AI-supported programming has taken giant leaps with tools such as Meta's Llama and openAI's chatGPT. These are examples of stochastic sources of programs and have already greatly influenced how we produce code and teach programming. If we consider input to such models as a stochastic source, a natural question is, what is the relation between the input and the output distributions, between the chatGPT prompt and the resulting program? In this paper, we will show how the relation between random Python programs generated from chatGPT can be described geometrically and topologically using Tree-edit distances between the program's syntax trees and without explicit modeling of the underlying space. A popular approach to studying high-dimensional samples in a metric space is to use low-dimensional embedding using, e.g., multidimensional scaling. Such methods imply errors depending on the data and dimension of the embedding space. In this article, we propose to restrict such projection methods to purely visualization purposes and instead use geometric summary statistics, methods from spatial point statistics, and topological data analysis to characterize the configurations of random programs that do not rely on embedding approximations. To demonstrate their usefulness, we compare two publicly available models: ChatGPT-4 and TinyLlama, on a simple problem related to image processing. Application areas include understanding how questions should be asked to obtain useful programs; measuring how consistently a given large language model answers; and comparing the different large language models as a programming assistant. Finally, we speculate that our approach may in the future give new insights into the structure of programming languages.

Statistical learning theory offers probabilistic guarantees on the accuracy of models learned from data. Most of these results assume that the data come from a realization of a sample of independent and identically distributed(i.i.d.) random variables, which allows one to build the theory upon standard concentration arguments. However, this assumption is often unrealistic as dependent data are ubiquitous in real-world applications, such as signal processing, speech recognition, biological sequence annotation (Baldi and Brunak, 2001), dynamical system identification (Ljung, 1987), or even handwritten character recognition where the images collected for training come from a string of letters forming a meaningful text. This paper extends several classical results to sequences of dependent data, such as risk bounds based on the Vapnik-Chervonenkis (VC) dimension or the Rademacher complexity. In particular, we focus on uniform risk bounds that are more suitable for nonconvex loss functions difficult to minimize in practice. As a motivating application, we also consider the consequences of these results in the framework of scenario-based optimization for solving uncertain optimization problems. Here, robust solutions are those that typically satisfy an infinite number of constraints: one for each value of the uncertain parameter of the problem.

It is believed that mechanisms including intermediate values enable composable inductive programming (CIP) to be used to produce software of any size. We present the results of a study that investigated the relationships between program size, the number of intermediate values and the number of test cases used to specify programs using CIP. In the study 96,000 programs of various sizes were randomly generated, decomposed into fragments and transformed into test cases. The test cases were then used to regenerate new versions of the original programs using Zoea. The results show linear relationships between the number of intermediate values and regenerated program size, and between the number of test cases and regenerated program size within the size range studied. In addition, as program size increases there is increasing scope for trading off the number of test cases against the number of intermediate values and vice versa.

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large. KEYWORDS: answer set programming, random logic programs.