Making Sense of Learning Machines

News and Updates

  • PI @ ELLIS Institute Finland November 17, 2025

    I am one of the Principal Investigators in the newly established ELLIS Institute Finland.

  • Program Chair for AISTATS 2026 August 12, 2025

    I’ve been invited to serve as Program Chair for AISTATS 2026 together with Prof. Aaditya Ramdas from Carnegie Mellon University.

  • Five papers presented at ICLR 2025 April 24, 2025

    This year my group is presenting works on diffusion models, computational methods, and RL at the International Conference on Learning Representations.

  • Associate Professor (with tenure) February 1, 2025

    I have been appointed Associate Professor in Machine Learning (with tenure) at Aalto University.

  • AI Researcher of the Year October 23, 2024

    I have been awarded ‘AI Researcher of the Year’ by AI Finland (Teknologiateollisuus).

  • Lassi Meronen awarded for best thesis March 21, 2024

    Lassi Meronen’s thesis ‘Uncertainty Quantification in Deep Learning’ has been awarded one of the best doctoral theses 2023 in the Aalto School of Science.

  • Finnish Doctoral Program Network in AI (AI-DOC) March 1, 2024

    I’m acting as Director of the new Finnish Doctoral Program Network in AI that is a joint venture of 10 universities in Finland.

  • Teacher of the Year 2023 December 20, 2023

    I have been awarded ‘Teacher of the Year 2023’ by the Aalto University Department of Computer Science.

  • ELLIS Doctoral Symposium August 28, 2023

    I’m acting as hosting faculty for the ELLIS Doctoral Symposium 2023 (EDS) of the ELLIS Doctoral Program.

  • Five papers presented at NeurIPS 2021 December 5, 2021

    My group is presenting five papers at the main conference and one workshop paper at NeurIPS this year.

  • Keynote at the NeurIPS Meetup Copenhagen December 5, 2021

    After a two-year break in travelling (since NeurIPS 2019), I’m giving a live keynote at the official NeurIPS satellite event in Copenhagen.

  • Appointed as ELLIS Scholar October 25, 2021

    I have been appointed as an ELLIS Scholar in Theory, Algorithms and Computations of Modern Learning Systems under European Laboratory for Learning and Intelligent Systems (ELLIS).

  • Academy of Finland Research Fellow September 1, 2021

    I have received five-year personal funding from the Academy of Finland to support my research.

  • Member of the Young Academy Finland September 1, 2021

    I have been appointed as member of the Young Academy Finland for the term 2021–2025.

Research Highlights

Illustration from Applied Stochastic Differential Equations

Simo SärkkäArno Solin

Applied Stochastic Differential Equations
Cambridge University Press 2019 Abstract: Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are...

Illustration from Free hunch: Denoiser covariance estimation for diffusion models without extra costs

Severi RissanenMarkus HeinonenArno Solin

Free hunch: Denoiser covariance estimation for diffusion models without extra costs
International Conference on Learning Representations (ICLR) 2025 Abstract: The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked...

Illustration from Streamlining prediction in Bayesian deep learning

Rui LiMarcus KlassonArno SolinMartin Trapp

Streamlining prediction in Bayesian deep learning
International Conference on Learning Representations (ICLR) 2025 Abstract: The rising interest in Bayesian deep learning (BDL) has led to a plethora of methods for estimating the posterior distribution. However, efficient computation of inferences, such as predictions, has been largely overlooked with Monte Carlo integration remaining the standard. In this work we examine streamlining prediction in BDL through a single forward pass without sampling. For this we use local linearisation on activation functions and local Gaussian approximations at linear layers. Thus...

Illustration from Equivariant denoisers cannot copy graphs: Align your graph diffusion models

Najwa LaabidSeveri RissanenMarkus HeinonenArno SolinVikas Garg

Equivariant denoisers cannot copy graphs: Align your graph diffusion models
International Conference on Learning Representations (ICLR) 2025 Abstract: Graph diffusion models, dominant in graph generative modeling, remain underexplored for graph-to-graph translation tasks like chemical reaction prediction. We demonstrate that standard permutation equivariant denoisers face fundamental limitations in these tasks due to their inability to break symmetries in noisy inputs. To address this, we propose aligning input and target graphs to break input symmetries while preserving permutation equivariance in non-matching graph portions. Using retrosynthesis (i.e., the task of predicting precursors for...

Illustration from Approximate Bayesian inference via bitstring representations

Aleksanteri SladekMartin TrappArno Solin

Approximate Bayesian inference via bitstring representations
Proceedings of the 41st Conference on Uncertainty in Artificial Intelligence (UAI) 2025 Abstract: The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex...

Illustration from DeSplat: Decomposed Gaussian splatting for distractor-free rendering

Yihao WangMarcus KlassonMatias TurkulainenShuzhe WangJuho KannalaArno Solin

DeSplat: Decomposed Gaussian splatting for distractor-free rendering
The IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) 2025 Abstract: Gaussian splatting enables fast novel view synthesis in static 3D environments. However, reconstructing real-world environments remains challenging as distractors or occluders break the multi-view consistency assumption required for accurate 3D reconstruction. Most existing methods rely on external semantic information from pre-trained models, introducing additional computational overhead as pre-processing steps or during optimization. In this work, we propose a novel method, DeSplat, that directly separates distractors and static scene elements purely based on...

Illustration from Gaussian splatting on the move: Blur and rolling shutter compensation for natural camera motion

Otto SeiskariJerry YlilammiValtteri KaatrasaloPekka RantalankilaMatias TurkulainenJuho KannalaEsa RahtuArno Solin

Gaussian splatting on the move: Blur and rolling shutter compensation for natural camera motion
Proceedings of European Conference on Computer Vision (ECCV) 2024 Abstract: High-quality scene reconstruction and novel view synthesis based on Gaussian Splatting (3DGS) typically require steady, high-quality photographs, often impractical to capture with handheld cameras. We present a method that adapts to camera motion and allows high-quality scene reconstruction with handheld video data suffering from motion blur and rolling shutter distortion. Our approach is based on detailed modelling of the physical image formation process and utilizes velocities estimated using visual-inertial odometry (VIO). Camera...

Illustration from Variational Gaussian process diffusion processes

Prakhar VermaVincent AdamArno Solin

Variational Gaussian process diffusion processes
Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024 Abstract: Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization...

Illustration from Sources of uncertainty in 3D scene reconstruction

Marcus KlassonRiccardo MereuJuho KannalaArno Solin

Sources of uncertainty in 3D scene reconstruction
Proceedings of European Conference on Computer Vision Workshops (ECCVW) 2024 Abstract: The process of 3D scene reconstruction can be affected by numerous uncertainty sources in real-world scenes. While Neural Radiance Fields (NeRFs) and 3D Gaussian Splatting (GS) achieve high-fidelity rendering, they lack built-in mechanisms to directly address or quantify uncertainties arising from the presence of noise, occlusions, confounding outliers, and imprecise camera pose inputs. In this paper, we introduce a taxonomy that categorizes different sources of uncertainty inherent in these methods. Moreover, we...

Illustration from Transport with support: Data-conditional diffusion bridges

Ella TamirMartin TrappArno Solin

Transport with support: Data-conditional diffusion bridges
Transactions on Machine Learning Research (TMLR) 2023 Abstract: The dynamic Schrödinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient iterative solvers. Recent works have demonstrated state-of-the-art results (eg. in modelling single-cell embryo RNA sequences or sampling from complex posteriors) but are limited to learning bridges with only initial and terminal constraints. Our work extends this paradigm by proposing the Iterative Smoothing...

Illustration from Generative modelling with inverse heat dissipation

Severi RissanenMarkus HeinonenArno Solin

Generative modelling with inverse heat dissipation
International Conference on Learning Representations (ICLR) 2023 Abstract: While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the empirical success of coarse-to-fine modelling, we propose a new diffusion-like model that generates images through stochastically reversing the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. We interpret...

Illustration from Stationary activations for uncertainty calibration in deep learning

Lassi MeronenChristabella IrwantoArno Solin

Stationary activations for uncertainty calibration in deep learning
Advances in Neural Information Processing Systems 33 (NeurIPS) 2020 Abstract: We introduce a new family of non-linear neural network activation functions that mimic the properties induced by the widely-used Matérn family of kernels in Gaussian process (GP) models. This class spans a range of locally stationary models of various degrees of mean-square differentiability. We show an explicit link to the corresponding GP models in the case that the network consists of one infinitely wide hidden layer. In the limit of infinite smoothness...

Illustration from Hilbert space methods for reduced-rank Gaussian process regression

Arno SolinSimo Särkkä

Hilbert space methods for reduced-rank Gaussian process regression
Statistics and Computing 2020 Abstract: This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of R^d. On this approximate eigenbasis the eigenvalues of the covariance function can be expressed as simple functions of the spectral density of the Gaussian process, which allows the GP inference to be solved...

Illustration from Know your boundaries: Constraining Gaussian processes by variational harmonic features

Arno SolinManon Kok

Know your boundaries: Constraining Gaussian processes by variational harmonic features
Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019 Abstract: Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in the domain of interest, which both constrains the GP and attains a low-rank representation that is used for speeding up inference. The method scales as O(nm^2) in prediction and O(m^3) in...

Illustration from Infinite-horizon Gaussian processes

Arno SolinJames HensmanRichard E. Turner

Infinite-horizon Gaussian processes
Advances in Neural Information Processing Systems 31 (NeurIPS) 2018 Abstract: Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by reducing the complexity to linear in the number of data points. The complexity is still cubic in the state dimension m which is an impediment to practical application. In certain special cases (Gaussian likelihood, regular spacing) the GP posterior will reach...

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