Related papers: The Linear Representation Hypothesis and the Geome…
Although natural language is the default medium for Large Language Models (LLMs), its limited expressive capacity creates a profound bottleneck for complex problem-solving. While recent advancements in AI have relied heavily on scaling,…
Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…
Static concreteness ratings are widely used in NLP, yet a word's concreteness can shift with context, especially in figurative language such as metaphor, where common concrete nouns can take abstract interpretations. While such shifts are…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
A two-part affine approximation has been found to be a good approximation for transformer computations over certain subject object relations. Adapting the Bigger Analogy Test Set, we show that the linear transformation Ws, where s is a…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
It has been hypothesized that neural networks with similar architectures trained on similar data learn shared representations relevant to the learning task. We build on this idea by extending the conceptual framework where representations…
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…
Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and…
The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
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…
Humans can effortlessly describe what they see, yet establishing a shared representational format between vision and language remains a significant challenge. Emerging evidence suggests that human brain representations in both vision and…
Understanding how linguistic structures are encoded in contextualized embedding could help explain their impressive performance across NLP@. Existing approaches for probing them usually call for training classifiers and use the accuracy,…
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying…