Related papers: Elaboration on Two Points Raised in ``Classifier T…
These lecture notes intend to form a short pedagogical introduction to inflationary cosmology, highlighting selected areas of recent progress such as reheating and the theory of cosmological perturbations. Problems of principle for…
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
This work studies improving large language model (LLM) generations at inference time by mitigating fact-conflicting hallucinations. Particularly, we propose a self-endorsement framework that leverages the fine-grained fact-level comparisons…
This article contributes to the search for a notion of postural style, focusing on the issue of classifying subjects in terms of how they maintain posture. Longer term, the hope is to make it possible to determine on a case by case basis…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…
Information overload and the rapid pace of scientific advancement make it increasingly difficult to evaluate and allocate resources to new research proposals. Is there a structure to scientific discovery that could inform such decisions? We…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
Technology-Enhanced Formative Assessment (TEFA) is a pedagogy for teaching with classroom response technology. Teacher Learning of TEFA is a five-year research project studying teacher change, in the context of an intensive professional…
This dissertation collects together results on Patience Sorting and its generalizations. It incorporates the results of math.CO/0506358, math.CO/0507031, and math.CO/0512122, as well as previously unpublished results.
[Note to the reader: properties (C2) and (C2)* are under development, in order to form a generalization of (C3) and (C3)*]
This paper presents the methodology for the system requirements and architecture w.r.t. their decomposition and refinement. It also introduces ideas of refinement layers and of refinement-based verification.
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
We propose a novel class incremental learning approach by incorporating a feature augmentation technique motivated by adversarial attacks. We employ a classifier learned in the past to complement training examples rather than simply play a…
In this work we develop some categorical aspects of the double structure of a module.
These notes are the second part of the tensor calculus documents which started with the previous set of introductory. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
Large Reasoning Models (LRMs) have become a central focus in today's large language model (LLM) research, where models are designed to output a step-by-step thinking process before arriving at a final answer to handle complex reasoning…
We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.