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Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell.

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak--strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.

As an illustrative example, consider solving a Sudoku.

We show that video generation models could reason now. Testing on tasks such as chess, maze, Sudoku, mental rotation, and Raven's Matrices, leading models such as Sora-2 achieve sixty percent success rates. We establish a robust experimental paradigm centered on the "Task Pair" design. We build a code framework, with 39 models available already, that supports this paradigm and allows for easy scaling - users can add models and tasks efficiently. We show our automated evaluation strongly correlates with human judgment, and therefore this paradigm is highly scalable. We see an opportunity, given the availability of our paradigm, to do reinforcement learning for improving reasoning in video models. You could checkout all of our raw $\href{https://grow-ai-like-a-child.com/video-reason/}{results}$ and our $\href{https://github.com/hokindeng/VMEvalKit}{VMEvalKit}$ codebase.

Post-training with reinforcement learning (RL) typically optimizes a single scalar objective and ignores structure in how solutions are produced. We ask whether a scalar hint toward a canonical solver ordering, used only during RL post-training, improves performance even when fine-tuned on randomized solution sequences. On Sudoku, we train a Transformer with standard fine-tuning on randomized solving orders, then post-train it with Group Relative Policy Optimization (GRPO) with two rewards: cell accuracy and an ordering reward that increases when the model's emission order aligns with the solver order. To compare signals cleanly, we combine them via fixed mixtures and use a simple bootstrapped scaling to equalize component magnitudes at initialization. Mixed rewards generally outperform cell-only optimization--the best mixture yields substantially higher test accuracy than the fine-tuned-only model trained on random-order and approaches the fine-tuned-only model trained on solver-order sequences in accuracy. These results suggest that coarse ordering signals can steer RL post-training toward solver-order trajectories without modifying supervised data or architecture.

Reinforcement Learning (RL) has proven highly effective for autoregressive language models, but adapting these methods to diffusion large language models (dLLMs) presents fundamental challenges. The core difficulty lies in likelihood approximation: while autoregressive models naturally provide token-level conditional probabilities essential for token-level RL objectives (e.g., GRPO), dLLMs generate sequences through iterative non-autoregressive denoising steps that lack this factorization. To address this fundamental mismatch, we propose ELBO-based Sequence-level Policy Optimization (ESPO), a principled RL framework that treats entire sequence generation as a single action and uses the ELBO as a tractable sequence-level likelihood proxy. Our method incorporates per-token normalization of importance ratios and robust KL-divergence estimation to ensure stable large-scale training. Extensive experiments on mathematical reasoning, coding, and planning tasks demonstrate that ESPO significantly outperforms token-level baselines, achieving dramatic improvements of 20-40 points on the Countdown task, while maintaining consistent gains on math and coding benchmarks. Our approach establishes sequence-level optimization as a principled and empirically effective paradigm for RL in dLLMs. Our code is available at https://github.com/ML-GSAI/ESPO. Large language models (LLMs) (OpenAI, 2023) have become a cornerstone of modern natural language processing, achieving remarkable progress across math (Guo et al., 2025), coding (Hui et al., 2024), and planning tasks (Y ao et al., 2023). While autoregressive (AR) modeling has long dominated this field, recent advances in diffusion large language models (dLLMs) have demonstrated strong potential as an alternative formulation (Ou et al., 2024; Shi et al., 2024; Sahoo et al., 2024; Nie et al., 2025; Y e et al., 2025). With the advent of powerful pretrained dLLMs, the next frontier lies in post-training (Ouyang et al., 2022) to further enhance their capabilities. Among various post-training paradigms, reinforcement learning (RL) has emerged as a powerful approach that enables test-time scaling (Snell et al., 2025) through verifiable rewards (Guo et al., 2025). It has yielded substantial gains on reasoning tasks in recent AR models (OpenAI, 2024), such as math (Cobbe et al., 2021b), coding (Chen et al., 2021), and reasoning (Liu et al., 2023b).

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