Related papers: Basic Reasoning with Tensor Product Representation…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Representation is a key notion in neuroscience and artificial intelligence (AI). However, a longstanding philosophical debate highlights that specifying what counts as representation is trickier than it seems. With this brief opinion paper…

Existing question answering systems can only predict answers without explicit reasoning processes, which hinder their explainability and make us overestimate their ability of understanding and reasoning over natural language. In this work,…

In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…

We introduce an architecture, the Tensor Product Recurrent Network (TPRN). In our application of TPRN, internal representations learned by end-to-end optimization in a deep neural network performing a textual question-answering (QA) task…

Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…

Abstractive summarization, the task of generating a concise summary of input documents, requires: (1) reasoning over the source document to determine the salient pieces of information scattered across the long document, and (2) composing a…

Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…

In this paper we study MapReduce computations from a complexity-theoretic perspective. First, we formulate a uniform version of the MRC model of Karloff et al. (2010). We then show that the class of regular languages, and moreover all of…

Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome…

Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…

Since the inception of the classicalist vs. connectionist debate, it has been argued that the ability to systematically combine symbol-like entities into compositional representations is crucial for human intelligence. In connectionist…

This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…

Sequential Recommendation (SeqRec) aims to predict the next item by capturing sequential patterns from users' historical interactions, playing a crucial role in many real-world recommender systems. However, existing approaches predominantly…

Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…

Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a…

We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…