Lukas Franken

Felix Wagner, Florian Nachtigall, Lukas Franken et al.

Climate change mitigation in urban mobility requires policies reconfiguring urban form to increase accessibility and facilitate low-carbon modes of transport. However, current policy research has insufficiently assessed urban form effects on car travel at three levels: (1) Causality -- Can causality be established beyond theoretical and correlation-based analyses? (2) Generalizability -- Do relationships hold across different cities and world regions? (3) Context specificity -- How do relationships vary across neighborhoods of a city? Here, we address all three gaps via causal graph discovery and explainable machine learning to detect urban form effects on intra-city car travel, based on mobility data of six cities across three continents. We find significant causal effects of urban form on trip emissions and inter-feature effects, which had been neglected in previous work. Our results demonstrate that destination accessibility matters most overall, while low density and low connectivity also sharply increase CO$_2$ emissions. These general trends are similar across cities but we find idiosyncratic effects that can lead to substantially different recommendations. In more monocentric cities, we identify spatial corridors -- about 10--50 km from the city center -- where subcenter-oriented development is more relevant than increased access to the main center. Our work demonstrates a novel application of machine learning that enables new research addressing the needs of causality, generalizability, and contextual specificity for scaling evidence-based urban climate solutions.

Bogdan Georgiev, Lukas Franken, Mayukh Mukherjee et al.

A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights' stable ranks. Intuitively, the latter are indicators of the effective number of parameters in the net. In this work, we address some natural questions regarding the space of DNNs conditioned on the layers' stable rank, where we study feed-forward dynamics, initialization, training and expressivity. To this end, we first propose a random DNN model with a new sampling scheme based on stable rank. Then, we show how feed-forward maps are affected by the constraint and how training evolves in the overparametrized regime (via Neural Tangent Kernels). Our results imply that stable ranks appear layerwise essentially as linear factors whose effect accumulates exponentially depthwise. Moreover, we provide empirical analysis suggesting that stable rank initialization alone can lead to convergence speed ups.

Raoul Heese, Moritz Wolter, Sascha Mücke et al.

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

Bogdan Georgiev, Lukas Franken, Mayukh Mukherjee

In the present work we study classifiers' decision boundaries via Brownian motion processes in ambient data space and associated probabilistic techniques. Intuitively, our ideas correspond to placing a heat source at the decision boundary and observing how effectively the sample points warm up. We are largely motivated by the search for a soft measure that sheds further light on the decision boundary's geometry. En route, we bridge aspects of potential theory and geometric analysis (Mazya, 2011, Grigoryan-Saloff-Coste, 2002) with active fields of ML research such as adversarial examples and generalization bounds. First, we focus on the geometric behavior of decision boundaries in the light of adversarial attack/defense mechanisms. Experimentally, we observe a certain capacitory trend over different adversarial defense strategies: decision boundaries locally become flatter as measured by isoperimetric inequalities (Ford et al, 2019); however, our more sensitive heat-diffusion metrics extend this analysis and further reveal that some non-trivial geometry invisible to plain distance-based methods is still preserved. Intuitively, we provide evidence that the decision boundaries nevertheless retain many persistent "wiggly and fuzzy" regions on a finer scale. Second, we show how Brownian hitting probabilities translate to soft generalization bounds which are in turn connected to compression and noise stability (Arora et al, 2018), and these bounds are significantly stronger if the decision boundary has controlled geometric features.

Lukas Franken, Bogdan Georgiev, Sascha Mücke et al.

Variational quantum circuits build the foundation for various classes of quantum algorithms. In a nutshell, the weights of a parametrized quantum circuit are varied until the empirical sampling distribution of the circuit is sufficiently close to a desired outcome. Numerical first-order methods are applied frequently to fit the parameters of the circuit, but most of the time, the circuit itself, that is, the actual composition of gates, is fixed. Methods for optimizing the circuit design jointly with the weights have been proposed, but empirical results are rather scarce. Here, we consider a simple evolutionary strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We evaluate our method both via simulation and on actual quantum hardware. Our benchmark problems include the transverse field Ising Hamiltonian and the Sherrington-Kirkpatrick spin model. Despite the shortcomings of current noisy intermediate-scale quantum hardware, we find only a minor slowdown on actual quantum machines compared to simulations. Moreover, we investigate which mutation operations most significantly contribute to the optimization. The results provide intuition on how randomized search heuristics behave on actual quantum hardware and lay out a path for further refinement of evolutionary quantum gate circuits.