Related papers: On Sharing, Memoization, and Polynomial Time (Long…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
This work proposes a way to align statistical modeling with decision making. We provide a method that propagates the uncertainty in predictive modeling to the uncertainty in operational cost, where operational cost is the amount spent by…
In this paper, we shall study the uniqueness problems on meromorphic functions sharing a polynomial. We give a complete answer to a problem posed by Fang Mingliang. Our results improve or generalize those given by Fang and Hua, Yang and…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
In the design of probabilistic timed systems, bounded requirements concerning behaviour that occurs within a given time, energy, or more generally cost budget are of central importance. Traditionally, such requirements have been…
We develop a new algorithm for the quantisation of systems with first-class constraints. Our approach lies within the (History Projection Operator) continuous-time histories quantisation programme. In particular, the Hamiltonian treatment…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…
Matrix factorization is a common machine learning technique for recommender systems. Despite its high prediction accuracy, the Bayesian Probabilistic Matrix Factorization algorithm (BPMF) has not been widely used on large scale data because…
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…
The $\pi$-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how $\pi$-calculus processes can be controlled so that computations…
We study to which extent additive fairness metrics (statistical parity, equal opportunity and equalized odds) can be influenced in a multi-class classification problem by memorizing a subset of the population. We give explicit expressions…
In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…
Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they…
Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on…
Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely…
It is well known that quantifying uncertainty in the action-value estimates is crucial for efficient exploration in reinforcement learning. Ensemble sampling offers a relatively computationally tractable way of doing this using randomized…