Scaling the interaction horizon—the maximum number of environment interactions per episode—improves LLM agents on long-horizon tasks, and curriculum-based methods that progressively expand the horizon outperform fixed-horizon alternatives. However, existing schedules are open-loop: they monotonically increase the horizon until a manually specified maximum, with no mechanism to detect when further expansion stops helping. We propose the effective interaction frontier hypothesis: a dynamic boundary beyond which additional interactions yield diminishing returns while cost grows linearly. We then introduce Elastic Horizon, a closed-loop controller that tracks this boundary via the 90th percentile of successful trajectory lengths. On AppWorld and BFCL, fixed-horizon sweeps reveal clear saturation plateaus; Elastic Horizon stabilizes the horizon inside the saturation band from both under- and over-capacity initializations, attains the best success rates across 7B and 14B backbones, and saves up to 25% of per-step trajectory tokens. Our work shifts the paradigm from how to scale interaction horizons to when to stop scaling.

Large reasoning models enhanced by reinforcement learning with verifiable rewards have achieved significant performance gains by extending their chain-of-thought. However, this paradigm incurs substantial deployment costs as models often exhibit excessive verbosity on simple queries. Existing efficient reasoning methods relying on explicit length penalties often introduce optimization conflicts and leave the generative mechanisms driving overthinking largely unexamined. In this paper, we identify a phenomenon termed length shift where models increasingly generate unnecessary reasoning on trivial inputs during training. To address this, we introduce Dynamic Outlier Truncation (DOT), a training-time intervention that selectively suppresses redundant tokens. This method targets only the extreme tail of response lengths within fully correct rollout groups while preserving long-horizon reasoning capabilities for complex problems. To complement this intervention and ensure stable convergence, we further incorporate auxiliary KL regularization and predictive dynamic sampling. Experimental results across multiple model scales demonstrate that our approach significantly pushes the efficiency-performance Pareto frontier outward. Notably, on the AIME-24, our method reduces inference token usage by 78% while simultaneously increasing accuracy compared to the initial policy and surpassing state-of-the-art efficient reasoning methods.

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model’s reflective ability. Though some studies attempted to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes.In this work, we propose to enhance LLM’s reasoning ability by Learning from Errors for MatheMatical Advancement (LEMMA). LEMMA constructs data consists of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an error-type grounded mistake augmentation method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. By fine-tuning on the constructed dataset, the model is able to self-correct errors autonomously within the generation process without relying on external critique models. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong models with less than 90k data.

Rapid advances in Large Language Models (LLMs) have spurred demand for processing extended context sequences in contemporary applications. However, this progress faces two challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues limit LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using QK dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a few critical KV cache tokens in attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we design the Selection Cache based on observations of consecutive Query similarity and implemented the efficient Paged Dot Product Kernel, significantly reducing the selection overhead. A comprehensive evaluation of TokenSelect demonstrates up to 23.84× speedup in attention computation and up to 2.28× acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.