Because of the generality of Definition 1.1, it may be that

For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs and examples show that this geometric similarity between dataset and model is essential to trustworthy interpolation and perturbation, and we conjecture that this new concept will add value to the current debate regarding the unclear relationship between "overfitting" and "generalization" in applications of deeplearning. In typical DNN applications, an explicit geometric description of the model is impossible, but parallax can estimate topological features (components, cycles, voids, etc.) in the model by examining the effect on the Rips complex of geodesic distortions using the reference dataset. Thus, parallax indicates whether the model shares similar multiscale geometric features with the dataset. Parallax presents theoretically via topological data analysis [TDA] as a bi-filtered persistence module, and the key properties of this module are stable under perturbation of the reference dataset.

This study aimed to evaluate the proficiency of prominent Large Language Models (LLMs), namely OpenAI's ChatGPT 3.5 and 4.0, Google's Bard(LaMDA), and Microsoft's Bing AI in discerning the truthfulness of news items using black box testing. A total of 100 fact-checked news items, all sourced from independent fact-checking agencies, were presented to each of these LLMs under controlled conditions. Their responses were classified into one of three categories: True, False, and Partially True/False. The effectiveness of the LLMs was gauged based on the accuracy of their classifications against the verified facts provided by the independent agencies. The results showed a moderate proficiency across all models, with an average score of 65.25 out of 100. Among the models, OpenAI's GPT-4.0 stood out with a score of 71, suggesting an edge in newer LLMs' abilities to differentiate fact from deception. However, when juxtaposed against the performance of human fact-checkers, the AI models, despite showing promise, lag in comprehending the subtleties and contexts inherent in news information. The findings highlight the potential of AI in the domain of fact-checking while underscoring the continued importance of human cognitive skills and the necessity for persistent advancements in AI capabilities. Finally, the experimental data produced from the simulation of this work is openly available on Kaggle.

Many tasks aim to measure machine reading comprehension (MRC), often focusing on question types presumed to be difficult. Rarely, however, do task designers start by considering what systems should in fact comprehend. In this paper we make two key contributions. First, we argue that existing approaches do not adequately define comprehension; they are too unsystematic about what content is tested. Second, we present a detailed definition of comprehension -- a "Template of Understanding" -- for a widely useful class of texts, namely short narratives. We then conduct an experiment that strongly suggests existing systems are not up to the task of narrative understanding as we define it.

We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties of entropy. CDER applies to a training set of labeled pointclouds embedded in a common Euclidean space. If typical pointclouds corresponding to distinct labels tend to differ at any scale in any sub-region, CDER can identify these differences in (typically) linear time, creating a set of distributional coordinates which act as a feature extraction mechanism for supervised learning. We describe theoretical properties and implementation details of CDER, and illustrate its benefits on several synthetic examples.

Genome-wide association studies (GWAS) offer new opportunities to identify genetic risk factors for Alzheimer's disease (AD). Recently, collaborative efforts across different institutions emerged that enhance the power of many existing techniques on individual institution data. However, a major barrier to collaborative studies of GWAS is that many institutions need to preserve individual data privacy. To address this challenge, we propose a novel distributed framework, termed Local Query Model (LQM) to detect risk SNPs for AD across multiple research institutions. To accelerate the learning process, we propose a Distributed Enhanced Dual Polytope Projection (D-EDPP) screening rule to identify irrelevant features and remove them from the optimization. To the best of our knowledge, this is the first successful run of the computationally intensive model selection procedure to learn a consistent model across different institutions without compromising their privacy while ranking the SNPs that may collectively affect AD. Empirical studies are conducted on 809 subjects with 5.9 million SNP features which are distributed across three individual institutions. D-EDPP achieved a 66-fold speed-up by effectively identifying irrelevant features.