Thinking Long, but Short: Stable Sequential Test-Time Scaling for Large Reasoning Models

2026-01-14

AI Summary

This work proposes Min-Seek, a training-free dynamic KV cache management mechanism that addresses the accuracy degradation and instability commonly observed in existing sequential inference methods when scaling to longer contexts, which often require cumbersome length-specific tuning. By discarding positional encodings and retaining only the most recent key-value (KV) pairs, Min-Seek dynamically re-encodes the context prior to each decoding step, enabling continuous inference beyond the model’s native context window. This approach eliminates the need for inference-length hyperparameter tuning, significantly improves long-sequence reasoning accuracy across diverse tasks, and maintains linear computational complexity, thereby achieving both efficiency and robustness.

Technology Category

• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• sequential test-time scaling
• reasoning length
• model instability
• accuracy degradation
• large reasoning models

Innovation

• sequential test-time scaling
• Min-Seek
• KV cache optimization
• position embedding
• linear complexity