Related papers: Program algebra with a jump-shift instruction
Pretraining has been widely explored to augment the adaptability of graph learning models to transfer knowledge from large datasets to a downstream task, such as link prediction or classification. However, the gap between training…
This work identifies a simple pre-training mechanism that leads to representations exhibiting better continual and transfer learning. This mechanism -- the repeated resetting of weights in the last layer, which we nickname "zapping" -- was…
Instruction tuning commonly means finetuning a language model on instruction-response pairs. We discover two forms of adaptation (tuning) that are deficient compared to instruction tuning, yet still yield instruction following; we call this…
Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps…
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…
Many sequences of $p$-adic integers project modulo $p^\alpha$ to $p$-automatic sequences for every $\alpha \geq 0$. Examples include algebraic sequences of integers, which satisfy this property for every prime $p$, and some cocycle…
Image-language models with prompt learning have shown remarkable advances in numerous downstream vision tasks. Nevertheless, conventional prompt learning methods overfit their training distribution and lose the generalization ability on…
Neural networks, especially the recent proposed neural operator models, are increasingly being used to find the solution operator of differential equations. Compared to traditional numerical solvers, they are much faster and more efficient…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple…
Recent research identified a temporary performance drop on previously learned tasks when transitioning to a new one. This drop is called the stability gap and has great consequences for continual learning: it complicates the direct…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
Transition Algebra (TA) is a type of infinite logic introduced to discuss rewriting systems. The natural deductive proof systems already introduced in TA satisfy completeness for countable signatures. However, it lacks compactness, making…
We study Transformers on the task \emph{program trace generation} (PTG), where models produce step-by-step execution traces for synthetic programs. Unlike existing algorithmic problems, PTG externalizes reasoning through long traces where…
This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
We study the computational power of parsing expression grammars (PEGs). We begin by constructing PEGs with unexpected behaviour, and surprising new examples of languages with PEGs, including the language of palindromes whose length is a…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution…