Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations. Our approach is based on a stabilization term that, when added to the original dynamics, renders the constraint manifold provably asymptotically stable. Due to its simplicity, our method is compatible with all common neural differential equation (NDE) models and broadly applicable. In extensive empirical evaluations, we demonstrate that SNDEs outperform existing methods while broadening the types of constraints that can be incorporated into NDE training.
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Mitigating the disparate impact of statistical machine learning methods is crucial for ensuring fairness. While extensive research aims to reduce disparity, the effect of using a \emph{finite dataset} -- as opposed to the entire population -- remains unclear. This paper explores the statistical foundations of fair binary classification with two protected groups, focusing on controlling demographic disparity, defined as the difference in acceptance rates between the groups. Although fairness may come at the cost of accuracy even with infinite data, we show that using a finite sample incurs additional costs due to the need to estimate group-specific acceptance thresholds. We study the minimax optimal classification error while constraining demographic disparity to a user-specified threshold. To quantify the impact of fairness constraints, we introduce a novel measure called \emph{fairness-aware excess risk} and derive a minimax lower bound on this measure that all classifiers must satisfy. Furthermore, we propose FairBayes-DDP+, a group-wise thresholding method with an offset that we show attains the minimax lower bound. Our lower bound proofs involve several innovations. Experiments support that FairBayes-DDP+ controls disparity at the user-specified level, while being faster and having a more favorable fairness-accuracy tradeoff than several baselines.
Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-developed in the literature. It is common practice to introduce a measurement error into SAR models. The measurement error serves to distinguish the noise component from the spatial process. However, the previous literature has not considered adding a measurement error to the SAR models with missing data. The maximum likelihood estimation for such models with large datasets is challenging and computationally expensive. This paper proposes two efficient likelihood-based estimation methods: the marginal maximum likelihood (ML) and expectation-maximisation (EM) algorithms for estimating SAR models with both measurement errors and missing data in the response variable. The spatial error model (SEM) and the spatial autoregressive model (SAM), two popular SAR model types, are considered. The missing data mechanism is assumed to follow missing at random (MAR). While naive calculation approaches lead to computational complexities of $O(n^3)$, where n is the total number of observations, our computational approaches for both the marginal ML and EM algorithms are designed to reduce the computational complexity. The performance of the proposed methods is investigated empirically using simulated and real datasets.
Visual planning methods are promising to handle complex settings where extracting the system state is challenging. However, none of the existing works tackles the case of multiple heterogeneous agents which are characterized by different capabilities and/or embodiment. In this work, we propose a method to realize visual action planning in multi-agent settings by exploiting a roadmap built in a low-dimensional structured latent space and used for planning. To enable multi-agent settings, we infer possible parallel actions from a dataset composed of tuples associated with individual actions. Next, we evaluate feasibility and cost of them based on the capabilities of the multi-agent system and endow the roadmap with this information, building a capability latent space roadmap (C-LSR). Additionally, a capability suggestion strategy is designed to inform the human operator about possible missing capabilities when no paths are found. The approach is validated in a simulated burger cooking task and a real-world box packing task.
The efficacy of machine learning has traditionally relied on the availability of increasingly larger datasets. However, large datasets pose storage challenges and contain non-influential samples, which could be ignored during training without impacting the final accuracy of the model. In response to these limitations, the concept of distilling the information on a dataset into a condensed set of (synthetic) samples, namely a distilled dataset, emerged. One crucial aspect is the selected architecture (usually ConvNet) for linking the original and synthetic datasets. However, the final accuracy is lower if the employed model architecture differs from the model used during distillation. Another challenge is the generation of high-resolution images, e.g., 128x128 and higher. In this paper, we propose Latent Dataset Distillation with Diffusion Models (LD3M) that combine diffusion in latent space with dataset distillation to tackle both challenges. LD3M incorporates a novel diffusion process tailored for dataset distillation, which improves the gradient norms for learning synthetic images. By adjusting the number of diffusion steps, LD3M also offers a straightforward way of controlling the trade-off between speed and accuracy. We evaluate our approach in several ImageNet subsets and for high-resolution images (128x128 and 256x256). As a result, LD3M consistently outperforms state-of-the-art distillation techniques by up to 4.8 p.p. and 4.2 p.p. for 1 and 10 images per class, respectively.
Symbolic reasoning systems have been used in cognitive architectures to provide inference and planning capabilities. However, defining domains and problems has proven difficult and prone to errors. Moreover, Large Language Models (LLMs) have emerged as tools to process natural language for different tasks. In this paper, we propose the use of LLMs to tackle these problems. This way, this paper proposes the integration of LLMs in the ROS 2-integrated cognitive architecture MERLIN2 for autonomous robots. Specifically, we present the design, development and deployment of how to leverage the reasoning capabilities of LLMs inside the deliberative processes of MERLIN2. As a result, the deliberative system is updated from a PDDL-based planner system to a natural language planning system. This proposal is evaluated quantitatively and qualitatively, measuring the impact of incorporating the LLMs in the cognitive architecture. Results show that a classical approach achieves better performance but the proposed solution provides an enhanced interaction through natural language.
Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
Incorporating knowledge graph into recommender systems has attracted increasing attention in recent years. By exploring the interlinks within a knowledge graph, the connectivity between users and items can be discovered as paths, which provide rich and complementary information to user-item interactions. Such connectivity not only reveals the semantics of entities and relations, but also helps to comprehend a user's interest. However, existing efforts have not fully explored this connectivity to infer user preferences, especially in terms of modeling the sequential dependencies within and holistic semantics of a path. In this paper, we contribute a new model named Knowledge-aware Path Recurrent Network (KPRN) to exploit knowledge graph for recommendation. KPRN can generate path representations by composing the semantics of both entities and relations. By leveraging the sequential dependencies within a path, we allow effective reasoning on paths to infer the underlying rationale of a user-item interaction. Furthermore, we design a new weighted pooling operation to discriminate the strengths of different paths in connecting a user with an item, endowing our model with a certain level of explainability. We conduct extensive experiments on two datasets about movie and music, demonstrating significant improvements over state-of-the-art solutions Collaborative Knowledge Base Embedding and Neural Factorization Machine.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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