Weight Tying Biases Token Embeddings Towards the Output Space

TL;DR

This paper investigates how weight tying in language models biases the shared embedding matrix towards output prediction, affecting input representation and early-layer computations, with implications for model performance.

Contribution

It provides mechanistic evidence that weight tying primarily optimizes embeddings for output prediction, explaining potential performance drawbacks.

Findings

Tied embeddings align more with output matrices than input embeddings.

Output gradients dominate early training, shaping the shared matrix.

Scaling input gradients reduces the bias, confirming gradient imbalance's role.

Abstract

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, we 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, we 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, compromising its role in input representation. These results help explain why weight tying can harm performance at scale and have implications for training smaller LLMs, where the embedding matrix contributes substantially to total parameter count.