Related papers: Murmurations: a case study in AI-assisted mathemat…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
This paper is focused on the coherent effects that appear in tracer statistics in two-dimensional incompressible turbulence in the presence of an average velocity. We show that this determines strong modifications of the transport and…
This paper proposes an Artificial Intelligence (AI) Grounded Theory for management studies. We argue that this novel and rigorous approach that embeds topic modelling will lead to the latent knowledge to be found. We illustrate this…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
Big data and machine learning are driving comprehensive economic and social transformations and are rapidly re-shaping the toolbox and the methodologies of applied scientists. Machine learning tools are designed to learn functions from data…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…
Enhancing the ability of Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) to interpret sheet music is a crucial step toward building AI musicians. However, current research lacks both evaluation benchmarks and…
Stuttering is a speech disorder during which the flow of speech is interrupted by involuntary pauses and repetition of sounds. Stuttering identification is an interesting interdisciplinary domain research problem which involves pathology,…
How can we make sense of large-scale recordings of neural activity across learning? Theories of neural network learning with their origins in statistical physics offer a potential answer: for a given task, there are often a small set of…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We present a new theoretical perspective of data noising in recurrent neural network language models (Xie et al., 2017). We show that each variant of data noising is an instance of Bayesian recurrent neural networks with a particular…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
Reputation is a central element of social communications, be it with human or artificial intelligence (AI), and as such can be the primary target of malicious communication strategies. There is already a vast amount of literature on trust…
Models of bags of words typically assume topic mixing so that the words in a single bag come from a limited number of topics. We show here that many sets of bag of words exhibit a very different pattern of variation than the patterns that…
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…
Natural and artificial audition can in principle acquire different solutions to a given problem. The constraints of the task, however, can nudge the cognitive science and engineering of audition to qualitatively converge, suggesting that a…
While the utility of well-chosen abstractions for understanding and predicting the behaviour of complex systems is well appreciated, precisely what an abstraction $\textit{is}$ has so far has largely eluded mathematical formalization. In…