Related papers: Peano: Learning Formal Mathematical Reasoning
Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Computational learning approaches to solving visual reasoning tests, such as Raven's Progressive Matrices (RPM), critically depend on the ability to identify the visual concepts used in the test (i.e., the representation) as well as the…
Learning to code, and more broadly, learning about computer science is a growing field of activity and research. Under the label of computational thinking, computational concepts are increasingly used as cognitive tools in many subject…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts…
Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic…
Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weight…
Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications.…
Humans learn compositional and causal abstraction, \ie, knowledge, in response to the structure of naturalistic tasks. When presented with a problem-solving task involving some objects, toddlers would first interact with these objects to…
Humans flexibly solve new problems that differ qualitatively from those they were trained on. This ability to generalize is supported by learned concepts that capture structure common across different problems. Here we develop a…
With the rapid development of deep learning, most of current state-of-the-art techniques in natural langauge processing are based on deep learning models trained with argescaled static textual corpora. However, we human beings learn and…
We present AlgCo (Algebraic Coinductives), a practical framework for inductive reasoning over commonly used coinductive types such as conats, streams, and infinitary trees with finite branching factor. The key idea is to exploit the notion…
The currently dominating artificial intelligence and machine learning technology, neural networks, builds on inductive statistical learning. Neural networks of today are information processing systems void of understanding and reasoning…
Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform…
A hallmark of human intelligence is the ability to infer abstract rules from limited experience and apply these rules to unfamiliar situations. This capacity is widely studied in the visual domain using the Raven's Progressive Matrices.…
Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of…
Learning abstractions directly from data is a core challenge in robotics. Humans naturally operate at an abstract level, reasoning over high-level subgoals while delegating execution to low-level motor skills -- an ability that enables…
How did humanity coax mathematics from the aether? We explore the Platonic view that mathematics can be discovered from its axioms - a game of conjecture and proof. We describe Minimo (Mathematics from Intrinsic Motivation): an agent that…