Related papers: End-to-End Learning of Geometrical Shaping Maximiz…

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at…

Adversarial training, especially projected gradient descent (PGD), has proven to be a successful approach for improving robustness against adversarial attacks. After adversarial training, gradients of models with respect to their inputs…

End-to-end multimodal learning on knowledge graphs has been left largely unaddressed. Instead, most end-to-end models such as message passing networks learn solely from the relational information encoded in graphs' structure: raw values, or…

We introduce a simplified method for calculating the loss function for use in geometric shaping, allowing for the optimisation of high dimensional constellations. We design constellations up to 12D with 4096 points, with gains up to 0.31 dB…

We introduce a principled method to train end-to-end analog neural networks by stochastic gradient descent. In these analog neural networks, the weights to be adjusted are implemented by the conductances of programmable resistive devices…

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…

The proximal generalized alternating direction method of multipliers (p-GADMM) is substantially efficient for solving convex composite programming problems of high-dimensional to moderate accuracy. The global convergence of this method was…

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…

The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This…

Learn to Optimize (L2O) trains deep neural network-based solvers for optimization, achieving success in accelerating convex problems and improving non-convex solutions. However, L2O lacks rigorous theoretical backing for its own training…

We consider nonconvex-concave minimax problems, $\min_{\mathbf{x}} \max_{\mathbf{y} \in \mathcal{Y}} f(\mathbf{x}, \mathbf{y})$, where $f$ is nonconvex in $\mathbf{x}$ but concave in $\mathbf{y}$ and $\mathcal{Y}$ is a convex and bounded…

Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure…

Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…

Meeting the high data rate demands of modern applications necessitates the utilization of high-frequency spectrum bands, including millimeter-wave and sub-terahertz bands. However, these frequencies require precise alignment of narrow…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the…

We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly…