Related papers: Basic Reasoning with Tensor Product Representation…

idely used recurrent units, including Long-short Term Memory (LSTM) and the Gated Recurrent Unit (GRU), perform well on natural language tasks, but their ability to learn structured representations is still questionable. Exploiting reduced…

An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…

We study machine learning formulations of inductive program synthesis; given input-output examples, we try to synthesize source code that maps inputs to corresponding outputs. Our aims are to develop new machine learning approaches based on…

We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural…

For a given base class of sequence-to-next-token generators, we consider learning prompt-to-answer mappings obtained by iterating a fixed, time-invariant generator for multiple steps, thus generating a chain-of-thought, and then taking the…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

In this note we give an elementary demonstration of the fact that AB=I implies BA=I for square matrices A,B with coefficients in a field K. By elementary we mean that our proof follows from the very definitions of matrix and product of a…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Expressive text encoders such as RNNs and Transformer Networks have been at the center of NLP models in recent work. Most of the effort has focused on sentence-level tasks, capturing the dependencies between words in a single sentence, or…

Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…

We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…

A core component of human intelligence is the ability to identify abstract patterns inherent in complex, high-dimensional perceptual data, as exemplified by visual reasoning tasks such as Raven's Progressive Matrices (RPM). Motivated by the…

In the pursuit of enhancing the efficacy and flexibility of interpretable, data-driven classification models, this work introduces a novel incorporation of user-defined preferences with Abstract Argumentation and Case-Based Reasoning (CBR).…

Large-scale, pre-trained language models (LMs) have achieved human-level performance on a breadth of language understanding tasks. However, evaluations only based on end task performance shed little light on machines' true ability in…

This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…

This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

In this paper, we investigate the problem of reasoning over natural language statements. Prior neural based approaches do not explicitly consider the inter-dependency among answers and their proofs. In this paper, we propose PRobr, a novel…

Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…