Related papers: Automatic Generation of Theorems and Proofs on Enu…
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in…
Auto-regressive models are widely used in sequence generation problems. The output sequence is typically generated in a predetermined order, one discrete unit (pixel or word or character) at a time. The models are trained by teacher-forcing…
Beyond maximum likelihood estimation (MLE), the standard objective of a language model (LM) that optimizes good examples probabilities, many studies have explored ways that also penalize bad examples for enhancing the quality of output…
Dyck paths are one of the most important objects in enumerative combinatorics, and there are many papers devoted to counting selected families of Dyck paths. Here we present two approaches for the automatic counting of many such families,…
We use the cluster method to enumerate permutations avoiding consecutive patterns. We reprove and generalize in a unified way several known results and obtain new ones, including some patterns of length 4 and 5, as well as some infinite…
Automatic prompt engineering aims to enhance the generation quality of large language models (LLMs). Recent works utilize feedbacks generated from erroneous cases to guide the prompt optimization. During inference, they may further retrieve…
Adequate sampling space coverage is the keystone to effectively train trustworthy Machine Learning models. Unfortunately, real data do carry several inherent risks due to the many potential biases they exhibit when gathered without a proper…
Since data is the fuel that drives machine learning models, and access to labeled data is generally expensive, semi-supervised methods are constantly popular. They enable the acquisition of large datasets without the need for too many…
Building a good predictive model requires an array of activities such as data imputation, feature transformations, estimator selection, hyper-parameter search and ensemble construction. Given the large, complex and heterogenous space of…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work,…
We determine all 242 Wilf classes of triples of 4-letter patterns by showing that there are 32 non-singleton Wilf classes. There are 317 symmetry classes of triples of 4-letter patterns and after computer calculation of initial terms, the…
Induction lies at the heart of mathematics and computer science. However, automated theorem proving of inductive problems is still limited in its power. In this abstract, we first summarize our progress in automating inductive theorem…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
We study generating abstractive summaries that are faithful and factually consistent with the given articles. A novel contrastive learning formulation is presented, which leverages both reference summaries, as positive training data, and…
Analogies help learners understand unfamiliar concepts by relating them to known concepts. Despite recent advances, large language models (LLMs) continue to struggle to generate analogies of comparable quality to those produced by humans.…
Learning distributed sentence representations remains an interesting problem in the field of Natural Language Processing (NLP). We want to learn a model that approximates the conditional latent space over the representations of a logical…
Active learning (AL) seeks to reduce annotation costs by selecting the most informative samples for labeling, making it particularly valuable in resource-constrained settings. However, traditional evaluation methods, which focus solely on…
We examine whether data generated by explanation techniques, which promote a process of self-reflection, can improve classifier performance. Our work is based on the idea that humans have the ability to make quick, intuitive decisions as…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…