Related papers: A heuristic prover for real inequalities
Predictive uncertainties in classification tasks are often a consequence of model inadequacy or insufficient training data. In popular applications, such as image processing, we are often required to scrutinise these uncertainties by…
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
Metric search commonly involves finding objects similar to a given sample object. We explore a generalization, where the desired result is a fair tradeoff between multiple query objects. This builds on previous results on complex queries,…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
The emergence of large-scale pretrained language models has posed unprecedented challenges in deriving explanations of why the model has made some predictions. Stemmed from the compositional nature of languages, spurious correlations have…
We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…
In multi-prover interactive proofs, the verifier interrogates the provers and attempts to steal their knowledge. Other than that, the verifier's role has not been studied. We have discovered that the verifier plays a much more important…
When explaining the decisions of deep neural networks, simple stories are tempting but dangerous. Especially in computer vision, the most popular explanation approaches give a false sense of comprehension to its users and provide an overly…
We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…
We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…
Bell inequalities play a central role in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
There is growing concern about tacit collusion using algorithmic pricing, and regulators need tools to help detect the possibility of such collusion. This paper studies how to design a hypothesis testing framework in order to decide whether…
There is a broad consensus on the importance of deep learning models in tasks involving complex data. Often, an adequate understanding of these models is required when focusing on the transparency of decisions in human-critical…
Algorithmic transparency entails exposing system properties to various stakeholders for purposes that include understanding, improving, and contesting predictions. Until now, most research into algorithmic transparency has predominantly…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
Heterogeneity is one important feature of complex systems, leading to the complexity of their construction and analysis. Moving the heterogeneity at model level helps in mastering the difficulty of composing heterogeneous models which…