Repeat After Me: Transformers are Better than State Space Models at Copying (AI summary)

Key Points

- Transformers outperform generalized state space models (GSSMs) in terms of copying from the input context.

- The theoretical analysis showed that transformers can copy exponential lengths of strings, while GSSMs are limited by their fixed-size latent state.

- Empirical results demonstrated that transformers are much more efficient and generalizable at learning copying tasks compared to GSSMs on synthetic tasks.

- The study also found that transformers dramatically outperformed GSSMs at memory-intensive tasks, such as copying and retrieving information from context.

- The theoretical comparison between state space models and transformers suggested that GSSMs fail to solve the copying task unless their latent state grows linearly with the sequence length.

- Experimentation showed that, unlike transformers, GSSMs cannot effectively retrieve and copy from the input context, which indicates a significant limitation of GSSMs on practical tasks.

- Pre-trained transformer models substantially outperformed GSSMs in tasks such as copying long natural language strings and retrieval and few-shot question answering, even when GSSMs had lower perplexity as a language model.

- The study suggests that future work should focus on developing hybrid architectures that combine the advantages of both transformers and state space models for efficient and effective sequence modeling.

- The paper highlighted that although transformers excel at tasks involving copying and accessing arbitrary parts of the context, GSSMs have their own advantages, such as better memory and computational complexity for processing long inputs.

Summary

Comparative Analysis of Transformers and GSSMs
The paper compares transformers with generalized state space models (GSSMs) in terms of their ability to copy input context. The authors conduct theoretical analysis and empirical experiments to demonstrate that transformers outperform GSSMs in tasks that require copying from the input context. The theoretical analysis shows that while transformers are capable of copying inputs of exponential length using Õ(L) input-dependent memory, GSSMs fail to copy long sequences unless their latent state grows linearly with the sequence length. Empirically, the authors find that transformers outperform GSSMs in terms of training efficiency, length generalization, and retrieval of information from context. The experiments also demonstrate that pretrained transformers outperform pretrained GSSMs at memory-intensive tasks, including copying and retrieving information from the context. The results suggest a fundamental disparity between transformers and GSSMs in tasks of practical interest.

Advantages of State Space Models over Transformers
The paper emphasizes that state space models have advantages over transformers, such as memory and computational complexity not increasing with input length, making them better for training and inference on long inputs. The authors acknowledge that while transformers outperform GSSMs in copying tasks, there are tasks where GSSMs outperform transformers, such as tracking state variables across long sequences. They propose future work on hybrid architectures that endow state space models with an attention-like mechanism to allow them to retrieve relevant pieces of text from their input. Overall, the paper demonstrates that while transformers excel at certain tasks, GSSMs have their own strengths and may be more suitable for other applications.

Insights and Future Research Opportunities
The paper provides insights into the capabilities and limitations of transformers and GSSMs in handling tasks that involve processing and retrieving information from input contexts. It lays the groundwork for potential future research in developing hybrid models that combine the strengths of both transformer and state space models.

Reference: https://arxiv.org/abs/2402.010...