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 Constraint-Based Reasoning


Systems Challenges for Trustworthy Embodied Systems

arXiv.org Artificial Intelligence

A new generation of increasingly autonomous and self-learning systems, which we call embodied systems, is about to be developed. When deploying these systems into a real-life context we face various engineering challenges, as it is crucial to coordinate the behavior of embodied systems in a beneficial manner, ensure their compatibility with our human-centered social values, and design verifiably safe and reliable human-machine interaction. We are arguing that raditional systems engineering is coming to a climacteric from embedded to embodied systems, and with assuring the trustworthiness of dynamic federations of situationally aware, intent-driven, explorative, ever-evolving, largely non-predictable, and increasingly autonomous embodied systems in uncertain, complex, and unpredictable real-world contexts. We are also identifying a number of urgent systems challenges for trustworthy embodied systems, including robust and human-centric AI, cognitive architectures, uncertainty quantification, trustworthy self-integration, and continual analysis and assurance.


Lazy Lagrangians with Predictions for Online Learning

arXiv.org Machine Learning

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a Follow-The-Regularized-Leader iteration with prediction-adaptive dynamic steps. The algorithm achieves $\mathcal O(T^{\frac{3-\beta}{4}})$ regret and $\mathcal O(T^{\frac{1+\beta}{2}})$ constraint violation bounds that are tunable via parameter $\beta\!\in\![1/2,1)$ and have constant factors that shrink with the predictions quality, achieving eventually $\mathcal O(1)$ regret for perfect predictions. Our work extends the FTRL framework for this constrained OCO setting and outperforms the respective state-of-the-art greedy-based solutions, without imposing conditions on the quality of predictions, the cost functions or the geometry of constraints, beyond convexity.


Scaling Knowledge Graph Embedding Models

arXiv.org Artificial Intelligence

Developing scalable solutions for training Graph Neural Networks (GNNs) for link prediction tasks is challenging due to the high data dependencies which entail high computational cost and huge memory footprint. We propose a new method for scaling training of knowledge graph embedding models for link prediction to address these challenges. Towards this end, we propose the following algorithmic strategies: self-sufficient partitions, constraint-based negative sampling, and edge mini-batch training. Both, partitioning strategy and constraint-based negative sampling, avoid cross partition data transfer during training. In our experimental evaluation, we show that our scaling solution for GNN-based knowledge graph embedding models achieves a 16x speed up on benchmark datasets while maintaining a comparable model performance as non-distributed methods on standard metrics.


Super-Reparametrizations of Weighted CSPs: Properties and Optimization Perspective

arXiv.org Artificial Intelligence

The notion of reparametrizations of Weighted CSPs (WCSPs) (also known as equivalence-preserving transformations of WCSPs) is well-known and finds its use in many algorithms to approximate or bound the optimal WCSP value. In contrast, the concept of super-reparametrizations (which are changes of the weights that keep or increase the WCSP objective for every assignment) was already proposed but never studied in detail. To fill this gap, we present a number of theoretical properties of super-reparametrizations and compare them to those of reparametrizations. Furthermore, we propose a framework for computing upper bounds on the optimal value of the (maximization version of) WCSP using super-reparametrizations. We show that it is in principle possible to employ arbitrary (under some technical conditions) constraint propagation rules to improve the bound. For arc consistency in particular, the method reduces to the known Virtual AC (VAC) algorithm. Newly, we implemented the method for singleton arc consistency (SAC) and compared it to other strong local consistencies in WCSPs on a public benchmark. The results show that the bounds obtained from SAC are superior for many instance groups.


A Constraint Programming Approach to Weighted Isomorphic Mapping of Fragment-based Shape Signatures

arXiv.org Artificial Intelligence

Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference to the full underlying chemical structure, which is essential to deal with chemical databases containing millions of compounds. However, finding the optimal match of a part of the fragmented compound can be time-consuming. In this paper, we use constraint programming to solve this specific problem. It involves finding a weighted assignment of fragments subject to connectivity constraints. Our experiments demonstrate the practical relevance of our approach and open new perspectives, including generating multiple, diverse solutions. Our approach constitutes an original use of a constraint solver in a real time setting, where propagation allows to avoid an enumeration of weighted paths. The model must remain robust to the addition of constraints making some instances not tractable. This particular context requires the use of unusual criteria for the choice of the model: lightweight, standard propagation algorithms, data structures without prohibitive constant cost. The objective is not to design new, complex algorithms to solve difficult instances.


Constraint-based Diversification of JOP Gadgets

Journal of Artificial Intelligence Research

Modern software deployment process produces software that is uniform, and hence vulnerable to large-scale code-reuse attacks, such as Jump-Oriented Programming (JOP) attacks. Compiler-based diversification improves the resilience and security of software systems by automatically generating different assembly code versions of a given program. Existing techniques are efficient but do not have a precise control over the quality, such as the code size or speed, of the generated code variants.  This paper introduces Diversity by Construction (DivCon), a constraint-based compiler approach to software diversification. Unlike previous approaches, DivCon allows users to control and adjust the conflicting goals of diversity and code quality. A key enabler is the use of Large Neighborhood Search (LNS) to generate highly diverse assembly code efficiently. For larger problems, we propose a combination of LNS with a structural decomposition  of the problem. To further improve the diversification efficiency of DivCon against JOP attacks, we propose an application-specific distance measure tailored to the characteristics of JOP attacks.  We evaluate DivCon with 20 functions from a popular benchmark suite for embedded systems. These experiments show that DivCon's combination of LNS and our application-specific distance measure generates binary programs that are highly resilient against JOP  attacks (they share between 0.15% to 8% of JOP gadgets) with an optimality gap of 10%. Our results confirm that there is a trade-off between the quality of each assembly code version and the diversity of the entire pool of versions. In particular, the experiments  show that DivCon is able to generate binary programs that share a very small number of  gadgets, while delivering near-optimal code.  For constraint programming researchers and practitioners, this paper demonstrates that LNS is a valuable technique for finding diverse solutions. For security researchers and software  engineers, DivCon extends the scope of compiler-based diversification to performance-critical and resource-constrained applications.  


The effective noise of Stochastic Gradient Descent

arXiv.org Machine Learning

Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted according to the performance on this specific subset of examples. The mini-batch sampling procedure introduces a stochastic dynamics to the gradient descent, with a non-trivial state-dependent noise. We characterize the stochasticity of SGD and a recently-introduced variant, persistent SGD, in a prototypical neural network model. In the under-parametrized regime, where the final training error is positive, the SGD dynamics reaches a stationary state and we define an effective temperature from the fluctuation-dissipation theorem, computed from dynamical mean-field theory. We use the effective temperature to quantify the magnitude of the SGD noise as a function of the problem parameters. In the over-parametrized regime, where the training error vanishes, we measure the noise magnitude of SGD by computing the average distance between two replicas of the system with the same initialization and two different realizations of SGD noise. We find that the two noise measures behave similarly as a function of the problem parameters. Moreover, we observe that noisier algorithms lead to wider decision boundaries of the corresponding constraint satisfaction problem.


Pretrained Cost Model for Distributed Constraint Optimization Problems

arXiv.org Artificial Intelligence

Distributed Constraint Optimization Problems (DCOPs) are an important subclass of combinatorial optimization problems, where information and controls are distributed among multiple autonomous agents. Previously, Machine Learning (ML) has been largely applied to solve combinatorial optimization problems by learning effective heuristics. However, existing ML-based heuristic methods are often not generalizable to different search algorithms. Most importantly, these methods usually require full knowledge about the problems to be solved, which are not suitable for distributed settings where centralization is not realistic due to geographical limitations or privacy concerns. To address the generality issue, we propose a novel directed acyclic graph representation schema for DCOPs and leverage the Graph Attention Networks (GATs) to embed graph representations. Our model, GAT-PCM, is then pretrained with optimally labelled data in an offline manner, so as to construct effective heuristics to boost a broad range of DCOP algorithms where evaluating the quality of a partial assignment is critical, such as local search or backtracking search. Furthermore, to enable decentralized model inference, we propose a distributed embedding schema of GAT-PCM where each agent exchanges only embedded vectors, and show its soundness and complexity. Finally, we demonstrate the effectiveness of our model by combining it with a local search or a backtracking search algorithm. Extensive empirical evaluations indicate that the GAT-PCM-boosted algorithms significantly outperform the state-of-the-art methods in various benchmarks. The pretrained model is available at https://github.com/dyc941126/GAT-PCM.


SaDe: Learning Models that Provably Satisfy Domain Constraints

arXiv.org Artificial Intelligence

With increasing real world applications of machine learning, models are often required to comply with certain domain based requirements, e.g., safety guarantees in aircraft systems, legal constraints in a loan approval model. A natural way to represent these properties is in the form of constraints. Including such constraints in machine learning is typically done by the means of regularization, which does not guarantee satisfaction of the constraints. In this paper, we present a machine learning approach that can handle a wide variety of constraints, and guarantee that these constraints will be satisfied by the model even on unseen data. We cast machine learning as a maximum satisfiability problem, and solve it using a novel algorithm SaDe which combines constraint satisfaction with gradient descent. We demonstrate on three use cases that this approach learns models that provably satisfy the given constraints.


Enhanced Self-Organizing Map Solution for the Traveling Salesman Problem

arXiv.org Artificial Intelligence

Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the benchmark work brought consistent results and may inspire future efforts to improve this algorithm and apply it to different problems.