Hybrid models combining Transformers and State Space Models (SSMs) are promising for balancing performance and efficiency. However, optimizing these hybrid models, particularly by addressing the potential redundancy inherent within the Transformer components, remains a significant challenge. In this paper, we propose RAD (Redundancy-Aware Distillation), a novel framework that uses self-speculative decoding as a diagnostic tool to identify redundant attention layers within the model. These identified layers are then selectively replaced with SSM components, followed by targeted (self-)distillation. Specifically, RAD focuses knowledge transfer on the components identified as redundant, considering architectural changes and specific weight initialization strategies. We experimentally demonstrate that self-distillation using RAD significantly surpasses the performance of the original base model on mathematical and coding tasks. Furthermore, RAD is also effective in standard knowledge distillation settings, achieving up to approximately 2x faster convergence compared to baseline methods. Notably, while a baseline model distilled from a Llama-3.1 70B teacher achieves scores of 46.17 on GSM8K and 22.75 on CRUX, RAD achieves significantly higher scores of 71.27 on GSM8K and 28.25 on CRUX, even when using a much smaller Llama-3.1 8B teacher. RAD offers a new pathway for efficient optimization and performance enhancement in the distillation of hybrid models.

The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as ``sequence modeling." Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs. In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives. Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.

Racing car aficionados will probably send me hate mail for this, but my experience has been that there is only one case, in normal driving, where a good automatic transmission is inferior to a manual transmission. Similarly in software development: in almost every case, automatic memory management is superior to manual memory management and results in far greater programmer productivity. If you were developing desktop applications in the early years of Windows, Microsoft offered you two ways to do it: writing C code which calls the Windows API directly and managing your own memory, or using Visual Basic and getting your memory managed for you. These are the two development environments I have used the most, personally, over the last 13 years or so, and I know them inside-out, and my experience has been that Visual Basic is significantly more productive. Often I've written the same code, once in C calling the Windows API and once in Visual Basic, and C always took three or four times as much work.