Melih Kandemir

Gulcin Baykal, Melih Kandemir, Gozde Unal

Codebook collapse is a common problem in training deep generative models with discrete representation spaces like Vector Quantized Variational Autoencoders (VQ-VAEs). We observe that the same problem arises for the alternatively designed discrete variational autoencoders (dVAEs) whose encoder directly learns a distribution over the codebook embeddings to represent the data. We hypothesize that using the softmax function to obtain a probability distribution causes the codebook collapse by assigning overconfident probabilities to the best matching codebook elements. In this paper, we propose a novel way to incorporate evidential deep learning (EDL) instead of softmax to combat the codebook collapse problem of dVAE. We evidentially monitor the significance of attaining the probability distribution over the codebook embeddings, in contrast to softmax usage. Our experiments using various datasets show that our model, called EdVAE, mitigates codebook collapse while improving the reconstruction performance, and enhances the codebook usage compared to dVAE and VQ-VAE based models. Our code can be found at https://github.com/ituvisionlab/EdVAE .

Hamish Flynn, David Reeb, Melih Kandemir et al.

We present improved algorithms with worst-case regret guarantees for the stochastic linear bandit problem. The widely used "optimism in the face of uncertainty" principle reduces a stochastic bandit problem to the construction of a confidence sequence for the unknown reward function. The performance of the resulting bandit algorithm depends on the size of the confidence sequence, with smaller confidence sets yielding better empirical performance and stronger regret guarantees. In this work, we use a novel tail bound for adaptive martingale mixtures to construct confidence sequences which are suitable for stochastic bandits. These confidence sequences allow for efficient action selection via convex programming. We prove that a linear bandit algorithm based on our confidence sequences is guaranteed to achieve competitive worst-case regret. We show that our confidence sequences are tighter than competitors, both empirically and theoretically. Finally, we demonstrate that our tighter confidence sequences give improved performance in several hyperparameter tuning tasks.

Gulcin Baykal, Melih Kandemir, Gozde Unal

Disentangled representation learning aims to represent the underlying generative factors of a dataset in a latent representation independently of one another. In our work, we propose a discrete variational autoencoder (VAE) based model where the ground truth information about the generative factors are not provided to the model. We demonstrate the advantages of learning discrete representations over learning continuous representations in facilitating disentanglement. Furthermore, we propose incorporating an inductive bias into the model to further enhance disentanglement. Precisely, we propose scalar quantization of the latent variables in a latent representation with scalar values from a global codebook, and we add a total correlation term to the optimization as an inductive bias. Our method called FactorQVAE combines optimization based disentanglement approaches with discrete representation learning, and it outperforms the former disentanglement methods in terms of two disentanglement metrics (DCI and InfoMEC) while improving the reconstruction performance. Our code can be found at https://github.com/ituvisionlab/FactorQVAE.

Andreas Look, Melih Kandemir, Barbara Rakitsch et al.

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM) generalizes this framework to dynamical systems of unknown parametric form, where the transition and emission models are described by neural networks with uncertain weights. In this work, we propose the first deterministic inference algorithm for models of this type. Our framework allows efficient approximations for training and testing. We demonstrate in our experiments that our new method can be employed for a variety of tasks and enjoys a superior balance between predictive performance and computational budget.

Çağatay Yıldız, Melih Kandemir, Barbara Rakitsch

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian process ordinary differential equations, our model infers both independent dynamics and their interactions with reliable uncertainty estimates. In our formulation, each object is represented as a graph node and interactions are modeled by accumulating the messages coming from neighboring objects. We show that efficient inference of such a complex network of variables is possible with modern variational sparse Gaussian process inference techniques. We empirically demonstrate that our model improves the reliability of long-term predictions over neural network based alternatives and it successfully handles missing dynamic or static information. Furthermore, we observe that only our model can successfully encapsulate independent dynamics and interaction information in distinct functions and show the benefit from this disentanglement in extrapolation scenarios.

Manuel Haussmann, Mustafa Mert Çelikok, Melih Kandemir

While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains largely confined to tabular or linearizable settings. We identify the cause of this gap as an emergent isolation of three traditions: (i) measure-theoretic MDP foundations on general spaces limit their analysis to exact dynamic programming and ignore all error sources of a learning process; (ii) deterministic error propagation analysis addresses the approximation error via concentrability coefficients without a finite-sample analysis of the estimation error; and (iii) PAC generalization bounds characterize the estimation errors of simplified topologies. We bridge these traditions with a unified theoretical framework for fitted Q-iteration (FQI) on general measurable Borel spaces. Our main result provides a finite-sample, adaptive-data performance bound by chaining measure-theoretic probability with Bellman-operator contraction in Banach spaces. We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection. We further extend this analysis to provide the first cumulative, pathwise online regret guarantee for FQI in continuous spaces. These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.

Hamish Flynn, David Reeb, Melih Kandemir et al.

PAC-Bayes has recently re-emerged as an effective theory with which one can derive principled learning algorithms with tight performance guarantees. However, applications of PAC-Bayes to bandit problems are relatively rare, which is a great misfortune. Many decision-making problems in healthcare, finance and natural sciences can be modelled as bandit problems. In many of these applications, principled algorithms with strong performance guarantees would be very much appreciated. This survey provides an overview of PAC-Bayes bounds for bandit problems and an experimental comparison of these bounds. On the one hand, we found that PAC-Bayes bounds are a useful tool for designing offline bandit algorithms with performance guarantees. In our experiments, a PAC-Bayesian offline contextual bandit algorithm was able to learn randomised neural network polices with competitive expected reward and non-vacuous performance guarantees. On the other hand, the PAC-Bayesian online bandit algorithms that we tested had loose cumulative regret bounds. We conclude by discussing some topics for future work on PAC-Bayesian bandit algorithms.

Hamish Flynn, David Reeb, Melih Kandemir et al.

We present a PAC-Bayesian analysis of lifelong learning. In the lifelong learning problem, a sequence of learning tasks is observed one-at-a-time, and the goal is to transfer information acquired from previous tasks to new learning tasks. We consider the case when each learning task is a multi-armed bandit problem. We derive lower bounds on the expected average reward that would be obtained if a given multi-armed bandit algorithm was run in a new task with a particular prior and for a set number of steps. We propose lifelong learning algorithms that use our new bounds as learning objectives. Our proposed algorithms are evaluated in several lifelong multi-armed bandit problems and are found to perform better than a baseline method that does not use generalisation bounds.

Bahareh Tasdighi, Abdullah Akgül, Manuel Haussmann et al.

Actor-critic algorithms address the dual goals of reinforcement learning (RL), policy evaluation and improvement via two separate function approximators. The practicality of this approach comes at the expense of training instability, caused mainly by the destructive effect of the approximation errors of the critic on the actor. We tackle this bottleneck by employing an existing Probably Approximately Correct (PAC) Bayesian bound for the first time as the critic training objective of the Soft Actor-Critic (SAC) algorithm. We further demonstrate that online learning performance improves significantly when a stochastic actor explores multiple futures by critic-guided random search. We observe our resulting algorithm to compare favorably against the state-of-the-art SAC implementation on multiple classical control and locomotion tasks in terms of both sample efficiency and regret.

Magnus Victor Boock, Abdullah Akgül, Mustafa Mert Çelikok et al.

We present a new operator-theoretic representation learning framework for offline reinforcement learning that recovers the directed temporal geometry of a controlled Markov process from hitting time observations. While prior art often produces symmetric distances or fails to satisfy the triangle inequality, our framework learns a Hilbert-space displacement geometry where expected hitting times are realized as linear functionals of latent displacements. We prove that this representation exists under latent linear closure and is uniquely identifiable up to a bounded linear isomorphism. For finite-dimensional implementations, we show that global hitting-time error is bounded by one-step transition error amplified by the environment's transient spectral radius. Furthermore, we provide finite-sample guarantees accounting for approximation, statistical complexity, and trajectory-label mismatch. Derived from this theory, we curate Isomorphic Embedding Learning (IEL) as a new goal-agnostic foundation policy learning algorithm that anchors a HILP-style consistency objective with explicit hitting-time regression to ensure that the learned geometry reflects actual decision-time progress. This asymmetric and compositional structure enables robust graph-based multi-stage planning for long-horizon navigation. Our experiments demonstrate that IEL improves the state of the art of learning foundation policy policies from offline maze locomotion data. Our code can be found on https://github.com/MagnusBoock/IEL

Orhun Buğra Baran, Melih Kandemir, Ramazan Gokberk Cinbis

Autoregressive (AR) models are highly effective for image generation, yet their standard maximum-likelihood estimation training lacks direct optimization for sample quality and diversity. While reinforcement learning (RL) has been used to align diffusion models, these methods typically suffer from output diversity collapse. Similarly, concurrent RL methods for AR models rely strictly on instance-level rewards, often trading off distributional coverage for quality. To address these limitations, we propose a lightweight RL framework that casts token-based AR synthesis as a Markov Decision Process, optimized via Group Relative Policy Optimization (GRPO). Our core contribution is the introduction of a novel distribution-level Leave-One-Out FID (LOO-FID) reward; by leveraging an exponential moving average of feature moments, it explicitly encourages sample diversity and prevents mode collapse during policy updates. We integrate this with composite instance-level rewards (CLIP and HPSv2) for strict semantic and perceptual fidelity, and stabilize the multi-objective learning with an adaptive entropy regularization term. Extensive experiments on LlamaGen and VQGAN architectures demonstrate clear improvements across standard quality and diversity metrics within only a few hundred tuning iterations. The results also show that the model can be updated to produce competitive samples even without Classifier-Free Guidance, and bypass its 2x inference cost.

Aritra Dutta, El Houcine Bergou, Soumia Boucherouite et al.

Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood, their convergence for nonconvex functions stands on weak mathematical foundations. Most existing studies on the nonconvex convergence of SGD show the complexity results based on either the minimum of the expected gradient norm or the functional sub-optimality gap (for functions with extra structural property) by searching the entire range of iterates. Hence the last iterations of SGDs do not necessarily maintain the same complexity guarantee. This paper shows that an $ε$-stationary point exists in the final iterates of SGDs, given a large enough total iteration budget, $T$, not just anywhere in the entire range of iterates -- a much stronger result than the existing one. Additionally, our analyses allow us to measure the density of the $ε$-stationary points in the final iterates of SGD, and we recover the classical $O(\frac{1}{\sqrt{T}})$ asymptotic rate under various existing assumptions on the objective function and the bounds on the stochastic gradient. As a result of our analyses, we addressed certain myths and legends related to the nonconvex convergence of SGD and posed some thought-provoking questions that could set new directions for research.

Juliane Weilbach, Sebastian Gerwinn, Melih Kandemir et al.

Counterfactual analysis is intuitively performed by humans on a daily basis eg. "What should I have done differently to get the loan approved?". Such counterfactual questions also steer the formulation of scientific hypotheses. More formally it provides insights about potential improvements of a system by inferring the effects of hypothetical interventions into a past observation of the system's behaviour which plays a prominent role in a variety of industrial applications. Due to the hypothetical nature of such analysis, counterfactual distributions are inherently ambiguous. This ambiguity is particularly challenging in continuous settings in which a continuum of explanations exist for the same observation. In this paper, we address this problem by following a hierarchical Bayesian approach which explicitly models such uncertainty. In particular, we derive counterfactual distributions for a Bayesian Warped Gaussian Process thereby allowing for non-Gaussian distributions and non-additive noise. We illustrate the properties our approach on a synthetic and on a semi-synthetic example and show its performance when used within an algorithmic recourse downstream task.

Nicklas Werge, Yi-Shan Wu, Abdullah Akgül et al.

We study non-stationary linear contextual bandits through the lens of sequential Bayesian inference. Whereas existing algorithms typically rely on the Weighted Regularized Least-Squares (WRLS) objective, we study Weighted Sequential Bayesian (WSB), which maintains a posterior distribution over the time-varying reward parameters. Our main contribution is a novel concentration inequality for WSB posteriors, which introduces a prior-dependent term that quantifies the influence of initial beliefs. We show that this influence decays over time and derive tractable upper bounds that make the result useful for both analysis and algorithm design. Building on WSB, we introduce three algorithms: WSB-LinUCB, WSB-RandLinUCB, and WSB-LinTS. We establish frequentist regret guarantees: WSB-LinUCB matches the best-known WRLS-based guarantees, while WSB-RandLinUCB and WSB-LinTS improve upon them, all while preserving the computational efficiency of WRLS-based algorithms.

Abdullah Akgül, Gozde Unal, Melih Kandemir

We study the problem of fitting a model to a dynamical environment when new modes of behavior emerge sequentially. The learning model is aware when a new mode appears, but it cannot access the true modes of individual training sequences. The state-of-the-art continual learning approaches cannot handle this setup, because parameter transfer suffers from catastrophic interference and episodic memory design requires the knowledge of the ground-truth modes of sequences. We devise a novel continual learning method that overcomes both limitations by maintaining a \textit{descriptor} of the mode of an encountered sequence in a neural episodic memory. We employ a Dirichlet Process prior on the attention weights of the memory to foster efficient storage of the mode descriptors. Our method performs continual learning by transferring knowledge across tasks by retrieving the descriptors of similar modes of past tasks to the mode of a current sequence and feeding this descriptor into its transition kernel as control input. We observe the continual learning performance of our method to compare favorably to the mainstream parameter transfer approach.

Gulcin Baykal, Abdullah Akgül, Manuel Haussmann et al.

ObjectRL is an open-source Python codebase for deep reinforcement learning (RL), designed for research-oriented prototyping with minimal programming effort. Unlike existing codebases, ObjectRL is built on Object-Oriented Programming (OOP) principles, providing a clear structure that simplifies the implementation, modification, and evaluation of new algorithms. ObjectRL lowers the entry barrier for deep RL research by organizing best practices into explicit, clearly separated components, making them easier to understand and adapt. Each algorithmic component is a class with attributes that describe key RL concepts and methods that intuitively reflect their interactions. The class hierarchy closely follows common ontological relationships, enabling data encapsulation, inheritance, and polymorphism, which are core features of OOP. We demonstrate the efficiency of ObjectRL's design through representative use cases that highlight its flexibility and suitability for rapid prototyping. The documentation and source code are available at https://objectrl.readthedocs.io and https://github.com/adinlab/objectrl .

Amelia Jiménez-Sánchez, Natalia-Rozalia Avlona, Sarah de Boer et al.

Datasets play a critical role in medical imaging research, yet issues such as label quality, shortcuts, and metadata are often overlooked. This lack of attention may harm the generalizability of algorithms and, consequently, negatively impact patient outcomes. While existing medical imaging literature reviews mostly focus on machine learning (ML) methods, with only a few focusing on datasets for specific applications, these reviews remain static -- they are published once and not updated thereafter. This fails to account for emerging evidence, such as biases, shortcuts, and additional annotations that other researchers may contribute after the dataset is published. We refer to these newly discovered findings of datasets as research artifacts. To address this gap, we propose a living review that continuously tracks public datasets and their associated research artifacts across multiple medical imaging applications. Our approach includes a framework for the living review to monitor data documentation artifacts, and an SQL database to visualize the citation relationships between research artifact and dataset. Lastly, we discuss key considerations for creating medical imaging datasets, review best practices for data annotation, discuss the significance of shortcuts and demographic diversity, and emphasize the importance of managing datasets throughout their entire lifecycle. Our demo is publicly available at http://inthepicture.itu.dk/.

Bahareh Tasdighi, Manuel Haussmann, Nicklas Werge et al.

Reinforcement learning (RL) for continuous control under delayed rewards is an under-explored problem despite its significance in real-world applications. Many complex skills are based on intermediate ones as prerequisites. For instance, a humanoid locomotor must learn how to stand before it can learn to walk. To cope with delayed reward, an agent must perform deep exploration. However, existing deep exploration methods are designed for small discrete action spaces, and their generalization to state-of-the-art continuous control remains unproven. We address the deep exploration problem for the first time from a PAC-Bayesian perspective in the context of actor-critic learning. To do this, we quantify the error of the Bellman operator through a PAC-Bayes bound, where a bootstrapped ensemble of critic networks represents the posterior distribution, and their targets serve as a data-informed function-space prior. We derive an objective function from this bound and use it to train the critic ensemble. Each critic trains an individual soft actor network, implemented as a shared trunk and critic-specific heads. The agent performs deep exploration by acting epsilon-softly on a randomly chosen actor head. Our proposed algorithm, named {\it PAC-Bayesian Actor-Critic (PBAC)}, is the only algorithm to consistently discover delayed rewards on continuous control tasks with varying difficulty.

Abdullah Akgül, Gulcin Baykal, Manuel Haußmann et al.

Optimal control of complex environments with robotic systems faces two complementary and intertwined challenges: efficient organization of sensory state information and far-sighted action planning. Because the reinforcement learning framework addresses only the latter, it tends to deliver sample-inefficient solutions. Active inference is the state-of-the-art process theory that explains how biological brains handle this dual problem. However, its applications to artificial intelligence have thus far been limited to extensions of existing model-based approaches. We present a formal abstraction of reinforcement learning algorithms that spans model-based, distributional, and model-free approaches. This abstraction seamlessly integrates active inference into the distributional reinforcement learning framework, making its performance advantages accessible without transition dynamics modeling.

Nicklas Werge, Yi-Shan Wu, Bahareh Tasdighi et al.

Off-policy reinforcement learning in continuous control tasks depends critically on accurate $Q$-value estimates. Conservative aggregation over ensembles, such as taking the minimum, is commonly used to mitigate overestimation bias. However, these static rules are coarse, discard valuable information from the ensemble, and cannot adapt to task-specific needs or different learning regimes. We propose Directional Ensemble Aggregation (DEA), an aggregation method that adaptively combines $Q$-value estimates in actor-critic frameworks. DEA introduces two fully learnable directional parameters: one that modulates critic-side conservatism and another that guides actor-side policy exploration. Both parameters are learned using ensemble disagreement-weighted Bellman errors, which weight each sample solely by the direction of its Bellman error. This directional learning mechanism allows DEA to adjust conservatism and exploration in a data-driven way, adapting aggregation to both uncertainty levels and the phase of training. We evaluate DEA across continuous control benchmarks and learning regimes - from interactive to sample-efficient - and demonstrate its effectiveness over static ensemble strategies.

Abdullah Akgül, Gulcin Baykal, Manuel Haußmann et al.

Continuous control of non-stationary environments is a major challenge for deep reinforcement learning algorithms. The time-dependency of the state transition dynamics aggravates the notorious stability problems of model-free deep actor-critic architectures. We posit that two properties will play a key role in overcoming non-stationarity in transition dynamics: (i)~preserving the plasticity of the critic network and (ii) directed exploration for rapid adaptation to changing dynamics. We show that performing on-policy reinforcement learning with an evidential critic provides both. The evidential design ensures a fast and accurate approximation of the uncertainty around the state value, which maintains the plasticity of the critic network by detecting the distributional shifts caused by changes in dynamics. The probabilistic critic also makes the actor training objective a random variable, enabling the use of directed exploration approaches as a by-product. We name the resulting algorithm \emph{Evidential Proximal Policy Optimization (EPPO)} due to the integral role of evidential uncertainty quantification in both policy evaluation and policy improvement stages. Through experiments on non-stationary continuous control tasks, where the environment dynamics change at regular intervals, we demonstrate that our algorithm outperforms state-of-the-art on-policy reinforcement learning variants in both task-specific and overall return.

Abdullah Akgül, Manuel Haußmann, Melih Kandemir

Current approaches to model-based offline reinforcement learning often incorporate uncertainty-based reward penalization to address the distributional shift problem. These approaches, commonly known as pessimistic value iteration, use Monte Carlo sampling to estimate the Bellman target to perform temporal difference-based policy evaluation. We find out that the randomness caused by this sampling step significantly delays convergence. We present a theoretical result demonstrating the strong dependency of suboptimality on the number of Monte Carlo samples taken per Bellman target calculation. Our main contribution is a deterministic approximation to the Bellman target that uses progressive moment matching, a method developed originally for deterministic variational inference. The resulting algorithm, which we call Moment Matching Offline Model-Based Policy Optimization (MOMBO), propagates the uncertainty of the next state through a nonlinear Q-network in a deterministic fashion by approximating the distributions of hidden layer activations by a normal distribution. We show that it is possible to provide tighter guarantees for the suboptimality of MOMBO than the existing Monte Carlo sampling approaches. We also observe MOMBO to converge faster than these approaches in a large set of benchmark tasks.

Bahareh Tasdighi, Nicklas Werge, Yi-Shan Wu et al.

Off-policy actor-critic algorithms have shown strong potential in deep reinforcement learning for continuous control tasks. Their success primarily comes from leveraging pessimistic state-action value function updates, which reduce function approximation errors and stabilize learning. However, excessive pessimism can limit exploration, preventing the agent from effectively refining its policies. Conversely, optimism can encourage exploration but may lead to high-risk behaviors and unstable learning if not carefully managed. To address this trade-off, we propose Utility Soft Actor-Critic (USAC), a novel framework that allows independent, interpretable control of pessimism and optimism for both the actor and the critic. USAC dynamically adapts its exploration strategy based on the uncertainty of critics using a utility function, enabling a task-specific balance between optimism and pessimism. This approach goes beyond binary choices of pessimism or optimism, making the method both theoretically meaningful and practically feasible. Experiments across a variety of continuous control tasks show that adjusting the degree of pessimism or optimism significantly impacts performance. When configured appropriately, USAC consistently outperforms state-of-the-art algorithms, demonstrating its practical utility and feasibility.

Busra Asan, Abdullah Akgül, Alper Unal et al.

Seasonal forecasting is a crucial task when it comes to detecting the extreme heat and colds that occur due to climate change. Confidence in the predictions should be reliable since a small increase in the temperatures in a year has a big impact on the world. Calibration of the neural networks provides a way to ensure our confidence in the predictions. However, calibrating regression models is an under-researched topic, especially in forecasters. We calibrate a UNet++ based architecture, which was shown to outperform physics-based models in temperature anomalies. We show that with a slight trade-off between prediction error and calibration error, it is possible to get more reliable and sharper forecasts. We believe that calibration should be an important part of safety-critical machine learning applications such as weather forecasters.

Andreas Look, Melih Kandemir, Barbara Rakitsch et al.

Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems, modeling is much more challenging for stochastic systems in which one is interested in obtaining a predictive distribution over future trajectories. Existing methods are either computationally slow since they rely on Monte Carlo sampling or make simplifying assumptions such that the predictive distribution is unimodal. In this work, we present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system. The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules. Our moment matching scheme can be exploited for sample-free inference, leading to more efficient and stable training compared to Monte Carlo alternatives. Furthermore, we propose structured approximations to the covariance matrices of the Gaussian components in order to scale up to systems with many agents. We benchmark our novel framework on two challenging autonomous driving datasets. Both confirm the benefits of our method compared to state-of-the-art methods. We further demonstrate the usefulness of our individual contributions in a carefully designed ablation study and provide a detailed runtime analysis of our proposed covariance approximations. Finally, we empirically demonstrate the generalization ability of our method by evaluating its performance on unseen scenarios.

Krista Longi, Jakob Lindinger, Olaf Duennbier et al.

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic differential equations, but inference for long sequences with fast and slow transitions is difficult. Fast transitions need tight discretizations whereas slow transitions require backpropagating the gradients over long subtrajectories. We propose a novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution, to model effects on different timescales. The combined model allows traversing time on adaptive scales, providing efficient inference for arbitrarily long sequences with complex dynamics. We benchmark our novel method on semi-synthetic data and on an engine modeling task. In both experiments, our approach compares favorably against its state-of-the-art alternatives that operate on a single time-scale only.

Juliane Weilbach, Sebastian Gerwinn, Christian Weilbach et al.

Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and are less amenable for further expert investigation. Alternatively, the dynamics can be analysed via symbolic regression. In this paper, we extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems based on observations from the resulting trajectories. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available. Although the proposed approach performs best on this benchmark, we observed difficulties of all the compared symbolic regression approaches on more complex systems, such as Cart-Pole.

Melih Kandemir, Abdullah Akgül, Manuel Haussmann et al.

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii) accurately identifies queries coming out of the target domain and rejects them. We introduce an original combination of Evidential Deep Learning, Neural Processes, and Neural Turing Machines capable of providing all three essential properties mentioned above for total uncertainty quantification. We observe our method on five classification tasks to be the only one that can excel all three aspects of total calibration with a single standalone predictor. Our unified solution delivers an implementation-friendly and compute efficient recipe for safety clearance and provides intellectual economy to an investigation of algorithmic roots of epistemic awareness in deep neural nets.

Andreas Look, Simona Doneva, Melih Kandemir et al.

In this paper, we introduce an efficient backpropagation scheme for non-constrained implicit functions. These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable as a learnable layer in a neural network. We demonstrate our scheme on different applications: (i) neural ODEs with the implicit Euler method, and (ii) system identification in model predictive control.

Manuel Haussmann, Sebastian Gerwinn, Andreas Look et al.

Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification of the large set of free parameters. This paper presents a recipe to improve the prediction accuracy of such models in three steps: i) accounting for epistemic uncertainty by assuming probabilistic weights, ii) incorporation of partial knowledge on the state dynamics, and iii) training the resultant hybrid model by an objective derived from a PAC-Bayesian generalization bound. We observe in our experiments that this recipe effectively translates partial and noisy prior knowledge into an improved model fit.

Andreas Look, Melih Kandemir, Barbara Rakitsch et al.

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been remained unexplored so far. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme which accurately approximates the transition kernel, when dynamics is governed by a NSDE. Our method introduces a bidimensional moment matching algorithm: vertical along the neural net layers and horizontal along the time direction, which benefits from an original combination of effective approximations. Our deterministic approximation of the transition kernel is applicable to both training and prediction. We observe in multiple experiments that the uncertainty calibration quality of our method can be matched by Monte Carlo sampling only after introducing high computational cost. Thanks to the numerical stability of deterministic training, our method also improves prediction accuracy.

Andreas Look, Melih Kandemir

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power of their deterministic counterpart. We assign Bayesian Neural Nets (BNNs) to both the drift and the diffusion terms of a Stochastic Differential Equation (SDE) that models the flow of the activation map in time. We infer the posterior on the BNN weights using a straightforward adaptation of Stochastic Gradient Langevin Dynamics (SGLD). We illustrate significantly improved stability on two synthetic time series prediction tasks and report better model fit on UCI regression benchmarks with our method when compared to its non-Bayesian counterpart.

Manuel Haussmann, Fred A. Hamprecht, Melih Kandemir

Model selection is treated as a standard performance boosting step in many machine learning applications. Once all other properties of a learning problem are fixed, the model is selected by grid search on a held-out validation set. This is strictly inapplicable to active learning. Within the standardized workflow, the acquisition function is chosen among available heuristics a priori, and its success is observed only after the labeling budget is already exhausted. More importantly, none of the earlier studies report a unique consistently successful acquisition heuristic to the extent to stand out as the unique best choice. We present a method to break this vicious circle by defining the acquisition function as a learning predictor and training it by reinforcement feedback collected from each labeling round. As active learning is a scarce data regime, we bootstrap from a well-known heuristic that filters the bulk of data points on which all heuristics would agree, and learn a policy to warp the top portion of this ranking in the most beneficial way for the character of a specific data distribution. Our system consists of a Bayesian neural net, the predictor, a bootstrap acquisition function, a probabilistic state definition, and another Bayesian policy network that can effectively incorporate this input distribution. We observe on three benchmark data sets that our method always manages to either invent a new superior acquisition function or to adapt itself to the a priori unknown best performing heuristic for each specific data set.

Manuel Haussmann, Sebastian Gerwinn, Melih Kandemir

We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving closed-form access to predictive uncertainty. We employ it to model aleatoric uncertainty and extend it to account also for epistemic uncertainty by converting it to a Bayesian Neural Net. While extending its uncertainty quantification capabilities, we maintain its analytically accessible predictive distribution model by performing progressive moment matching for the first time for approximate weight marginalization. The eventual model introduces a prohibitively large number of hyperparameters for stable training. We overcome this drawback by deriving a vacuous PAC bound that comprises the marginal likelihood of the predictor and a complexity penalty. We observe on regression, classification, and out-of-domain detection benchmarks that our method improves model fit and uncertainty quantification.

Murat Sensoy, Lance Kaplan, Melih Kandemir

Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indirectly infer prediction uncertainty through weight uncertainties, we propose explicit modeling of the same using the theory of subjective logic. By placing a Dirichlet distribution on the class probabilities, we treat predictions of a neural net as subjective opinions and learn the function that collects the evidence leading to these opinions by a deterministic neural net from data. The resultant predictor for a multi-class classification problem is another Dirichlet distribution whose parameters are set by the continuous output of a neural net. We provide a preliminary analysis on how the peculiarities of our new loss function drive improved uncertainty estimation. We observe that our method achieves unprecedented success on detection of out-of-distribution queries and endurance against adversarial perturbations.

Manuel Haussmann, Fred A. Hamprecht, Melih Kandemir

We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variational inference on this construction enables a sampling-free computation of the evidence lower bound which is a more effective approximation than the widely applied Monte Carlo sampling and CLT related techniques. We evaluate the model on a range of regression and classification tasks against BNN inference alternatives, showing competitive or improved performance over the current state-of-the-art.