Related papers: Program algebra with a jump-shift instruction
A discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. One-way jumping finite automata change their states…
Knowledge tracing aims to model students' past answer sequences to track the change in their knowledge acquisition during exercise activities and to predict their future learning performance. Most existing approaches ignore the fact that…
The last two decades, since the seminal work of Selig, has seen projective geometric algebra (PGA) gain popularity as a modern coordinate-free framework for doing classical Euclidean geometry and other Cayley-Klein geometries. This…
To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA)…
This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational…
Backpropagation has rapidly become the workhorse credit assignment algorithm for modern deep learning methods. Recently, modified forms of predictive coding (PC), an algorithm with origins in computational neuroscience, have been shown to…
Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not…
Recent developments in sequential experimental design look to construct a policy that can efficiently navigate the design space, in a way that maximises the expected information gain. Whilst there is work on achieving tractable policies for…
The a priori analysis (APA) is discussed as a tool to assess the reliability of grades in standard curricular courses. This unusual, but striking application is presented when teaching the section on data treatment of a Laboratory Course to…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
Chain of Thought (CoT) prompting has been shown to significantly improve the performance of large language models (LLMs), particularly in arithmetic and reasoning tasks, by instructing the model to produce intermediate reasoning steps.…
The PICUP Collection of Exercise Sets (https://www.compadre.org/PICUP/exercises/) contains over 60 peer-reviewed computation-infused activities for use in various physics courses from high school through graduate study. Each Exercise Set…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
Final outputs hide when a checkpoint commits to its next-token prediction. We introduce the convergence gap, a model-diffing diagnostic that decodes each layer's next-token distribution and measures its distance to the model's own final…
In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…
We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…
Minimizing expected loss measured by a proper scoring rule, such as Brier score or log-loss (cross-entropy), is a common objective while training a probabilistic classifier. If the data have experienced dataset shift where the class…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Graph learning models have demonstrated great prowess in learning expressive representations from large-scale graph data in a wide variety of real-world scenarios. As a prevalent strategy for training powerful graph learning models, the…
This note explores state space search to find efficient instruction sequences that perform particular data manipulations. Once found, the instruction sequences are hard-wired in the code generator that needs these data manipulations. Since…