Keywords: language modeling, state space models, efficiency
TL;DR: We study the expressivity gap between state space models (SSMs) and attention on language modeling and reduce the hardware barrier between SSMs and attention.
Abstract: State space models (SSMs) have demonstrated state-of-the-art sequence modeling performance in some modalities, but underperform attention in language modeling. Moreover, despite scaling nearly linearly in sequence length instead of quadratically, SSMs are still slower than Transformers due to poor hardware utilization. In this paper, we make progress on understanding the expressivity gap between SSMs and attention in language modeling, and on reducing the hardware barrier between SSMs and attention. First, we use synthetic language modeling tasks to understand the gap between SSMs and attention. We find that existing SSMs struggle with two capabilities: recalling earlier tokens in the sequence and comparing tokens across the sequence. To understand the impact on language modeling, we propose a new SSM layer, H3, that is explicitly designed for these abilities. H3 matches attention on the synthetic languages and comes within 0.4 PPL of Transformers on OpenWebText. Furthermore, a hybrid H3-attention model that retains two attention layers surprisingly outperforms Transformers on OpenWebText by 1.0 PPL. When trained on the Pile at small/medium scale (125M and 355M parameters), hybrid H3-attention language models display promising initial results, achieving lower perplexity than Transformers and outperforming Transformers in zero- and few-shot learning on a majority of tasks in the SuperGLUE benchmark. Next, to improve the efficiency of training SSMs on modern hardware, we propose FlashFFTConv. FlashFFTConv uses a fused block FFT algorithm to improve efficiency on sequences up to 8K, and introduces a novel state passing algorithm that exploits the recurrent properties of SSMs to scale to longer sequences. FlashFFTConv yields 2$\times$ speedup on the long-range arena benchmark and allows hybrid language models to generate text 1.6$\times$ faster than Transformers.
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