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.

Recent advances in Instruction-fine-tuned Vision and Language Models (IVLMs), such as GPT-4V and InstructBLIP, have prompted some studies have started an in-depth analysis of the reasoning capabilities of IVLMs. However, Inductive Visual Reasoning, a vital skill for text-image understanding, remains underexplored due to the absence of benchmarks. In this paper, we introduce Find-the-Common (FTC): a new vision and language task for Inductive Visual Reasoning. In this task, models are required to identify an answer that explains the common attributes across visual scenes. We create a new dataset for the FTC and assess the performance of several contemporary approaches including Image-Based Reasoning, Text-Based Reasoning, and Image-Text-Based Reasoning with various models. Extensive experiments show that even state-of-the-art models like GPT-4V can only archive with 48% accuracy on the FTC, for which, the FTC is a new challenge for the visual reasoning research community. Our dataset has been released and is available online: https://github.com/SSSSSeki/Find-the-common.