@inproceedings{14093, abstract = { We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or require carefully increasing the batch size over the course of the algorithm’s execution, which leads to computing full gradients. In contrast, the proposed method, equipped with a stochastic average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques. In applications we put special emphasis on problems with a large number of separable constraints. Such problems are prevalent among semidefinite programming (SDP) formulations arising in machine learning and theoretical computer science. We provide numerical experiments on matrix completion, unsupervised clustering, and sparsest-cut SDPs. }, author = {Dresdner, Gideon and Vladarean, Maria-Luiza and Rätsch, Gunnar and Locatello, Francesco and Cevher, Volkan and Yurtsever, Alp}, booktitle = {Proceedings of the 25th International Conference on Artificial Intelligence and Statistics}, issn = {2640-3498}, location = {Virtual}, pages = {8439--8457}, publisher = {ML Research Press}, title = {{ Faster one-sample stochastic conditional gradient method for composite convex minimization}}, volume = {151}, year = {2022}, } @inproceedings{14106, abstract = {We show that deep networks trained to satisfy demographic parity often do so through a form of race or gender awareness, and that the more we force a network to be fair, the more accurately we can recover race or gender from the internal state of the network. Based on this observation, we investigate an alternative fairness approach: we add a second classification head to the network to explicitly predict the protected attribute (such as race or gender) alongside the original task. After training the two-headed network, we enforce demographic parity by merging the two heads, creating a network with the same architecture as the original network. We establish a close relationship between existing approaches and our approach by showing (1) that the decisions of a fair classifier are well-approximated by our approach, and (2) that an unfair and optimally accurate classifier can be recovered from a fair classifier and our second head predicting the protected attribute. We use our explicit formulation to argue that the existing fairness approaches, just as ours, demonstrate disparate treatment and that they are likely to be unlawful in a wide range of scenarios under US law.}, author = {Lohaus, Michael and Kleindessner, Matthäus and Kenthapadi, Krishnaram and Locatello, Francesco and Russell, Chris}, booktitle = {36th Conference on Neural Information Processing Systems}, isbn = {9781713871088}, location = {New Orleans, LA, United States}, pages = {16548--16562}, publisher = {Neural Information Processing Systems Foundation}, title = {{Are two heads the same as one? Identifying disparate treatment in fair neural networks}}, volume = {35}, year = {2022}, } @inproceedings{14107, abstract = {Amodal perception requires inferring the full shape of an object that is partially occluded. This task is particularly challenging on two levels: (1) it requires more information than what is contained in the instant retina or imaging sensor, (2) it is difficult to obtain enough well-annotated amodal labels for supervision. To this end, this paper develops a new framework of Self-supervised amodal Video object segmentation (SaVos). Our method efficiently leverages the visual information of video temporal sequences to infer the amodal mask of objects. The key intuition is that the occluded part of an object can be explained away if that part is visible in other frames, possibly deformed as long as the deformation can be reasonably learned. Accordingly, we derive a novel self-supervised learning paradigm that efficiently utilizes the visible object parts as the supervision to guide the training on videos. In addition to learning type prior to complete masks for known types, SaVos also learns the spatiotemporal prior, which is also useful for the amodal task and could generalize to unseen types. The proposed framework achieves the state-of-the-art performance on the synthetic amodal segmentation benchmark FISHBOWL and the real world benchmark KINS-Video-Car. Further, it lends itself well to being transferred to novel distributions using test-time adaptation, outperforming existing models even after the transfer to a new distribution.}, author = {Yao, Jian and Hong, Yuxin and Wang, Chiyu and Xiao, Tianjun and He, Tong and Locatello, Francesco and Wipf, David and Fu, Yanwei and Zhang, Zheng}, booktitle = {36th Conference on Neural Information Processing Systems}, location = {New Orleans, LA, United States}, title = {{Self-supervised amodal video object segmentation}}, doi = {10.48550/arXiv.2210.12733}, year = {2022}, } @inproceedings{14114, abstract = {Algorithmic fairness is frequently motivated in terms of a trade-off in which overall performance is decreased so as to improve performance on disadvantaged groups where the algorithm would otherwise be less accurate. Contrary to this, we find that applying existing fairness approaches to computer vision improve fairness by degrading the performance of classifiers across all groups (with increased degradation on the best performing groups). Extending the bias-variance decomposition for classification to fairness, we theoretically explain why the majority of fairness methods designed for low capacity models should not be used in settings involving high-capacity models, a scenario common to computer vision. We corroborate this analysis with extensive experimental support that shows that many of the fairness heuristics used in computer vision also degrade performance on the most disadvantaged groups. Building on these insights, we propose an adaptive augmentation strategy that, uniquely, of all methods tested, improves performance for the disadvantaged groups.}, author = {Zietlow, Dominik and Lohaus, Michael and Balakrishnan, Guha and Kleindessner, Matthaus and Locatello, Francesco and Scholkopf, Bernhard and Russell, Chris}, booktitle = {2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition}, isbn = {9781665469470}, issn = {2575-7075}, location = {New Orleans, LA, United States}, pages = {10400--10411}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Leveling down in computer vision: Pareto inefficiencies in fair deep classifiers}}, doi = {10.1109/cvpr52688.2022.01016}, year = {2022}, } @inproceedings{14168, abstract = {Recent work has seen the development of general purpose neural architectures that can be trained to perform tasks across diverse data modalities. General purpose models typically make few assumptions about the underlying data-structure and are known to perform well in the large-data regime. At the same time, there has been growing interest in modular neural architectures that represent the data using sparsely interacting modules. These models can be more robust out-of-distribution, computationally efficient, and capable of sample-efficient adaptation to new data. However, they tend to make domain-specific assumptions about the data, and present challenges in how module behavior (i.e., parameterization) and connectivity (i.e., their layout) can be jointly learned. In this work, we introduce a general purpose, yet modular neural architecture called Neural Attentive Circuits (NACs) that jointly learns the parameterization and a sparse connectivity of neural modules without using domain knowledge. NACs are best understood as the combination of two systems that are jointly trained end-to-end: one that determines the module configuration and the other that executes it on an input. We demonstrate qualitatively that NACs learn diverse and meaningful module configurations on the NLVR2 dataset without additional supervision. Quantitatively, we show that by incorporating modularity in this way, NACs improve upon a strong non-modular baseline in terms of low-shot adaptation on CIFAR and CUBs dataset by about 10%, and OOD robustness on Tiny ImageNet-R by about 2.5%. Further, we find that NACs can achieve an 8x speedup at inference time while losing less than 3% performance. Finally, we find NACs to yield competitive results on diverse data modalities spanning point-cloud classification, symbolic processing and text-classification from ASCII bytes, thereby confirming its general purpose nature.}, author = {Rahaman, Nasim and Weiss, Martin and Locatello, Francesco and Pal, Chris and Bengio, Yoshua and Schölkopf, Bernhard and Li, Li Erran and Ballas, Nicolas}, booktitle = {36th Conference on Neural Information Processing Systems}, location = {New Orleans, United States}, title = {{Neural attentive circuits}}, volume = {35}, year = {2022}, } @inproceedings{14170, abstract = {The idea behind object-centric representation learning is that natural scenes can better be modeled as compositions of objects and their relations as opposed to distributed representations. This inductive bias can be injected into neural networks to potentially improve systematic generalization and performance of downstream tasks in scenes with multiple objects. In this paper, we train state-of-the-art unsupervised models on five common multi-object datasets and evaluate segmentation metrics and downstream object property prediction. In addition, we study generalization and robustness by investigating the settings where either a single object is out of distribution -- e.g., having an unseen color, texture, or shape -- or global properties of the scene are altered -- e.g., by occlusions, cropping, or increasing the number of objects. From our experimental study, we find object-centric representations to be useful for downstream tasks and generally robust to most distribution shifts affecting objects. However, when the distribution shift affects the input in a less structured manner, robustness in terms of segmentation and downstream task performance may vary significantly across models and distribution shifts. }, author = {Dittadi, Andrea and Papa, Samuele and Vita, Michele De and Schölkopf, Bernhard and Winther, Ole and Locatello, Francesco}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, location = {Baltimore, MD, United States}, pages = {5221--5285}, publisher = {ML Research Press}, title = {{Generalization and robustness implications in object-centric learning}}, volume = {2022}, year = {2022}, } @inproceedings{14171, abstract = {This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.}, author = {Rolland, Paul and Cevher, Volkan and Kleindessner, Matthäus and Russel, Chris and Schölkopf, Bernhard and Janzing, Dominik and Locatello, Francesco}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, location = {Baltimore, MD, United States}, pages = {18741--18753}, publisher = {ML Research Press}, title = {{Score matching enables causal discovery of nonlinear additive noise models}}, volume = {162}, year = {2022}, } @inproceedings{14172, abstract = {An important component for generalization in machine learning is to uncover underlying latent factors of variation as well as the mechanism through which each factor acts in the world. In this paper, we test whether 17 unsupervised, weakly supervised, and fully supervised representation learning approaches correctly infer the generative factors of variation in simple datasets (dSprites, Shapes3D, MPI3D) from controlled environments, and on our contributed CelebGlow dataset. In contrast to prior robustness work that introduces novel factors of variation during test time, such as blur or other (un)structured noise, we here recompose, interpolate, or extrapolate only existing factors of variation from the training data set (e.g., small and medium-sized objects during training and large objects during testing). Models that learn the correct mechanism should be able to generalize to this benchmark. In total, we train and test 2000+ models and observe that all of them struggle to learn the underlying mechanism regardless of supervision signal and architectural bias. Moreover, the generalization capabilities of all tested models drop significantly as we move from artificial datasets towards more realistic real-world datasets. Despite their inability to identify the correct mechanism, the models are quite modular as their ability to infer other in-distribution factors remains fairly stable, providing only a single factoris out-of-distribution. These results point to an important yet understudied problem of learning mechanistic models of observations that can facilitate generalization.}, author = {Schott, Lukas and Kügelgen, Julius von and Träuble, Frederik and Gehler, Peter and Russell, Chris and Bethge, Matthias and Schölkopf, Bernhard and Locatello, Francesco and Brendel, Wieland}, booktitle = {10th International Conference on Learning Representations}, location = {Virtual}, title = {{Visual representation learning does not generalize strongly within the same domain}}, year = {2022}, } @inproceedings{14173, abstract = {Since out-of-distribution generalization is a generally ill-posed problem, various proxy targets (e.g., calibration, adversarial robustness, algorithmic corruptions, invariance across shifts) were studied across different research programs resulting in different recommendations. While sharing the same aspirational goal, these approaches have never been tested under the same experimental conditions on real data. In this paper, we take a unified view of previous work, highlighting message discrepancies that we address empirically, and providing recommendations on how to measure the robustness of a model and how to improve it. To this end, we collect 172 publicly available dataset pairs for training and out-of-distribution evaluation of accuracy, calibration error, adversarial attacks, environment invariance, and synthetic corruptions. We fine-tune over 31k networks, from nine different architectures in the many- and few-shot setting. Our findings confirm that in- and out-of-distribution accuracies tend to increase jointly, but show that their relation is largely dataset-dependent, and in general more nuanced and more complex than posited by previous, smaller scale studies.}, author = {Wenzel, Florian and Dittadi, Andrea and Gehler, Peter Vincent and Carl-Johann Simon-Gabriel, Carl-Johann Simon-Gabriel and Horn, Max and Zietlow, Dominik and Kernert, David and Russell, Chris and Brox, Thomas and Schiele, Bernt and Schölkopf, Bernhard and Locatello, Francesco}, booktitle = {36th Conference on Neural Information Processing Systems}, isbn = {9781713871088}, location = {New Orleans, LA, United States}, pages = {7181--7198}, publisher = {Neural Information Processing Systems Foundation}, title = {{Assaying out-of-distribution generalization in transfer learning}}, volume = {35}, year = {2022}, } @inproceedings{14174, abstract = {Building sample-efficient agents that generalize out-of-distribution (OOD) in real-world settings remains a fundamental unsolved problem on the path towards achieving higher-level cognition. One particularly promising approach is to begin with low-dimensional, pretrained representations of our world, which should facilitate efficient downstream learning and generalization. By training 240 representations and over 10,000 reinforcement learning (RL) policies on a simulated robotic setup, we evaluate to what extent different properties of pretrained VAE-based representations affect the OOD generalization of downstream agents. We observe that many agents are surprisingly robust to realistic distribution shifts, including the challenging sim-to-real case. In addition, we find that the generalization performance of a simple downstream proxy task reliably predicts the generalization performance of our RL agents under a wide range of OOD settings. Such proxy tasks can thus be used to select pretrained representations that will lead to agents that generalize.}, author = {Dittadi, Andrea and Träuble, Frederik and Wüthrich, Manuel and Widmaier, Felix and Gehler, Peter and Winther, Ole and Locatello, Francesco and Bachem, Olivier and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {10th International Conference on Learning Representations}, location = {Virtual}, title = {{The role of pretrained representations for the OOD generalization of reinforcement learning agents}}, year = {2022}, } @inproceedings{14175, abstract = {Predicting the future trajectory of a moving agent can be easy when the past trajectory continues smoothly but is challenging when complex interactions with other agents are involved. Recent deep learning approaches for trajectory prediction show promising performance and partially attribute this to successful reasoning about agent-agent interactions. However, it remains unclear which features such black-box models actually learn to use for making predictions. This paper proposes a procedure that quantifies the contributions of different cues to model performance based on a variant of Shapley values. Applying this procedure to state-of-the-art trajectory prediction methods on standard benchmark datasets shows that they are, in fact, unable to reason about interactions. Instead, the past trajectory of the target is the only feature used for predicting its future. For a task with richer social interaction patterns, on the other hand, the tested models do pick up such interactions to a certain extent, as quantified by our feature attribution method. We discuss the limits of the proposed method and its links to causality.}, author = {Makansi, Osama and Kügelgen, Julius von and Locatello, Francesco and Gehler, Peter and Janzing, Dominik and Brox, Thomas and Schölkopf, Bernhard}, booktitle = {10th International Conference on Learning Representations}, location = {Virtual}, title = {{You mostly walk alone: Analyzing feature attribution in trajectory prediction}}, year = {2022}, } @inproceedings{14215, abstract = {Geospatial Information Systems are used by researchers and Humanitarian Assistance and Disaster Response (HADR) practitioners to support a wide variety of important applications. However, collaboration between these actors is difficult due to the heterogeneous nature of geospatial data modalities (e.g., multi-spectral images of various resolutions, timeseries, weather data) and diversity of tasks (e.g., regression of human activity indicators or detecting forest fires). In this work, we present a roadmap towards the construction of a general-purpose neural architecture (GPNA) with a geospatial inductive bias, pre-trained on large amounts of unlabelled earth observation data in a self-supervised manner. We envision how such a model may facilitate cooperation between members of the community. We show preliminary results on the first step of the roadmap, where we instantiate an architecture that can process a wide variety of geospatial data modalities and demonstrate that it can achieve competitive performance with domain-specific architectures on tasks relating to the U.N.'s Sustainable Development Goals.}, author = {Rahaman, Nasim and Weiss, Martin and Träuble, Frederik and Locatello, Francesco and Lacoste, Alexandre and Bengio, Yoshua and Pal, Chris and Li, Li Erran and Schölkopf, Bernhard}, booktitle = {36th Conference on Neural Information Processing Systems}, location = {New Orleans, LA, United States}, title = {{A general purpose neural architecture for geospatial systems}}, year = {2022}, } @unpublished{14216, abstract = {CLIP proved that aligning visual and language spaces is key to solving many vision tasks without explicit training, but required to train image and text encoders from scratch on a huge dataset. LiT improved this by only training the text encoder and using a pre-trained vision network. In this paper, we show that a common space can be created without any training at all, using single-domain encoders (trained with or without supervision) and a much smaller amount of image-text pairs. Furthermore, our model has unique properties. Most notably, deploying a new version with updated training samples can be done in a matter of seconds. Additionally, the representations in the common space are easily interpretable as every dimension corresponds to the similarity of the input to a unique entry in the multimodal dataset. Experiments on standard zero-shot visual benchmarks demonstrate the typical transfer ability of image-text models. Overall, our method represents a simple yet surprisingly strong baseline for foundation multi-modal models, raising important questions on their data efficiency and on the role of retrieval in machine learning.}, author = {Norelli, Antonio and Fumero, Marco and Maiorca, Valentino and Moschella, Luca and Rodolà, Emanuele and Locatello, Francesco}, booktitle = {arXiv}, title = {{ASIF: Coupled data turns unimodal models to multimodal without training}}, doi = {10.48550/arXiv.2210.01738}, year = {2022}, } @unpublished{14220, abstract = {Although reinforcement learning has seen remarkable progress over the last years, solving robust dexterous object-manipulation tasks in multi-object settings remains a challenge. In this paper, we focus on models that can learn manipulation tasks in fixed multi-object settings and extrapolate this skill zero-shot without any drop in performance when the number of objects changes. We consider the generic task of bringing a specific cube out of a set to a goal position. We find that previous approaches, which primarily leverage attention and graph neural network-based architectures, do not generalize their skills when the number of input objects changes while scaling as K2. We propose an alternative plug-and-play module based on relational inductive biases to overcome these limitations. Besides exceeding performances in their training environment, we show that our approach, which scales linearly in K, allows agents to extrapolate and generalize zero-shot to any new object number.}, author = {Mambelli, Davide and Träuble, Frederik and Bauer, Stefan and Schölkopf, Bernhard and Locatello, Francesco}, booktitle = {arXiv}, title = {{Compositional multi-object reinforcement learning with linear relation networks}}, doi = {10.48550/arXiv.2201.13388}, year = {2022}, } @article{14355, abstract = {Purpose: The mediator (MED) multisubunit-complex modulates the activity of the transcriptional machinery, and genetic defects in different MED subunits (17, 20, 27) have been implicated in neurologic diseases. In this study, we identified a recurrent homozygous variant in MED11 (c.325C>T; p.Arg109Ter) in 7 affected individuals from 5 unrelated families. Methods: To investigate the genetic cause of the disease, exome or genome sequencing were performed in 5 unrelated families identified via different research networks and Matchmaker Exchange. Deep clinical and brain imaging evaluations were performed by clinical pediatric neurologists and neuroradiologists. The functional effect of the candidate variant on both MED11 RNA and protein was assessed using reverse transcriptase polymerase chain reaction and western blotting using fibroblast cell lines derived from 1 affected individual and controls and through computational approaches. Knockouts in zebrafish were generated using clustered regularly interspaced short palindromic repeats/Cas9. Results: The disease was characterized by microcephaly, profound neurodevelopmental impairment, exaggerated startle response, myoclonic seizures, progressive widespread neurodegeneration, and premature death. Functional studies on patient-derived fibroblasts did not show a loss of protein function but rather disruption of the C-terminal of MED11, likely impairing binding to other MED subunits. A zebrafish knockout model recapitulates key clinical phenotypes. Conclusion: Loss of the C-terminal of MED subunit 11 may affect its binding efficiency to other MED subunits, thus implicating the MED-complex stability in brain development and neurodegeneration. (C) 2022 The Authors. Published by Elsevier Inc. on behalf of American College of Medical Genetics and Genomics.}, author = {Cali, Elisa and Lin, Sheng-Jia and Rocca, Clarissa and Sahin, Yavuz and Al Shamsi, Aisha and El Chehadeh, Salima and Chaabouni, Myriam and Mankad, Kshitij and Galanaki, Evangelia and Efthymiou, Stephanie and Sudhakar, Sniya and Athanasiou-Fragkouli, Alkyoni and Celik, Tamer and Narli, Nejat and Bianca, Sebastiano and Murphy, David and Moreira, Francisco Martins De Carvalho and Accogli, Andrea and Petree, Cassidy and Huang, Kevin and Monastiri, Kamel and Edizadeh, Masoud and Nardello, Rosaria and Ognibene, Marzia and De Marco, Patrizia and Ruggieri, Martino and Zara, Federico and Striano, Pasquale and Sahin, Yavuz and Al-Gazali, Lihadh and Warde, Marie Therese Abi and Gerard, Benedicte and Zifarelli, Giovanni and Beetz, Christian and Fortuna, Sara and Soler, Miguel and Valente, Enza Maria and Varshney, Gaurav and Maroofian, Reza and Salpietro, Vincenzo and Houlden, Henry and Grp, SYNaPS Study}, issn = {1098-3600}, journal = {Genetics in Medicine}, keywords = {Human mediator complex, MED11, MEDopathies}, number = {10}, pages = {2194--2203}, publisher = {Elsevier}, title = {{A homozygous MED11 C-terminal variant causes a lethal neurodegenerative disease}}, doi = {10.1016/j.gim.2022.07.013}, volume = {24}, year = {2022}, } @article{14381, abstract = {Expander graphs (sparse but highly connected graphs) have, since their inception, been the source of deep links between Mathematics and Computer Science as well as applications to other areas. In recent years, a fascinating theory of high-dimensional expanders has begun to emerge, which is still in a formative stage but has nonetheless already lead to a number of striking results. Unlike for graphs, in higher dimensions there is a rich array of non-equivalent notions of expansion (coboundary expansion, cosystolic expansion, topological expansion, spectral expansion, etc.), with differents strengths and applications. In this talk, we will survey this landscape of high-dimensional expansion, with a focus on two main results. First, we will present Gromov’s Topological Overlap Theorem, which asserts that coboundary expansion (a quantitative version of vanishing mod 2 cohomology) implies topological expansion (roughly, the property that for every map from a simplicial complex to a manifold of the same dimension, the images of a positive fraction of the simplices have a point in common). Second, we will outline a construction of bounded degree 2-dimensional topological expanders, due to Kaufman, Kazhdan, and Lubotzky.}, author = {Wagner, Uli}, issn = {2102-622X}, journal = {Bulletin de la Societe Mathematique de France}, pages = {281--294}, publisher = {Societe Mathematique de France}, title = {{High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others)}}, doi = {10.24033/ast.1188}, volume = {438}, year = {2022}, } @article{14437, abstract = {Future LEDs could be based on lead halide perovskites. A breakthrough in preparing device-compatible solids composed of nanoscale perovskite crystals overcomes a long-standing hurdle in making blue perovskite LEDs.}, author = {Utzat, Hendrik and Ibáñez, Maria}, issn = {1476-4687}, journal = {Nature}, keywords = {Multidisciplinary}, number = {7941}, pages = {638--639}, publisher = {Springer Nature}, title = {{Molecular engineering enables bright blue LEDs}}, doi = {10.1038/d41586-022-04447-0}, volume = {612}, year = {2022}, } @misc{14520, abstract = {This dataset comprises all data shown in the figures of the submitted article "Compact vacuum gap transmon qubits: Selective and sensitive probes for superconductor surface losses" at arxiv.org/abs/2206.14104. Additional raw data are available from the corresponding author on reasonable request.}, author = {Zemlicka, Martin and Redchenko, Elena and Peruzzo, Matilda and Hassani, Farid and Trioni, Andrea and Barzanjeh, Shabir and Fink, Johannes M}, publisher = {Zenodo}, title = {{Compact vacuum gap transmon qubits: Selective and sensitive probes for superconductor surface losses}}, doi = {10.5281/ZENODO.8408897}, year = {2022}, } @unpublished{14597, abstract = {Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow. In the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε1/2). Our approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of "gradient flow calibrations" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.}, author = {Fischer, Julian L and Marveggio, Alice}, booktitle = {arXiv}, title = {{Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow}}, doi = {10.48550/ARXIV.2203.17143}, year = {2022}, } @unpublished{14600, abstract = {We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks.}, author = {Zikelic, Dorde and Lechner, Mathias and Henzinger, Thomas A and Chatterjee, Krishnendu}, booktitle = {arXiv}, title = {{Learning control policies for stochastic systems with reach-avoid guarantees}}, doi = {10.48550/ARXIV.2210.05308}, year = {2022}, }