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The Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) is a generative, few-shot fluid intelligence benchmark. Although humans effortlessly solve ARC-AGI, it remains extremely difficult for even the most advanced…
Jackendoff (2002) posed four challenges that linguistic combinatoriality and rules of language present to theories of brain function. The essence of these problems is the question of how to neurally instantiate the rapid construction and…
Support vector machines (SVMs) have been successful in solving many computer vision tasks including image and video category recognition especially for small and mid-scale training problems. The principle of these non-parametric models is…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
We present a novel application of category theory for deep learning. We show how category theory can be used to understand and work with the linear layer functions of group equivariant neural networks whose layers are some tensor power…
This paper develops an innovative method that enables neural networks to generate and utilize knowledge graphs, which describe their concept-level knowledge and optimize network parameters through alignment with human-provided knowledge.…
Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is…
This paper introduces the Token Space framework, a novel mathematical construct designed to enhance the interpretability and effectiveness of deep learning models through the application of category theory. By establishing a categorical…
Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…
Using Frequency-domain Holographic Reduced Representations (FHRRs), we extend a Vector-Symbolic Architecture (VSA) encoding of Lisp 1.5 with primitives for arithmetic operations using Residue Hyperdimensional Computing (RHC). Encoding a…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…
A key challenge in artificial intelligence and neuroscience is understanding how neural systems learn representations that capture the underlying dynamics of the world. Most world models represent the transition function with unstructured…
It is very attractive to formulate vision in terms of pattern theory \cite{Mumford2010pattern}, where patterns are defined hierarchically by compositions of elementary building blocks. But applying pattern theory to real world images is…
Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data…
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…
We marry two powerful ideas: deep representation learning for visual recognition and language understanding, and symbolic program execution for reasoning. Our neural-symbolic visual question answering (NS-VQA) system first recovers a…
Vector-space models, from word embeddings to neural network parsers, have many advantages for NLP. But how to generalise from fixed-length word vectors to a vector space for arbitrary linguistic structures is still unclear. In this paper we…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Dynamic arrays, also referred to as vectors, are fundamental data structures used in many programs. Modeling their semantics efficiently is crucial when reasoning about such programs. The theory of arrays is widely supported but is not…