Ahmad Mousavi

Ahmad Mousavi

Assistant Prof. of Data Science,
Dept. of Math. and Stat.,
American University

Research

My research develops mathematical methods for sparse and structured learning, with emphasis on exact sparsity, constrained optimization, and machine learning. The unifying idea is to put structure into models directly—how many assets a portfolio may hold, how curved a classifier may be, how text and images should be fused—rather than hoping a generic method will discover that structure on its own. Current work follows three directions that share a common base in nonconvex constrained optimization, listed below from the most recent line of work to the earlier ones. Papers within each section are in the same reverse-chronological order.

The summaries below are written for students as well as colleagues. Each section names a few representative papers, explains what the method is doing in plain language, and shows a figure from the paper when one is available. The full list is on the Publications page.

Working With Students

I welcome students who are persistent, motivated to learn, and willing to work carefully. You do not need to already know all of the mathematics. A foundation in programming, machine learning, optimization, or natural language processing is enough to start. Typical first projects include reproducing a figure from a paper, implementing a block of an algorithm, or running a controlled experiment on a public dataset. Several class projects have continued as practicum or independent research, including work with collaborators at AU and at other universities.

If you would like to work together, email mousavi@american.edu with your CV and a short note on your interests (coursework, projects, or links to code). Geographic location is not a limitation; remote collaboration is fully supported.

Robust Multi-Scale And Multi-Modal Learning

Real systems mix sources: a social media post is text plus an image plus a timestamp; an EEG recording is many channels over time; a large language model may need to forget some facts without collapsing on the rest. Distribution shift, class imbalance, and weak alignment between modalities are the usual failure modes. This direction builds lightweight, attention-based models that stay accurate across subjects, events, and domains, and that remain efficient enough to train and inspect.

BLADE: Bilevel Low-Rank Augmented-Lagrangian Erasure for LLM Unlearning

Md Toufikuzzaman, A. Mousavi, D. Lee. EMNLP 2026 (main conference, to appear).

Unlearning asks a language model to forget targeted content (privacy, copyright, or outdated facts) without destroying the rest of its behavior. BLADE treats this as a constrained bilevel problem: forget in the outer loop, repair retain quality in the inner loop, with a low-rank (LoRA) bottleneck and an augmented-Lagrangian safeguard. The figure below is the practical test. A competing method collapses when the forget set grows or when unlearning is applied in sequence; BLADE stays stable.

Two-panel plot showing BLADE remaining stable as forget-set size and sequential unlearning steps increase, while a baseline method collapses.
BLADE remains stable as the forget set grows and as unlearning is applied repeatedly; a strong baseline collapses. Figure from Toufikuzzaman, Mousavi, and Lee, EMNLP 2026.

E-CaTCH: Event-Centric Cross-Modal Attention with Temporal Consistency and Class-Imbalance Handling for Misinformation Detection

A. Mousavi, Y. Abdollahinejad, R. Corizzo, N. Japkowicz, Z. Boukouvalas. IEEE Transactions on Computational Social Systems, 2026.

Most detectors score posts one at a time. Misinformation, however, often spreads as a story: related posts, over days, with text that may not match the image. E-CaTCH groups posts into pseudo-events, aligns BERT text features with ResNet image features through intra- and cross-modal attention, and tracks how the event evolves with a trend-aware temporal encoder. Training uses class weighting, temporal consistency, and hard-example mining so rare deceptive events are not ignored.

Architecture diagram of E-CaTCH showing text and image encoders, cross-modal attention with soft gating, an event-level temporal encoder, and an imbalance-aware loss.
E-CaTCH pipeline: encode text and image, fuse them with gated cross-modal attention, model the event over time, and train with an imbalance-aware, temporally consistent loss. Figure from Mousavi et al., IEEE TCSS 2026.

MOMENTA: Mixture-of-Experts over Multimodal Embeddings with Neural Temporal Aggregation for Misinformation Detection

Y. Abdollahinejad, A. Mousavi, N. Hassan, K. Shu, N. Japkowicz, S. Khosravi, A. Karami. arXiv:2604.16172, 2026 (submitted).

MOMENTA is a mixture-of-experts architecture in the same family. Separate experts specialize per modality, bidirectional co-attention aligns text and image, and a temporal branch tracks drift and momentum so a campaign that changes story over time is still recognized. The figure is useful for students because it makes the design pattern explicit: encode, specialize, align, fuse, then aggregate over time.

MOMENTA architecture from text and image encoders through mixture-of-experts, cross-modal fusion, temporal aggregation, and the multi-objective training loss.
MOMENTA: mixture-of-experts encoders, cross-modal fusion, temporal aggregation, and a multi-objective training loss. Figure from Abdollahinejad et al., arXiv:2604.16172.

MURAL: Multimodal Uncertainty-Aware Recommendation via Adaptive Edge Learning

A. Mousavi, M. Alikhani (equal contribution), Y.-C. Lee, R. Corizzo, Y. Abdollahinejad. arXiv:2609.04574, 2026.

Multimodal recommenders often freeze an item-item graph from a one-time similarity computation, then fuse every modality with the same weight. MURAL treats the graph as something to learn: an Adaptive Edge Learner finds item-item links as preferences change, and Uncertainty-Aware Fusion down-weights noisy views (a blurry frame, thin text, background audio) so the collaborative signal is not washed out. The figure is the pipeline: align modalities with behavior, learn edges, fuse with uncertainty, then recommend.

MURAL pipeline from interaction and modality features through behavior alignment, adaptive edge learning, uncertainty-aware fusion, graph convolution, and the ranking and contrastive losses.
MURAL: adaptive item-item edges plus uncertainty-aware fusion of text, image, and audio, trained with ranking and contrastive losses. Figure from Mousavi, Alikhani, Lee, Corizzo, and Abdollahinejad, arXiv:2609.04574.

EMO-CARE: EEG Multi-Scale Temporal Modeling with Channel-Aware Feature Attention for Robust Subject-Independent Emotion Recognition

Y. Abdollahinejad, A. Mousavi, P. Siaplaouras, Z. Boukouvalas, R. Corizzo. IEEE Open Journal of the Computer Society, 2026.

EEG emotion models often look strong when trained and tested on the same person, then fail on a new person. EMO-CARE is a lightweight network that reads the signal at several time scales and uses feature-level attention to weight the scales that matter. Evaluated under leave-one-subject-out protocols on SEED, SEED-V, and DREAMER, it is built for the harder, more realistic setting: the test subject was never seen in training. A related IEEE Access survey reviews EEG and physiological emotion recognition methods in healthcare.

EMO-CARE pipeline from EEG datasets and preprocessing through dilated temporal convolutions, feature fusion with multi-head attention, classification, and leave-one-subject-out evaluation.
EMO-CARE: multi-scale temporal convolutions and channel-aware attention, trained and tested leave-one-subject-out so the person at test time was never seen in training. Figure from Abdollahinejad et al., IEEE OJCS 2026.

Related projects, also from newest to oldest, include physics-conditioned attention for next-day wildfire spread prediction, CAM-Soft for soft hate speech detection, and an IEEE BigData 2024 paper on event-based multimodal fusion for misinformation detection during high-impact events.

Cardinality-Constrained Structured Optimization

Many real problems ask for a solution that is not just accurate, but also simple in a precise way: hold at most k stocks, keep only a few features, or recover a signal that is sparse. Convex relaxations are convenient, but they often cannot enforce that exact budget. I develop penalty decomposition methods that treat cardinality and related constraints directly, with convergence guarantees and algorithms that stay practical on real data.

In finance this means portfolios that are sparse (few assets, lower trading cost), volatile enough to be useful, and, when desired, mean-reverting, so prices tend to oscillate around a level rather than wander. The same algorithmic ideas extend to sparse symmetric sets, hybrid quantum-classical compressive sensing, low-rank quadratic optimization, and application-layer protection of quantum optimization jobs that run on untrusted cloud hardware.

The Rank-Collapse Principle for Quadratic Optimization

M. Soltanalian, A. Mousavi. arXiv:2608.07828, 2026.

This preprint studies when a quadratic optimization problem collapses to a low-rank form. The practical message is that some high-dimensional quadratic models are governed by a much smaller effective dimension, which can make them easier to analyze and to solve.

Two-dimensional rank-space plot of projected vertices, an optimal shadow, and a supporting hyperplane illustrating quadratic rank collapse.
Rank collapse in two-dimensional rank space: the quadratic problem reduces to exposing a low-dimensional shadow, so a high-dimensional quadratic is governed by a much smaller effective geometry. Figure from Soltanalian and Mousavi, arXiv:2608.07828.

Weaver: A Hybrid Quantum-Classical Optimization Method for Binary Compressive Sensing under Matrix Uncertainty

K. Jayathilake, A. Mousavi, R. Ayanzadeh. Submitted to AAAI 2027, July 2026.

Weaver combines classical optimization with a quantum subroutine for binary compressive sensing when the measurement matrix is uncertain. The goal is a hybrid method that can recover a sparse binary signal without pretending the sensing matrix is known exactly.

Flowchart of Weaver: measurements with an uncertain sensing matrix, a classical uncertainty-elimination step, a quantum binary search step, a reduced objective, and a global-optimality certificate.
Schematic of Weaver: a classical step eliminates matrix uncertainty, a quantum step searches the binary signal, and a certificate bounds the support of any better solution. Jayathilake, Mousavi, and Ayanzadeh, submitted to AAAI 2027.

Enigma: Beyond Circuit-Level Security through Application-Layer Obfuscation for Quantum Optimization

R. Ayanzadeh, A. Mousavi, A. Basareh, N. Alavisamani, K. Taram. Submitted to EuroSys 2027 Fall.

Quantum optimization workloads will run on expensive cloud machines, so the problem instance itself can leak. Circuit-level protections need large quantum networks or full error correction, which are not practical yet. Enigma obfuscates the instance at the application layer: it scrambles coefficients, inserts decoy structure, and prunes variables, then recovers the original solution from the solver output.

Sparse Extended Mean-Variance-CVaR Portfolios with Short-Selling

A. Mousavi, M. Salahi, Z. Boukouvalas. Japan Journal of Industrial and Applied Mathematics, 2026.

This paper extends the sparse-portfolio line to mean-variance-CVaR models that allow short-selling. Cardinality still caps the number of assets, while CVaR brings a tail-risk measure into the same penalty-decomposition framework.

Four-panel plot of return, risk, Sharpe ratio, and CVaR versus number of stocks for a direct solver, PADM, and the proposed algorithm.
Sparse mean-variance-CVaR portfolios as the cardinality budget grows. The penalty methods match the direct solver on return, risk, Sharpe ratio, and tail risk (CVaR). Figure from Mousavi, Salahi, and Boukouvalas, JJIAM 2026.

An Efficient Penalty Decomposition Algorithm for Minimization over Sparse Symmetric Sets

A. Mousavi, M. Kimiaei, S. Babaie-Kafaki, V. Kungurtsev. arXiv:2601.12383, 2026 (under review at Mathematical Programming Computation).

Here the feasible set is both sparse and symmetric. A quasi-Newton penalty decomposition method keeps the per-iteration cost manageable while still enforcing exact sparsity, rather than a convex surrogate.

Four performance-profile panels comparing PD-LM1-a with iterative hard thresholding on function evaluations and runtime at two accuracy targets.
Performance profiles on sparse symmetric problems: PD-LM1-a solves a larger fraction of instances than iterative hard thresholding, in both function evaluations and runtime. Figure from Mousavi, Kimiaei, Babaie-Kafaki, and Kungurtsev, arXiv:2601.12383.

Statistical Proxy Based Mean-Reverting Portfolios with Sparsity and Volatility Constraints

A. Mousavi, G. Michailidis. International Transactions in Operational Research, 2025.

Mean reversion can be measured in more than one way (predictability, portmanteau, and crossing statistics). This paper puts those proxies into one optimization model with sparsity and volatility constraints, and solves it with a unifying penalty decomposition method. On S&P 500 data, the crossing-statistics proxy produces the most attractive sparse portfolios among the three.

Time series of sparse mean-reverting portfolio spreads, daily returns, and cumulative profit for three statistical proxies with cardinality five.
Sparse mean-reverting portfolios with cardinality k = 5. Spreads, daily returns, and cumulative profit for the three statistical proxies; the crossing-statistics portfolio (green) accumulates the strongest gain in this example. Figure from Mousavi and Michailidis, ITOR 2025.

Cardinality Constrained Mean-Variance Portfolios: A Penalty Decomposition Algorithm

A. Mousavi, G. Michailidis. Computational Optimization and Applications, 2025.

Markowitz mean-variance optimization is classical, but asking for “exactly k assets” makes the problem nonconvex. Regularization can encourage sparsity without letting the investor set k directly. This paper solves the cardinality-constrained problem with a penalty decomposition method whose block updates have closed form, and shows that the method is faster than strong commercial and penalty baselines on real indexes while matching their risk-return profile.

Three-panel plot of CPU time versus sparsity level for 226, 476, and 2196 assets, comparing CCMV-PADM, CCMV-PD, and Mosek.
CPU time versus sparsity on indexes of 226, 476, and 2,196 assets. Penalty decomposition stays far below a commercial mixed-integer solver as the universe grows. Figure from Mousavi and Michailidis, COAP 2025.

A Penalty Decomposition Algorithm with Greedy Improvement for Mean-Reverting Portfolios with Sparsity and Volatility Constraints

A. Mousavi, J. Shen. International Transactions in Operational Research, 2023.

An earlier paper in this line builds sparse, volatile, mean-reverting portfolios with a two-stage method: penalty decomposition to a stationary point, then a greedy improvement step based on semidefinite relaxations of restricted subproblems.

Time series of portfolio spreads, daily ROI, and cumulative profit for a sparse mean-reverting portfolio with cardinality five, comparing penalty decomposition with greedy improvement to an SDP baseline.
Sparse mean-reverting portfolio with cardinality k = 5. Spreads, daily returns, and cumulative profit: the penalty method with greedy improvement (PD-G) accumulates a stronger gain than the SDP baseline in this example. Figure from Mousavi and Shen, ITOR 2023.

Sparse And Structured Quadratic Surface Support Vector Machines

A linear SVM draws a flat wall between two classes. That is easy to interpret, but many datasets are separated by a curve. Kernel SVMs can bend the boundary, at the cost of choosing a kernel and losing a direct geometric picture. Kernel-free quadratic surface SVMs (QSVMs) fit a quadratic surface in the original features, so the boundary can curve without a kernel. The price is that the number of parameters grows like the square of the dimension. My work uses sparsity and Universum data so the quadratic model stays flexible without becoming a dense, hard-to-read surface.

Quadratic Surface Twin Support Vector Machine for Imbalanced Data

H. Moosaei, M. Hladík, A. Mousavi, Z. Gao, H. Fu. International Journal of Machine Learning and Cybernetics, 2026.

When one class is rare, a single decision surface often hugs the majority class. This twin model fits two nonparallel quadratic surfaces and uses Universum points to support the minority class, so the classifier is less biased on imbalanced data.

Scatter plot of two classes and Universum points with two nonparallel quadratic surfaces fitted by a twin quadratic SVM.
Twin quadratic surfaces on imbalanced data. The two nonparallel curves (red and green) separate the classes; Universum points (stars) sit in the gap and support the minority class. Figure from Moosaei, Hladik, Mousavi, Gao, and Fu, IJMLC 2026.

An Ensemble Learning Approach Based on Random Sparse Quadratic Twin Parametric-Margin SVMs

P. Yang, J. Luo, A. Mousavi, R. Corizzo, Z. Gao. SSRN 7022004, 2026 (submitted).

Instead of one large quadratic classifier, this work trains many small sparse twin QSVMs on random subspaces and combines them. The ensemble keeps the kernel-free geometry while spreading the quadratic parameter cost across weaker models.

Accuracy versus number of estimators for a sparse quadratic twin SVM ensemble on eight datasets.
Ensemble accuracy as the number of sparse twin base learners grows. Most datasets stay stable once a modest number of estimators is reached; Ionosphere continues to gain. Figure from Yang, Luo, Mousavi, Corizzo, and Gao, SSRN 7022004.

ℓ0-Regularized Quadratic Surface Support Vector Machines

A. Mousavi, R. Zandvakili, Z. Gao. arXiv:2501.11268, 2025 (journal version under review).

ℓ1 encourages sparsity; ℓ0 asks for an exact number of nonzero quadratic coefficients. A penalty decomposition algorithm produces surfaces that satisfy first-order optimality conditions, with subproblems that admit closed-form or efficient dual solutions. The heatmap below is the practical payoff: most entries of the quadratic matrix W are driven to zero, so the classifier remains nonlinear but uses only a few interactions among features.

Heatmap of a sparse symmetric quadratic coefficient matrix W and vector b, with many exact zeros.
Exact sparsity in an ℓ0-regularized QSVM: many quadratic coefficients are zero, while the remaining entries define the curved boundary. Figure from Mousavi, Zandvakili, and Gao, arXiv:2501.11268.

Sparse ℓ1-Norm Quadratic Surface Support Vector Machine with Universum Data

H. Moosaei, A. Mousavi, M. Hladík, Z. Gao. Soft Computing, 2023.

Universum points are examples that belong to neither class. They sit in the gap and tell the classifier where not to put the boundary. Combined with a quadratic surface and ℓ1 sparsity, they improve generalization, especially when labeled data are limited.

Schematic of two classes on quadratic curves with Universum points in the middle band between f(x) equals 1 and f(x) equals minus 1.
Universum points (triangles) occupy the region between the two classes and regularize the quadratic decision surface. Figure from Moosaei, Mousavi, Hladík, and Gao, Soft Computing 2023.

Quadratic Surface Support Vector Machine with ℓ1 Norm Regularization

A. Mousavi, Z. Gao, L. Han, A. Lim. Journal of Industrial and Management Optimization, 2022.

ℓ1 regularization on the quadratic coefficients does two useful things. If the data are essentially linear, a large penalty flattens the surface toward an ordinary SVM. If the data are quadratic, the same penalty can recover the sparse pattern in the true surface. The figure below is the simplest picture of why the extra curvature matters: a linear SVM cuts through a U-shaped class structure, while the quadratic model follows it.

Scatter plot of two classes with a U-shaped boundary. A linear SVM cuts across the curve, while L1-regularized quadratic SVM follows it.
Linear SVM versus quadratic surface SVM on quadratically separable data. The curved boundary separates the two classes; the linear hyperplane cannot. Figure from Mousavi, Gao, Han, and Lim, JIMO 2022.