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Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling…
In this paper we will study an important but rather technical result which is called The Reduction Property. The result tells us how much arithmetical conservation there is between two arithmetical theories. Both theories essentially speak…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Crash classification models in transportation safety are typically evaluated using accuracy, F1, or AUC, metrics that cannot reveal whether a model is silently overfitting. We introduce a spectral diagnostic framework grounded in Random…
In recent years, Karr's difference field theory has been extended to the so-called $R\Pi\Sigma$-extensions in which one can represent not only indefinite nested sums and products that can be expressed by transcendental ring extensions, but…
In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that…
There exist many techniques for automatically deriving parametric resource (or cost) bounds by analyzing the source code of a program. These techniques work effectively for a large class of programs and language features. However, non-local…
We introduce a framework for filtering features that employs the Hilbert-Schmidt Independence Criterion (HSIC) as a measure of dependence between the features and the labels. The key idea is that good features should maximise such…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
The motivation of this study is to leverage recent breakthroughs in artificial intelligence research to unlock novel solutions to important scientific problems encountered in computational science. To address the human intelligence…
We study cohomology for classical Lie superalgebras $\mathfrak{g}$ (e.g. gl(m|n)) over the complex numbers. Using results from invariant theory, we show that there exist subsuperalgebras which detect the cohomology of $\mathfrak{g}.$…
We investigate the set of Pi-1-2 sentences which are Pi-1-1 conservative over the theories of reverse mathematics RCA0+ISigma_n and ACA0. We exhibit new elements of these sets and conclude that the sets are Pi_2 complete. Along the way, we…
We describe a construction of a model of second order arithmetic in which (boldface) $\bm{\Pi^1_n}$-determinacy holds, but (lightface) $\Pi^1_{n+2}$-$\mathsf{DC}$ fails, thus showing that no projective level of determinacy implies full…
We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental Theorem of Statistical Learning, which characterizes PAC…
Standard supervised classification trains models to imitate the exact labels provided by a perfect oracle. This imitation happens in a single pass, restricting the model to a fixed compute budget even when inputs vary in complexity.…
We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{ \pm 1\}$ only. A basic case of our results states that for…
The Axiom of Choice (AC for short) is the most (in)famous axiom of the usual foundations of mathematics, ZFC set theory. The (non-)essential use of AC in mathematics has been well-studied and thoroughly classified. Now, fragments of…
We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,\epsilon$ such that $Y=\sum_{k\in \pi}\alpha_kX_k+\epsilon$ with $\pi\subseteq \{1,...,m\}$ and $\alpha_k\in…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
We show that $\mathbf{C}$, a weak theory of sets with Axiom Beta, proves the scheme of Elementary, or $\Delta_0$ Transfinite Recursion and can generate, for every set, the corresponding relativized constructible hierarchy. We show that the…