2 research outputs found
An Asymmetric Contrastive Loss for Handling Imbalanced Datasets
Contrastive learning is a representation learning method performed by
contrasting a sample to other similar samples so that they are brought closely
together, forming clusters in the feature space. The learning process is
typically conducted using a two-stage training architecture, and it utilizes
the contrastive loss (CL) for its feature learning. Contrastive learning has
been shown to be quite successful in handling imbalanced datasets, in which
some classes are overrepresented while some others are underrepresented.
However, previous studies have not specifically modified CL for imbalanced
datasets. In this work, we introduce an asymmetric version of CL, referred to
as ACL, in order to directly address the problem of class imbalance. In
addition, we propose the asymmetric focal contrastive loss (AFCL) as a further
generalization of both ACL and focal contrastive loss (FCL). Results on the
FMNIST and ISIC 2018 imbalanced datasets show that AFCL is capable of
outperforming CL and FCL in terms of both weighted and unweighted
classification accuracies. In the appendix, we provide a full axiomatic
treatment on entropy, along with complete proofs.Comment: 15 pages, 5 figure
Adaptive Monte Carlo Search for Conjecture Refutation in Graph Theory
Graph theory is an interdisciplinary field of study that has various
applications in mathematical modeling and computer science. Research in graph
theory depends on the creation of not only theorems but also conjectures.
Conjecture-refuting algorithms attempt to refute conjectures by searching for
counterexamples to those conjectures, often by maximizing certain score
functions on graphs. This study proposes a novel conjecture-refuting algorithm,
referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by
modifying the Monte Carlo tree search algorithm. Evaluated based on its success
in finding counterexamples to several graph theory conjectures, AMCS
outperforms existing conjecture-refuting algorithms. The algorithm is further
utilized to refute six open conjectures, two of which were chemical graph
theory conjectures formulated by Liu et al. in 2021 and four of which were
formulated by the AutoGraphiX computer system in 2006. Finally, four of the
open conjectures are strongly refuted by generalizing the counterexamples
obtained by AMCS to produce a family of counterexamples. It is expected that
the algorithm can help researchers test graph-theoretic conjectures more
effectively.Comment: 27 pages, 11 figures, 3 tables; Milo Roucairol pointed out that both
of our papers used an incorrect formula for the harmonic of a graph. The
revised Conjecture 4 was able to be refuted. This paper and the GitHub
repository have been updated accordingl