Means-Ends Analysis Helps LLMs Plan in Continuous-State Domains

Frontier large language models (LLMs) can generate heuristic functions that guide search to achieve state-of-the-art performance in satisficing planning, where any plan is acceptable. However, these heuristics are not guaranteed to be admissible and can lead to suboptimal plans. We introduce LeanPlan, the first planning system that finds optimal plans with LLM-generated heuristics whose admissibility is machine-checked. Given a domain description and training tasks, an agentic loop uses planner feedback to iteratively improve a reusable domain-specific heuristic, its admissibility proof and the required domain assumptions. LeanPlan implements the heuristic, its proof and an efficient planner with machine-checked grounding and search in Lean 4. We evaluate LeanPlan on ten domains from the International Planning Competition and three new domains, using test tasks with up to 57 times as many objects as the training tasks. With GPT-5.6 Sol in the agentic loop, we successfully generate heuristics and admissibility proofs for all these domains. With the resulting heuristics, LeanPlan usually expands fewer states than the state-of-the-art Scorpion planner and solves more tasks overall.

Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and early token commitments in discrete reasoning traces. Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states. However, many such methods optimize latent states end to end without a trained interface for intermediate textual readout, and several representative configurations use a pre-defined number of latent steps during inference. In this work, we introduce PLaT (Planning with Latent Thoughts), a framework that decouples latent planning from verbalization. The Planner deterministically evolves latent planning states, while an independent Decoder provides textual readouts when needed. Answer-aware textual stopping allows the latent rollout to use a problem-dependent number of groups rather than a pre-specified chain length. PLaT achieves competitive coverage at larger $k$ in several mathematical settings, with lower Pass@1: on Llama-1B GSM8K, it reaches 80.59% Pass@128 versus CODI's 72.37%. These results support PLaT as a candidate-generation interface supplying multiple textual readouts for downstream verification or reranking.

When LLMs exhibit uneven performance across planning tasks, these gaps are often attributed to task difficulty. We argue that this explanation is incomplete, as task-level variation may reflect distinct latent planning competencies rather than differences along a single ability spectrum. We study this question on ACPBench-Hard by evaluating multiple LLM families under varying test-time reasoning budgets and applying a multidimensional item response theory model to uncover the latent competency structure underlying LLM planning. The analysis reveals two principal dimensions that shape planning performance: operational reasoning, the ability to evaluate local action applicability and immediate state transitions, and structural enumeration, the ability to reason about goal reachability and landmark structure. Operational reasoning improving under model scaling and longer reasoning traces, while structural enumeration remains comparatively insensitive. Our findings motivate competency-level evaluation of LLM planning, shifting the focus from whether models improve overall to which planning competencies improve, under what conditions, and why.