Related papers: Semantic Identity Compression: Zero-Error Laws, Ra…
Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add…
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…
Modern self-supervised predictive architectures excel at capturing complex statistical correlations from high-dimensional data but lack mechanisms to internalize verifiable human logic, leaving them susceptible to spurious correlations and…
Learning is a distinctive feature of intelligent behaviour. High-throughput experimental data and Big Data promise to open new windows on complex systems such as cells, the brain or our societies. Yet, the puzzling success of Artificial…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
How do artificial neural networks bind concepts to form complex semantic structures? Here, we propose a simple neural code, whereby the existence and the type of relations between entities are represented by the distance and the direction…
Complementary Learning Systems theory holds that intelligent agents need two learning systems. Semantic memory is encoded in the neocortex with dense, overlapping representations and acquires structured knowledge. Episodic memory is encoded…
We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in…
Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture…
One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
Representations pervade our daily experience, from letters representing sounds to bit strings encoding digital files. While such representations require externally defined decoders to convey meaning, conscious experience appears…
Understanding a neural code requires knowledge both of the elementary symbols that transmit information and of the algorithm for translating these symbols into sensory signals or motor actions. We show that these questions can be separated:…
To understand cognitive reasoning in the brain, it has been proposed that symbols and compositions of symbols are represented by activity patterns (vectors) in a large population of neurons. Formal models implementing this idea [Plate…
Lossy image coding standards such as JPEG and MPEG have successfully achieved high compression rates for human consumption of multimedia data. However, with the increasing prevalence of IoT devices, drones, and self-driving cars, machines…
With the evolution of storage and communication protocols, ultra-low bitrate image compression has become a highly demanding topic. However, existing compression algorithms must sacrifice either consistency with the ground truth or…
Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…