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The linear representation hypothesis states that language models (LMs) encode concepts as directions in their latent space, forming organized, multidimensional manifolds. Prior work has largely focused on identifying specific geometries for…

Artificial Intelligence · Computer Science 2026-04-08 Federico Tiblias , Irina Bigoulaeva , Jingcheng Niu , Simone Balloccu , Iryna Gurevych

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind…

Machine Learning · Computer Science 2014-04-24 Yoshua Bengio , Aaron Courville , Pascal Vincent

Large language models (LLMs) form implicit beliefs (posteriors over latent variables) from prompts, but we lack a mechanistic account of how these beliefs are encoded in representation space, how they update with new evidence, and how…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Machine Learning · Computer Science 2018-01-08 Elif Vural , Christine Guillemot

Large Language Models (LLMs) have started to demonstrate the ability to persuade humans, yet our understanding of how this dynamic transpires is limited. Recent work has used linear probes, lightweight tools for analyzing model…

Computation and Language · Computer Science 2025-08-08 Brandon Jaipersaud , David Krueger , Ekdeep Singh Lubana

Self-supervised visual representation learning has recently attracted significant research interest. While a common way to evaluate self-supervised representations is through transfer to various downstream tasks, we instead investigate the…

Computer Vision and Pattern Recognition · Computer Science 2022-09-08 Iro Laina , Yuki M. Asano , Andrea Vedaldi

There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation…

Machine Learning · Computer Science 2025-05-27 Alexander Modell , Patrick Rubin-Delanchy , Nick Whiteley

This work explores whether language models encode meaningfully grounded representations of sounds of objects. We learn a linear probe that retrieves the correct text representation of an object given a snippet of audio related to that…

Computation and Language · Computer Science 2024-08-19 Jerry Ngo , Yoon Kim

Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…

Computation and Language · Computer Science 2025-03-25 Sharan Maiya , Yinhong Liu , Ramit Debnath , Anna Korhonen

It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related…

Machine Learning · Computer Science 2012-07-19 Yoshua Bengio , Grégoire Mesnil , Yann Dauphin , Salah Rifai

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

Computation and Language · Computer Science 2026-05-18 Kiho Park , Yo Joong Choe , Victor Veitch

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

Computer Vision and Pattern Recognition · Computer Science 2013-05-20 Elif Vural , Pascal Frossard

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods either focus on input-oriented feature extraction, such as supervised…

Computation and Language · Computer Science 2025-12-03 Marco Bronzini , Carlo Nicolini , Bruno Lepri , Jacopo Staiano , Andrea Passerini

Probing is widely used to study which features can be decoded from language model representations. However, the common decoding probe approach has two limitations that we aim to solve with our new encoding probe approach: contributions of…

Computation and Language · Computer Science 2026-05-04 Gaofei Shen , Martijn Bentum , Tom Lentz , Afra Alishahi , Grzegorz Chrupała

Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…

Machine Learning · Computer Science 2025-11-25 David D. Baek , Yuxiao Li , Max Tegmark

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn…

Machine Learning · Computer Science 2020-01-06 Jean-Yves Franceschi , Aymeric Dieuleveut , Martin Jaggi

Linguistic representation learning in deep neural language models (LMs) has been studied for decades, for both practical and theoretical reasons. However, finding representations in LMs remains an unsolved problem, in part due to a dilemma…

Computation and Language · Computer Science 2026-03-26 Joshua Rozner , Cory Shain

There is general consensus that learning representations is useful for a variety of reasons, e.g. efficient use of labeled data (semi-supervised learning), transfer learning and understanding hidden structure of data. Popular techniques for…

Machine Learning · Computer Science 2017-06-15 Sanjeev Arora , Andrej Risteski

A common approach in neuroscience is to study neural representations as a means to understand a system -- increasingly, by relating the neural representations to the internal representations learned by computational models. However, a…

Neurons and Cognition · Quantitative Biology 2025-08-14 Andrew Kyle Lampinen , Stephanie C. Y. Chan , Yuxuan Li , Katherine Hermann

It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…

Machine Learning · Computer Science 2026-04-01 Allen Liu
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