Algorithms, while straightforward in theory, become challenging to deploy in real-world scenarios.

Algorithms, while straightforward in theory, become challenging to deploy in real-world scenarios.

We introduce an unsupervised learning algorithm that combines probabilistic modeling with solver-based techniques for program synthesis. We apply our techniques to both a visual learning domain and a language learning problem, showing that our algorithm can learn many visual concepts from only a few examples and that it can recover some English inflectional morphology. Taken together, these results give both a new approach to unsupervised learning of symbolic compositional structures, and a technique for applying program synthesis tools to noisy data.

In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to represent the semantic difference between syntactically equivalent expressions. We then construct a diagrammatic calculus to model parsing and handling of effects, providing a method to efficiently compute the denotations for sentences.

Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We make the case that human languages are similarly organized around the give and pull of pure values and impure processes, and we'll aim to show how denotational techniques from computer science can be leveraged to support elegant and illuminating analyses of natural language composition.

We develop an algorithm to semantically parse linear ordering problems, which require a model to arrange entities using deductive reasoning. Our method takes as input a number of premises and candidate statements, parsing them to a first-order logic of an ordering domain, and then utilizes constraint logic programming to infer the truth of proposed statements about the ordering. Our semantic parser transforms Heim and Kratzer's syntax-based compositional formal semantic rules to a computational algorithm. This transformation involves introducing abstract types and templates based on their rules, and introduces a dynamic component to interpret entities within a contextual framework. Our symbolic system, the Formal Semantic Logic Inferer (FSLI), is applied to answer multiple choice questions in BIG-bench's logical_deduction multiple choice problems, achieving perfect accuracy, compared to 67.06% for the best-performing LLM (GPT-4) and 87.63% for the hybrid system Logic-LM. These promising results demonstrate the benefit of developing a semantic parsing algorithm driven by first-order logic constructs.

We investigates the concept of strong equivalence within the extended framework of Answer Set Programming with constraints. Two groups of rules are considered strongly equivalent if, informally speaking, they have the same meaning in any context. We demonstrate that, under certain assumptions, strong equivalence between rule sets in this extended setting can be precisely characterized by their equivalence in the logic of Here-and-There with constraints. Furthermore, we present a translation from the language of several clingo-based answer set solvers that handle constraints into the language of Here-and-There with constraints. This translation enables us to leverage the logic of Here-and-There to reason about strong equivalence within the context of these solvers. We also explore the computational complexity of determining strong equivalence in this context.

Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of the GNN matches an iteration of the algorithm. In this paper we study neurally solving algorithms from a different perspective: since the algorithm's solution is often an equilibrium, it is possible to find the solution directly by solving an equilibrium equation. Our approach requires no information on the ground-truth number of steps of the algorithm, both during train and test time. Furthermore, the proposed method improves the performance of GNNs on executing algorithms and is a step towards speeding up existing NAR models. Our empirical evidence, leveraging algorithms from the CLRS-30 benchmark, validates that one can train a network to solve algorithmic problems by directly finding the equilibrium. We discuss the practical implementation of such models and propose regularisations to improve the performance of these equilibrium reasoners.

Recently, a simple but powerful language for expressing and learning general policies and problem decompositions (sketches) has been introduced in terms of rules defined over a set of Boolean and numerical features. In this work, we consider three extensions of this language aimed at making policies and sketches more flexible and reusable: internal memory states, as in finite state controllers; indexical features, whose values are a function of the state and a number of internal registers that can be loaded with objects; and modules that wrap up policies and sketches and allow them to call each other by passing parameters. In addition, unlike general policies that select state transitions rather than ground actions, the new language allows for the selection of such actions. The expressive power of the resulting language for policies and sketches is illustrated through a number of examples.

We introduce an unsupervised learning algorithm that combines probabilistic modeling with solver-based techniques for program synthesis. We apply our techniques to both a visual learning domain and a language learning problem, showing that our algorithm can learn many visual concepts from only a few examples and that it can recover some English inflectional morphology. Taken together, these results give both a new approach to unsupervised learning of symbolic compositional structures, and a technique for applying program synthesis tools to noisy data.