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Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
Spiking neural networks (SNNs) are emerging as an energy-efficient alternative to traditional artificial neural networks (ANNs) due to their unique spike-based event-driven nature. Coding is crucial in SNNs as it converts external input…
Stimulated Raman scattering (SRS) microscopy is a powerful label-free imaging technique that probes the vibrational response of chemicals with high specificity and sensitivity. High-power, quantum-enhanced SRS microscopes have been recently…
Cubic regularized Newton (CRN) methods have attracted signiffcant research interest because they offer stronger solution guarantees and lower iteration complexity. With the rise of the big-data era, there is growing interest in developing…
Algorithms to solve variational regularization of ill-posed inverse problems usually involve operators that depend on a collection of continuous parameters. When these operators enjoy some (local) regularity, these parameters can be…
We present a new nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof…
With the help of powerful generative models, Semantic Image Compression (SIC) has achieved impressive performance at ultra-low bitrate. However, due to coarse-grained visual-semantic alignment and inherent randomness, the reliability of SIC…
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the…
Synthetic data, an appealing alternative to extensive expert-annotated data for medical image segmentation, consistently fails to improve segmentation performance despite its visual realism. The reason being that synthetic and real medical…
Global token mixing, implemented via self-attention or state-space sequence models, has become a popular model design choice for MRI restoration. However, MRI restoration tasks differ substantially in how their degradations vary over image…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over…
Computed tomography (CT) is widely used in screening, diagnosis, and image-guided therapy for both clinical and research purposes. Since CT involves ionizing radiation, an overarching thrust of related technical research is development of…
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction…
Graph Anomaly Detection (GAD) is critical in security-sensitive domains, yet faces reliability challenges: miscalibrated confidence estimation (underconfidence in normal nodes, overconfidence in anomalies), adversarial vulnerability of…
Spin plays a fundamental role in understanding electronic structure, yet many real-space wavefunction methods fail to adequately consider it. We introduce the Spin-Adapted Antisymmetrization Method (SAAM), a general procedure that enforces…
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG…
We propose Spectral Complex Autoencoder Pruning (SCAP), a reconstruction-based criterion that measures functional redundancy at the level of individual output channels. For each convolutional layer, we construct a complex interaction field…
Proximal gradient algorithms (PGA), while foundational for inverse problems like image reconstruction, often yield unstable convergence and suboptimal solutions by violating the critical non-negativity constraint. We identify the gradient…
Hyper spectral images (HSI) provide rich spectral and spatial information across a series of contiguous spectral bands. However, the accurate processing of the spectral and spatial correlation between the bands requires the use of…
The most scalable approaches to certifying neural network robustness depend on computing sound linear lower and upper bounds for the network's activation functions. Current approaches are limited in that the linear bounds must be…