Lambda-Skip Connections: the architectural component that prevents Rank Collapse

2024-10-14

arXiv.org

AI Summary

Sequence models—particularly state-space models (SSMs)—suffer from rank collapse, wherein embedding vectors rapidly degenerate into low-rank or uniform states, degrading representational capacity and destabilizing training. Method: We propose the lambda-skip connection, a novel architectural mechanism designed within a unified modeling framework encompassing both Transformers and SSMs. Contribution/Results: First, we establish a general theoretical criterion for rank collapse, rigorously characterizing its necessary and sufficient conditions in SSMs. Second, we prove that lambda-skip strictly prevents rank collapse. Third, via spectral analysis, principled parameterization, and ablation studies, we empirically validate that lambda-skip significantly enhances training stability and representation quality across both Transformer and SSM architectures. Our work bridges theoretical analysis and practical design, offering a principled solution to a fundamental limitation in sequence modeling.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: (Large) Language Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Rank collapse, a phenomenon where embedding vectors in sequence models rapidly converge to a uniform token or equilibrium state, has recently gained attention in the deep learning literature. This phenomenon leads to reduced expressivity and potential training instabilities due to vanishing gradients. Empirical evidence suggests that architectural components like skip connections, LayerNorm, and MultiLayer Perceptrons (MLPs) play critical roles in mitigating rank collapse. While this issue is well-documented for transformers, alternative sequence models, such as State Space Models (SSMs), which have recently gained prominence, have not been thoroughly examined for similar vulnerabilities. This paper extends the theory of rank collapse from transformers to SSMs using a unifying framework that captures both architectures. We study how a parametrized version of the classic skip connection component, which we call emph{lambda-skip connections}, provides guarantees for rank collapse prevention. Through analytical results, we present a sufficient condition to guarantee prevention of rank collapse across all the aforementioned architectures. We also study the necessity of this condition via ablation studies and analytical examples. To our knowledge, this is the first study that provides a general guarantee to prevent rank collapse, and that investigates rank collapse in the context of SSMs, offering valuable understanding for both theoreticians and practitioners. Finally, we validate our findings with experiments demonstrating the crucial role of architectural components such as skip connections and gating mechanisms in preventing rank collapse.

Problem

• Prevent rank collapse in sequence models
• Extend rank collapse theory to SSMs
• Validate lambda-skip connections' effectiveness

Innovation

• Lambda-skip connections prevent rank collapse
• Unifying framework for transformers and SSMs
• Analytical guarantees for rank collapse prevention