Related papers: Mathematics, Recursion, and Universals in Human La…
Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge…
Recent advances in large language models (LLMs) and multimodal LLMs (MLLMs) have led to strong reasoning ability across a wide range of tasks. However, their ability to perform mathematical reasoning from spoken input remains underexplored.…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many…
Machine learning is increasingly used to inform decision-making in sensitive situations where decisions have consequential effects on individuals' lives. In these settings, in addition to requiring models to be accurate and robust, socially…
The fundamentals of formal logic, theory of sets and mathematical structures are narrated in terms of relations language.
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
Providing plausible responses to why questions is a challenging but critical goal for language based human-machine interaction. Explanations are challenging in that they require many different forms of abstract knowledge and reasoning.…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
Cross-lingual summarization is the task of generating a summary in one language (e.g., English) for the given document(s) in a different language (e.g., Chinese). Under the globalization background, this task has attracted increasing…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words,…
Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like…
Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue…