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Implicit graph neural networks (GNNs) have emerged as a potential approach to enable GNNs to capture long-range dependencies effectively. However, poorly designed implicit GNN layers can experience over-smoothing or may have limited adaptability to learn data geometry, potentially hindering their performance in graph learning problems. To address these issues, we introduce a geometric framework to design implicit graph diffusion layers based on a parameterized graph Laplacian operator. Our framework allows learning the geometry of vertex and edge spaces, as well as the graph gradient operator from data. We further show how implicit GNN layers can be viewed as the fixed-point solution of a Dirichlet energy minimization problem and give conditions under which it may suffer from over-smoothing. To overcome the over-smoothing problem, we design our implicit graph diffusion layer as the solution of a Dirichlet energy minimization problem with constraints on vertex features, enabling it to trade off smoothing with the preservation of node feature information. With an appropriate hyperparameter set to be larger than the largest eigenvalue of the parameterized graph Laplacian, our framework guarantees a unique equilibrium and quick convergence. Our models demonstrate better performance than leading implicit and explicit GNNs on benchmark datasets for node and graph classification tasks, with substantial accuracy improvements observed for some datasets.

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.

The design of a neural image compression network is governed by how well the entropy model matches the true distribution of the latent code. Apart from the model capacity, this ability is indirectly under the effect of how close the relaxed quantization is to the actual hard quantization. Optimizing the parameters of a rate-distortion variational autoencoder (R-D VAE) is ruled by this approximated quantization scheme. In this paper, we propose a feature-level frequency disentanglement to help the relaxed scalar quantization achieve lower bit rates by guiding the high entropy latent features to include most of the low-frequency texture of the image. In addition, to strengthen the de-correlating power of the transformer-based analysis/synthesis transform, an augmented self-attention score calculation based on the Hadamard product is utilized during both encoding and decoding. Channel-wise autoregressive entropy modeling takes advantage of the proposed frequency separation as it inherently directs high-informational low-frequency channels to the first chunks and conditions the future chunks on it. The proposed network not only outperforms hand-engineered codecs, but also neural network-based codecs built on computation-heavy spatially autoregressive entropy models.

Adversarial training (AT) is widely considered the state-of-the-art technique for improving the robustness of deep neural networks (DNNs) against adversarial examples (AE). Nevertheless, recent studies have revealed that adversarially trained models are prone to unfairness problems, restricting their applicability. In this paper, we empirically observe that this limitation may be attributed to serious adversarial confidence overfitting, i.e., certain adversarial examples with overconfidence. To alleviate this problem, we propose HAM, a straightforward yet effective framework via adaptive Hard Adversarial example Mining.HAM concentrates on mining hard adversarial examples while discarding the easy ones in an adaptive fashion. Specifically, HAM identifies hard AEs in terms of their step sizes needed to cross the decision boundary when calculating loss value. Besides, an early-dropping mechanism is incorporated to discard the easy examples at the initial stages of AE generation, resulting in efficient AT. Extensive experimental results on CIFAR-10, SVHN, and Imagenette demonstrate that HAM achieves significant improvement in robust fairness while reducing computational cost compared to several state-of-the-art adversarial training methods. The code will be made publicly available.

Visual Question Answering (VQA) based on multi-modal data facilitates real-life applications such as home robots and medical diagnoses. One significant challenge is to devise a robust decentralized learning framework for various client models where centralized data collection is refrained due to confidentiality concerns. This work aims to tackle privacy-preserving VQA by decoupling a multi-modal model into representation modules and a contrastive module and leveraging inter-module gradients sharing and inter-client weight sharing. To this end, we propose Bidirectional Contrastive Split Learning (BiCSL) to train a global multi-modal model on the entire data distribution of decentralized clients. We employ the contrastive loss that enables a more efficient self-supervised learning of decentralized modules. Comprehensive experiments are conducted on the VQA-v2 dataset based on five SOTA VQA models, demonstrating the effectiveness of the proposed method. Furthermore, we inspect BiCSL's robustness against a dual-key backdoor attack on VQA. Consequently, BiCSL shows much better robustness to the multi-modal adversarial attack compared to the centralized learning method, which provides a promising approach to decentralized multi-modal learning.

Optical flow and disparity are two informative visual features for autonomous driving perception. They have been used for a variety of applications, such as obstacle and lane detection. The concept of "U-V-Disparity" has been widely explored in the literature, while its counterpart in optical flow has received relatively little attention. Traditional motion analysis algorithms estimate optical flow by matching correspondences between two successive video frames, which limits the full utilization of environmental information and geometric constraints. Therefore, we propose a novel strategy to model optical flow in the collision-free space (also referred to as drivable area or simply freespace) for intelligent vehicles, with the full utilization of geometry information in a 3D driving environment. We provide explicit representations of optical flow and deduce the quadratic relationship between the optical flow component and the vertical coordinate. Through extensive experiments on several public datasets, we demonstrate the high accuracy and robustness of our model. Additionally, our proposed freespace optical flow model boasts a diverse array of applications within the realm of automated driving, providing a geometric constraint in freespace detection, vehicle localization, and more. We have made our source code publicly available at //mias.group/FSOF.

Hyperproperties extend trace properties to express properties of sets of traces, and they are increasingly popular in specifying various security and performance-related properties in domains such as cyber-physical systems, smart grids, and automotive. This paper introduces a model checking algorithm for a new formalism, HyperTWTL, which extends Time Window Temporal Logic (TWTL) -- a domain-specific formal specification language for robotics, by allowing explicit and simultaneous quantification over multiple execution traces. We present HyperTWTL with both \emph{synchronous} and \emph{asynchronous} semantics, based on the alignment of the timestamps in the traces. Consequently, we demonstrate the application of HyperTWTL in formalizing important information-flow security policies and concurrency for robotics applications. Finally, we propose a model checking algorithm for verifying fragments of HyperTWTL by reducing the problem to a TWTL model checking problem.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.