Related papers: From Type Spaces to Probability Frames and Back, v…

Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint…

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…

Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…

Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other…

Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One…

While internet-scale data often comes in pairs (e.g., audio/image, image/text), we often want to perform inferences over modalities unseen together in the training data (e.g., audio/text). Empirically, this can often be addressed by…

Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…

This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

Language model representations often contain linear directions that correspond to high-level concepts. Here, we study the dynamics of these representations: how representations evolve along these dimensions within the context of (simulated)…

The study of linguistic typology is rooted in the implications we find between linguistic features, such as the fact that languages with object-verb word ordering tend to have post-positions. Uncovering such implications typically amounts…

A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…

Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human…

Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…

Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to…

The Theory of Proportions and Symbolic Allusions applied Interdisciplinary (TPASAI) is a framework that integrates mathematics, linguistics, psychology, and game theory to uncover hidden patterns and proportions in reality. Its central idea…