Related papers: Token embeddings violate the manifold hypothesis
Large language models (LLMs) have recently shown promise in recommendation by providing rich semantic knowledge. While most existing approaches rely on external textual corpora to align LLMs with recommender systems, we revisit a more…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
This research aims to unravel how large language models (LLMs) iteratively refine token predictions through internal processing. We utilized a logit lens technique to analyze the model's token predictions derived from intermediate…
Language Confusion is a phenomenon where Large Language Models (LLMs) generate text that is neither in the desired language, nor in a contextually appropriate language. This phenomenon presents a critical challenge in text generation by…
Current research in adversarial robustness of LLMs focuses on discrete input manipulations in the natural language space, which can be directly transferred to closed-source models. However, this approach neglects the steady progression of…
We study high-dimensional analogues of spaces of long knots. These are spaces of compactly-supported embeddings (modulo immersions) of $\mathbb{R}^m$ into $\mathbb{R}^n$. We view the space of embeddings as the value of a certain functor at…
Recent advances in representation learning have emphasized the role of embedding geometry in capturing semantic structure. Traditional sentence embeddings typically reside in unconstrained Euclidean spaces, which may limit their ability to…
We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry. Our framework unifies the Linear Representation Hypothesis with…
Large language models (LLMs) are known to be vulnerable to jailbreak attacks, which typically rely on carefully designed prompts containing explicit semantic structure. These attacks generally operate by fixing an adversarial instruction…
Large language models fail at counting repeated tokens despite strong performance on broader reasoning benchmarks. These failures are commonly attributed to limitations in internal count tracking. We show this attribution is wrong. Linear…
The remarkable success of large language models (LLMs) has motivated researchers to adapt them as universal predictors for various graph tasks. As a widely recognized paradigm, Graph-Tokenizing LLMs (GTokenLLMs) compress complex graph data…
Standard evaluations of Large language models (LLMs) focus on task performance, offering limited insight into whether correct behavior reflects appropriate underlying mechanisms and risking confirmation bias. We introduce a simple,…
Language models lack the notion of interchangeable tokens: symbols that are semantically equivalent yet distinct, such as bound variables in formal logic. This limitation prevents generalization to larger vocabularies and hinders the…
This paper provides a theoretical framework for interpreting acoustic neighbor embeddings, which are representations of the phonetic content of variable-width audio or text in a fixed-dimensional embedding space. A probabilistic…
Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable…
Foundation models based on large language models (LLMs) have shown great success in handling various tasks and modalities. However, adapting these models for general-purpose audio-language tasks is challenging due to differences in acoustic…
Large Language Models (LLMs) exhibit impressive capabilities yet suffer from sensitivity to slight input context variations, hampering reliability. Conventional metrics like accuracy and perplexity fail to assess local prediction…
We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r\geq 1$. Under some assumptions on the normal bundle and a…
Despite the widespread use of Transformer-based text embedding models in NLP tasks, surprising 'sticky tokens' can undermine the reliability of embeddings. These tokens, when repeatedly inserted into sentences, pull sentence similarity…
One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional manifold embedded in a high-dimensional observation space by a given set of data points from the manifold. We derive a local lower…