The increasing level of autonomy of robots poses challenges of trust and social acceptance, especially in human-robot interaction scenarios. This requires an interpretable implementation of robotic cognitive capabilities, possibly based on formal methods as logics for the definition of task specifications. However, prior knowledge is often unavailable in complex realistic scenarios. In this paper, we propose an offline algorithm based on inductive logic programming from noisy examples to extract task specifications (i.e., action preconditions, constraints and effects) directly from raw data of few heterogeneous (i.e., not repetitive) robotic executions. Our algorithm leverages on the output of any unsupervised action identification algorithm from video-kinematic recordings. Combining it with the definition of very basic, almost task-agnostic, commonsense concepts about the environment, which contribute to the interpretability of our methodology, we are able to learn logical axioms encoding preconditions of actions, as well as their effects in the event calculus paradigm. Since the quality of learned specifications depends mainly on the accuracy of the action identification algorithm, we also propose an online framework for incremental refinement of task knowledge from user feedback, guaranteeing safe execution. Results in a standard manipulation task and benchmark for user training in the safety-critical surgical robotic scenario, show the robustness, data- and time-efficiency of our methodology, with promising results towards the scalability in more complex domains.
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent proof step, and reasoning about it, given the multitude of possibilities, remains a daunting task for novice users. To improve the situation, several investigations have developed machine learning based guidance for tactic selection. Such approaches struggle to learn non-trivial relationships between the chosen tactic and the structure of the proof state and represent them as symbolic expressions. To address these issues we (i) We represent the problem as an Inductive Logic Programming (ILP) task, (ii) Using the ILP representation we enriched the feature space by encoding additional, computationally expensive properties as background knowledge predicates, (iii) We use this enriched feature space to learn rules explaining when a tactic is applicable to a given proof state, (iv) we use the learned rules to filter the output of an existing tactic selection approach and empirically show improvement over the non-filtering approaches.
This paper presents PROB-IRM, an approach that learns robust reward machines (RMs) for reinforcement learning (RL) agents from noisy execution traces. The key aspect of RM-driven RL is the exploitation of a finite-state machine that decomposes the agent's task into different subtasks. PROB-IRM uses a state-of-the-art inductive logic programming framework robust to noisy examples to learn RMs from noisy traces using the Bayesian posterior degree of beliefs, thus ensuring robustness against inconsistencies. Pivotal for the results is the interleaving between RM learning and policy learning: a new RM is learned whenever the RL agent generates a trace that is believed not to be accepted by the current RM. To speed up the training of the RL agent, PROB-IRM employs a probabilistic formulation of reward shaping that uses the posterior Bayesian beliefs derived from the traces. Our experimental analysis shows that PROB-IRM can learn (potentially imperfect) RMs from noisy traces and exploit them to train an RL agent to solve its tasks successfully. Despite the complexity of learning the RM from noisy traces, agents trained with PROB-IRM perform comparably to agents provided with handcrafted RMs.
We introduce a novel approach to program synthesis that decomposes complex functional tasks into simpler relational synthesis sub-tasks. We demonstrate the effectiveness of our approach using an off-the-shelf inductive logic programming (ILP) system on three challenging datasets. Our results show that (i) a relational representation can outperform a functional one, and (ii) an off-the-shelf ILP system with a relational encoding can outperform domain-specific approaches.
We introduce AutoCoder, the first Large Language Model to surpass GPT-4 Turbo (April 2024) and GPT-4o in pass@1 on the Human Eval benchmark test ($\mathbf{90.9\%}$ vs. $\mathbf{90.2\%}$). In addition, AutoCoder offers a more versatile code interpreter compared to GPT-4 Turbo and GPT-4o. It's code interpreter can install external packages instead of limiting to built-in packages. AutoCoder's training data is a multi-turn dialogue dataset created by a system combining agent interaction and external code execution verification, a method we term \textbf{\textsc{AIEV-Instruct}} (Instruction Tuning with Agent-Interaction and Execution-Verified). Compared to previous large-scale code dataset generation methods, \textsc{AIEV-Instruct} reduces dependence on proprietary large models and provides execution-validated code dataset. The code and the demo video is available in \url{https://github.com/bin123apple/AutoCoder}.
A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use constraint solvers to efficiently join rules. Our experiments on many domains, including game playing and drug design, show that our approach can (i) learn rules with more than 100 literals, and (ii) drastically outperform existing approaches in terms of predictive accuracies.
With the ever-increasing potential of AI to perform personalised tasks, it is becoming essential to develop new machine learning techniques which are data-efficient and do not require hundreds or thousands of training data. In this paper, we explore an Inductive Logic Programming approach for one-shot text classification. In particular, we explore the framework of Meta-Interpretive Learning (MIL), along with using common-sense background knowledge extracted from ConceptNet. Results indicate that MIL can learn text classification rules from a small number of training examples. Moreover, the higher complexity of chosen examples, the higher accuracy of the outcome.
Many inductive logic programming approaches struggle to learn programs from noisy data. To overcome this limitation, we introduce an approach that learns minimal description length programs from noisy data, including recursive programs. Our experiments on several domains, including drug design, game playing, and program synthesis, show that our approach can outperform existing approaches in terms of predictive accuracies and scale to moderate amounts of noise.
We introduce the higher-order refactoring problem, where the goal is to compress a logic program by discovering higher-order abstractions, such as map, filter, and fold. We implement our approach in Stevie, which formulates the refactoring problem as a constraint optimisation problem. Our experiments on multiple domains, including program synthesis and visual reasoning, show that refactoring can improve the learning performance of an inductive logic programming system, specifically improving predictive accuracies by 27% and reducing learning times by 47%. We also show that Stevie can discover abstractions that transfer to multiple domains.
Partially Observable Monte Carlo Planning (POMCP) is an efficient solver for Partially Observable Markov Decision Processes (POMDPs). It allows scaling to large state spaces by computing an approximation of the optimal policy locally and online, using a Monte Carlo Tree Search based strategy. However, POMCP suffers from sparse reward function, namely, rewards achieved only when the final goal is reached, particularly in environments with large state spaces and long horizons. Recently, logic specifications have been integrated into POMCP to guide exploration and to satisfy safety requirements. However, such policy-related rules require manual definition by domain experts, especially in real-world scenarios. In this paper, we use inductive logic programming to learn logic specifications from traces of POMCP executions, i.e., sets of belief-action pairs generated by the planner. Specifically, we learn rules expressed in the paradigm of answer set programming. We then integrate them inside POMCP to provide soft policy bias toward promising actions. In the context of two benchmark scenarios, rocksample and battery, we show that the integration of learned rules from small task instances can improve performance with fewer Monte Carlo simulations and in larger task instances. We make our modified version of POMCP publicly available at https://github.com/GiuMaz/pomcp_clingo.git.
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention. Combining these two features allows an ILP system to generalise better by learning rules with universally quantified body-only variables. We implement our idea in NOPI, which can learn normal logic programs with predicate invention, including Datalog programs with stratified negation. Our experimental results on multiple domains show that our approach can improve predictive accuracies and learning times.
Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NUMSYNTH, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.
Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In contrast, gradient descent provides an efficient way to find solutions within such high-dimensional spaces. Neuro-symbolic ILP approaches have not fully exploited this so far. We propose extending the {\delta}ILP approach to inductive synthesis with large-scale predicate invention, thus allowing us to exploit the efficacy of high-dimensional gradient descent. We show that large-scale predicate invention benefits differentiable inductive synthesis through gradient descent and allows one to learn solutions for tasks beyond the capabilities of existing neuro-symbolic ILP systems. Furthermore, we achieve these results without specifying the precise structure of the solution within the language bias.
A magic value in a program is a constant symbol that is essential for the execution of the program but has no clear explanation for its choice. Learning programs with magic values is difficult for existing program synthesis approaches. To overcome this limitation, we introduce an inductive logic programming approach to efficiently learn programs with magic values. Our experiments on diverse domains, including program synthesis, drug design, and game playing, show that our approach can (i) outperform existing approaches in terms of predictive accuracies and learning times, (ii) learn magic values from infinite domains, such as the value of pi, and (iii) scale to domains with millions of constant symbols.
Inductive logic reasoning is a fundamental task in graph analysis, which aims to generalize patterns from data. This task has been extensively studied for traditional graph representations, such as knowledge graphs (KGs), using techniques like inductive logic programming (ILP). Existing ILP methods assume learning from KGs with static facts and binary relations. Beyond KGs, graph structures are widely present in other applications such as procedural instructions, scene graphs, and program executions. While ILP is beneficial for these applications, applying it to those graphs is nontrivial: they are more complex than KGs, which usually involve timestamps and n-ary relations, effectively a type of hypergraph with temporal events. In this work, we propose temporal inductive logic reasoning (TILR), an ILP method that reasons on temporal hypergraphs. To enable hypergraph reasoning, we introduce the multi-start random B-walk, a novel graph traversal method for hypergraphs. By combining it with a path-consistency algorithm, TILR learns logic rules by generalizing from both temporal and relational data. To address the lack of hypergraph benchmarks, we create and release two temporal hypergraph datasets: YouCook2-HG and nuScenes-HG. Experiments on these benchmarks demonstrate that TILR achieves superior reasoning capability over various strong baselines.
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an approach where we learn small non-separable programs and combine them. We implement our approach in a constraint-driven ILP system. Our approach can learn optimal and recursive programs and perform predicate invention. Our experiments on multiple domains, including game playing and program synthesis, show that our approach can drastically outperform existing approaches in terms of predictive accuracies and learning times, sometimes reducing learning times from over an hour to a few seconds.
Relational machine learning programs like those developed in Inductive Logic Programming (ILP) offer several advantages: (1) The ability to model complex relationships amongst data instances; (2) The use of domain-specific relations during model construction; and (3) The models constructed are human-readable, which is often one step closer to being human-understandable. However, these ILP-like methods have not been able to capitalise fully on the rapid hardware, software and algorithmic developments fuelling current developments in deep neural networks. In this paper, we treat relational features as functions and use the notion of generalised composition of functions to derive complex functions from simpler ones. We formulate the notion of a set of $\text{M}$-simple features in a mode language $\text{M}$ and identify two composition operators ($\rho_1$ and $\rho_2$) from which all possible complex features can be derived. We use these results to implement a form of "explainable neural network" called Compositional Relational Machines, or CRMs, which are labelled directed-acyclic graphs. The vertex-label for any vertex $j$ in the CRM contains a feature-function $f_j$ and a continuous activation function $g_j$. If $j$ is a "non-input" vertex, then $f_j$ is the composition of features associated with vertices in the direct predecessors of $j$. Our focus is on CRMs in which input vertices (those without any direct predecessors) all have $\text{M}$-simple features in their vertex-labels. We provide a randomised procedure for constructing and learning such CRMs. Using a notion of explanations based on the compositional structure of features in a CRM, we provide empirical evidence on synthetic data of the ability to identify appropriate explanations; and demonstrate the use of CRMs as 'explanation machines' for black-box models that do not provide explanations for their predictions.
The topic of comprehensibility of machine-learned theories has recently drawn increasing attention. Inductive Logic Programming (ILP) uses logic programming to derive logic theories from small data based on abduction and induction techniques. Learned theories are represented in the form of rules as declarative descriptions of obtained knowledge. In earlier work, the authors provided the first evidence of a measurable increase in human comprehension based on machine-learned logic rules for simple classification tasks. In a later study, it was found that the presentation of machine-learned explanations to humans can produce both beneficial and harmful effects in the context of game learning. We continue our investigation of comprehensibility by examining the effects of the ordering of concept presentations on human comprehension. In this work, we examine the explanatory effects of curriculum order and the presence of machine-learned explanations for sequential problem-solving. We show that 1) there exist tasks A and B such that learning A before B has a better human comprehension with respect to learning B before A and 2) there exist tasks A and B such that the presence of explanations when learning A contributes to improved human comprehension when subsequently learning B. We propose a framework for the effects of sequential teaching on comprehension based on an existing definition of comprehensibility and provide evidence for support from data collected in human trials. Empirical results show that sequential teaching of concepts with increasing complexity a) has a beneficial effect on human comprehension and b) leads to human re-discovery of divide-and-conquer problem-solving strategies, and c) studying machine-learned explanations allows adaptations of human problem-solving strategy with better performance.
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily-solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.
The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first discovers where not to search. We use given BK to discover constraints on hypotheses, such as that a number cannot be both even and odd. We use the constraints to bootstrap a constraint-driven ILP system. Our experiments on multiple domains (including program synthesis and game playing) show that our approach can (i) substantially reduce learning times by up to 97%, and (ii) scale to domains with millions of facts.