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Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a…

We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

Recurrent Neural Networks (RNNs) have been shown to capture various aspects of syntax from raw linguistic input. In most previous experiments, however, learning happens over unrealistic corpora, which do not reflect the type and amount of…

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and…

We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…

Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…

In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…

How can we best encode structured data into sequential form for use in large language models (LLMs)? In this work, we introduce a parameter-efficient method to explicitly represent structured data for LLMs. Our method, GraphToken, learns an…

Developments in Graph-Language Models (GLMs) aim to integrate the structural reasoning capabilities of Graph Neural Networks (GNNs) with the semantic understanding of Large Language Models (LLMs). However, we demonstrate that current…

Programming languages possess rich semantic information - such as data flow - that is represented by graphs and not available from the surface form of source code. Recent code language models have scaled to billions of parameters, but model…

We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…

Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax…

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.…

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic…

Humans naturally interpret numbers non-literally, effortlessly combining context, world knowledge, and speaker intent. We investigate whether large language models (LLMs) interpret numbers similarly, focusing on hyperbole and pragmatic halo…

We demonstrate a declarative differentiable programming framework based on the language of Lifted Relational Neural Networks, where small parameterized logic programs are used to encode relational learning scenarios. When presented with…

While large language models (LLMs) have advanced the field of natural language processing (NLP), their "black box" nature obscures their decision-making processes. To address this, researchers developed structured approaches using higher…

We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with…

The success of pretrained contextual encoders, such as ELMo and BERT, has brought a great deal of interest in what these models learn: do they, without explicit supervision, learn to encode meaningful notions of linguistic structure? If so,…