Probabilistic Tiny Recursive Model

Recursive models show promise on reasoning and language tasks, yet their test-time scaling lacks a principled criterion for selecting trajectories or determining recurrent depth. We introduce \textbf{Energy-guided Recursive Model (ERM)}, which uses Hopfield-type memories of valid local and global structures to assign intrinsic energies to candidate trajectories. These energies guide candidate selection and suggest an effective range of recurrent depths, implying that deeper recurrence does not necessarily improve reasoning accuracy. They also enable sampling methods such as parallel tempering to improve exploration. For reasoning tasks, ERM achieves optimal solutions on Sudoku ($98.97\%$), Pencil Puzzle Bench (PPBench, $88.04\%$) and Maze ($99.30\%$), reaching the best accuracy in recursive modeling. On language modeling, ERM reduces RedPajama-V2 perplexity by $1.74\%$ with marginal inference overhead. The results support energy guidance as a practical framework for improving test-time scaling in recursive models.

Hard symbolic-reasoning tasks such as Sudoku, maze pathfinding, and ARC remain challenging for LLMs due to their fixed-depth autoregressive reasoning, which limits systematic search, refinement, and backtracking. While recursive models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) address this limitation through iterative latent-state refinement, they are typically task-specific and do not leverage pretrained language priors. We propose R-Qwen, a recursive reasoning framework built upon a pretrained Qwen backbone. R-Qwen repeatedly refines a candidate solution through programmatic self-recursion and deep supervision, combining the structured iterative computation of recursive models with the linguistic and reasoning priors of pretrained LLMs. We further adapt Hierarchical Supervision Weighting (HSW) to autoregressive models by exponentially weighting losses across recursive steps. HSW reduces gradient variance by at least 50%, improves the signal-to-noise ratio of stochastic gradients, and accelerates convergence. Across eight challenging benchmarks, R-Qwen consistently outperforms prior recursive reasoning models and substantially larger LLMs while using a comparable number of trainable parameters. Notably, on ARC-AGI dataset, our model achieves a 27.6% improvement over the baseline, highlighting the effectiveness of recursive refinement for general symbolic reasoning. These results suggest that recursive reasoning mechanisms and pretrained language model priors are complementary approaches for improving symbolic puzzle-solving. Code and models will be released after acceptance.

Chain-of-Thought (CoT) prompting has become the dominant paradigm for eliciting reasoning in Large Language Models (LLMs), yet it creates substantial computational overhead by forcing models to externalize intermediate reasoning steps as discrete tokens. Recent latent reasoning approaches attempt to internalize this process within continuous hidden states. One of the latest advancements in the field of latent reasoning, Tiny Recursive Models (TRMs) excel at symbolic reasoning but struggle to preserve semantic coherence in natural language settings. To bridge this gap, we introduce ReLIT (Recursive Latent Implicit Transformer), a hybrid framework that grounds deep recursive reasoning within the rich semantic representations of a foundational model. ReLIT augments a frozen LLM backbone (TinyLlama-1.1B) with a lightweight, trainable recursive block that iteratively refines its latent thinking (z) before committing to a final output, structurally solving linguistic intuition from algorithmic processing and enabling "deep thinking" via gradient-isolated recurrent loops without the latency of explicit token generation. Empirically, ReLIT achieves high parameter efficiency on the GLoRE logical reasoning benchmark, matching or outperforming significantly larger models on challenging tasks such as ProofWriter and RuleTaker despite minimal supervision. These results demonstrate that reasoning capability can be scaled efficiently through recurrent depth rather than parameter width, offering a principled framework for semantically grounded implicit reasoning.