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We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of…
Although the cosmic concordance cosmology is quite successful in fitting data, fine tuning and coincidence problems apparently weaken it. We review several possibilities to ease its problems, by considering various kinds of dynamical Dark…
The hard problem in consciousness is the problem of understanding how physical processes in the brain could give rise to subjective conscious experience. In this paper, I suggest that in order to understand the relationship between…
The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.
Autonomous systems are soon to be ubiquitous, spanning manufacturing, agriculture, healthcare, entertainment, and other industries. Most of these systems are developed with modular sub-components for decision-making, planning, and control…
Reasoning has become a central paradigm for large language models (LLMs), consistently boosting accuracy across diverse benchmarks. Yet its suitability for precision-sensitive tasks remains unclear. We present the first systematic study of…
This paper presents an efficient algorithm to solve the sleeping bandit with multiple plays problem in the context of an online recommendation system. The problem involves bounded, adversarial loss and unknown i.i.d. distributions for arm…
Despite substantial advances, large language models (LLMs) continue to exhibit hallucinations, generating plausible yet incorrect responses. In this paper, we highlight a critical yet previously underexplored class of hallucinations driven…
Although large language models (LLMs) have demonstrated remarkable proficiency in modeling text and generating human-like text, they may exhibit biases acquired from training data in doing so. Specifically, LLMs may be susceptible to a…
We discuss coin-weighing problems with a new type of coin: a chameleon. A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently. We consider a mix of $N$ coins that include…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
There is an increasing interest in the role of macroscopic environments to our understanding of the basics of quantum theory. The knowledge of the implications of the quantum theory to other theories, especially to the statistical mechanics…
To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms).…
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…
Traditional language models face a challenge from hallucinations. Their very presence casts a large, dangerous shadow over the promising realm of natural language processing. It becomes crucial to understand the various kinds of…
Randomness is an intrinsic feature of quantum theory. The outcome of any quantum measurement will be random, sampled from a probability distribution that is defined by the measured quantum state. The task of sampling from a prescribed…
Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…
In this article we investigate the effects of shifting position decoherence, arisen from the tunneling effect in the experimental realization of the quantum walk, on the one-dimensional discreet time quantum walk. We show that in the regime…
Color constancy is the problem of inferring the color of the light that illuminated a scene, usually so that the illumination color can be removed. Because this problem is underconstrained, it is often solved by modeling the statistical…
We examine cyclic phantom models for the universe, in which the universe is dominated sequentially by radiation, matter, and a phantom dark energy field, followed by a standard inflationary phase. Since this cycle repeats endlessly, the…