Reward-Gated On-Policy Distillation

On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.

OpenThoughts-Agent: Data Recipes for Agentic Models

Agentic language models dramatically expand the applications of AI yet little is publicly known about how to curate training data for broadly capable agents. Existing open efforts such as SWE-Smith, SERA, and Nemotron-Terminal typically target a single benchmark, leaving open the question of how to train models that generalize across diverse agentic tasks. The OpenThoughts-Agent (OT-Agent) project addresses this gap with a fully open data curation pipeline for training agentic models. We conduct more than 100 controlled ablation experiments to systematically investigate each stage of the pipeline, yielding insights on the importance of task sources and diversity. We then assemble a training set of 100K examples from our pipeline and fine-tune Qwen3-32B on this dataset, which yields an average accuracy of 44.8% across seven agentic benchmarks and a 3.9 percentage point improvement over the strongest existing open data agentic model (Nemotron-Terminal-32B, 40.9%). Moreover, our training data exhibits strong scaling properties, outperforming alternative open datasets at every training set size in compute-controlled comparisons. We publicly release our training sets, data pipeline, experimental data, and models at openthoughts.ai to support future open research on agentic model training.

Understanding Parallel Samplers in Masked Diffusion via Random Walks on Graphs

In this paper, we propose using random walks on graphs as a verifiable sandbox to study different parallel sampling strategies in masked diffusion models (MDMs). We train an MDM on random walk samples from a fixed graph. The graph or the transition kernel is never shown to the model explicitly and plays the role of latent structure in the sequences, albeit one that is controllable and can be used for quantitative evaluation. Thus, this framework enjoys a Sudoku-like validity check: verifying that an output is a valid walk and estimating the Markov kernel from the walks to measure distribution fidelity. Using simple graphs, we theoretically prove that parallel unmasking via widely used scores like lowest entropy is not uniformly better than a random parallel sampler; the performance critically depends on the structure of the underlying graph. We develop a new bisection sampler for random walks, which takes logarithmic steps in the sequence length and is provably exact under perfect training. Experiments on various graph walk tasks show that different parallel samplers are better for different graphs even in practice. Our initial experiments on a pretrained OpenWebText MDM show that the bisection-style samplers improve speed-quality tradeoffs even for language generation. Together, these results position graph random walks as a mechanistic benchmark for diagnosing and designing parallel samplers for masked diffusion models.

Test-Time Speculation

Speculative decoding accelerates LLM inference by using a fast draft model to generate tokens and a more accurate target model to verify them. Its performance depends on the $\textit{acceptance length}$, or number of draft tokens accepted by the target. Our studies show that the acceptance length of even state-of-the-art speculators, like DFlash, EAGLE-3 and PARD degrade with generation length, reaching values close to 1 (i.e. no speedup) within just a few thousand output tokens, making speculators ineffective for long-response tasks. Acceptance lengths decline because most speculators are trained offline on short sequences, but are forced to match the target model on much longer outputs at inference, well beyond their training distribution. To address this issue, we propose $\textit{Test-Time Speculation (TTS)}$, an online distillation approach that continuously adapts the speculator at test-time. TTS leverages the key insight that the token verification step already invokes the target model for each draft token, providing the training signal needed to adapt the draft at no additional cost. Treating the draft as the student and the target as a teacher, TTS adjusts the draft over several speculation rounds, with each update improving the draft's accuracy as generation proceeds. Our results across multiple models from the Qwen-3, Qwen-3.5, and Llama3.1 families show that TTS improves acceptance lengths over state-of-the-art speculators by up to $72\%$ and $41\%$ on average, with the benefits scaling with increased generation lengths.

EntRGi: Entropy Aware Reward Guidance for Diffusion Language Models

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

MURPHY: Multi-Turn GRPO for Self Correcting Code Generation

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful framework for enhancing the reasoning capabilities of large language models (LLMs). However, existing approaches such as Group Relative Policy Optimization (GRPO) and its variants, while effective on reasoning benchmarks, struggle with agentic tasks that require iterative decision-making. We introduce Murphy, a multi-turn reflective optimization framework that extends GRPO by incorporating iterative self-correction during training. By leveraging both quantitative and qualitative execution feedback, Murphy enables models to progressively refine their reasoning across multiple turns. Evaluations on code generation benchmarks with model families such as Qwen and OLMo show that Murphy consistently improves performance, achieving up to a 8% relative gain in pass@1 over GRPO, on similar compute budgets.

Context-Free Synthetic Data Mitigates Forgetting

Fine-tuning a language model often results in a degradation of its existing performance on other tasks, due to a shift in the model parameters; this phenomenon is often referred to as (catastrophic) forgetting. We are interested in mitigating this, in settings where we only have access to the model weights but no access to its training data/recipe. A natural approach is to penalize the KL divergence between the original model and the new one. Our main realization is that a simple process - which we term context-free generation - allows for an approximate unbiased estimation of this KL divergence. We show that augmenting a fine-tuning dataset with context-free generations mitigates forgetting, in two settings: (a) preserving the zero-shot performance of pretrained-only models, and (b) preserving the reasoning performance of thinking models. We show that contextual synthetic data, and even a portion of the pretraining data, are less effective. We also investigate the effect of choices like generation temperature, data ratios etc. We present our results for OLMo-1B for pretrained-only setting and R1-Distill-Llama-8B for the reasoning setting.

Asymptotically-Optimal Gaussian Bandits with Side Observations

We study the problem of Gaussian bandits with general side information, as first introduced by Wu, Szepesvari, and Gyorgy. In this setting, the play of an arm reveals information about other arms, according to an arbitrary a priori known side information matrix: each element of this matrix encodes the fidelity of the information that the ``row'' arm reveals about the ``column'' arm. In the case of Gaussian noise, this model subsumes standard bandits, full-feedback, and graph-structured feedback as special cases. In this work, we first construct an LP-based asymptotic instance-dependent lower bound on the regret. The LP optimizes the cost (regret) required to reliably estimate the suboptimality gap of each arm. This LP lower bound motivates our main contribution: the first known asymptotically optimal algorithm for this general setting.

InfoPO: On Mutual Information Maximization for Large Language Model Alignment

We study the post-training of large language models (LLMs) with human preference data. Recently, direct preference optimization and its variants have shown considerable promise in aligning language models, eliminating the need for reward models and online sampling. Despite these benefits, these methods rely on explicit assumptions about the Bradley-Terry (BT) model, which makes them prone to overfitting and results in suboptimal performance, particularly on reasoning-heavy tasks. To address these challenges, we propose a principled preference fine-tuning algorithm called InfoPO, which effectively and efficiently aligns large language models using preference data. InfoPO eliminates the reliance on the BT model and prevents the likelihood of the chosen response from decreasing. Extensive experiments confirm that InfoPO consistently outperforms established baselines on widely used open benchmarks, particularly in reasoning tasks.

Geometric Median Matching for Robust k-Subset Selection from Noisy Data

Data pruning -- the combinatorial task of selecting a small and representative subset from a large dataset, is crucial for mitigating the enormous computational costs associated with training data-hungry modern deep learning models at scale. Since large scale data collections are invariably noisy, developing data pruning strategies that remain robust even in the presence of corruption is critical in practice. However, existing data pruning methods often fail under high corruption rates due to their reliance on empirical mean estimation, which is highly sensitive to outliers. In response, we propose Geometric Median (GM) Matching, a novel k-subset selection strategy that leverages Geometric Median -- a robust estimator with an optimal breakdown point of 1/2; to enhance resilience against noisy data. Our method iteratively selects a k-subset such that the mean of the subset approximates the GM of the (potentially) noisy dataset, ensuring robustness even under arbitrary corruption. We provide theoretical guarantees, showing that GM Matching enjoys an improved O(1/k) convergence rate -- a quadratic improvement over random sampling, even under arbitrary corruption. Extensive experiments across image classification and image generation tasks demonstrate that GM Matching consistently outperforms existing pruning approaches, particularly in high-corruption settings and at high pruning rates; making it a strong baseline for robust data pruning.