# What Cosine Similarity of Label Representations Can and Cannot Tell us

arXiv: https://arxiv.org/abs/2603.29488 · HTML: https://mlsanity.com/paper/2603.29488/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [Fishing for Magikarp: Automatically Detecting Under-trained Tokens in Large Language Models](https://mlsanity.com/paper/2405.05417/) (2024)
- [Shared Global and Local Geometry of Language Model Embeddings](https://mlsanity.com/paper/2503.21073/) (2025)
- [Low-Rank Softmax Can Have Unargmaxable Classes in Theory but Rarely in Practice](https://mlsanity.com/paper/2203.06462/) (2022)
- [Taming the Sigmoid Bottleneck: Provably Argmaxable Sparse Multi-Label Classification](https://mlsanity.com/paper/2310.10443/) (2023)
- [Prediction hubs are context-informed frequent tokens in LLMs](https://mlsanity.com/paper/2502.10201/) (2025)

## Built on by (most cited first, 1 of 1)

- [Cosine Similarity Is Not Evidence: Measuring the Noise Floor of Interpretability Transfer Under Quantization](https://mlsanity.com/paper/2609.30275/) (2026)

## Abstract (arXiv)

Cosine similarity is often used to measure the similarity of vector representations of neural network models. However, the cosine similarity of representations is not guaranteed to tell us anything about model probabilities. In this paper we show that for a softmax classifier, be it an image classifier or an autoregressive language model, the cosine similarity between label representations (called unembeddings in the paper) does not give any information on the probabilities assigned by the model. Specifically, we prove that given two unembeddings, it is possible to create another model which assigns the same probabilities for all inputs, but where the cosine similarity between the representations is now either 1 or -1. We also show that for a sigmoid classifier (where each input can be assigned multiple labels), all pairwise cosine similarities between the unembeddings define the set of possible label combinations. However, for softmax classifiers (where each input is assigned a ranking of the labels from most to least likely), we need all pairwise cosine similarities between all differences of unembeddings to know which rankings the model can predict. We conclude that it is misleading to interpret the cosine similarity between unembeddings without reference to the classifier that produced them.