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Hybrid Quantum Neural Networks (HQNNs) combine classical learning with parameterized quantum circuits, but their practical performance is often limited by (i) the noise of Noisy Intermediate-Scale Quantum (NISQ) devices and (ii) the large,…

While Convolutional Neural Networks (CNNs) have long been investigated and applied, as well as theorized, we aim to provide a slightly different perspective into their nature -- through the perspective of their Hessian maps. The reason is…

Hierarchical quantum classifiers, such as quantum convolutional neural networks (QCNNs), represent recent progress toward designing effective and feasible architectures for quantum classification. However, their performance on near-term…

When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

Adaptive robot navigation in dynamic environments requires policies that can reach the target reliably while producing efficient and stable trajectories. This paper presents Q-SpiRL, a quantum spiking reinforcement learning framework for…

Lagrangian Neural Networks (LNNs) present a principled and interpretable framework for learning the system dynamics by utilizing inductive biases. While traditional dynamics models struggle with compounding errors over long horizons, LNNs…

We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…

Hypercomplex neural networks have proven to reduce the overall number of parameters while ensuring valuable performance by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by…

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel…

Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…

There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain…

Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…

The research presented in this paper advances the integration of Hebbian learning into Convolutional Neural Networks (CNNs) for image processing, systematically exploring different architectures to build an optimal configuration, adhering…

The high dimensionality of kinetic equations with stochastic parameters poses major computational challenges for uncertainty quantification (UQ). Traditional Monte Carlo (MC) sampling methods, while widely used, suffer from slow convergence…

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve…

Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph…

Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing…