相关论文: The Future of Set Theory

Many proposed methods for explaining machine learning predictions are in fact challenging to understand for nontechnical consumers. This paper builds upon an alternative consumer-driven approach called TED that asks for explanations to be…

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

Advances in deep learning systems have allowed large models to match or surpass human accuracy on a number of skills such as image classification, basic programming, and standardized test taking. As the performance of the most capable…

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…

Session-based recommender systems aim to improve recommendations in short-term sessions that can be found across many platforms. A critical challenge is to accurately model user intent with only limited evidence in these short sessions. For…

Participation in conferences is an important part of every scientific career. Conferences provide an opportunity for a fast dissemination of latest results, discussion and exchange of ideas, and broadening of scientists' collaboration…

Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…

We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation…

Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent…

Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…

The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest.…

In neural dialogue modeling, a neural network is trained to predict the next utterance, and at inference time, an approximate decoding algorithm is used to generate next utterances given previous ones. While this autoregressive framework…

This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…

My assignment at this conference is to assess where we are in high-energy physics and speculate on where we might be going. This frees me from any obligation to summarize all that went on here and allows me to talk just about those topics…

Given a malfunctioning system, sequential diagnosis aims at identifying the root cause of the failure in terms of abnormally behaving system components. As initial system observations usually do not suffice to deterministically pin down…

Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. As more taxa are added, the new source trees may begin to tell a different evolutionary story when…

This paper summarizes my thoughts, given in an invited review at the IAU symposium 341 "Challenges in Panchromatic Galaxy Modelling with Next Generation Facilities", about how machine learning methods can help us solve some of the big data…

A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.

Event prediction is the ability of anticipating future events, i.e., future real-world occurrences, and aims to support the user in deciding on actions that change future events towards a desired state. An event prediction method learns the…

As Artificial Intelligence (AI) systems continue to grow in size and complexity, so does the difficulty of the quest for AI transparency. In a world of large models and complex AI systems, why do we explain AI and what should we explain?…