Sequential test-time scaling is a promising training-free method to improve large reasoning model accuracy, but as currently implemented, significant limitations have been observed. Inducing models to think for longer can increase their accuracy, but as the length of reasoning is further extended, it has also been shown to result in accuracy degradation and model instability. This work presents a novel sequential test-time scaling method, Min-Seek, which improves model accuracy significantly over a wide range of induced thoughts, stabilizing the accuracy of sequential scaling, and removing the need for reasoning length fine-tuning. Beyond improving model accuracy over a variety of reasoning tasks, our method is inherently efficient, as only the KV pairs of one additional induced thought are kept in the KV cache during reasoning. With a custom KV cache which stores keys without position embeddings, by dynamically encoding them contiguously before each new generated thought, our method can continue to reason well beyond a model’s maximum context length, and under mild conditions has linear computational complexity.

The quadratic computational cost of traditional attention mechanisms poses a major bottleneck to the scalability and practical deployment of large language models (LLMs), particularly in long-context scenarios. To improve efficiency, existing approaches often enforce rigid structural constraints such as local attention windows. However, these strategies typically lead to substantial performance degradation on tasks requiring precise long-range recall. In this work, we propose MATCH, a scalable and efficient framework that augments sparsified attention mechanisms with dynamically integrated in-context information through an efficient retrieval system. Empirical results show that MATCH significantly improves the performance of sparse-attention models on both synthetic and real-world natural-language tasks. These findings highlight the versatility of MATCH as a general approach for enhancing in-context retrieval capabilities while maintaining the efficiency benefits of sparse attention architectures.

Post-training hybridization of large language models (LLMs) often replaces quadratic self-attention with sliding-window attention (SWA) to reduce KV cache usage and improve latency. Existing hybridization schemes are typically defined either at the layer level (e.g., interleaving) or at the head level via static rankings from local to global. Layer-level schemes ignore that local and global dependencies are routed through heads within the same layer, while static head-level rankings suffer from entanglement: a head’s local/global behavior can change after hybridization. We propose BOSCH, Black-box Binary Optimization for Short-context Head Selection, a training-free method that formulates the problem as a Large Neighborhood Search and decomposes it into three subproblems: (i) layer-importance detection via small-budget black-box probes, (ii) adaptive per-layer SWA-ratio assignment based on these sensitivities, and (iii) grouped head-level optimization within ratio buckets. Extensive experiments on 4 LLMs ranging from 1.7B to 30B parameters, across 4 SWA ratios, show that BOSCH consistently outperforms layer-level heuristics and 6 strong static head-level methods, with larger gains at higher SWA ratios. Under continual pretraining, BOSCH recover original long-context performance faster and to a higher level. Analysis of the selected heads reveals substantial turnover for BOSCH across different SWA ratios, underscoring the importance of performing head-level selection for each target ratio rather than relying on fixed locality rankings.