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Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a blending for a seamless transition between the warped images. We propose to leverage coord-based neural networks to represent such warpings and blendings of face images. During training, we exploit the smoothness and flexibility of such networks by combining energy functionals employed in classical approaches without discretizations. Additionally, our method is time-dependent, allowing a continuous warping/blending of the images. During morphing inference, we need both direct and inverse transformations of the time-dependent warping. The first (second) is responsible for warping the target (source) image into the source (target) image. Our neural warping stores those maps in a single network dismissing the need for inverting them. The results of our experiments indicate that our method is competitive with both classical and generative models under the lens of image quality and face-morphing detectors. Aesthetically, the resulting images present a seamless blending of diverse faces not yet usual in the literature.

We propose GNNInfer, the first automatic property inference technique for GNNs. To tackle the challenge of varying input structures in GNNs, GNNInfer first identifies a set of representative influential structures that contribute significantly towards the prediction of a GNN. Using these structures, GNNInfer converts each pair of an influential structure and the GNN to their equivalent FNN and then leverages existing property inference techniques to effectively capture properties of the GNN that are specific to the influential structures. GNNINfer then generalizes the captured properties to any input graphs that contain the influential structures. Finally, GNNInfer improves the correctness of the inferred properties by building a model (either a decision tree or linear regression) that estimates the deviation of GNN output from the inferred properties given full input graphs. The learned model helps GNNInfer extend the inferred properties with constraints to the input and output of the GNN, obtaining stronger properties that hold on full input graphs. Our experiments show that GNNInfer is effective in inferring likely properties of popular real-world GNNs, and more importantly, these inferred properties help effectively defend against GNNs' backdoor attacks. In particular, out of the 13 ground truth properties, GNNInfer re-discovered 8 correct properties and discovered likely correct properties that approximate the remaining 5 ground truth properties. Using properties inferred by GNNInfer to defend against the state-of-the-art backdoor attack technique on GNNs, namely UGBA, experiments show that GNNInfer's defense success rate is up to 30 times better than existing baselines.

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and computational complexity constraints. However, the efficiency of these methods depends on the preconditioner utilized. The development of the preconditioner normally requires some insight into the sparse linear system and the desired trade-off of generating the preconditioner and the reduction in the number of iterations. Incomplete factorization methods tend to be black box methods to generate these preconditioners but may fail for a number of reasons. These reasons include numerical issues that require searching for adequate scaling, shifting, and fill-in while utilizing a difficult to parallelize algorithm. With a move towards heterogeneous computing, many sparse applications find GPUs that are optimized for dense tensor applications like training neural networks being underutilized. In this work, we demonstrate that a simple artificial neural network trained either at compile time or in parallel to the running application on a GPU can provide an incomplete sparse Cholesky factorization that can be used as a preconditioner. This generated preconditioner is as good or better in terms of reduction of iterations than the one found using multiple preconditioning techniques such as scaling and shifting. Moreover, the generated method also works and never fails to produce a preconditioner that does not reduce the iteration count.

Consider a committee election consisting of (i) a set of candidates who are divided into arbitrary groups each of size \emph{at most} two and a diversity constraint that stipulates the selection of \emph{at least} one candidate from each group and (ii) a set of voters who are divided into arbitrary populations each approving \emph{at most} two candidates and a representation constraint that stipulates the selection of \emph{at least} one candidate from each population who has a non-null set of approved candidates. The DiRe (Diverse + Representative) committee feasibility problem (a.k.a. the minimum vertex cover problem on unweighted undirected graphs) concerns the determination of the smallest size committee that satisfies the given constraints. Here, for this problem, we discover an unconditional deterministic polynomial-time algorithm that is an amalgamation of maximum matching, breadth-first search, maximal matching, and local minimization.

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation with initial conditions on the sphere. This finite-dimensional characterization unlocks an efficient sampling-based estimation algorithm to accurately over-approximate reachable sets. We also study the structure of the boundary of the reachable convex hulls and derive error bounds for the estimation algorithm. We give applications to neural feedback loop analysis and robust MPC.

We derive and study time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across all sample sizes. Inspired by the original work of Catoni and Giulini, we unify and extend their analysis to cover both the sequential setting and to handle a variety of distributional assumptions. Our results include an empirical-Bernstein CSS for bounded random vectors (resulting in a novel empirical-Bernstein confidence interval with asymptotic width scaling proportionally to the true unknown variance), CSSs for sub-$\psi$ random vectors (which includes sub-gamma, sub-Poisson, and sub-exponential), and CSSs for heavy-tailed random vectors (two moments only). Finally, we provide two CSSs that are robust to contamination by Huber noise. The first is a robust version of our empirical-Bernstein CSS, and the second extends recent work in the univariate setting to heavy-tailed multivariate distributions.

Multimodal datasets contain observations generated by multiple types of sensors. Most works to date focus on uncovering latent structures in the data that appear in all modalities. However, important aspects of the data may appear in only one modality due to the differences between the sensors. Uncovering modality-specific attributes may provide insights into the sources of the variability of the data. For example, certain clusters may appear in the analysis of genetics but not in epigenetic markers. Another example is hyper-spectral satellite imaging, where various atmospheric and ground phenomena are detectable using different parts of the spectrum. In this paper, we address the problem of uncovering latent structures that are unique to a single modality. Our approach is based on computing a graph representation of datasets from two modalities and analyzing the differences between their connectivity patterns. We provide an asymptotic analysis of the convergence of our approach based on a product manifold model. To evaluate the performance of our method, we test its ability to uncover latent structures in multiple types of artificial and real datasets.

We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness of standard Neural Networks (NNs) because it requires searching the parameters' space for safe weights. Moreover, tight and complete approaches for the verification of standard NNs, such as those based on Mixed-Integer Linear Programming (MILP), cannot be directly used for the verification of BNNs because of the polynomial terms resulting from the consecutive multiplication of variables encoding the weights. Our algorithms efficiently and effectively search the parameters' space for safe weights by using iterative expansion and the network's gradient and can be used with any verification algorithm of choice for BNNs. In addition to proving that our algorithms compute tighter bounds than the SoA, we also evaluate our algorithms against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that our algorithms compute bounds up to 40% tighter than the SoA.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

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.