseen latent regions. We analyze this behavior through per-step decoding, latent drift tracking, and gradient decomposit...