Euclidean spaces – semialgebraic sets – latent, embedded manifolds – topology – function spaces – metric spaces
Generative models, inference (UQ) and topology
- ‘Globally injective ReLU networks’, J. Mach. Learn. Res. 23 (2022) 1-55, with M. Puthawala, K. Kothari, M. Lassas and I. Dokmanić. View
- ‘Universal joint approximation of manifolds and densities by simple injective flows’, ICML 162 (2022) 17959-17983, with M. Puthawala, M. Lassas and I. Dokmanić. View ; ‘TRUMPETS: Injective flows for inference and inverse problems’, Uncertainty in Artificial Intelligence ’21 (2021) 1269-1278, with K. Kothari, A.E. Khorashadizadeh and I. Dokmanić. View . ‘Conditional injective flows for Bayesian imaging’, IEEE Trans. Comput. Imaging 9 (2023) 224-237, with A.E. Khorashadizadeh, K. Kothari, L. Salsi, A.A. Harandi and I. Dokmanić. View
- ‘Deep invertible approximation of topologically rich maps between manifolds’ (2025), with M. Puthawala, M. Lassas, I. Dokmanić and P. Pankka. View
- ‘Deep invertible approximation of topologically nontrivial fibrations’ (2026), with M. Puthawala, M. Lassas and I. Dokmanić, not available yet.
Hilbert spaces, approximating probability distributions, memorization
- ‘Conditional score-based diffusion models for Bayesian inference in infinite dimensions’, NeurIPS Proceedings: Advances in Neural Processing Systems 36 (2023) 24262-24290, with L. Baldassari, A. Siahkoohi, J. Garnier and K. Sølna. View
- ‘Preconditioned Langevin dynamics with score-based generative models for infinite-dimensional linear Bayesian inverse problems’, NeurIPS Proceedings: Advances in Neural Processing Systems (2025) in print, with L. Baldassari, J. Garnier and K. Sølna. View
- ‘On the convergence of Hilbert space MCMC with score-based priors and classifier-free guidance for nonlinear inverse problems’ (2025), with L. Baldassari, J. Garnier and K. Sølna, not available yet.
- ‘Diffeomorphism equivariant sampling methods via Bézier curves in Bayes Hilbert spaces’ (2025), with D. Mis and M. Lassas, not available yet.
Low-dimensional structure and manifolds
- ‘Reconstructing manifolds of large reach via measure learning in Bayes Hilbert spaces’ (2026), with D. Mis and M. Lassas, not available yet.
Foundation models
- ‘Learned conditioning operators yielding a foundation model for Bayesian inference’ (2026), not available yet.
Neural operators, surrogate models and adjoint states, SciML
- ‘Globally injective and bijective neural operators’, NeurIPS Proceedings: Advances in Neural Processing Systems 36 (2023) 57713-57753, with T. Furuya, M. Puthawala and M. Lassas. View
- ‘Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation’, J. Comp. Phys. 513 (2024) 113168, with J.A. Lara Benitez, T. Furuya, F. Faucher, A. Kratsios and X. Tricoche. View
- ‘Maps between graph measures and transformers for operator learning’ (2026), with K. Alkire, T. Furuya and M. Lassas, not available yet.
Computing
- ‘Mixture of experts softens the curse of dimensionality in operator learning’ (2024), with A. Kratsios, T. Furuya, J.A. Lara Benitez and M. Lassas. View
- ‘Can neural operators always be continuously discretized?’, NeurIPS (2024) in print, with T. Furuya, M. Puthawala and M. Lassas. View
- ‘The algebra of neural operator approximation’ (2026), with T. Furuya, M. Puthawala and M. Lassas, not available yet.
Deep learning, interpretability and inverse problems
- ‘Learning the geometry of wave-based imaging’, NeurIPS Proceedings: Advances in Neural Processing Systems 33 (2020) 8318-8329, with K. Kothari and I. Dokmanić. View
- ‘Learning double fibration transforms is data efficient’ (2025), with T.M. Roddenberry, L. Tzou, I. Dokmanić and R.G. Baraniuk, not available yet.
- ‘Deep learning architectures for nonlinear operator functions and nonlinear inverse problems’, Mathematical Statistics and Learning 4 (2022) 1-86, doi:10.4171/MSL/28, with M. Lassas and C.A. Wong. View
- ‘Convergence rates for learning linear operators from noisy data’, SIAM/ASA Journal on Uncertainty Quantification 11 (2023) 480-513, with N.B. Kovachki, N.H. Nelson and A.M. Stuart. View
- ‘Approximating the Electrical Impedance Tomography inversion operator’ (2025), with N.B. Kovachki, M. Lassas and N.H. Nelson, not available yet.
Semialgebraic sets
- ‘Semialgebraic Neural Networks: From roots to representations’, ICLR (2025) in print, with D. Mis and M. Lassas. View
- ‘Generative equilibrium operators’ (2026), not available yet.
Foundation models, measures and (interacting) particle systems
- ‘An approximation theory for metric space-valued functions with a view towards deep learning’ (2023), with A. Kratsios, C. Liu, M. Lassas, and I. Dokmanić. View
- ‘Transformers are universal in-context learners’, ICLR (2025) in print, with T. Furuya and G. Peyré. View
- ‘Transformers through the lens of support-preserving maps between measures’ (2025), with T. Furuya and M. Lassas. View
Kinetic theory context, collisions
- ‘Neural equilibria for long-term prediction of nonlinear conservation laws’ (2025), with J.A. Lara Benitez, J. Guo, K. Hegazy, I. Dokmanić and M.W. Mahoney. View
- ‘Operator state space models from nonlinear conservation laws’ (2026), with H. Schluter, I. Dokmanić and M. Lassas, not available yet.
- ‘Limit of transformers, reasoning and Boltzmann equation’, (2026), with T. Furuya, not available yet.
Training dynamics and feature dynamics
- ‘Training dynamics of infinitely deep and wide transformers’ (2025), not available yet.
- ‘Hypernetworks inducing heavy tailed distributions of weights while flattening the loss landscape’ (2025), not available yet.
- ‘Training of infinitely deep residual “sequential” neural operators and optimal control’ (2026), not available yet.
- ‘Dynamics of feature learning in injective flows through the embedding gap’ (2026), not available yet.
