The application of graph neural networks (GNNs) to learn heuristic functions in classical planning is gaining traction. Despite the variety of methods proposed in the literature to encode classical planning tasks for GNNs, a comparative study evaluating their relative performances has been lacking. Moreover, some encodings have been assessed solely for their expressiveness rather than practical effectiveness in planning. This paper provides an extensive comparative analysis of existing encodings. Our results indicate that the smallest encoding based on Gaifman graphs, not yet applied in planning, outperforms the rest due to its fast evaluation times and the informativeness of the resulting heuristic. The overall coverage measured on the IPC almost reaches that of the state-of-the-art planner LAMA while exhibiting rather complementary strengths across different domains.

Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between the problem’s variables. While the framework has yielded promising results in various combinatorial problems, we show that the performance of PI-GNNs systematically plummets with an increasing density of the combinatorial problem graphs. Our analysis reveals an interesting phase transition in the PI-GNNs’ training dynamics, associated with degenerate solutions for the denser problems, highlighting a discrepancy between the relaxed, real-valued model outputs and the binary-valued problem solutions. To address the discrepancy, we propose principled alternatives to the naive strategy used in PI-GNNs by building on insights from fuzzy logic and binarized neural networks. Our experiments demonstrate that the portfolio of proposed methods significantly improves the performance of PI-GNNs in increasingly dense settings.

Transformer models have continuously expanded into all machine learning domains convertible to the underlying sequence-to-sequence representation, including tabular data. However, while ubiquitous, this representation restricts its extension to the more general case of relational databases . In this article, we introduce a modular neural message-passing scheme that closely adheres to the formal relational model, enabling direct end-to-end learning of tabular transformers from database storage systems. We address the associated challenges of appropriate learning data representation and loading, which are critical in the database setting, and compare our approach against a number of representative models from various related fields across a significantly wide range of datasets. Our results then demonstrate superior performance of this newly proposed class of neural architectures.

The Rubik's cube, a widely recognized combinatorial puzzle with an astronomically vast state space, has been the subject of various research experiments with neural networks used as heuristic estimators to navigate the state-space exploration. However, prior efforts have overlooked the intriguing symmetries inherent to this domain. Drawing on geometric deep learning principles, this article introduces a novel neural architecture that explicitly leverages these symmetries, grounded in a rigorous group-theoretical analysis. The design of the proposed symmetry-invariant model is then validated empirically through an innovative universal procedure for detecting model symmetry invariance. Finally, experimental results demonstrate that the symmetry-aware neural architecture exhibits enhanced generalization and problem-solving efficacy compared with the state of the art.

Graph Neural Networks (GNNs) have become the standard method of choice for learning with structured data, demonstrating particular promise in classical planning. Their inherent invariance under symmetries of the input graphs endows them with superior generalization capabilities, compared to their symmetry-oblivious counterparts. However, this comes at the cost of limited expressive power. Particularly, GNNs cannot distinguish between graphs that satisfy identical sentences of C2 logic. To leverage GNNs for learning policies in PDDL domains, one needs to encode the contextual representation of the planning states as graphs. The expressiveness of this encoding, coupled with a specific GNN architecture, then hinges on the absence of indistinguishable states necessitating distinct actions. This paper provides a comprehensive theoretical and statistical exploration of such situations in PDDL domains across diverse natural encoding schemes and GNN models.

Despite their significant success, all the existing deep neural architectures based on static computational graphs processing fixed tensor representations necessarily face fundamental limitations when presented with dynamically sized and structured data. Examples of these are sparse multi-relational structures present everywhere from biological networks and complex knowledge hyper-graphs to logical theories. Likewise, given the cryptic nature of generalization and representation learning in neural networks, potential integration with the sheer amounts of existing symbolic abstractions present in human knowledge remains highly problematic. Here, we argue that these abilities, naturally present in symbolic approaches based on the expressive power of relational logic, are necessary to be adopted for further progress of neural networks, and present a well founded learning framework for integration of deep and symbolic approaches based on the lifted modelling paradigm.

To perform sophisticated traffic analysis, such as intrusion detection, network monitoring tools firstly need to extract higher-level information from lower-level data by reconstructing events and activities from as primitive information as individual network packets or traffic flows. Aggregating communication data into meaningful entities is an open problem and existing, typically clustering-based, solutions are often highly suboptimal, producing results that may misinterpret the extracted information and consequently miss many network events. We propose a novel method for the extraction of various predefined types of network events from raw network flow data. The new method is based on analysis of computational properties of the event types as prescribed by their attributes in a given descriptive language. The corresponding events are then extracted with a supreme recall as compared to a respective event extraction part of an in-production intrusion detection system Camnep.

We propose a method to combine the interpretability and expressive power of firstorder logic with the effectiveness of neural network learning. In particular, we introduce a lifted framework in which first-order rules are used to describe the structure of a given problem setting. These rules are then used as a template for constructing a number of neural networks, one for each training and testing example. As the different networks corresponding to different examples share their weights, these weights can be efficiently learned using stochastic gradient descent. Our framework provides a flexible way for implementing and combining a wide variety of modelling constructs. In particular, the use of first-order logic allows for a declarative specification of latent relational structures, which can then be efficiently discovered in a given data set using neural network learning. Experiments on 78 relational learning benchmarks clearly demonstrate the effectiveness of the framework.