# Reasoning as Energy Minimization over Structured Latent Trajectories

arXiv: https://arxiv.org/abs/2603.28248 · HTML: https://mlsanity.com/paper/2603.28248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 12 of 12)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [Neural Arithmetic Logic Units](https://mlsanity.com/paper/1808.00508/) (2018)
- [Latent Thought Models with Variational Bayes Inference-Time Computation](https://mlsanity.com/paper/2502.01567/) (2025)
- [Efficient Planning with Latent Diffusion](https://mlsanity.com/paper/2310.00311/) (2023)
- [Learning Latent Space Hierarchical EBM Diffusion Models](https://mlsanity.com/paper/2405.13910/) (2024)
- [Hitchhiker's guide on the relation of Energy-Based Models with other generative models, sampling and statistical physics: a comprehensive review](https://mlsanity.com/paper/2406.13661/) (2024)
- [nabla-Reasoner: LLM Reasoning via Test-Time Gradient Descent in Latent Space](https://mlsanity.com/paper/2603.04948/) (2026)
- [Kolmogorov-Arnold Energy Models: Fast, Interpretable Generative Modeling](https://mlsanity.com/paper/2506.14167/) (2025)

## Abstract (arXiv)

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 z1:T under a learned energy function E(hx, 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 zT. We identify a critical failure mode: on CNF logic satisfaction, latent planning reduces accuracy from ≈ 95% to ≈ 56%. This degradation arises from a distribution mismatch, where the decoder is trained on encoder outputs hx but evaluated on planner outputs zT that drift into unseen latent regions. We analyze this behavior through per-step decoding, latent drift tracking, and gradient decomposition. To address it, we propose dual-path decoder training and latent anchoring. We further introduce a six-part ablation protocol covering component contributions, trajectory length, planner dynamics, initialization, decoder training distribution, and anchor weight. Experiments on three synthetic tasks show that energy decreases monotonically and induces structured latent trajectories on graph and logic tasks, while remaining flat on arithmetic (r = 0.073), indicating a negative result. Code is available at https://github.com/dkjo8/ebr-via-structured-latent-planning.