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Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
What does it mean for a machine to recognize beauty? While beauty remains a culturally and experientially compelling but philosophically elusive concept, deep learning systems increasingly appear capable of modeling aesthetic judgment. In…
Lock-in feedback circuits are routinely used in physics laboratories all around the world to extract small signals out of a noisy environment. In a recent paper (M. Kaptein, R. van Emden, and D. Iannuzzi, paper under review), we have shown…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…
We investigate a recently proposed model for cortical computation which performs relational inference. It consists of several interconnected, structurally equivalent populations of leaky integrate-and-fire (LIF) neurons, which are trained…
The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study a coupled quintessence scenario in which the scalar field evolves…
This paper presents an in-depth statistical analysis of an experiment designed to measure the extent to which players in a simple game behave according to a popular behavioral economic model. The p-beauty contest is a multi-player number…
The growth in prominence of large language models (LLMs) in everyday life can be largely attributed to their generative abilities, yet some of this is also owed to the risks and costs associated with their use. On one front is their…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Trust is the foundation of every area of life. Without it, it is difficult to build lasting relationships. Unfortunately, in recent years, trust has been severely damaged by the spread of fake news and disinformation, which has become a…
Visual illusions may be explained by the likelihood of patches in real-world images, as argued by input-driven paradigms in Neuro-Science. However, neither the data nor the tools existed in the past to extensively support these…
Hallucinations are one of the major issues affecting LLMs, hindering their wide adoption in production systems. While current research solutions for detecting hallucinations are mainly based on heuristics, in this paper we introduce a…
Even though the brain operates in pure darkness, within the skull, it can infer the most likely causes of its sensory input. An approach to modelling this inference is to assume that the brain has a generative model of the world, which it…
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can…
In the era of large language models (LLMs), hallucination (i.e., the tendency to generate factually incorrect content) poses great challenge to trustworthy and reliable deployment of LLMs in real-world applications. To tackle the LLM…
The hallucination problem of Large Language Models (LLMs) significantly limits their reliability and trustworthiness. Humans have a self-awareness process that allows us to recognize what we don't know when faced with queries. Inspired by…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
Despite great performance on many tasks, language models (LMs) still struggle with reasoning, sometimes providing responses that cannot possibly be true because they stem from logical incoherence. We call such responses \textit{strong…