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Large language models often struggle to recognize their knowledge limits in closed-book question answering, leading to confident hallucinations. While decomposed prompting is typically used to improve accuracy, we investigate its impact on…
We provide a proof of the union-closed sets conjecture, by means of a suitable refinement of the breakthrough entropy-approach introduced by Gilmer. The novelty here is to consider a convex combination of $A$ and $A\cup B$, where $A,B$ are…
Statistically resolving the underlying haplotype pair for a genotype measurement is an important intermediate step in gene mapping studies, and has received much attention recently. Consequently, a variety of methods for this problem have…
The widespread success of deep learning models today is owed to the curation of extensive datasets significant in size and complexity. However, such models frequently pick up inherent biases in the data during the training process, leading…
Community detection techniques are widely used to infer hidden structures within interconnected systems. Despite demonstrating high accuracy on benchmarks, they reproduce the external classification for many real-world systems with a…
Forecast of football outcomes in terms of Home Win, Draw and Away Win relies largely on ex ante probability elicitation of these events and ex post verification of them via computation of probability scoring rules (Brier, Ranked…
Deception detection is gaining increasing interest due to ethical and security concerns. This paper explores the application of convolutional neural networks for the purpose of multimodal deception detection. We use a dataset built by…
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…
Bias issues of neural networks garner significant attention along with its promising advancement. Among various bias issues, mitigating two predominant biases is crucial in advancing fair and trustworthy AI: (1) ensuring neural networks…
The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph $G$ with ${n+1\choose 2}$ edges admits an edge decomposition $G=H_1\oplus\cdots \oplus H_n$ such that $H_i$ has $i$ edges and it is isomorphic to a subgraph of…
As Artificial Intelligence (AI) is increasingly used in areas that significantly impact human lives, concerns about fairness and transparency have grown, especially regarding their impact on protected groups. Recently, the intersection of…
The way the media presents events can significantly affect public perception, which in turn can alter people's beliefs and views. Media bias describes a one-sided or polarizing perspective on a topic. This article summarizes the research on…
Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…
In this survey paper we present recent results obtained by Khare, Wintenberger and the author that have led to a proof of Serre's conjecture, such as existence of compatible families, modular upper bounds for universal deformation rings and…
We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.
Causal effect estimation from observational data is one of the essential problems in causal inference. However, most estimation methods rely on the strong assumption that all confounders are observed, which is impractical and untestable in…
Multimodal learning has witnessed remarkable advancements in recent years, particularly with the integration of attention-based models, leading to significant performance gains across a variety of tasks. Parallel to this progress, the…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
In this paper we present a new proof of a proposition presented in the article: Complexes of tournaments, directionality filtrations and persistent homology. This paper is part of Joaqu\'in Casta\~neda's undergraduate thesis.