In this paper, we investigate the output token probability information in the output embedding of language models. We find an approximate common log-linear encoding of output token probabilities within the output embedding vectors and empirically demonstrate that it is accurate and sparse. As a causality examination, we steer the encoding in output embedding to modify the output probability distribution accurately. Moreover, the sparsity we find in output probability encoding suggests that a large number of dimensions in the output embedding do not contribute to causal language modeling. Therefore, we attempt to delete the output-unrelated dimensions and find more than 30% of the dimensions can be deleted without significant movement in output distribution and sequence generation. Additionally, in the pre-training dynamics of language models, we find that the output embeddings capture the corpus token frequency information in early steps, even before an obvious convergence of parameters starts.

In-Context Learning (ICL) typically utilizes classification criteria from output probabilities of manually selected label tokens. However, we argue that such token-based classification criteria lead to suboptimal decision boundaries, despite delicate calibrations through translation and constrained rotation applied. To address this problem, we propose Hidden Calibration, which renounces token probabilities and uses the nearest centroid classifier on the LM’s last hidden states. In detail, we assign the label of the nearest centroid previously estimated from a calibration set to the test sample as the predicted label. Our experiments on 6 models and 10 classification datasets indicate that Hidden Calibration consistently outperforms current token-based baselines by about 20%~50%, achieving a strong state-of-the-art in ICL. Our further analysis demonstrates that Hidden Calibration finds better classification criteria with less inter-class overlap, and LMs provide linearly separable intra-class clusters with the help of demonstrations, which supports Hidden Calibration and gives new insights into the principle of ICL. Our official code implementation can be found at https://github.com/hc495/Hidden_Calibration.