Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07549
Lőrincz, András Cristian
Let either $GL(E)times SO(F)$ or $GL(E)times Sp(F)$ act naturally on the space of matrices $Eotimes F$. There are only finitely many orbits, and the orbit closures are orthogonal and symplectic generalizations of determinantal varieties, which can be described similarly using rank conditions. In this paper, we study the singularities of these varieties and describe their defining equations. We prove that in the symplectic case, the orbit closures are normal with good filtrations, and in characteristic $0$ have rational singularities. In the orthogonal case we show that most orbit closures will have the same properties, and determine precisely the exceptions to this.
{"title":"Singularities of orthogonal and symplectic determinantal varieties","authors":"Lőrincz, András Cristian","doi":"10.48550/arxiv.2311.07549","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07549","url":null,"abstract":"Let either $GL(E)times SO(F)$ or $GL(E)times Sp(F)$ act naturally on the space of matrices $Eotimes F$. There are only finitely many orbits, and the orbit closures are orthogonal and symplectic generalizations of determinantal varieties, which can be described similarly using rank conditions. In this paper, we study the singularities of these varieties and describe their defining equations. We prove that in the symplectic case, the orbit closures are normal with good filtrations, and in characteristic $0$ have rational singularities. In the orthogonal case we show that most orbit closures will have the same properties, and determine precisely the exceptions to this.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"106 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136353008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07564
Aggazzotti, Cristina, Andrews, Nicholas, Smith, Elizabeth Allyn
Authorship verification is the problem of determining if two distinct writing samples share the same author and is typically concerned with the attribution of written text. In this paper, we explore the attribution of transcribed speech, which poses novel challenges. The main challenge is that many stylistic features, such as punctuation and capitalization, are not available or reliable. Therefore, we expect a priori that transcribed speech is a more challenging domain for attribution. On the other hand, other stylistic features, such as speech disfluencies, may enable more successful attribution but, being specific to speech, require special purpose models. To better understand the challenges of this setting, we contribute the first systematic study of speaker attribution based solely on transcribed speech. Specifically, we propose a new benchmark for speaker attribution focused on conversational speech transcripts. To control for spurious associations of speakers with topic, we employ both conversation prompts and speakers' participating in the same conversation to construct challenging verification trials of varying difficulties. We establish the state of the art on this new benchmark by comparing a suite of neural and non-neural baselines, finding that although written text attribution models achieve surprisingly good performance in certain settings, they struggle in the hardest settings we consider.
{"title":"Can Authorship Attribution Models Distinguish Speakers in Speech\u0000 Transcripts?","authors":"Aggazzotti, Cristina, Andrews, Nicholas, Smith, Elizabeth Allyn","doi":"10.48550/arxiv.2311.07564","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07564","url":null,"abstract":"Authorship verification is the problem of determining if two distinct writing samples share the same author and is typically concerned with the attribution of written text. In this paper, we explore the attribution of transcribed speech, which poses novel challenges. The main challenge is that many stylistic features, such as punctuation and capitalization, are not available or reliable. Therefore, we expect a priori that transcribed speech is a more challenging domain for attribution. On the other hand, other stylistic features, such as speech disfluencies, may enable more successful attribution but, being specific to speech, require special purpose models. To better understand the challenges of this setting, we contribute the first systematic study of speaker attribution based solely on transcribed speech. Specifically, we propose a new benchmark for speaker attribution focused on conversational speech transcripts. To control for spurious associations of speakers with topic, we employ both conversation prompts and speakers' participating in the same conversation to construct challenging verification trials of varying difficulties. We establish the state of the art on this new benchmark by comparing a suite of neural and non-neural baselines, finding that although written text attribution models achieve surprisingly good performance in certain settings, they struggle in the hardest settings we consider.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"106 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136353016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}