Background: Recently, ChatGPT and similar generative AI models have attracted hundreds of millions of users and become part of the public discourse. Many believe that such models will disrupt society and will result in a significant change in the education system and information generation in the future. So far, this belief is based on either colloquial evidence or benchmarks from the owners of the models -- both lack scientific rigour. Objective: Through a large-scale study comparing human-written versus ChatGPT-generated argumentative student essays, we systematically assess the quality of the AI-generated content. Methods: A large corpus of essays was rated using standard criteria by a large number of human experts (teachers). We augment the analysis with a consideration of the linguistic characteristics of the generated essays. Results: Our results demonstrate that ChatGPT generates essays that are rated higher for quality than human-written essays. The writing style of the AI models exhibits linguistic characteristics that are different from those of the human-written essays, e.g., it is characterized by fewer discourse and epistemic markers, but more nominalizations and greater lexical diversity. Conclusions: Our results clearly demonstrate that models like ChatGPT outperform humans in generating argumentative essays. Since the technology is readily available for anyone to use, educators must act immediately. We must re-invent homework and develop teaching concepts that utilize these AI models in the same way as math utilized the calculator: teach the general concepts first and then use AI tools to free up time for other learning objectives.
Written answers to open-ended questions can have a higher long-term effect on learning than multiple-choice questions. However, it is critical that teachers immediately review the answers, and ask to redo those that are incoherent. This can be a difficult task and can be time-consuming for teachers. A possible solution is to automate the detection of incoherent answers. One option is to automate the review with Large Language Models (LLM). In this paper, we analyze the responses of fourth graders in mathematics using three LLMs: GPT-3, BLOOM, and YOU. We used them with zero, one, two, three and four shots. We compared their performance with the results of various classifiers trained with Machine Learning (ML). We found that LLMs perform worse than MLs in detecting incoherent answers. The difficulty seems to reside in recursive questions that contain both questions and answers, and in responses from students with typical fourth-grader misspellings. Upon closer examination, we have found that the ChatGPT model faces the same challenges.
The performance of Large Language Models (LLMs) in reasoning tasks depends heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency being critical methods that enhance this ability. However, these methods do not fully exploit the answers generated by the LLM to guide subsequent responses. This paper proposes a new prompting method, named Progressive-Hint Prompting (PHP), that enables automatic multiple interactions between users and LLMs by using previously generated answers as hints to progressively guide toward the correct answers. PHP is orthogonal to CoT and self-consistency, making it easy to combine with state-of-the-art techniques to further improve performance. We conducted extensive and comprehensive experiments on seven benchmarks. The results show that PHP significantly improves accuracy while remaining highly efficient. For instance, with text-davinci-003, we observed a 4.2% improvement on GSM8K with greedy decoding compared to Complex CoT, and a 46.17% reduction in sample paths with self-consistency. With GPT-4 and PHP, we achieve state-of-the-art performances on SVAMP (89.1% -> 91.9%), GSM8K (92% -> 95.5%), AQuA (76.4% -> 79.9%) and MATH (50.3% -> 53.9%).
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has emerged as a promising direction for solving math word problems, but prior approaches such as Program-Aided Language model (PAL) are biased towards simple procedural problems and less effective for problems that require declarative reasoning. We propose an approach that combines an LLM that can incrementally formalize word problems as a set of variables and equations with an external symbolic solver that can solve the equations. Our approach achieves comparable accuracy to the original PAL on the GSM8K benchmark of math word problems and outperforms PAL by an absolute 20% on ALGEBRA, a new dataset of more challenging word problems extracted from Algebra textbooks. Our work highlights the benefits of using declarative and incremental representations when interfacing with an external tool for solving complex math word problems. Our data and prompts are publicly available at https://github.com/joyheyueya/declarative-math-word-problem.
Textbooks are one of the main mediums for delivering high-quality education to students. In particular, explanatory and illustrative visuals play a key role in retention, comprehension and general transfer of knowledge. However, many textbooks lack these interesting visuals to support student learning. In this paper, we investigate the effectiveness of vision-language models to automatically enhance textbooks with images from the web. We collect a dataset of e-textbooks in the math, science, social science and business domains. We then set up a text-image matching task that involves retrieving and appropriately assigning web images to textbooks, which we frame as a matching optimization problem. Through a crowd-sourced evaluation, we verify that (1) while the original textbook images are rated higher, automatically assigned ones are not far behind, and (2) the precise formulation of the optimization problem matters. We release the dataset of textbooks with an associated image bank to inspire further research in this intersectional area of computer vision and NLP for education.
Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their individual utility. Accordingly, considerable ranking metrics have been developed and learning-to-rank algorithms that have been designed to optimize these simple performance metrics have been widely used in modern IR systems. As applications evolve, however, people's need for information retrieval have shifted from simply retrieving relevant documents to more advanced information services that satisfy their complex working and entertainment needs. Thus, more complicated and user-centric objectives such as user satisfaction and engagement have been adopted to evaluate modern IR systems today. Those objectives, unfortunately, are difficult to be optimized under existing learning-to-rank frameworks as they are subject to great variance and complicated structures that cannot be explicitly explained or formulated with math equations like those simple performance metrics. This leads to the following research question -- how to optimize result ranking for complex ranking metrics without knowing their internal structures? To address this question, we conduct formal analysis on the limitation of existing ranking optimization techniques and describe three research tasks in \textit{Metric-agnostic Ranking Optimization}. Through the discussion of potential solutions to these tasks, we hope to encourage more people to look into the problem of ranking optimization in complex search and recommendation scenarios.
The usage of mathematical formulas as concise representations of a document's key ideas is common practice. Correctly interpreting these formulas, by identifying mathematical symbols and extracting their descriptions, is an important task in document understanding. This paper makes the following contributions to the mathematical identifier description reading (MIDR) task: (i) introduces the Math Formula Question Answering Dataset (MFQuAD) with $7508$ annotated identifier occurrences; (ii) describes novel variations of the noun phrase ranking approach for the MIDR task; (iii) reports experimental results for the SOTA noun phrase ranking approach and our novel variations of the approach, providing problem insights and a performance baseline; (iv) provides a position on the features that make an effective dataset for the MIDR task.
Manipulatives used in the right way help improve mathematical concepts leading to better learning outcomes. In this paper, we present a phygital (physical + digital) curriculum inspired teaching system for kids aged 5-8 to learn geometry using shape tile manipulatives. Combining smaller shapes to form larger ones is an important skill kids learn early on which requires shape tiles to be placed close to each other in the play area. This introduces a challenge of oriented object detection for densely packed objects with arbitrary orientations. Leveraging simulated data for neural network training and light-weight mobile architectures, we enable our system to understand user interactions and provide real-time audiovisual feedback. Experimental results show that our network runs real-time with high precision/recall on consumer devices, thereby providing a consistent and enjoyable learning experience.
Evaluating the general abilities of foundation models to tackle human-level tasks is a vital aspect of their development and application in the pursuit of Artificial General Intelligence (AGI). Traditional benchmarks, which rely on artificial datasets, may not accurately represent human-level capabilities. In this paper, we introduce AGIEval, a novel benchmark specifically designed to assess foundation model in the context of human-centric standardized exams, such as college entrance exams, law school admission tests, math competitions, and lawyer qualification tests. We evaluate several state-of-the-art foundation models, including GPT-4, ChatGPT, and Text-Davinci-003, using this benchmark. Impressively, GPT-4 surpasses average human performance on SAT, LSAT, and math competitions, attaining a 95% accuracy rate on the SAT Math test and a 92.5% accuracy on the English test of the Chinese national college entrance exam. This demonstrates the extraordinary performance of contemporary foundation models. In contrast, we also find that GPT-4 is less proficient in tasks that require complex reasoning or specific domain knowledge. Our comprehensive analyses of model capabilities (understanding, knowledge, reasoning, and calculation) reveal these models' strengths and limitations, providing valuable insights into future directions for enhancing their general capabilities. By concentrating on tasks pertinent to human cognition and decision-making, our benchmark delivers a more meaningful and robust evaluation of foundation models' performance in real-world scenarios. The data, code, and all model outputs are released in https://github.com/ruixiangcui/AGIEval.
Resource limitations make it hard to provide all students with one of the most effective educational interventions: personalized instruction. Reinforcement learning could be a key tool to reduce the development cost and improve the effectiveness of intelligent tutoring software that aims to provide the right support, at the right time, to a student. Here we illustrate that deep reinforcement learning can be used to provide adaptive pedagogical support to students learning about the concept of volume in a narrative storyline software. Using explainable artificial intelligence tools, we extracted interpretable insights about the pedagogical policy learned and demonstrated that the resulting policy had similar performance in a different student population. Most importantly, in both studies, the reinforcement-learning narrative system had the largest benefit for those students with the lowest initial pretest scores, suggesting the opportunity for AI to adapt and provide support for those most in need.
Becoming a (super) hero is almost every kid's dream. During their sheltered childhood, they do whatever it takes to grow up to be one. Work hard, play hard -- all day long. But as they're getting older, distractions are more and more likely to occur. They're getting off track. They start discovering what is feared as simple math. Finally, they end up as a researcher, writing boring, non-impressive papers all day long because they only rely on simple mathematics. No top-tier conferences, no respect, no groupies. Life's over. To finally put an end to this tragedy, we propose a fundamentally new algorithm, dubbed zero2hero, that turns every research paper into a scientific masterpiece. Given a LaTeX document containing ridiculously simple math, based on next-generation large language models, our system automatically over-complicates every single equation so that no one, including yourself, is able to understand what the hell is going on. Future reviewers will be blown away by the complexity of your equations, immediately leading to acceptance. zero2hero gets you back on track, because you deserve to be a hero$^{\text{TM}}$. Code leaked at \url{https://github.com/mweiherer/zero2hero}.
The success of ChatGPT has recently attracted numerous efforts to replicate it, with instruction-tuning strategies being a key factor in achieving remarkable results. Instruction-tuning not only significantly enhances the model's performance and generalization but also makes the model's generated results more consistent with human speech patterns. However current research rarely studies the impact of different amounts of instruction data on model performance, especially in the real-world use cases. In this paper we explore the performance of large language models based on instruction tuning across different scales of instruction data. An evaluation dataset consisting of 12 major online use cases is constructed in the experiment. With Bloomz-7B1-mt as the base model, the results show that 1) merely increasing the amount of instruction data leads to continuous improvement in tasks such as open-ended generation, 2) in tasks such as math and code, the model performance curve remains quite flat while increasing data size. We further analyze the possible causes of these phenomena and propose potential future research directions such as effectively selecting high-quality training data, scaling base models and training methods specialized for hard tasks. We will release our training and evaluation datasets, as well as model checkpoints.
This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open Linked Data cloud. The proposed model is intended for applications that extract mathematical facts from natural language mathematical texts and represent these facts as Linked Open Data. The model is used in development of a new version of the OntoMath${}^{\mathrm{PRO}}$ ontology of professional mathematics is described. OntoMath${}^{\mathrm{PRO}}$ underlies a semantic publishing platform, that takes as an input a collection of mathematical papers in LaTeX format and builds their ontology-based Linked Open Data representation. The semantic publishing platform, in turn, is a central component of OntoMath digital ecosystem, an ecosystem of ontologies, text analytics tools, and applications for mathematical knowledge management, including semantic search for mathematical formulas and a recommender system for mathematical papers. According to the new model, the ontology is organized into three layers: a foundational ontology layer, a domain ontology layer and a linguistic layer. The domain ontology layer contains language-independent math concepts. The linguistic layer provides linguistic grounding for these concepts, and the foundation ontology layer provides them with meta-ontological annotations. The concepts are organized in two main hierarchies: the hierarchy of objects and the hierarchy of reified relationships.
Deep hashing has been extensively applied to massive image retrieval due to its efficiency and effectiveness. Recently, several adversarial attacks have been presented to reveal the vulnerability of deep hashing models against adversarial examples. However, existing attack methods suffer from degraded performance or inefficiency because they underutilize the semantic relations between original samples or spend a lot of time learning these relations with a deep neural network. In this paper, we propose a novel Pharos-guided Attack, dubbed PgA, to evaluate the adversarial robustness of deep hashing networks reliably and efficiently. Specifically, we design pharos code to represent the semantics of the benign image, which preserves the similarity to semantically relevant samples and dissimilarity to irrelevant ones. It is proven that we can quickly calculate the pharos code via a simple math formula. Accordingly, PgA can directly conduct a reliable and efficient attack on deep hashing-based retrieval by maximizing the similarity between the hash code of the adversarial example and the pharos code. Extensive experiments on the benchmark datasets verify that the proposed algorithm outperforms the prior state-of-the-arts in both attack strength and speed.
Cognitive psychology delves on understanding perception, attention, memory, language, problem-solving, decision-making, and reasoning. Large language models (LLMs) are emerging as potent tools increasingly capable of performing human-level tasks. The recent development in the form of GPT-4 and its demonstrated success in tasks complex to humans exam and complex problems has led to an increased confidence in the LLMs to become perfect instruments of intelligence. Although GPT-4 report has shown performance on some cognitive psychology tasks, a comprehensive assessment of GPT-4, via the existing well-established datasets is required. In this study, we focus on the evaluation of GPT-4's performance on a set of cognitive psychology datasets such as CommonsenseQA, SuperGLUE, MATH and HANS. In doing so, we understand how GPT-4 processes and integrates cognitive psychology with contextual information, providing insight into the underlying cognitive processes that enable its ability to generate the responses. We show that GPT-4 exhibits a high level of accuracy in cognitive psychology tasks relative to the prior state-of-the-art models. Our results strengthen the already available assessments and confidence on GPT-4's cognitive psychology abilities. It has significant potential to revolutionize the field of AI, by enabling machines to bridge the gap between human and machine reasoning.
We report the development of GPT-4, a large-scale, multimodal model which can accept image and text inputs and produce text outputs. While less capable than humans in many real-world scenarios, GPT-4 exhibits human-level performance on various professional and academic benchmarks, including passing a simulated bar exam with a score around the top 10% of test takers. GPT-4 is a Transformer-based model pre-trained to predict the next token in a document. The post-training alignment process results in improved performance on measures of factuality and adherence to desired behavior. A core component of this project was developing infrastructure and optimization methods that behave predictably across a wide range of scales. This allowed us to accurately predict some aspects of GPT-4's performance based on models trained with no more than 1/1,000th the compute of GPT-4.
Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset ($78.7\%\rightarrow92.5\%$) evaluated using 175B parameter GPT-based LLM.
Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST is based on module~LWE, and current publicly available PQ Homomorphic Encryption (HE) libraries are based on ring LWE. The security of LWE-based PQ cryptosystems is critical, but certain implementation choices could weaken them. One such choice is sparse binary secrets, desirable for PQ HE schemes for efficiency reasons. Prior work, SALSA, demonstrated a machine learning-based attack on LWE with sparse binary secrets in small dimensions ($n \le 128$) and low Hamming weights ($h \le 4$). However, this attack assumes access to millions of eavesdropped LWE samples and fails at higher Hamming weights or dimensions. We present PICANTE, an enhanced machine learning attack on LWE with sparse binary secrets, which recovers secrets in much larger dimensions (up to $n=350$) and with larger Hamming weights (roughly $n/10$, and up to $h=60$ for $n=350$). We achieve this dramatic improvement via a novel preprocessing step, which allows us to generate training data from a linear number of eavesdropped LWE samples ($4n$) and changes the distribution of the data to improve transformer training. We also improve the secret recovery methods of SALSA and introduce a novel cross-attention recovery mechanism allowing us to read off the secret directly from the trained models. While PICANTE does not threaten NIST's proposed LWE standards, it demonstrates significant improvement over SALSA and could scale further, highlighting the need for future investigation into machine learning attacks on LWE with sparse binary secrets.
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible transformations. This paper presents new computational techniques for building the Knothe--Rosenblatt (KR) rearrangement based on general separable functions. We first introduce a new construction of the KR rearrangement -- with guaranteed invertibility in its numerical implementation -- based on approximating the density of the target random variable using tensor-product spectral polynomials and downward closed sparse index sets. Compared to other constructions of KR arrangements based on either multi-linear approximations or nonlinear optimizations, our new construction only relies on a weighted least square approximation procedure. Then, inspired by the recently developed deep tensor trains (Cui and Dolgov, Found. Comput. Math. 22:1863--1922, 2022), we enhance the approximation power of sparse polynomials by preconditioning the density approximation problem using compositions of maps. This is particularly suitable for high-dimensional and concentrated probability densities commonly seen in many applications. We approximate the complicated target density by a composition of self-reinforced KR rearrangements, in which previously constructed KR rearrangements -- based on the same approximation ansatz -- are used to precondition the density approximation problem for building each new KR rearrangement. We demonstrate the efficiency of our proposed methods and the importance of using the composite map on several inverse problems governed by ordinary differential equations (ODEs) and partial differential equations (PDEs).
In this article, we show existence of minimizers in the loss landscape for residual artificial neural networks (ANNs) with multi-dimensional input layer and one hidden layer with ReLU activation. Our work contrasts earlier results in [D. Gallon, A. Jentzen, and F. Lindner, preprint, arXiv:2211.15641, 2022] and [P. Petersen, M. Raslan, and F. Voigtlaender, Found. Comput. Math., 21 (2021), pp. 375-444] which showed that in many situations minimizers do not exist for common smooth activation functions even in the case where the target functions are polynomials. The proof of the existence property makes use of a closure of the search space containing all functions generated by ANNs and additional discontinuous generalized responses. As we will show, the additional generalized responses in this larger space are suboptimal so that the minimum is attained in the original function class.