Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking—wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide LLM TTS without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating step-wise uncertainty over time. To support flexible inference-time control, we introduce -control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by over 45% on average while improving accuracy by 0.33–3.46%.

Advancing LLM reasoning skills has captivated wide interest. However, current post-training techniques rely heavily on supervisory signals, such as outcome supervision or auxiliary reward models, which face the problem of scalability and high annotation costs. This motivates us to enhance LLM reasoning without the need for external supervision. Given the input query, the LLM seeks the globally optimal response by stepwise sampling and self-rewarding, and optimizes itself with the collected responses. Genius offers some technical solutions to address the following key challenges. To tackle the problem of how to determine the steps in the response via self-rewarding, Genius introduces a stepwise foresight re-sampling strategy to sample and estimate the step value by simulating future outcomes. Recognizing the intrinsic noise and uncertainty of self-supervision, we propose an advantage-calibrated optimization (ACO) loss function to mitigate estimation inconsistencies. In short, Genius provides an advanced initial step towards self-improve LLM reasoning with general queries and without supervision, revolutionizing reasoning scaling laws given the vast availability of general queries.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named 𝜙-Decoding. To provide a precise and expressive estimation of step value, 𝜙-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show 𝜙-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets.