arXiv subjects

Maryam Bagherian

Publications and source records attributed to Maryam Bagherian.

8 recordsLinked to original sources

arXiv2026

Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing

Many biomedical challenges can be posed as tensor completion problems where the observed entries of a multidimensional array (a tensor) are used to impute the missing values. In such settings, incorporating side information about the modes of the tensor, such as gene-gene similarity, can significantly enhance the solutions of the completion problem. Most existing tensor completion methods can only incorporate side information in the form of matrices. In this study, we introduce a novel framework to incorporate side information in the form of tensors. Our new approach, called Coupled Tensor-Tensor Completion (CTTC), leverages the hidden connections among multimodal tensors to improve tensor completion performance. In addition to practical utility, CTTC has theoretical foundations in distance metric learning and group theory. We derive an alternating algorithm to solve the CTTC optimization problem and establish its convergence to a stationary point. Finally, we show that CTTC outperforms state-of-the-art tensor completion methods at predicting drug effects. Results: Compared with other tensor completion methods, including HaLRTC, CTRC, Cell, and NTDDR, CTTC demonstrates superior run-time and RSE tensor completion accuracy on two benchmark datasets, DTD and LINCS.

math.NA↗

arXiv2026

Universal Approximation of Operators with Transformers and Neural Integral Operators

We study the universal approximation properties of transformers and neural integral operators for operators in Banach spaces. In particular, we show that the transformer architecture is a universal approximator of integral operators between Hölder spaces. Moreover, we show that a generalized version of neural integral operators, based on the Gavurin integral, are universal approximators of arbitrary operators between Banach spaces. Lastly, we show that a modified version of transformer, which uses Leray-Schauder mappings, is a universal approximator of operators between arbitrary Banach spaces.

cs.LG↗

arXiv2026

Axiomatic Foundation of Quantum-Inspired Distance Metrics

We develop a comprehensive axiomatic framework for quantum-inspired distance metrics on projective Hilbert spaces, providing a unified foundation that organizes and generalizes existing measures in quantum information theory. Starting from five fundamental axioms, projective invariance, unitary covariance, superposition sensitivity, entanglement awareness, and measurement contextuality, we show that any admissible distance depends solely on state overlap and establish the uniqueness of the Fubini-Study metric as the canonical geodesic distance. Our framework further yields a hierarchy of comparison results relating the Fubini-Study metric, Bures distance, Euclidean distance, measurement-based pseudometrics, and entanglement-sensitive distances. Key contributions include an entanglement-geometry complementarity principle, high-dimensional concentration bounds, and operational interpretations connecting distances to state discrimination and quantum metrology. This work places the geometry of quantum state spaces on a rigorous axiomatic footing, bridging abstract metric theory, information geometry, and operational quantum principles.

quant-ph↗

arXiv2026

No-Rank Tensor Decomposition Using Metric Learning

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor decomposition framework based on metric learning, which replaces reconstruction objectives with a similarity-driven optimization. By combining a triplet loss with diversity and uniformity regularization, the method learns embeddings where distances naturally reflect semantic and physical relationships, supported by theoretical guarantees on convergence and metric properties. We evaluate the approach on diverse datasets, including face recognition (LFW, Olivetti), brain connectivity (ABIDE), and simulated physical systems (galaxies, crystals). In comprehensive comparisons against classical methods (PCA, t-SNE, UMAP), tensor decompositions (CP, Tucker, t-SVD), and deep learning models (VAE, DEC, transformer based embeddings), our method produces embeddings that preserve physically and semantically relevant relationships and achieve competitive clustering performance. While transformers often excel in predictive accuracy on large datasets, our method provides interpretable embeddings and remains effective in small-data regimes where transformer training may be infeasible. This work establishes metric learning as a principled paradigm for tensor analysis, emphasizing physical interpretability and semantic relevance over pixel-level reconstruction, and offering an efficient and robust alternative in data-scarce scientific domains.

cs.LG↗

arXiv2024

FIMP: Foundation Model-Informed Message Passing for Graph Neural Networks

Foundation models have achieved remarkable success across many domains, relying on pretraining over vast amounts of data. Graph-structured data often lacks the same scale as unstructured data, making the development of graph foundation models challenging. In this work, we propose Foundation-Informed Message Passing (FIMP), a Graph Neural Network (GNN) message-passing framework that leverages pretrained non-textual foundation models in graph-based tasks. We show that the self-attention layers of foundation models can effectively be repurposed on graphs to perform cross-node attention-based message-passing. Our model is evaluated on a real-world image network dataset and two biological applications (single-cell RNA sequencing data and fMRI brain activity recordings) in both finetuned and zero-shot settings. FIMP outperforms strong baselines, demonstrating that it can effectively leverage state-of-the-art foundation models in graph tasks.

cs.LG↗

arXiv2022

A Bilevel Optimization Method for Tensor Recovery Under Metric Learning Constraints

Tensor completion and tensor decomposition are important problems in many domains. In this work, we leverage the connection between these problems to learn a distance metric that improves both decomposition and completion. We show that the optimal Mahalanobis distance metric for the completion task is closely related to the Tucker decomposition of the completed tensor. Then, we formulate a bilevel optimization problem to perform joint tensor completion and decomposition, subject to metric learning constraints. The metric learning constraints also allow us to flexibly incorporate similarity side information and coupled matrices, when available, into the tensor recovery process. We derive an algorithm to solve the bilevel optimization problem and prove its global convergence. When evaluated on real data, our approach performs significantly better compared to previous methods.

math.OC↗

arXiv2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries

We investigate field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest. Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the nonretarded plasmon dispersion relations, eigenmodes, and fields are then calculated for several geometric entities of use in nanoscience and nanotechnology. From the classical energy of the charge density oscillations in the modeled nanoparticle, we then derive the Hamiltonian of the system, which is used for quantization. The quantized plasmon field is obtained and, employing an interaction Hamiltonian derived from the first-order perturbation theory within the hydrodynamic model of the electron gas, we obtain an analytical expression for the radiative decay rate of the plasmons. The established treatment is applied to multiple geometries to investigate the quantized charge density oscillations on their bounding surfaces. Specifically, using one sheet of a two-sheeted hyperboloid of revolution, paraboloid of revolution, and cylindrical domains, all with one infinite dimension, and the finite spheroidal and toroidal domains are treated. ...

cond-mat.mes-hall↗

arXiv2019

General Approach to Study Geometric Effects on Classical & Quantum Fields & Eigenmodes of Particles with Finite & Infinite Extend for Applications in Plasmonics & Scanning Probe Microscopy

This manuscript provides a general approach to the investigation of field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest. Within the quasistatic framework, the nanostructure material domains with frequency-dependent dielectric functions are presented. Quantities associated with the normal modes of the electronic systems, the nonretarded plasmon dispersion relations, eigenmodes, and fields are then calculated for several geometric entities of use in nanoscience and nanotechnology. From the classical energy of the charge density oscillations in the modeled nanoparticle, the Hamiltonian of the system, which is used for quantization, is derived. The quantized plasmon field is obtained and, employing an interaction Hamiltonian derived from the first-order perturbation theory within the hydrodynamic model of the electron gas, an analytical expression for the radiative decay rate of the plasmons could be obtained. The established treatment could be applied to multiple geometries to investigate the quantized charge density oscillations on their bounding surfaces.

cond-mat.mes-hall↗