Related papers: The Linear Representation Hypothesis and the Geome…
We study linear and hermitian representations of finite $C_2$-graded groups. We prove that the category of linear representations is equivalent to a category of antilinear representations as an $\infty$-category. We also prove that the…
Interpretability is a key challenge in fostering trust for Large Language Models (LLMs), which stems from the complexity of extracting reasoning from model's parameters. We present the Frame Representation Hypothesis, a theoretically robust…
Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…
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…
Bolukbasi et al. (2016) presents one of the first gender bias mitigation techniques for word representations. Their method takes pre-trained word representations as input and attempts to isolate a linear subspace that captures most of the…
Black-box probing models can reliably extract linguistic features like tense, number, and syntactic role from pretrained word representations. However, the manner in which these features are encoded in representations remains poorly…
Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
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…
We investigate the Platonic Representation Hypothesis (PRH) through a tripartite statistical framework of representations: signal, bias, and noise. {1) Signal:} We propose that Platonic alignment arises from the universal relationship…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
Large scale neural models show impressive performance across a wide array of linguistic tasks. Despite this they remain, largely, black-boxes - inducing vector-representations of their input that prove difficult to interpret. This limits…
Transformer language models (LMs) have been shown to represent concepts as directions in the latent space of hidden activations. However, for any human-interpretable concept, how can we find its direction in the latent space? We present a…
We study visual representation learning from a structural and topological perspective. We begin from a single hypothesis: that visual understanding presupposes a semantic language for vision, in which many perceptual observations correspond…
Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the…
Why is it that we can recognize object identity and 3D shape from line drawings, even though they do not exist in the natural world? This paper hypothesizes that the human visual system perceives line drawings as if they were approximately…
Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose…
This paper develops a geometric framework for modeling belief, motivation, and influence across cognitively heterogeneous agents. Each agent is represented by a personalized value space, a vector space encoding the internal dimensions…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results of Linear Geomery that depend on the flat hulls: flats, exchange, rank, regularity,…