相关论文: The Existential Theory of Research: Why Discovery …

We prove a PCP theorem for the existential theory of the reals, showing that MAX-ETR-INV is $\exists\mathbb{R}$-hard to approximate to within some constant factor. The existential theory of the reals (ETR) is a decision problem asking if…

The Existential Theory of the Reals (ETR) consists of existentially quantified Boolean formulas over equalities and inequalities of polynomial functions of variables in $\mathbb{R}$. In this paper we propose and study the approximate…

Consistent confirmations obtained independently of each other lend credibility to a scientific result. We refer to results satisfying this consistency as reproducible and assume that reproducibility is a desirable property of scientific…

This paper explores the concept of "entropy of knowledge" (EoN) as a framework for understanding the challenges and complexities of scientific discovery. Drawing from principles in thermodynamics and information theory, I propose that the…

Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…

Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…

It has long been known that scientific output proceeds on an exponential increase, or more properly, a logistic growth curve. The interplay between effort and discovery is clear, and the nature of the functional form has been thought to be…

This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…

Current Retrieval-Augmented Generation (RAG) systems predominantly rely on relevance-based dense retrieval, sequentially fetching documents to maximize semantic similarity with the query. However, in knowledge-intensive and real-world…

Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…

Many published research results are false, and controversy continues over the roles of replication and publication policy in improving the reliability of research. Addressing these problems is frustrated by the lack of a formal framework…

Exploration is a significant challenge in practical reinforcement learning (RL), and uncertainty-aware exploration that incorporates the quantification of epistemic and aleatory uncertainty has been recognized as an effective exploration…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form…

Causal and attribution studies are essential for earth scientific discoveries and critical for informing climate, ecology, and water policies. However, the current generation of methods needs to keep pace with the complexity of scientific…

Tactical selection of experiments to estimate an underlying model is an innate task across various fields. Since each experiment has costs associated with it, selecting statistically significant experiments becomes necessary. Classic linear…

Controversy about the significance of underdetermination of theories persists in the philosophy and conduct of science. The issue has practical import when research is used to inform decision making, because scientific uncertainty yields…

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…

Recently, various natural algorithmic problems have been shown to be $\exists \mathbb{R}$-complete. The reduction relied in many cases on the $\exists \mathbb{R}$-completeness of the problem ETR-INV, which served as a useful intermediate…

In spite of the fact that statistical predictions of quantum theory (QT) can only be tested if large amount of data is available a claim has been made that QT provides the most complete description of an individual physical system.…