# List of publications and preprints

My publications are listed here (Google Scholar)

*How Infinitely Wide Neural Networks Can Benefit from Multi-task Learning – an Exact Macroscopic Characterization*

J Heiss, J Teichmann, H Wutte. arxiv 2022.

We provide an exact quantitative characterization of the inductive bias of infinitely wide L2-regularized ReLU-neural networks (NNs) in function space. This provides insights into the multi-task learning ability due to representation learning, while many other infinite width limits in the literature (such as NTK) only study settings where no benefit from multi-task learning is possible.

*Reducing the number of neurons of deep ReLU networks based on the current theory of Regularization*

J Heiss, A Stockinger, J Teichmann. OpenReview 2020.

Work in progress: The theory in the paper above shows that wide L2-regularized neural networks are sparse in function space. We have developed an algorithm that exploits this sparseness in function space to compress the neural network to a smaller number of neurons after training by applying specific transformations on the weight matrices. More experimental evaluation is still needed.

*Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework*

W. Andersson, J. Heiss, F. Krach, J Teichmann. arxiv 2023.

The Path-Dependent Neural Jump ODE (PD-NJ-ODE) is a model to learns optimal forecasts given irregularly sampled time series of incomplete past observations. So far the process itself and the coordinate-wise observation times were assumed to be independent and observations were assumed to be noiseless.
In this work we discuss two extensions to lift these restrictions and provide theoretical guarantees as well as empirical examples for them.

*NOMU: Neural Optimization-based Model Uncertainty*

J Heiss, J Weissteiner, H Wutte, S Seuken, J Teichmann. ICML 2022.

We study methods for estimating model uncertainty for neural networks (NNs) in regression. We introduce five important desiderata regarding model uncertainty that any method should satisfy. However, we find that established benchmarks often fail to reliably capture some of these desiderata. We introduce a new approach for capturing model uncertainty for NNs, which we call NOMU.

*How Implicit Regularization of ReLU Neural Networks Characterizes the Learned Function – Part I: the 1-D Case of Two Layers with Random First Layer*

J Heiss, J Teichmann, H Wutte. arxiv 2019.

We consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. We rigorously show that early stopping or L2 regularization on parameter space both corresponds to regularizing the second derivative in function space (similar to
smoothing splines) as the number of hidden nodes tends to infinity

*How (Implicit) Regularization of ReLU Neural Networks Characterizes the Learned Function – Part II: the Multi-D Case of Two Layers with Random First Layer*

J Heiss, J Teichmann, H Wutte. arxiv 2023.

We extend the results of part I to the multi-dimensional case. We show that (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained correspond in function space to a generalized additive model (GAM)-typed regression in which infinitely many directions are considered: the infinite generalized additive model (IGAM).

*Monotone-Value Neural Networks: Exploiting Preference Monotonicity in Combinatorial Assignment*

J Weissteiner, J Heiss, J Siems, S Seuken. IJCAI 2022.

We outperform the previous state of the art in machine learning based combinatorial assignment problems by introducing monotone-value neural networks (MVNNs). MVNNs are capturing prior knowledge on combinatorial valuations by enforcing monotonicity and normality, while solving the corresponding winner determination problem is still practically feasible via our MILP formulation.

*Bayesian Optimization-based Combinatorial Assignment*

J Weissteiner, J Heiss, J Siems, S Seuken. AAAI 2023.

We further improve the performance of machine learning based combinatorial assignment problems by combining MVNNs and NOMU. We use the uncertainty obtained by an adapted version of NOMU to promote exploration by using the upper confidence bounds as acquisition function. (Short and simple video-summary: https://youtu.be/6YH9K6LDHPY)

*Machine Learning-powered Combinatorial Clock Auction*

E Soumalias, J Weissteiner, J Heiss, S Seuken. arxiv 2023.

For real world combinatorial auctions (CAs) the combinatorial clock auction (CCA) is the most popular method in practice. While we have previously introduced ML-powered CAs that ask value queries (i.e., "What is your value for the bundle {A,B}?"), the CCA asks demand queries (i.e., "At prices p, what is your most preferred bundle of items?"). We introduce a machine learning-powered CCA that only asks demand queries and still outperforms the classical CCA significantly, while not changing the interaction-paradigm compared to the classical CCA.