Atharva Awari
Atharva Awari

Atharva Awari

PhD researcher, University of Mons
Postdoc at SimulaMet, Oslo, from 2027

I design optimization algorithms for low-rank models that go beyond linearity.

Classical factorizations write data as X ≈ WH. My work studies the nonlinear version X ≈ f(WH), and its tensor counterpart, which describes sparse, binary, bounded or clipped data with far fewer factors. I build these models into a single ADMM framework and release the code openly.

Download CV GitHub Google Scholar LinkedIn

atharvaabhijit.awari at umons.ac.be
Department of Mathematics and Operational Research, Faculty of Engineering, University of Mons, Belgium

ResearchFrom my thesis, Beyond Linearity: Nonlinear Matrix and Tensor Decompositions

Sparse data and the ReLU

X ≈ max(0, WH)

A sparse matrix can have high rank and still be the ReLU of a matrix of very low rank: the zeros only ask for nonpositive entries, and that freedom lowers the rank. The identity matrix of any size is the ReLU of a rank-3 matrix.

On a dictionary of sparse face features, a rank-20 ReLU decomposition reaches 3% error where the best linear rank-20 approximation stays at 78%. I developed accelerated algorithms for this model (A-NMD, 3B-NMD) and the first coordinate descent method that solves the original problem directly.

MLSP 2023, EUSIPCO 2024

A rank-3 matrix (teal positive, violet negative) whose ReLU is the full-rank identity.

Binary and bounded data

X ≈ σ(WH)

With the sigmoid, the model fits data with entries in [0, 1] or of a binary nature, such as presence/absence patterns, ratings or adjacency matrices. A block coordinate descent method with a scaling step and a TSVD-based initialization compresses binary data sets and completes missing entries better than the truncated SVD and ReLU-NMD.

MLSP 2025, with H. Nguyen

A binary matrix (left) and a rank-2 approximation σ(WH) (right).

One algorithm for many models

minW,H d(X, f(WH))

Splitting T = WH gives an ADMM scheme in which only one entrywise update depends on the nonlinearity f and the loss d. Four nonlinearities (ReLU, square, MinMax, modulus) and three losses (Frobenius, ℓ1, Kullback–Leibler) give twelve models, with missing data handled for free.

Matching the loss to the noise matters: under Poisson noise, MinMax with the KL divergence recovers the image with 9.9% error, against 19.9% for the Frobenius norm. For ReLU-NMD the same framework beats coordinate descent and a tuned Adam baseline.

Signal Processing (Elsevier), 2026, arXiv:2512.17473

MIT logo corrupted by Poisson noisePoisson noise
Rank-4 reconstruction with MinMax and KL divergence, noise removedMinMax + KL, rank 4
ReLU-NMD on MNIST, relative error over 10 seconds.

From matrices to tensors

𝒳 ≈ f(⟦A, B, C⟧)

The same splitting carries over to the canonical polyadic decomposition: a global ADMM scheme fits CPD under the Frobenius, ℓ1 and KL losses, succeeds more often than AO-ADMM on synthetic tensors, and denoises the Indian Pines hyperspectral cube (307 × 307 × 162) under Poisson noise with 0.7% error.

With a clipping nonlinearity, the model handles values censored at an instrument's limit of detection, as in NMR metabolomics, and recovers the underlying patterns more faithfully than treating those entries as missing or imputing them.

EUSIPCO 2026; arXiv:2610.05339 (ICASSP 2027 submission)

Indian Pines, band 20, cleanClean
Indian Pines, band 20, with Poisson noisePoisson noise
Indian Pines, band 20, reconstructed by ADMM with KL divergenceADMM + KL
Hyperspectral denoising (band 20) and, below, a schematic spectrum censored at a detection limit.

Positions and education

  • 2027–
    Postdoctoral researcherSimula Metropolitan Centre for Digital Engineering (SimulaMet), Oslo, NorwaySupervisor: Dr. Evrim Acar
  • Mar–Jun 2026
    Visiting researcherSimula Metropolitan Centre for Digital Engineering (SimulaMet), Oslo, NorwayHost: Dr. Evrim Acar
  • 2023–2026
    PhD in Applied MathematicsUniversity of Mons, BelgiumThesis: Beyond Linearity: Nonlinear Matrix and Tensor DecompositionsSupervisors: Prof. Nicolas Gillis and Prof. Arnaud Vandaele
  • 2020–2022
    MSc in Applied MathematicsIndian Institute of Technology Delhi, IndiaThesis: Linear and Non-linear Eigenvalue ProblemsSupervisor: Prof. Punit Sharma
  • 2016–2019
    BSc in MathematicsFergusson College, Pune University, India

Publications

Journal papers

  • Alternating direction method of multipliers for nonlinear matrix decompositions A. Awari, N. Gillis, A. Vandaele Signal Processing (Elsevier), 2026, accepted
    arXiv Code
    Cite
    @article{awari2025alternating,
  title={Alternating direction method of multipliers for nonlinear matrix decompositions},
  author={Awari, Atharva and Gillis, Nicolas and Vandaele, Arnaud},
  journal={Signal Processing},
  publisher={Elsevier},
  year={2026},
  note={Accepted for publication; arXiv:2512.17473}
}

Under review

  • Nonlinear tensor decomposition for pattern discovery A. Awari, G. R. van der Ploeg, A. Vandaele, N. Gillis, E. Acar Submitted to IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2027
    arXiv Code
    Cite
    @article{awari2026nonlinear,
  title={Nonlinear Tensor Decomposition for Pattern Discovery},
  author={Awari, Atharva and van der Ploeg, Geert Roelof and Vandaele, Arnaud and Gillis, Nicolas and Acar, Evrim},
  journal={arXiv preprint arXiv:2610.05339},
  year={2026}
}

Conference papers

  • A simple and flexible ADMM-based framework for tensor decompositions A. Awari, S. Saha, N. Gillis, A. Vandaele European Signal Processing Conference (EUSIPCO), 2026
    Preprint Code
    Cite
    @inproceedings{awarisimple,
  title={A Simple and Flexible ADMM-Based Framework for Tensor Decompositions},
  author={Awari, Atharva and Saha, Subhayan and Gillis, Nicolas and Vandaele, Arnaud},
  booktitle={European Signal Processing Conference (EUSIPCO)},
  year={2026}
}
  • Nonlinear matrix decomposition with the sigmoid function H. Nguyen, A. Awari, A. Vandaele, N. Gillis IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Istanbul, 2025
    Paper Code
    Cite
    @inproceedings{nguyen2025nonlinear,
  title={Nonlinear matrix decomposition with the sigmoid function},
  author={Nguyen, Harrison and Awari, Atharva and Vandaele, Arnaud and Gillis, Nicolas},
  booktitle={2025 IEEE 35th International Workshop on Machine Learning for Signal Processing (MLSP)},
  pages={1--6},
  year={2025},
  organization={IEEE}
}
  • Coordinate descent algorithm for nonlinear matrix decomposition with the ReLU function A. Awari, H. Nguyen, S. Wertz, A. Vandaele, N. Gillis European Signal Processing Conference (EUSIPCO), 2024
    Paper Code
    Cite
    @inproceedings{awari2024coordinate,
  title={Coordinate descent algorithm for nonlinear matrix decomposition with the ReLU function},
  author={Awari, Atharva and Nguyen, Harrison and Wertz, Samuel and Vandaele, Arnaud and Gillis, Nicolas},
  booktitle={2024 32nd European Signal Processing Conference (EUSIPCO)},
  pages={2622--2626},
  year={2024},
  organization={IEEE}
}
  • Accelerated algorithms for nonlinear matrix decomposition with the ReLU function G. Seraghiti, A. Awari, A. Vandaele, M. Porcelli, N. Gillis IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2023
    Paper arXiv Code
    Cite
    @inproceedings{seraghiti2023accelerated,
  title={Accelerated algorithms for nonlinear matrix decomposition with the ReLU function},
  author={Seraghiti, Giovanni and Awari, Atharva and Vandaele, Arnaud and Porcelli, Margherita and Gillis, Nicolas},
  booktitle={2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)},
  pages={1--6},
  year={2023},
  organization={IEEE}
}

Thesis

  • Beyond linearity: nonlinear matrix and tensor decompositions A. Awari, supervised by N. Gillis and A. Vandaele PhD thesis, University of Mons, 2026

SoftwareCode for every paper, with the experiments

  • ADMM for Nonlinear CP Decompositions

    ADMM for nonlinear CP decompositions, where an element-wise nonlinearity models clipped or censored data, such as values below a limit of detection in metabolomics or saturated audio recordings.

  • ADMM for NMDsMATLAB

    ADMM for twelve nonlinear matrix decompositions (ReLU, square, MinMax, modulus with Frobenius, ℓ1 or KL), with missing data and an adaptive penalty.

  • ADMM for Generalized Tensor DecompositionsPython

    Global ADMM for the canonical polyadic decomposition under Frobenius, ℓ1 and KL losses, with the AO-ADMM comparison.

  • Coordinate Descent for ReLU-NMDMATLAB, Julia, C++

    Exact coordinate descent for ReLU-NMD, solving each scalar subproblem by sweeping its breakpoints; multithreaded.

  • Accelerated ReLU-NMDMATLAB

    A-NMD and 3B-NMD with nuclear-norm initialization, with N. Gillis and G. Seraghiti.

  • Sigmoid NMDPython

    Block coordinate descent for the sigmoid decomposition, with H. Nguyen.

Talks and conferences

  • 2026
    European Signal Processing Conference (EUSIPCO)Low-rank matrix and tensor decompositions session, Bruges, Belgium
  • 2025
    EUROPT Workshop on Advances in Continuous OptimizationSouthampton, UK
  • 2025
    Biennial Numerical Analysis ConferenceGlasgow, UK
  • 2024
    EUROPT Workshop on Advances in Continuous OptimizationLund, Sweden
  • 2024
    SIAM Conference on Applied Linear AlgebraParis, France
  • 2024
    Belgian Mathematical Optimization WorkshopLa Roche-en-Ardenne, Belgium
  • 2023
    Foundations of Computational Mathematics (FoCM)Paris, France

News

  • Starting as a postdoctoral researcher in Evrim Acar's group at SimulaMet, Oslo.
  • Public PhD defence at the University of Mons.
  • Alternating direction method of multipliers for nonlinear matrix decompositions accepted in Signal Processing (Elsevier).
  • Passed my private PhD defence at the University of Mons.
  • Nonlinear tensor decomposition for pattern discovery, with SimulaMet, submitted to ICASSP 2027 (arXiv).
  • PhD thesis Beyond Linearity: Nonlinear Matrix and Tensor Decompositions submitted.
  • ADMM for tensor decompositions presented at EUSIPCO 2026 in Bruges.
  • Visiting researcher in Evrim Acar's DataSci group at SimulaMet, Oslo, until June.
  • Preprint on ADMM for nonlinear matrix decompositions on arXiv.