Besides standard latent subsymbolic variables, our model exploits a probabilistic logic program to define a further structured representation, which is used for logical reasoning. The entire process is end-to-end differentiable. Once trained, VAEL can solve new unseen generation tasks by (i) leveraging the previously acquired knowledge encoded in the neural component and (ii) exploiting new logical programs on the structured latent space. Our experiments provide support on the benefits of this neuro-symbolic integration both in terms of task generalization and data efficiency. To the best of our knowledge, this work is the first to propose a general-purpose end-to-end framework integrating probabilistic logic programming into a deep generative model.

We present a neural program synthesis approach integrating components which write, execute, and assess code to navigate the search space of possible programs. We equip the search process with an interpreter or a read-eval-print-loop (REPL), which immediately executes partially written programs, exposing their semantics. The REPL addresses a basic challenge of program synthesis: tiny changes in syntax can lead to huge changes in semantics. We train a pair of models, a policy that proposes the new piece of code to write, and a value function that assesses the prospects of the code written so-far. At test time we can combine these models with a Sequential Monte Carlo algorithm.

Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver. Specifically, an LLM only translates a natural language problem into a satisfiability (SAT) problem that consists of first-order logic formulas, and a sound symbolic solver returns a mathematically correct solution. However, we discover that LLMs have difficulties to capture complex logical semantics hidden in the natural language during translation. To resolve this limitation, we propose a Compositional First-Order Logic Translation. An LLM first parses a natural language sentence into newly defined logical dependency structures that consist of an atomic subsentence and its dependents, then sequentially translate the parsed subsentences. Since multiple logical dependency structures and sequential translations are possible for a single sentence, we also introduce two Verification algorithms to ensure more reliable results. We utilize an SAT solver to rigorously compare semantics of generated first-order logic formulas and select the most probable one. We evaluate the proposed method, dubbed CLOVER, on seven logical reasoning benchmarks and show that it outperforms the previous neurosymbolic approaches and achieves new state-of-the-art results. Logical reasoning involves reaching conclusions through a structured process. It entails drawing inferences by converting the information provided in a set of premises into a final conclusion (Nunes, 2012; Bronkhorst et al., 2020). Logical reasoning ability is one of the most challenging metrics to measure intelligence. As the language model size grows exponentially, large language models (LLMs) (Brown, 2020; Chen et al., 2021; Thoppilan et al., 2022) unlock the ability of machine to reason. Chain-of-thought (CoT) prompting (Wei et al., 2022) significantly improve the performance of LLMs on simple logical reasoning tasks that require few forward reasoning steps. However, CoT falls short in complex logical reasoning tasks which need longer sequence of reasoning (Ye et al., 2024; Pan et al., 2023).

The goal of program synthesis from examples is to find a computer program that is consistent with a given set of input-output examples. Most learning-based approaches try to find a program that satisfies all examples at once. Our work, by contrast, considers an approach that breaks the problem into two stages: (a) find programs that satisfy only one example, and (b) leverage these per-example solutions to yield a program that satisfies all examples. We introduce the Cross Aggregator neural network module based on a multi-head attention mechanism that learns to combine the cues present in these per-example solutions to synthesize a global solution. Evaluation across programs of different lengths and under two different experimental settings reveal that when given the same time budget, our technique significantly improves the success rate over PCCoder [Zohar et.

Program synthesis aims to automatically generate an executable program that conforms to the given specification. Recent advancements have demonstrated that deep neural methodologies and large-scale pretrained language models are highly proficient in capturing program semantics.For robot programming, prior works have facilitated program synthesis by incorporating global environments. However, the assumption of acquiring a comprehensive understanding of the entire environment is often excessively challenging to achieve.In this work, we present a framework that learns to synthesize a program by rectifying potentially erroneous code segments, with the aid of partially observed environments. To tackle the issue of inadequate attention to partial observations, we propose to first learn an environment embedding space that can implicitly evaluate the impacts of each program token based on the precondition. Furthermore, by employing a graph structure, the model can aggregate both environmental and syntactic information flow and furnish smooth program rectification guidance.Extensive experimental evaluations and ablation studies on the partially observed VizDoom domain authenticate that our method offers superior generalization capability across various tasks and greater robustness when encountering noises.

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge.

This paper describes a Reinforcement Learning algorithm adapted to settings with sparse reward and weak supervision, and applies it to program synthesis, achieving state-of-the-art and even outperforming baselines with full supervision. The two first sections explain very clearly the motivation of this work, presenting the current limitations of reinforcement learning for tasks like contextual program synthesis. It is nicely written and pleasant to read. Section 3 presents the Reinforcement Learning framework that is the basis of the proposal, where the goal is to find a food approximation of the expected return objective. Section 4 presents the MAPO algorithm and his three key points: "(1) distributed sampling from inside and outside memory with an actor-learner architecture; (2) a marginal likelihood constraint over the memory to accelerate training; (3) systematic exploration to discover new high reward trajectories" (I did not find a better phrasing to summarize than the one in the abstract and the conclusion).

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented as basic action theories. A refinement mapping specifies how each high-level action is implemented by a low-level ConGolog program and how each high-level fluent can be translated into a low-level formula. We define a notion of sound abstraction between such action theories in terms of the existence of a suitable bisimulation between their respective models. Sound abstractions have many useful properties that ensure that we can reason about the agent's actions (e.g., executability, projection, and planning) at the abstract level, and refine and concretely execute them at the low level. We also characterize the notion of complete abstraction where all actions (including exogenous ones) that the high level thinks can happen can in fact occur at the low level. To facilitate verifying that one has a sound/complete abstraction relative to a mapping, we provide a set of necessary and sufficient conditions. Finally, we identify a set of basic action theory constraints that ensure that for any low-level action sequence, there is a unique high-level action sequence that it refines. This allows us to track/monitor what the low-level agent is doing and describe it in abstract terms (i.e., provide high-level explanations, for instance, to a client or manager).

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

Summary of paper ---------------- The paper presents a novel class of models, termed Neural Theorem Provers (NTPs), for automated knowledge base completion and automated theorem proving, using a deep neural network architecture. The recursive construction of the network is inspired by the backward chaining algorithm typically employed in logic programming (i.e., using the basic operations unification, conjunction and disjunction). Instead of directly operating on symbols, the neural network is employed to learn subsymbolic vector representations of entities and predicates, which are then exploited for assessing the similarity of symbols. Since the proposed architecture is fully differentiable, knowledge base completion can be performed using gradient descent. Thus, following the fundamental philosophy of neural-symbolic systems, the paper aims at combining the advantages of symbolic reasoning with those of subsymbolic inference.