Paper Overview
Field: NLP Authors: Antonio Lopardo, Avyukth Harish, Catherine Arnett Published: 2025-03-30 arXiv: 2503.23753
Summary
Weight tying, i.e. sharing parameters between input and output embedding matrices, is common practice in language model design, yet its impact on the learned embedding space remains poorly understood. In this paper, the authors show that tied embedding matrices align more closely with output (unembedding) matrices than with input embeddings of comparable untied models, indicating that the shared matrix is shaped primarily for output prediction rather than input representation.
This unembedding bias arises because output gradients dominate early in training. Using tuned lens analysis, the authors show this negatively affects early-layer computations, which contribute less effectively to the residual stream. Scaling input gradients during training reduces this bias, providing causal evidence for the role of gradient imbalance.
This is mechanistic evidence that weight tying optimizes the embedding matrix for output prediction, harming its role in input representation. These results help explain why weight tying may degrade performance at scale and have implications for training smaller LLMs, where embedding matrices account for a large fraction of total parameters.
Key Findings
- Tied embedding matrices align more closely with unembedding matrices than with input embeddings of comparable untied models.
- The bias stems from output gradients dominating early in training.
- Tuned lens analysis shows the bias weakens early-layer contributions to the residual stream.
- Scaling input gradients during training causally reduces the bias.