相关论文: Learning Formal Mathematics From Intrinsic Motivat…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
Humans excel in grasping objects through diverse and robust policies, many of which are so probabilistically rare that exploration-based learning methods hardly observe and learn. Inspired by the human learning process, we propose a method…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
Humans integrate multiple sensory modalities (e.g. visual and audio) to build a causal understanding of the physical world. In this work, we propose a novel type of intrinsic motivation for Reinforcement Learning (RL) that encourages the…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We consider an agent's uncertainty about its environment and the problem of generalizing this uncertainty across observations. Specifically, we focus on the problem of exploration in non-tabular reinforcement learning. Drawing inspiration…
In reinforcement learning, an agent interacts sequentially with an environment to maximize a reward, receiving only partial, probabilistic feedback. This creates a fundamental exploration-exploitation trade-off: the agent must explore to…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains…
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept…
Agent-based models (ABMs) are simulation models used in economics to overcome some of the limitations of traditional frameworks based on general equilibrium assumptions. However, agents within an ABM follow predetermined 'bounded rational'…
Although most theories posit that natural behavior can be explained as maximizing some form of extrinsic reward, often called utility, some behaviors appear to be reward independent. For instance, spontaneous motor babbling in human…
This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…
Learning complex robot behavior through interactions with the environment necessitates principled exploration. Effective strategies should prioritize exploring regions of the state-action space that maximize rewards, with optimistic…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Formal mathematics is mathematics done within the framework of a formal logic. It offers major benefits to mathematicians as well as to computing professionals, engineers, and scientists who use mathematics in their work. The standard…