Related papers: Rare Speed-up in Automatic Theorem Proving Reveals…

Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…

We propose a simple yet effective solution to tackle the often-competing goals of fairness and utility in classification tasks. While fairness ensures that the model's predictions are unbiased and do not discriminate against any particular…

A trade-off between accuracy and fairness is almost taken as a given in the existing literature on fairness in machine learning. Yet, it is not preordained that accuracy should decrease with increased fairness. Novel to this work, we…

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of…

A resource-bounded version of the statement "no algorithm recognizes all non-halting Turing machines" is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any coNP-complete language and also…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…

Data mining, machine learning, and natural language processing are powerful techniques that can be used together to extract information from large texts. Depending on the task or problem at hand, there are many different approaches that can…

We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…

We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…

This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is…

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

Prediction markets are powerful tools to elicit and aggregate beliefs from strategic agents. However, in current prediction markets, agents may exhaust the social welfare by competing to be the first to update the market. We initiate the…

We study the tradeoff between fundamental risk and time. A time-constrained agent has to solve a problem. She dynamically allocates effort between implementing a risky initial idea and exploring alternatives. Discovering an alternative…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…

We study collective decision-making in a model of human groups, with network interactions, performing two alternative choice tasks. We focus on the speed-accuracy tradeoff, i.e., the tradeoff between a quick decision and a reliable…

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this…

Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning…

The field of learning-augmented algorithms has gained significant attention in recent years. These algorithms, using potentially inaccurate predictions, must exhibit three key properties: consistency, robustness, and smoothness. In…