Abstract: The inherent quadratic complexity of the attention mechanism in transformer models has driven the research community to explore alternative architectures with sub-quadratic complexity, such as state-space models. Mamba has established itself as a leading model within this emerging paradigm, achieving state-of-the-art results in various language modeling benchmarks. However, despite its impressive performance, Mamba's effectiveness is limited by its pre-training context length, resulting in a pronounced degradation when the model is tasked with handling longer contexts. Our investigation reveals that Mamba's inability to generalize effectively to long contexts is primarily due to the out-of-distribution (OOD) discretization steps. To address this critical limitation, we introduce _**MambaExtend**_, a novel framework designed to significantly enhance the context extension capabilities of Mamba. Specifically, MambaExtend leverages a _**training-free**_ approach to calibrate _only_ the scaling factors of discretization modules for different layers. We demonstrate both gradient-based and gradient-free zeroth-order optimization to learn the optimal scaling factors for each Mamba layer, requiring orders of magnitude fewer updates as opposed to the parameter fine-tuning-based alternatives. Using this approach, we achieve a training-free context extension of up to 32x, expanding the context from 2k to 64k tokens with minimal increases in perplexity. In contrast to existing fine-tuning methods, MambaExtend selectively calibrates the scaling factors, requiring up to $\mathbf{5.42 * 10^6} \times$ fewer parameter updates and incurring up to $\mathbf{3.87} \times$ lower peak memory usage, while delivering comparable or superior long-context performance across multiple tasks. Codes and checkpoints are available here$^1$.