Summary of Provable Benefits Of Complex Parameterizations For Structured State Space Models, by Yuval Ran-milo et al.
Provable Benefits of Complex Parameterizations for Structured State Space Models
by Yuval Ran-Milo, Eden Lumbroso, Edo Cohen-Karlik, Raja Giryes, Amir Globerson, Nadav Cohen
First submitted to arxiv on: 17 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed paper investigates the benefits of complex parameterizations in structured state space models (SSMs), particularly S4 and Mamba. Unlike traditional neural network modules, SSMs often employ complex parameters. The study aims to theoretically explain why this is advantageous by examining gaps between real and complex diagonal SSMs. Key findings include a moderate dimension being sufficient for a complex SSM to express all mappings of a real SSM, but requiring a much higher dimension for the opposite. Additionally, the research reveals that even with a high-dimensional real SSM, parameters must hold exponentially large values to learn in practice, whereas complex SSMs can achieve this with moderate parameter values. Experimental results support these findings and suggest potential extensions to account for selectivity, a novel architectural feature leading to state-of-the-art performance. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Structured state space models (SSMs) are an important part of neural networks like S4 and Mamba. They use special structures to process information. The researchers looked at why using complex numbers in these models can be helpful. They found that even with a simple structure, complex numbers can make it easier to learn new things. This is because complex numbers allow the model to express more possibilities without needing as many calculations. In other words, complex SSMs are better at learning and doing tasks than real SSMs. |
Keywords
» Artificial intelligence » Neural network
