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Large language models (LLMs) make remarkable progress in reasoning tasks. Among different reasoning modes, inductive reasoning, due to its better alignment with human learning, attracts increasing interest. However, research on inductive…

The use of large pretrained neural networks to create contextualized word embeddings has drastically improved performance on several natural language processing (NLP) tasks. These computationally expensive models have begun to be applied to…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

Machine learning (ML) is revolutionizing the world, affecting almost every field of science and industry. Recent algorithms (in particular, deep networks) are increasingly data-hungry, requiring large datasets for training. Thus, the…

Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…

This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…

High-quality datasets are typically required for accomplishing data-driven tasks, such as training medical diagnosis models, predicting real-time traffic conditions, or conducting experiments to validate research hypotheses. Consequently,…

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level…

This paper proposes a Transformer-based model to generate equations for math word problems. It achieves much better results than RNN models when copy and align mechanisms are not used, and can outperform complex copy and align RNN models.…

Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the…

We introduce the task of algorithm class prediction for programming word problems. A programming word problem is a problem written in natural language, which can be solved using an algorithm or a program. We define classes of various…

Knowledge tagging for questions plays a crucial role in contemporary intelligent educational applications, including learning progress diagnosis, practice question recommendations, and course content organization. Traditionally, these…

Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques…

Context information around words helps in determining their actual meaning, for example "networks" used in contexts of artificial neural networks or biological neuron networks. Generative topic models infer topic-word distributions, taking…

In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry,…

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…