Reason in the Words You Speak: Idiolectal Paraphrasing Off-Policy Traces for Reasoning Distillation in VideoLLMs

Recent large language models achieve strong performance on complex reasoning tasks, where reinforcement learning with Group Relative Policy Optimization (GRPO) has emerged as a leading paradigm for optimizing models on self-generated trajectories. However, the on-policy nature of GRPO bounds the model to the reasoning skills it can already produce, restricting to learn more advanced capabilities. Prior works inject privileged reasoning traces from a stronger teacher policy to guide training, yet these traces are inherently out of distribution with respect to the student policy. We observe that this mismatch between on-policy and off-policy causes gradient clipping on semantically critical reasoning tokens, ultimately rewarding correct answers while leaving the reasoning that justifies them unlearned. Hence, we propose \textbf{Echo-GRPO}, a framework that lets the model reason in the words it speaks. Rather than imitating low-probability privileged traces from the teacher model, Echo-GRPO rewrites them into the student policy's own \textit{idiolect}, that is, its own characteristic vocabulary and expression patterns, while preserving their semantics via Dual-Reference Decoding. We instantiate this framework as \textbf{VideoEcho-R1} for video reasoning distillation, achieving consistent improvements across three multimodal LLM backbones and five benchmarks. Finally, we show that our idiolectal paraphrasing is a plug-in module that consistently improves both RL and supervised fine-tuning frameworks for reasoning distillation, demonstrating that policy-aligned supervision extends beyond GRPO.

Distilling Reasoning Traces into Advisory Prompts for Software Engineering Tasks

Language models are widely used for generating and otherwise processing code (e.g., identifying code hallucinations, possible inputs, or predicting outputs); however, LLMs can make mistakes, which can be serious. One key issue is that models are trained on (still) largely human-written, and thus imperfect, code; it's not easy to find sufficiently large code corpora that are entirely free of bugs. Thus, other inference-time ways of reducing LLM errors, without additional training, are desirable. "Reasoning" or "thinking" modes, exposed as a togglable feature by hybrid reasoning models, do reduce errors; however, reasoning consumes additional resources. This paper asks if better performance can be achieved without always incurring the cost of reasoning. Human students of programming learn to avoid mistakes by (a) identifying them, (b) reflecting upon the cognitive lapses that led to them (essentially, "thinking through" the errors), (c) inferring general rules or lessons from these reflections, and (d) internalizing these lessons into rules. In tutorial sessions with an instructor, this is a common Socratic interaction. Examples of such internalizable rules might include the nugget "Before coding, restate the requirements to clarify them." Inspired by this process, this paper describes an approach where we first identify examples in which "thinking mode" in a (low-resource) LLM avoids errors. These errors, and their avoidance via "thinking" in the same LLM, are then examined by a bigger LLM to generate summary explanations; these are then summarized by a large LLM into brief advisory prompts. This approach works on many modest-sized models; in some cases, the "advisory prompts" thus learned can also be gainfully transferred to other models. We also present investigations into the nature of coding errors that language models make, and a characterization of when this approach can be helpful.

X$^3$-OPD: Distilling Reasoning into Large Audio-Language Models via On-Policy Alignment

While large audio-language models have achieved remarkable progress in auditory perception, they still lag behind text-based large language models in deep logical reasoning, primarily due to the scarcity of high-quality audio reasoning data. To bridge this gap, we propose X$^3$-OPD, a cross-modal on-policy distillation framework that transfers reasoning capabilities from a powerful text teacher to an audio-language student. During training, the student generates reasoning trajectories conditioned on its own acoustic perception, while the teacher provides token-level guidance using matched textual inputs and verified answers. We further construct a three-tier symmetric corpus covering textual reasoning rendered into speech, audio-event reasoning grounded in complex acoustic scenes, and spoken-dialogue reasoning involving paralinguistic cues. This design extends cross-modal distillation beyond textually recoverable content to reasoning grounded in non-linguistic events, prosody, and conversational context. Experiments on MMSU, MMAU, BIG Bench Audio, and MMAR demonstrate that X$^3$-OPD substantially improves audio-grounded reasoning and chain-of-thought quality while largely preserving the model's existing capabilities under domain shift.

Better Starts, Better Ends: Bootstrapped Iterative Self-Reasoning Distillation for Compressed Reasoning

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.

DT-Guard: Intent-Driven Reasoning-Active Training for Reasoning-Free LLM Safety Guardrail

Large language models deployed in open-world applications require safety guardrails that are both robust to complex risks and efficient enough for low-latency runtime moderation. Existing guardrails face a practical trade-off between lightweight classification-based models, which are efficient but often struggle with concealed intent, ambiguous semantics, and borderline safety decisions, and reasoning-based guards, which improve judgment quality but introduce additional token generation and inference latency. We present DT-Guard, a content safety guardrail model based on a Reasoning-Active Training, Reasoning-Free Inference paradigm. The key idea is to use reasoning supervision during training while emitting only structured safety labels at inference time. DT-Guard formulates safety judgment as a progressive decision process, Intent - Category - Safety, and constructs an intent-driven dataset with intent labels, risk categories, safety labels, and structured reasoning trajectories. To further improve hard-case robustness, we propose Rollout-Guided Progressive Hard-Case Optimization (RG-PHO), which uses multi-rollout consistency to identify stably mastered, persistently failed, and preference-unstable samples, and applies targeted supervised and preference optimization accordingly. At inference time, DT-Guard directly generates structured labels without explicit reasoning traces, preserving deployment efficiency. Experiments on prompt-side and response-side safety benchmarks show that DT-Guard achieves average F1 scores of 0.886 and 0.870, respectively. With only a 4B backbone, it reaches a dual-side average F1 of 0.878, outperforming strong 8B guardrail baselines. These results demonstrate that reasoning supervision can be effectively internalized into low-latency safety discrimination.

Safe Alone, Unsafe Together: Safeguarding Against Implicit Toxicity When Benign Images Combine

Multi-image content has become an increasingly prevalent form of visual communication in social media, giving rise to a new safety issue, multi-image implicit toxicity (MIIT), where each image appears benign in isolation, but harmful semantics emerge when the images are interpreted jointly. MIIT is particularly challenging for existing commercial moderation APIs and models due to the lack of explicit risky cues in each image. This paper aims to study how to identify MIIT. We first provide a formal definition of MIIT and analyze three key challenges for its detection. To alleviate the scarcity of data in this area, we construct MIIT-dataset, an image-only multi-image safety dataset covering seven representative risk categories through an automatic generation pipeline. Finally, we train MiShield with progressively distilled reasoning supervision, enabling it to produce safety judgments accompanied by explicit analyses of the correlated entities that result in the hazards. Experiments show that MiShield-8B models outperform representative moderation services and even larger-scale models, revealing its effectiveness and practical value for this widely used visual format. Warning: This paper contains potentially sensitive content.

Finding the Evidence: Discovering Decision-Supporting Tokens for On-Policy Reasoning Distillation

On-policy distillation transfers reasoning ability through dense token-level supervision, yet the nature of the transferable signal remains unclear. We discover that reasoning chains contain two types of knowledge that require different discovery mechanisms: decisions (where to branch), which surface through student uncertainty, and evidence (intermediate steps that justify decisions), which hides in positions where the student is confident yet wrong. Current methods capture only decisions; the substantive knowledge in evidence tokens remains untransferred. We propose DEAR(Decision-Evidence Aware Reasoning Distillation), which first identifies decisions via student entropy, then discovers their supporting evidence through hidden-state cosine similarity to decision anchors, boosted by teacher-student divergence to prioritize the largest knowledge gaps. Across three student-teacher configurations on math and code benchmarks, DEAR consistently outperforms standard OPD, with up to +2.5pp on competition math and +5.7pp on code generation.

Weight-Space Geometry of Offline Reasoning Training

Offline reinforcement-learning losses (RFT, RIFT, DFT, Offline GRPO, DPO) are widely used to distill reasoning from large teachers into smaller students, and are typically compared on downstream accuracy alone. We ask whether they are mechanistically distinct or converge to a similar weight update. Training six methods (SFT, RFT, DFT, RIFT, Offline GRPO, DPO) on identical math rollouts from a single base model (Qwen3-4B) with attention-only LoRA, we analyze the resulting deltas via cosine similarity, principal-angle subspace analysis, linear mode connectivity, and CKA. We observe: (i) SFT, RFT, and RIFT have nearly colinear weight deltas (cosine >= 0.97, top-1 principal angle ~7 deg median over 144 modules) and comparable GSM8K accuracy (87-88%, n=1319; pairwise McNemar p >= 0.15); (ii) DFT diverges further in direction than any reward-weighted method despite using the same data; (iii) Offline GRPO adds a substantial component orthogonal to the SFT direction (~67% globally, up to ~86% in late layers) while staying in the SFT loss basin; (iv) DPO sits in a near-orthogonal subspace, shows a mode-connectivity barrier, and collapses late-layer CKA to ~0.46. DPO also reaches the highest accuracy in our protocol on both GSM8K (93.5%, McNemar p < 10^-9 vs. each other method) and AIME26 (30.0% vs. 3.3-10.0%); its training uses a 10x smaller learning rate than the others (the standard convention), so the update-norm and accuracy gaps reflect loss-function and optimizer choices jointly, and a learning-rate-matched DPO comparison is left for future work.

MARD: Mirror-Augmented Reasoning Distillation for Mechanism-Level Drug-Drug Interaction Prediction

Mechanism-level drug-drug interaction (DDI) prediction requires identifying which enzyme or pharmacodynamic axis is implicated, in which direction, and with which evidence -- not merely whether two drugs interact. We introduce a reproducible mechanism-level DDI labelling and evaluation protocol with a structured 7-family/147-subtype taxonomy, leakage-safe cold-split protocols, and auditable reasoning metrics for evaluating pharmacological prediction beyond flat interaction classification. We propose a pipeline that produces a 7B reasoning MARD (Mirror-Augmented Reasoning Distillation), combining three training innovations: a single-token KL divergence on direction tag that ties the model's prediction, per-loss PRM-weighted DPO with programmatic hard negatives, and a leakage-safe mechanism-aware retrieval channel. Process-reward step labels are automatically verifiable against DrugBank-structured fields, requiring no human or LLM judges. On the April-2026 DrugBank release, our MARD-7B is the only system in a 32-system comparison whose accuracy survives drug-pair novelty, beating the best baseline by +13.9 pp and GPT-4o by +6.7 pp at ~1% of frontier API cost. Further analysis reveals an anti-memorisation signature where accuracy improves on rarely seen drugs, suggesting that gain comes from structured pharmacological reasoning rather than drug-frequency memorisation. We release corpus, DDI-PRM, retrieval index, and training code.