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The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error…
State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge…
We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and first…
Logic reasoning is a significant ability of human intelligence and also an important task in artificial intelligence. The existing logic reasoning methods, quite often, need to design some reasoning patterns beforehand. This has led to an…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned…
As a pivotal component to attaining generalizable solutions in human intelligence, reasoning provides great potential for reinforcement learning (RL) agents' generalization towards varied goals by summarizing part-to-whole arguments and…
Causal reasoning is a cornerstone of human intelligence and a critical capability for artificial systems aiming to achieve advanced understanding and decision-making. This thesis delves into various dimensions of causal reasoning and…
We study the problem of disseminating a piece of information through all the nodes of a network, given that it is known originally only to a single node. In the absence of any structural knowledge on the network other than the nodes'…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
Temporal commonsense reasoning refers to the ability to understand the typical temporal context of phrases, actions, and events, and use it to reason over problems requiring such knowledge. This trait is essential in temporal natural…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and…
Interestingly, LLMs yet struggle with some basic tasks that humans find trivial to handle, e.g., counting the number of character r's in the word "strawberry". There are several popular conjectures (e.g., tokenization, architecture and…
The paper analizes a set of issues related to analogy and analogical reasoning, namely: 1) The problem of analogy and its duplicity; 2) The role of analogy in demonstrative reasoning; 3) The role of analogy in non-demonstrative reasoning;…
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
The seasonal production of fruit and seeds resembles opening a feeding station, such as a restaurant agents/ customers will arrive at a certain rate and pick fruit (get served) at a certain rate following some appropriate processes.…
Logic is one of the most male-dominated areas within the already hugely male-dominated subject of philosophy. Popular hypotheses for this disparity include a preponderance of confident, mathematically-minded male students in the classroom,…