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Constructing VAE Latent Spaces with Prescribed Topology
Authors:
Jilles S. van Hulst,
Jakub M. Tomczak,
W. P. M. H. Heemels,
Duarte J. Antunes
Abstract:
Variational autoencoders (VAEs) learn low-dimensional latent representations of high-dimensional data. When the data lies on a manifold with non-Euclidean topology, the standard Gaussian prior introduces a topological mismatch that degrades reconstruction quality and prevents faithful representation. We present a constructive mathematical framework that resolves this mismatch for all manifolds tha…
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Variational autoencoders (VAEs) learn low-dimensional latent representations of high-dimensional data. When the data lies on a manifold with non-Euclidean topology, the standard Gaussian prior introduces a topological mismatch that degrades reconstruction quality and prevents faithful representation. We present a constructive mathematical framework that resolves this mismatch for all manifolds that admit a product covering space. These are manifolds expressible as products of elementary factors (circles, intervals, or lines) or as quotients of such products by a finite symmetry group. The class includes cylinders, tori, Möbius strips, Klein bottles, and real projective spaces. Factorized distributions over the elementary factors yield product topologies with closed-form, decoupled KL divergences, so that each latent factor can be shaped independently while keeping training tractable. We catalogue reparametrizable encoder-prior pairs for periodic, bounded, and unbounded supports, and provide coordinate transformations that allow standard neural networks to output non-Euclidean parameters with smooth gradients. For quotient manifolds, the decoder receives group-invariant features of the covering-space coordinates, so that identified points produce identical outputs. Anchor constraints fix the coordinate system relative to the data or create soft topological holes. Experiments on synthetic manifolds and real-image datasets (rotated and cyclically shifted MNIST) confirm that a topology-matched prior aligns KL regularization with the data manifold. The resulting topology-aware models outperform the Gaussian baseline at all practically relevant regularization strengths. The code is available at https://github.com/JvHulst/VAE-Topology.
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Submitted 5 June, 2026;
originally announced June 2026.
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Bridging the Simulation-to-Reality Gap in Electron Microscope Calibration via VAE-EM Estimation
Authors:
Jilles S. van Hulst,
W. P. M. H. Heemels,
Duarte J. Antunes
Abstract:
Electron microscopy has enabled many scientific breakthroughs across multiple fields. A key challenge is the tuning of microscope parameters based on images to overcome optical aberrations that deteriorate image quality. This calibration problem is challenging due to the high-dimensional and noisy nature of the diagnostic images, and the fact that optimal parameters cannot be identified from a sin…
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Electron microscopy has enabled many scientific breakthroughs across multiple fields. A key challenge is the tuning of microscope parameters based on images to overcome optical aberrations that deteriorate image quality. This calibration problem is challenging due to the high-dimensional and noisy nature of the diagnostic images, and the fact that optimal parameters cannot be identified from a single image. We tackle the calibration problem for Scanning Transmission Electron Microscopes (STEM) by employing variational autoencoders (VAEs), trained on simulated data, to learn low-dimensional representations of images, whereas most existing methods extract only scalar values. We then simultaneously estimate the model that maps calibration parameters to encoded representations and the optimal calibration parameters using an expectation maximization (EM) approach. This joint estimation explicitly addresses the simulation-to-reality gap inherent in data-driven methods that train on simulated data from a digital twin. We leverage the known symmetry property of the optical system to establish global identifiability of the joint estimation problem, ensuring that a unique optimum exists. We demonstrate that our approach is substantially faster and more consistent than existing methods on a real STEM, achieving a 2x reduction in estimation error while requiring fewer observations. This represents a notable advance in automated STEM calibration and demonstrates the potential of VAEs for information compression in images. Beyond microscopy, the VAE-EM framework applies to inverse problems where simulated training data introduces a reality gap and where non-injective mappings would otherwise prevent unique solutions.
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Submitted 19 March, 2026; v1 submitted 17 March, 2026;
originally announced March 2026.
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Formal Entropy-Regularized Control of Stochastic Systems
Authors:
Menno van Zutphen,
Giannis Delimpaltadakis,
Duarte J. Antunes
Abstract:
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In continuous-state stochastic systems, accurate entropy analysis and control remains a challenge. In recent years, finite-state abstractions of continuous systems…
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Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In continuous-state stochastic systems, accurate entropy analysis and control remains a challenge. In recent years, finite-state abstractions of continuous systems have enabled control synthesis with formal performance guarantees on objectives such as stage costs. However, these results do not extend to entropy-based performance measures. We solve this problem by first obtaining bounds on the entropy of system discretizations using traditional formal-abstractions results, and then obtaining an additional bound on the difference between the entropy of a continuous distribution and that of its discretization. The resulting theory enables formal entropy-aware controller synthesis that trades predictability against control performance while preserving formal guarantees for the original continuous system. More specifically, we focus on minimizing the linear combination of the KL divergence of the system trajectory distribution to uniform -- our system entropy metric -- and a generic cumulative cost. We note that the bound we derive on the difference between the KL divergence to uniform of a given continuous distribution and its discretization can also be relevant in more general information-theoretic contexts. A set of case studies illustrates the effectiveness of the method.
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Submitted 5 March, 2026;
originally announced March 2026.
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Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise
Authors:
Felipe J. P. Antunes,
Yuri F. Saporito,
Sebastian Jaimungal
Abstract:
We present a novel numerical method for solving McKean--Vlasov forward--backward stochastic differential equations (MV--FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a pathwise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expec…
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We present a novel numerical method for solving McKean--Vlasov forward--backward stochastic differential equations (MV--FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a pathwise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise, without requiring computationally expensive nested Monte Carlo simulations. The mean-field interaction term is parameterized via a recurrent neural network trained to minimize an elicitable score, while the backward process is approximated through a hybrid feedforward and recurrent network representing the decoupling field. We validate the algorithm on a systemic-risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution. We further extend the model to quantile-mediated interactions, showcasing the flexibility of the elicitability framework beyond conditional means or moments. Finally, we apply the method to a non-stationary Aiyagari--Bewley--Huggett economic growth model with endogenous interest rates, illustrating its applicability to complex mean-field games without closed-form solutions.
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Submitted 11 June, 2026; v1 submitted 16 December, 2025;
originally announced December 2025.
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Smart Exploration in Reinforcement Learning using Bounded Uncertainty Models
Authors:
J. S. van Hulst,
W. P. M. H. Heemels,
D. J. Antunes
Abstract:
Reinforcement learning (RL) is a powerful framework for decision-making in uncertain environments, but it often requires large amounts of data to learn an optimal policy. We address this challenge by incorporating prior model knowledge to guide exploration and accelerate the learning process. Specifically, we assume access to a model set that contains the true transition kernel and reward function…
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Reinforcement learning (RL) is a powerful framework for decision-making in uncertain environments, but it often requires large amounts of data to learn an optimal policy. We address this challenge by incorporating prior model knowledge to guide exploration and accelerate the learning process. Specifically, we assume access to a model set that contains the true transition kernel and reward function. We optimize over this model set to obtain upper and lower bounds on the Q-function, which are then used to guide the exploration of the agent. We provide theoretical guarantees on the convergence of the Q-function to the optimal Q-function under the proposed class of exploring policies. Furthermore, we also introduce a data-driven regularized version of the model set optimization problem that ensures the convergence of the class of exploring policies to the optimal policy. Lastly, we show that when the model set has a specific structure, namely the bounded-parameter MDP (BMDP) framework, the regularized model set optimization problem becomes convex and simple to implement. In this setting, we also prove finite-time convergence to the optimal policy under mild assumptions. We demonstrate the effectiveness of the proposed exploration strategy, which we call BUMEX (Bounded Uncertainty Model-based Exploration), in a simulation study. The results indicate that the proposed method can significantly accelerate learning in benchmark examples. A toolbox is available at https://github.com/JvHulst/BUMEX.
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Submitted 21 August, 2026; v1 submitted 8 April, 2025;
originally announced April 2025.
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The MONET dataset: Multimodal drone thermal dataset recorded in rural scenarios
Authors:
Luigi Riz,
Andrea Caraffa,
Matteo Bortolon,
Mohamed Lamine Mekhalfi,
Davide Boscaini,
André Moura,
José Antunes,
André Dias,
Hugo Silva,
Andreas Leonidou,
Christos Constantinides,
Christos Keleshis,
Dante Abate,
Fabio Poiesi
Abstract:
We present MONET, a new multimodal dataset captured using a thermal camera mounted on a drone that flew over rural areas, and recorded human and vehicle activities. We captured MONET to study the problem of object localisation and behaviour understanding of targets undergoing large-scale variations and being recorded from different and moving viewpoints. Target activities occur in two different la…
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We present MONET, a new multimodal dataset captured using a thermal camera mounted on a drone that flew over rural areas, and recorded human and vehicle activities. We captured MONET to study the problem of object localisation and behaviour understanding of targets undergoing large-scale variations and being recorded from different and moving viewpoints. Target activities occur in two different land sites, each with unique scene structures and cluttered backgrounds. MONET consists of approximately 53K images featuring 162K manually annotated bounding boxes. Each image is timestamp-aligned with drone metadata that includes information about attitudes, speed, altitude, and GPS coordinates. MONET is different from previous thermal drone datasets because it features multimodal data, including rural scenes captured with thermal cameras containing both person and vehicle targets, along with trajectory information and metadata. We assessed the difficulty of the dataset in terms of transfer learning between the two sites and evaluated nine object detection algorithms to identify the open challenges associated with this type of data. Project page: https://github.com/fabiopoiesi/monet_dataset.
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Submitted 19 July, 2023; v1 submitted 11 April, 2023;
originally announced April 2023.
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Spatial-And-Context aware (SpACe) "virtual biopsy" radiogenomic maps to target tumor mutational status on structural MRI
Authors:
Marwa Ismail,
Ramon Correa,
Kaustav Bera,
Ruchika Verma,
Anas Saeed Bamashmos,
Niha Beig,
Jacob Antunes,
Prateek Prasanna,
Volodymyr Statsevych,
Manmeet Ahluwalia,
Pallavi Tiwari
Abstract:
With growing emphasis on personalized cancer-therapies,radiogenomics has shown promise in identifying target tumor mutational status on routine imaging (i.e. MRI) scans. These approaches fall into 2 categories: (1) deep-learning/radiomics (context-based), using image features from the entire tumor to identify the gene mutation status, or (2) atlas (spatial)-based to obtain likelihood of gene mutat…
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With growing emphasis on personalized cancer-therapies,radiogenomics has shown promise in identifying target tumor mutational status on routine imaging (i.e. MRI) scans. These approaches fall into 2 categories: (1) deep-learning/radiomics (context-based), using image features from the entire tumor to identify the gene mutation status, or (2) atlas (spatial)-based to obtain likelihood of gene mutation status based on population statistics. While many genes (i.e. EGFR, MGMT) are spatially variant, a significant challenge in reliable assessment of gene mutation status on imaging has been the lack of available co-localized ground truth for training the models. We present Spatial-And-Context aware (SpACe) "virtual biopsy" maps that incorporate context-features from co-localized biopsy site along with spatial-priors from population atlases, within a Least Absolute Shrinkage and Selection Operator (LASSO) regression model, to obtain a per-voxel probability of the presence of a mutation status (M+ vs M-). We then use probabilistic pair-wise Markov model to improve the voxel-wise prediction probability. We evaluate the efficacy of SpACe maps on MRI scans with co-localized ground truth obtained from corresponding biopsy, to predict the mutation status of 2 driver genes in Glioblastoma: (1) EGFR (n=91), and (2) MGMT (n=81). When compared against deep-learning (DL) and radiomic models, SpACe maps obtained training and testing accuracies of 90% (n=71) and 90.48% (n=21) in identifying EGFR amplification status,compared to 80% and 71.4% via radiomics, and 74.28% and 65.5% via DL. For MGMT status, training and testing accuracies using SpACe were 88.3% (n=61) and 71.5% (n=20), compared to 52.4% and 66.7% using radiomics,and 79.3% and 68.4% using DL. Following validation,SpACe maps could provide surgical navigation to improve localization of sampling sites for targeting of specific driver genes in cancer.
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Submitted 17 June, 2020;
originally announced June 2020.
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MRQy: An Open-Source Tool for Quality Control of MR Imaging Data
Authors:
Amir Reza Sadri,
Andrew Janowczyk,
Ren Zou,
Ruchika Verma,
Niha Beig,
Jacob Antunes,
Anant Madabhushi,
Pallavi Tiwari,
Satish E. Viswanath
Abstract:
We sought to develop a quantitative tool to quickly determine relative differences in MRI volumes both within and between large MR imaging cohorts (such as available in The Cancer Imaging Archive (TCIA)), in order to help determine the generalizability of radiomics and machine learning schemes to unseen datasets. The tool is intended to help quantify presence of (a) site- or scanner-specific varia…
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We sought to develop a quantitative tool to quickly determine relative differences in MRI volumes both within and between large MR imaging cohorts (such as available in The Cancer Imaging Archive (TCIA)), in order to help determine the generalizability of radiomics and machine learning schemes to unseen datasets. The tool is intended to help quantify presence of (a) site- or scanner-specific variations in image resolution, field-of-view, or image contrast, or (b) imaging artifacts such as noise, motion, inhomogeneity, ringing, or aliasing; which can adversely affect relative image quality between data cohorts. We present MRQy, a new open-source quality control tool to (a) interrogate MRI cohorts for site- or equipment-based differences, and (b) quantify the impact of MRI artifacts on relative image quality; to help determine how to correct for these variations prior to model development. MRQy extracts a series of quality measures (e.g. noise ratios, variation metrics, entropy and energy criteria) and MR image metadata (e.g. voxel resolution, image dimensions) for subsequent interrogation via a specialized HTML5 based front-end designed for real-time filtering and trend visualization. MRQy was used to evaluate (a) n=133 brain MRIs from TCIA (7 sites), and (b) n=104 rectal MRIs (3 local sites). MRQy measures revealed significant site-specific variations in both cohorts, indicating potential batch effects. Marked differences in specific MRQy measures were also able to identify outlier MRI datasets that needed to be corrected for common MR imaging artifacts. MRQy is designed to be a standalone, unsupervised tool that can be efficiently run on a standard desktop computer. It has been made freely accessible at \url{http://github.com/ccipd/MRQy} for wider community use and feedback.
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Submitted 17 August, 2020; v1 submitted 9 April, 2020;
originally announced April 2020.
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Attention Filtering for Multi-person Spatiotemporal Action Detection on Deep Two-Stream CNN Architectures
Authors:
João Antunes,
Pedro Abreu,
Alexandre Bernardino,
Asim Smailagic,
Daniel Siewiorek
Abstract:
Action detection and recognition tasks have been the target of much focus in the computer vision community due to their many applications, namely, security, robotics and recommendation systems. Recently, datasets like AVA, provide multi-person, multi-label, spatiotemporal action detection and recognition challenges. Being unable to discern which portions of the input to use for classification is a…
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Action detection and recognition tasks have been the target of much focus in the computer vision community due to their many applications, namely, security, robotics and recommendation systems. Recently, datasets like AVA, provide multi-person, multi-label, spatiotemporal action detection and recognition challenges. Being unable to discern which portions of the input to use for classification is a limitation of two-stream CNN approaches, once the vision task involves several people with several labels. We address this limitation and improve the state-of-the-art performance of two-stream CNNs. In this paper we present four contributions: our fovea attention filtering that highlights targets for classification without discarding background; a generalized binary loss function designed for the AVA dataset; miniAVA, a partition of AVA that maintains temporal continuity and class distribution with only one tenth of the dataset size; and ablation studies on alternative attention filters. Our method, using fovea attention filtering and our generalized binary loss, achieves a relative video mAP improvement of 20% over the two-stream baseline in AVA, and is competitive with the state-of-the-art in the UCF101-24. We also show a relative video mAP improvement of 12.6% when using our generalized binary loss over the standard sum-of-sigmoids.
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Submitted 21 July, 2019;
originally announced July 2019.
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Trajectory Tracking for Quadrotors with Attitude Control on $\mathcal{S}^2 \times \mathcal{S}^1$
Authors:
Dave Kooijman,
Angela P. Schoellig,
Duarte J. Antunes
Abstract:
The control of a quadrotor is typically split into two subsequent problems: finding desired accelerations to control its position, and controlling its attitude and the total thrust to track these accelerations and to track a yaw angle reference. While the thrust vector, generating accelerations, and the angle of rotation about the thrust vector, determining the yaw angle, can be controlled indepen…
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The control of a quadrotor is typically split into two subsequent problems: finding desired accelerations to control its position, and controlling its attitude and the total thrust to track these accelerations and to track a yaw angle reference. While the thrust vector, generating accelerations, and the angle of rotation about the thrust vector, determining the yaw angle, can be controlled independently, most attitude control strategies in the literature, relying on representations in terms of quaternions, rotation matrices or Euler angles, result in an unnecessary coupling between the control of the thrust vector and of the angle about this vector. This leads, for instance, to undesired position tracking errors due to yaw tracking errors. In this paper we propose to tackle the attitude control problem using an attitude representation in the Cartesian product of the 2-sphere and the 1-sphere, denoted by $\mathcal{S}^2\times \mathcal{S}^1$. We propose a non-linear tracking control law on $\mathcal{S}^2\times \mathcal{S}^1$ that decouples the control of the thrust vector and of the angle of rotation about the thrust vector, and guarantees almost global asymptotic stability. Simulation results highlight the advantages of the proposed approach over previous approaches.
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Submitted 17 June, 2019;
originally announced June 2019.
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Weighted Multisource Tradaboost
Authors:
João Antunes,
Alexandre Bernardino,
Asim Smailagic,
Daniel Siewiorek
Abstract:
In this paper we propose an improved method for transfer learning that takes into account the balance between target and source data. This method builds on the state-of-the-art Multisource Tradaboost, but weighs the importance of each datapoint taking into account the amount of target and source data available. A comparative study is then presented exposing the performance of four transfer learnin…
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In this paper we propose an improved method for transfer learning that takes into account the balance between target and source data. This method builds on the state-of-the-art Multisource Tradaboost, but weighs the importance of each datapoint taking into account the amount of target and source data available. A comparative study is then presented exposing the performance of four transfer learning methods as well as the proposed Weighted Multisource Tradaboost. The experimental results show that the proposed method is able to outperform the base method as the number of target samples increase. These results are promising in the sense that source-target ratio weighing may be a path to improve current methods of transfer learning. However, against the asymptotic conjecture, all transfer learning methods tested in this work get outperformed by a no-transfer SVM for large number on target samples.
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Submitted 26 March, 2019;
originally announced March 2019.
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A Study on the Use of Eye Tracking to Adapt Gameplay and Procedural Content Generation in First-Person Shooter Games
Authors:
João Antunes,
Pedro Santana
Abstract:
This paper studies the use of eye tracking in a First-Person Shooter (FPS) game as a~mechanism to: (1) control the attention of the player's avatar according to the attention deployed by the player, and (2) guide the gameplay and game's procedural content generation, accordingly. This results in a more natural use of eye tracking in comparison to a use in which the eye tracker directly substitutes…
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This paper studies the use of eye tracking in a First-Person Shooter (FPS) game as a~mechanism to: (1) control the attention of the player's avatar according to the attention deployed by the player, and (2) guide the gameplay and game's procedural content generation, accordingly. This results in a more natural use of eye tracking in comparison to a use in which the eye tracker directly substitutes control input devices, such as gamepads. The study was conducted on a custom endless runner FPS, Zombie Runner, using an affordable eye tracker. Evaluation sessions showed that the proposed use of eye tracking provides a more challenging and immersive experience to the player, when compared to its absence. However, a strong correlation between eye tracker calibration problems and player's overall experience was found. This means that eye tracking technology still needs to evolve but also means that once technology gets mature enough players are expected to benefit greatly from the inclusion of eye tracking in their gaming experience.
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Submitted 21 May, 2018; v1 submitted 4 January, 2018;
originally announced January 2018.