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We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the…

Computation and Language · Computer Science 2025-01-22 Karthik Viswanathan , Yuri Gardinazzi , Giada Panerai , Alberto Cazzaniga , Matteo Biagetti

Researchers have recently suggested that models share common representations. In our work, we find numerous geometric similarities across the token embeddings of large language models. First, we find ``global'' similarities: token…

Computation and Language · Computer Science 2025-07-16 Andrew Lee , Melanie Weber , Fernanda Viégas , Martin Wattenberg

We demonstrate the utility of a new methodological tool, neural-network word embedding models, for large-scale text analysis, revealing how these models produce richer insights into cultural associations and categories than possible with…

Computation and Language · Computer Science 2019-11-13 Austin C. Kozlowski , Matt Taddy , James A. Evans

Large language models encode the correlational structure present in natural language by fitting segments of utterances (tokens) into a high dimensional ambient latent space upon which the models then operate. We assert that in order to…

Differential Geometry · Mathematics 2024-10-14 Michael Robinson , Sourya Dey , Shauna Sweet

The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…

Computation and Language · Computer Science 2025-03-31 Zhuo-Yang Song , Zeyu Li , Qing-Hong Cao , Ming-xing Luo , Hua Xing Zhu

Transformer models learn to encode and decode an input text, and produce contextual token embeddings as a side-effect. The mapping from language into the embedding space maps words expressing similar concepts onto points that are close in…

Computation and Language · Computer Science 2025-09-03 Vivi Nastase , Paola Merlo

We present models for embedding words in the context of surrounding words. Such models, which we refer to as token embeddings, represent the characteristics of a word that are specific to a given context, such as word sense, syntactic…

Computation and Language · Computer Science 2017-06-13 Lifu Tu , Kevin Gimpel , Karen Livescu

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an…

Machine Learning · Computer Science 2026-05-12 Albert F. Modenbach

Understanding cell identity and function through single-cell level sequencing data remains a key challenge in computational biology. We present a novel framework that leverages gene-specific textual annotations from the NCBI Gene database…

Genomics · Quantitative Biology 2025-05-14 Douglas Jiang , Zilin Dai , Luxuan Zhang , Qiyi Yu , Haoqi Sun , Feng Tian

Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…

Computation and Language · Computer Science 2025-04-25 Christopher Nightingale , Dominic Lavington , Jonathan Thistlethwaite , Sebastian Penhaligon , Thomas Belinski , David Boldo

The development of single-cell and spatial transcriptomics has revolutionized our capacity to investigate cellular properties, functions, and interactions in both cellular and spatial contexts. However, the analysis of single-cell and…

Genomics · Quantitative Biology 2024-12-09 Shuang Ge , Shuqing Sun , Huan Xu , Qiang Cheng , Zhixiang Ren

Multimodal large language models (MLLMs) project visual tokens into the embedding space of language models, yet the internal structuring and processing of visual semantics remain poorly understood. In this work, we introduce a two-fold…

Computer Vision and Pattern Recognition · Computer Science 2026-03-03 Yingqi Fan , Junlong Tong , Anhao Zhao , Xiaoyu Shen

The ability of machine learning models to store input information in hidden layer vector embeddings, analogous to the concept of `memory', is widely employed but not well characterized. We find that language model embeddings typically…

Computation and Language · Computer Science 2026-05-20 Benjamin L. Badger

Recent advances in applying deep learning in genomics include DNA-language and single-cell foundation models. However, these models take only one data type as input. We introduce dynamic token adaptation and demonstrate how it combines…

Powerful sentence encoders trained for multiple languages are on the rise. These systems are capable of embedding a wide range of linguistic properties into vector representations. While explicit probing tasks can be used to verify the…

Computation and Language · Computer Science 2021-09-22 Maarten De Raedt , Fréderic Godin , Pieter Buteneers , Chris Develder , Thomas Demeester

How related are the representations learned by neural language models, translation models, and language tagging tasks? We answer this question by adapting an encoder-decoder transfer learning method from computer vision to investigate the…

Computation and Language · Computer Science 2025-12-11 Richard Antonello , Javier Turek , Vy Vo , Alexander Huth

Single-cell sequencing has a significant role to explore biological processes such as embryonic development, cancer evolution, and cell differentiation. These biological properties can be presented by a two-dimensional scatter plot.…

Genomics · Quantitative Biology 2021-10-19 Ziyi Liu , Minghui Liao , Fulin luo , Bo Du

A common approach for sequence tagging tasks based on contextual word representations is to train a machine learning classifier directly on these embedding vectors. This approach has two shortcomings. First, such methods consider single…

Large language models use high-dimensional latent spaces to encode and process textual information. Much work has investigated how the conceptual content of words translates into geometrical relationships between their vector…

Computation and Language · Computer Science 2025-05-26 Raphaël Sarfati , Haley Moller , Toni J. B. Liu , Nicolas Boullé , Christopher Earls

Large pre-trained language models have recently been expanded and applied to programming language tasks with great success, often through further pre-training of a strictly-natural language model--where training sequences typically contain…

Computation and Language · Computer Science 2024-02-13 Fenia Christopoulou , Guchun Zhang , Gerasimos Lampouras
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