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We investigate the internal structure of language model computations using causal analysis and demonstrate two motifs: (1) a form of adaptive computation where ablations of one attention layer of a language model cause another layer to…
The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}$-Lie algebra. A $\operatorname{D}$-Lie algebra $\tilde{L}$…
Let $A$ be a unital $C^*$-algebra and $\alpha$ be an injective, unital endomorphism of $A$. A covariant representation of $(A,\alpha)$ is a pair $(\pi,T)$ consisting of a $C^*$-representation $\pi$ of $A$ on a Hilbert space $H$ and a…
Self-supervised learning has become a popular approach in recent years for its ability to learn meaningful representations without the need for data annotation. This paper proposes a novel image augmentation technique, overlaying images,…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…
Multilingual Large Language Models considerably changed how technologies influence language. While previous technologies could mediate or assist humans, there is now a tendency to offload the task of writing itself to these technologies,…
We prove an algebraic extension theorem for the computably enumerable sets, $\mathcal{E}$. Using this extension theorem and other work we then show if $A$ and $\hat{A}$ are automorphic via $\Psi$ then they are automorphic via $\Lambda$…
Public image diffusion models are now powerful enough that an attacker without the resources to train a tabular-specific generator may repurpose one off the shelf. This study tests that possibility directly. An unmodified Stable Diffusion…
The diversity of human expression is the raw material of discovery. Generative artificial intelligence threatens this resource even as it promises to accelerate innovation, a paradox now visible across science, culture, and professional…
Self-supervision provides effective representations for downstream tasks without requiring labels. However, existing approaches lag behind fully supervised training and are often not thought beneficial beyond obviating or reducing the need…
Deep learning models tend not to be out-of-distribution robust primarily due to their reliance on spurious features to solve the task. Counterfactual data augmentations provide a general way of (approximately) achieving representations that…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…
Inference in large-scale AI models is typically performed on dense parameter matrices, leading to inference cost and system complexity that scale unsustainably with model size. This limitation does not arise from insufficient model…
We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are…
Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal…
Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…
Analogy is a central faculty of human intelligence, enabling abstract patterns discovered in one domain to be applied to another. Despite its central role in cognition, the mechanisms by which Transformers acquire and implement analogical…
Additive deformations of bialgebras in the sense of Wirth are deformations of the multiplication map of the bialgebra fulfilling a compatibility condition with the coalgebra structure and a continuity condition. Two problems concerning…