Notices by José A. Alonso (jose_a_alonso@mathstodon.xyz)

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José A. Alonso (jose_a_alonso@mathstodon.xyz)'s status on Thursday, 28-Nov-2024 16:49:27 JST José A. Alonso

Readings shared November 27, 2024. https://jaalonso.github.io/vestigium/posts/2024/11/27-readings_shared_11-27-24 #Haskell #FunctionalProgramming #AI #MachineLearning #Math
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  Readings shared November 27, 2024
  
  from José A. Alonso
  
  The readings shared in Mastodon on 27 November 2024 are Readings shared November 26, 2024. #ITP #Lean4 #IsabelleHOL #Logic #Math #Prolog #LogicProgramming #Z3 #SMT #AI #Education Haskell: A great pro
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José A. Alonso (jose_a_alonso@mathstodon.xyz)'s status on Monday, 15-May-2023 18:51:43 JST José A. Alonso

A univalent formalization of constructive affine schemes. ~ Max Zeuner, Anders Mörtberg. https://arxiv.org/abs/2212.02902 #ITP #Agda #Math
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  A Univalent Formalization of Constructive Affine Schemes
  
  We present a formalization of constructive affine schemes in the Cubical Agda proof assistant. This development is not only fully constructive and predicative, it also makes crucial use of univalence. By now schemes have been formalized in various proof assistants. However, most existing formalizations follow the inherently non-constructive approach of Hartshorne's classic "Algebraic Geometry" textbook, for which the construction of the so-called structure sheaf is rather straightforwardly formalizable and works the same with or without univalence. We follow an alternative approach that uses a point-free description of the constructive counterpart of the Zariski spectrum called the Zariski lattice and proceeds by defining the structure sheaf on formal basic opens and then lift it to the whole lattice. This general strategy is used in a plethora of textbooks, but formalizing it has proved tricky. The main result of this paper is that with the help of the univalence principle we can make this "lift from basis" strategy formal and obtain a fully formalized account of constructive affine schemes.
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José A. Alonso (jose_a_alonso@mathstodon.xyz)'s status on Monday, 15-May-2023 18:48:47 JST José A. Alonso

Is ChatGPT a good causal reasoner? A comprehensive evaluation. ~ Jinglong Gao, Xiao Ding, Bing Qin, Ting Liu. https://arxiv.org/abs/2305.07375 #AI #ChatGPT
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  Is ChatGPT a Good Causal Reasoner? A Comprehensive Evaluation
  
  Causal reasoning ability is crucial for numerous NLP applications. Despite the impressive emerging ability of ChatGPT in various NLP tasks, it is unclear how well ChatGPT performs in causal reasoning. In this paper, we conduct the first comprehensive evaluation of the ChatGPT's causal reasoning capabilities. Experiments show that ChatGPT is not a good causal reasoner, but a good causal interpreter. Besides, ChatGPT has a serious hallucination on causal reasoning, possibly due to the reporting biases between causal and non-causal relationships in natural language, as well as ChatGPT's upgrading processes, such as RLHF. The In-Context Learning (ICL) and Chain-of-Though (COT) techniques can further exacerbate such causal hallucination. Additionally, the causal reasoning ability of ChatGPT is sensitive to the words used to express the causal concept in prompts, and close-ended prompts perform better than open-ended prompts. For events in sentences, ChatGPT excels at capturing explicit causality rather than implicit causality, and performs better in sentences with lower event density and smaller lexical distance between events.
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José A. Alonso (jose_a_alonso@mathstodon.xyz)'s status on Monday, 15-May-2023 16:47:30 JST José A. Alonso

Mathematics of the impossible, Chapter 12, Data structures. https://emanueleviola.wordpress.com/2023/05/14/mathematics-of-the-impossible-chapter-12-data-structures/ #Math #CompSci
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  Mathematics of the impossible, Chapter 12, Data structures
  
  from Manu
  
  And as promised, here’s a chapter on data structures… in a complexity theory course! — Data structures aim to maintain data in memory so as to be able to support various operation…

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Notices by José A. Alonso (jose_a_alonso@mathstodon.xyz)

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