A major drawback of reasoning models is their excessive token usage, inflating computational cost, resource demand, and latency. We show this verbosity stems not from deeper reasoning but from reinforcement learning loss minimization when models produce incorrect answers. With unsolvable problems dominating training, this effect compounds into a systematic tendency toward longer outputs. Through theoretical analysis of PPO and GRPO, we prove that incorrect answers inherently drive policies toward verbosity \textit{even when} $γ=1$, reframing response lengthening as an optimization artifact. We further uncover a consistent correlation between conciseness and correctness across reasoning and non-reasoning models. Building on these insights, we propose a two-phase RL procedure where a brief secondary stage, trained on a small set of solvable problems, significantly reduces response length while preserving or improving accuracy. Finally, we show that while GRPO shares properties with PPO, it exhibits collapse modes, limiting its reliability for concise reasoning. Our claims are supported by extensive experiments.

As Large Language Models (LLMs) evolve into personal assistants with access to sensitive user data, they face a critical privacy challenge: while prior work has addressed output-level privacy, recent findings reveal that LLMs often leak private information through their internal reasoning processes, violating contextual privacy expectations. These leaky thoughts occur when models inadvertently expose sensitive details in their reasoning traces, even when final outputs appear safe. The challenge lies in preventing such leakage without compromising the model's reasoning capabilities, requiring a delicate balance between privacy and utility. We introduce Steering Activations towards Leakage-free Thinking (SALT), a lightweight test-time intervention that mitigates privacy leakage in model's Chain of Thought (CoT) by injecting targeted steering vectors into hidden state. We identify the high-leakage layers responsible for this behavior. Through experiments across multiple LLMs, we demonstrate that SALT achieves reductions including $18.2\%$ reduction in CPL on QwQ-32B, $17.9\%$ reduction in CPL on Llama-3.1-8B, and $31.2\%$ reduction in CPL on Deepseek in contextual privacy leakage dataset AirGapAgent-R while maintaining comparable task performance and utility. Our work establishes SALT as a practical approach for test-time privacy protection in reasoning-capable language models, offering a path toward safer deployment of LLM-based personal agents.

Test-time scaling has been shown to substantially improve large language models' (LLMs) mathematical reasoning. However, for a large portion of mathematical corpora, especially theorem proving, RLVR's scalability is limited: intermediate reasoning is crucial, while final answers are difficult to directly and reliably verify. Meanwhile, token-level SFT often degenerates into rote memorization rather than inducing longer chains of thought. Inspired by BERT's self-supervised tasks, we propose MR-RLVR (Masked-and-Reordered RLVR), which constructs process-level self-supervised rewards via "masked-then-fill" and "step reordering" to extract learnable signals from intermediate reasoning. Our training pipeline comprises two stages: we first perform self-supervised training on sampled mathematical calculation and proof data; we then conduct RLVR fine-tuning on mathematical calculation datasets where only outcomes are verifiable. We implement MR-RLVR on Qwen2.5-3B and DeepSeek-R1-Distill-Qwen-1.5B, and evaluate on AIME24, AIME25, AMC23, and MATH500. Under a fixed sampling and decoding budget, MR-RLVR achieves average relative gains over the original RLVR of +9.86% Pass@1, +5.27% Pass@5, and +4.00% Pass@8. These results indicate that incorporating process-aware self-supervised signals can effectively enhance RLVR's scalability and performance in only outcome-verifiable settings.

In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on performance than how those examples are ordered, leading to a focus on example selection. We revisit this assumption and conduct a systematic comparison between the effect of selection and ordering. Through controlled experiments on both classification and generation tasks, using multiple open-source model families (0.5B to 27B parameters) and GPT-5, we find that the variance in performance due to different example orderings is comparable to that from using entirely different example sets. Furthermore, we show that strong orderings can be identified using only a development set, achieving performance close to an oracle that selects the best ordering based on test labels. Our findings highlight the equal and intertwined importance of example selection and ordering in prompt design, calling for a reexamination of the assumptions held in ICL.

Large Language Models (LLMs) deliver state-of-the-art performance across many tasks but impose high computational and memory costs, limiting their deployment in resource-constrained or real-time settings. To address this, we propose HierRouter, a hierarchical routing approach that dynamically assembles inference pipelines from a pool of specialized, lightweight language models. Formulated as a finite-horizon Markov Decision Process (MDP), our approach trains a Proximal Policy Optimization (PPO)-based reinforcement learning agent to iteratively select which models to invoke at each stage of multi-hop inference. The agent conditions on the evolving context and accumulated cost to make context-aware routing decisions. Experiments with three open-source candidate LLMs across six benchmarks, including QA, code generation, and mathematical reasoning, show that HierRouter improves response quality by up to 2.4x compared to using individual models independently, while incurring only a minimal additional inference cost on average. These results highlight the promise of hierarchical routing for cost-efficient, high-performance LLM inference. All codes can be found here https://github.com/ Nikunj-Gupta/hierouter.

Background: Medical coding structures healthcare data for research, quality monitoring, and policy. This study assesses the potential of large language models (LLMs) to assign ICPC-2 codes using the output of a domain-specific search engine. Methods: A dataset of 437 Brazilian Portuguese clinical expressions, each annotated with ICPC-2 codes, was used. A semantic search engine (OpenAI's text-embedding-3-large) retrieved candidates from 73,563 labeled concepts. Thirty-three LLMs were prompted with each query and retrieved results to select the best-matching ICPC-2 code. Performance was evaluated using F1-score, along with token usage, cost, response time, and format adherence. Results: Twenty-eight models achieved F1-score > 0.8; ten exceeded 0.85. Top performers included gpt-4.5-preview, o3, and gemini-2.5-pro. Retriever optimization can improve performance by up to 4 points. Most models returned valid codes in the expected format, with reduced hallucinations. Smaller models (<3B) struggled with formatting and input length. Conclusions: LLMs show strong potential for automating ICPC-2 coding, even without fine-tuning. This work offers a benchmark and highlights challenges, but findings are limited by dataset scope and setup. Broader, multilingual, end-to-end evaluations are needed for clinical validation.

Large Language Models (LLMs) have demonstrated remarkable progress in complex reasoning tasks through both post-training and test-time scaling laws. While prevalent test-time scaling approaches are often realized by using external reward models to guide the model generation process, we find that only marginal gains can be acquired when scaling a model post-trained on specific reasoning tasks. We identify that the limited improvement stems from distribution discrepancies between the specific post-trained generator and the general reward model. To address this, we propose a framework that incentivizes LLMs to self-verify their own answers. By unifying answer generation and verification within a single reinforcement learning (RL) process, we train models that can effectively assess the correctness of their own solutions. The trained model can further scale its performance at inference time by verifying its generations, without the need for external verifiers. We train our self-verification models based on Qwen2.5-Math-7B and DeepSeek-R1-Distill-Qwen-1.5B, demonstrating their capabilities across varying reasoning context lengths. Experiments on multiple mathematical reasoning benchmarks show that our models can not only improve post-training performance but also enable effective test-time scaling.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6% (8.6% improvement beyond format correction), and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7% (7.0% non-format gain). This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which contains the aforementioned example. Furthermore, RLVR with only two examples even slightly exceeds these results (MATH500: 74.8%, average: 36.6%). Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples. In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-category generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by incorporating entropy loss with an appropriate coefficient) in 1-shot RLVR training. We also further discuss related observations about format correction, label robustness and prompt modification. These findings can inspire future work on RLVR efficiency and encourage a re-examination of recent progress and the underlying mechanisms in RLVR. All resources are open source at https://github.com/ypwang61/One-Shot-RLVR.

Recent trends in test-time scaling for reasoning models (e.g., OpenAI o1, DeepSeek R1) have led to a popular belief that extending thinking traces using prompts like "Wait" or "Let me rethink" can improve performance. This raises a natural question: Does thinking more at test-time truly lead to better reasoning? To answer this question, we perform a detailed empirical study across models and benchmarks, which reveals a consistent pattern of initial performance improvements from additional thinking followed by a decline, due to "overthinking". To understand this non-monotonic trend, we consider a simple probabilistic model, which reveals that additional thinking increases output variance-creating an illusion of improved reasoning while ultimately undermining precision. Thus, observed gains from "more thinking" are not true indicators of improved reasoning, but artifacts stemming from the connection between model uncertainty and evaluation metric. This suggests that test-time scaling through extended thinking is not an effective way to utilize the inference thinking budget. Recognizing these limitations, we introduce an alternative test-time scaling approach, parallel thinking, inspired by Best-of-N sampling. Our method generates multiple independent reasoning paths within the same inference budget and selects the most consistent response via majority vote, achieving up to 20% higher accuracy compared to extended thinking. This provides a simple yet effective mechanism for test-time scaling of reasoning models.

Large Language Models (LLMs) have been demonstrating increasingly strong reasoning capability with their chain-of-thoughts (CoT), which are routinely used by humans to judge answer quality. This reliance creates a powerful yet fragile basis for trust. In this work, we present an urgent but underexplored risk: attackers could induce LLMs to generate incorrect yet coherent CoTs that look plausible at first glance, while leaving no obvious manipulated traces, closely resembling the reasoning exhibited in benign scenarios. In particular, we introduce DecepChain, a novel backdoor attack paradigm that steers models to generate reasoning that appears benign while yielding incorrect conclusions eventually. At a high level, DecepChain exploits LLMs' own hallucination and amplifies it by fine-tuning on naturally erroneous rollouts generated by the model itself and then reinforces it via Group Relative Policy Optimization (GRPO) with a flipped reward on triggered inputs, plus a plausibility regularizer to preserve fluent, benign-looking reasoning. Across multiple benchmarks and models, DecepChain achieves high attack success rates with minimal performance degradation on benign scenarios. Moreover, a careful human evaluation showed that the human raters struggle to distinguish our manipulated reasoning processes from benign ones, underscoring our attack's stealthiness. Left unaddressed, this stealthy failure mode can quietly corrupt LLM answers and undermine human trust for LLM reasoning, emphasizing the urgency for future research into this alarming risk. Project page: https://decepchain.github.io/.