Related papers: Program algebra with a jump-shift instruction
Although reinforcement learning has seen tremendous success recently, this kind of trial-and-error learning can be impractical or inefficient in complex environments. The use of demonstrations, on the other hand, enables agents to benefit…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Safety post-training can improve the harmfulness and policy compliance of Large Language Models (LLMs), but it may also reduce general utility, a phenomenon often described as the \emph{alignment tax}. We study this trade-off through the…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
Threads as considered in basic thread algebra are primarily looked upon as behaviours exhibited by sequential programs on execution. It is a fact of life that sequential programs are often fragmented. Consequently, fragmented program…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…
The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…
In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite…
In this paper we provide an overview of the programmed instructions approach for the purpose of quantum software education. The article presents the programmed instructions method and recent successes in STEM fields before describing its…
Most studies in multiparameter estimation assume the dynamics is fixed and focus on identifying the optimal probe state and the optimal measurements. In practice, however, controls are usually available to alter the dynamics, which provides…
Following an instruction involves distinct sub-processes, such as reading content, reading the instruction, executing it, and producing an answer. We ask where, along the layer stack, instruction following begins, the point where reading…
The evolutionary Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SG) with preferential learning mechanism are studied in the Barab\'asi-Albert network. Simulation results demonstrate that the preferential learning of individuals…
The recent "pre-train, prompt, predict training" paradigm has gained popularity as a way to learn generalizable models with limited labeled data. The approach involves using a pre-trained model and a prompting function that applies a…