Block-Biased Mamba for Long-Range Sequence Processing (2505.09022v1)

Abstract: Mamba extends earlier state space models (SSMs) by introducing input-dependent dynamics, and has demonstrated strong empirical performance across a range of domains, including LLMing, computer vision, and foundation models. However, a surprising weakness remains: despite being built on architectures designed for long-range dependencies, Mamba performs poorly on long-range sequential tasks. Understanding and addressing this gap is important for improving Mamba's universality and versatility. In this work, we analyze Mamba's limitations through three perspectives: expressiveness, inductive bias, and training stability. Our theoretical results show how Mamba falls short in each of these aspects compared to earlier SSMs such as S4D. To address these issues, we propose $\text{B}_2\text{S}_6$, a simple extension of Mamba's S6 unit that combines block-wise selective dynamics with a channel-specific bias. We prove that these changes equip the model with a better-suited inductive bias and improve its expressiveness and stability. Empirically, $\text{B}_2\text{S}_6$ outperforms S4 and S4D on Long-Range Arena (LRA) tasks while maintaining Mamba's performance on LLMing benchmarks.

Block-Biased Mamba for Long-Range Sequence Processing

The paper "Block-Biased Mamba for Long-Range Sequence Processing" addresses the intriguing challenges encountered by Mamba models—a subclass of state-space models (SSMs)—when applied to long-range sequence tasks. Despite showing competitiveness with Transformer architectures in various domains through their input-dependent dynamics, Mamba models exhibit notable deficiencies concerning long-range sequential data. The authors' exploration follows three core aspects: expressiveness, inductive bias, and training stability of the Mamba architecture.

Analytical Insights

1. Expressiveness: The authors illustrate that Mamba's parameter-sharing mechanism across channels constrains the model's "effective width", adversely impacting its expressiveness. Unlike some SSM variants that maintain individual channels allowing for broader approximation capabilities, Mamba lacks universal approximation properties for a broad spectrum of sequence transformations. This is substantiated by theoretical comparisons against models like S4D, showcasing how Mamba's parameterization restricts its applicability in capturing complex, multi-dimensional data patterns.
2. Inductive Bias: The model's inductive bias stemming from its input-dependent memory dynamics appears to exacerbate its deficiency in retaining long-term dependencies. Mamba allows for a variable rate of information retention, guided largely by the input, which can result in premature discarding of necessary sequential information. The authors demonstrate via analytical and empirical methods how this variability in memory retention can significantly hinder performance on tasks with static long-range dependencies such as vision or time-series tasks with uniform significance across inputs.
3. Training Stability: The dynamic nature of input-dependent dynamics such as Mamba introduces considerable training instability, primarily attributed to the excessive gradient magnitudes with respect to input-related parameters as sequence length increases. This volatility in gradient dynamics can lead to unpredictable and non-convergent learning paths, particularly in the context of long-range sequence benchmarks. The authors analytically derive that the gradient magnitudes associated with Mamba's input selection mechanism tend to scale unfavorably with input length and size, challenging its trainability.

Proposed Solution: Block-Biased S6

In response to these highlighted issues, the paper proposes a novel extension, termed as Block-Biased-S6 ($B$), which aims to surmount these challenges inherent in Mamba. The proposed architecture modifies the S6 unit by integrating a block-wise partitioning strategy paired with a channel-specific bias, enhancing both its expressiveness and stability. Specifically, $B$ achieves:

• Enhanced Expressiveness: By segmenting the input into blocks and incorporating block-specific dynamics, $B$ can harness increased expressiveness without relying on cross-channel parameter sharing. This effectively restores universal approximation capabilities for the network model, fostering improved performance on complex, static sequence transformations.
• Mitigated Inductive Bias: The introduction of a channel-specific bias term helps to moderate the model’s sensitivity to input variations, curtailing the skew towards selective memory retention that is overly dependent on immediate input magnitudes. This considerate modulation of memory dynamics aligns better with a diverse range of task requirements, particularly in long-range tasks.
• Improved Training Stability: Channel-specific input-independent biases, paired with sectoral partitioning, provide a more balanced approach to gradient descent optimization, reducing oscillations in the loss landscape, even as sequence length increases.

Empirical Validation

Empirical analysis conducted using the Long-Range Arena (LRA) benchmark substantiate $B$’s superior performance over its predecessor as well as various SSM architectures, such as S4D and S5, on long-range sequential tasks. Additionally, preliminary evaluations on tasks such as LLMing using datasets such as SlimPajama demonstrate that these improvements need not compromise on performance in other domains where Mamba excels.

Implications

The research advances practical and theoretical knowledge in neural sequence models by addressing intrinsic architectural limitations of Mamba through principled improvements. The theoretical insights underpinning B’s development accentuate an important paradigm shift towards adaptable yet stable architectures suited for extensive dependencies. The approach and outcomes present opportunities for further refinements in SSM models and potentially broader applications across diverse AI domains, including but not limited to multi-modal, operational forecasting, and LLMing tasks.

Future investigations may delve into scaling $B$ for large-scale language and foundation model applications to further explore its impact on AI developments.