@article{7489, abstract = {In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy.}, author = {Fischer, Julian L and Hensel, Sebastian}, issn = {14320673}, journal = {Archive for Rational Mechanics and Analysis}, pages = {967--1087}, publisher = {Springer Nature}, title = {{Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension}}, doi = {10.1007/s00205-019-01486-2}, volume = {236}, year = {2020}, } @unpublished{10012, abstract = {We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a "gradient flow calibration" ensures that the route of steepest descent in the energy landscape is unique and stable.}, author = {Fischer, Julian L and Hensel, Sebastian and Laux, Tim and Simon, Thilo}, booktitle = {arXiv}, title = {{The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions}}, year = {2020}, } @article{8755, abstract = {The superconducting circuit community has recently discovered the promising potential of superinductors. These circuit elements have a characteristic impedance exceeding the resistance quantum RQ ≈ 6.45 kΩ which leads to a suppression of ground state charge fluctuations. Applications include the realization of hardware protected qubits for fault tolerant quantum computing, improved coupling to small dipole moment objects and defining a new quantum metrology standard for the ampere. In this work we refute the widespread notion that superinductors can only be implemented based on kinetic inductance, i.e. using disordered superconductors or Josephson junction arrays. We present modeling, fabrication and characterization of 104 planar aluminum coil resonators with a characteristic impedance up to 30.9 kΩ at 5.6 GHz and a capacitance down to ≤ 1 fF, with lowloss and a power handling reaching 108 intra-cavity photons. Geometric superinductors are free of uncontrolled tunneling events and offer high reproducibility, linearity and the ability to couple magnetically - properties that significantly broaden the scope of future quantum circuits. }, author = {Peruzzo, Matilda and Trioni, Andrea and Hassani, Farid and Zemlicka, Martin and Fink, Johannes M}, issn = {23317019}, journal = {Physical Review Applied}, number = {4}, publisher = {American Physical Society}, title = {{Surpassing the resistance quantum with a geometric superinductor}}, doi = {10.1103/PhysRevApplied.14.044055}, volume = {14}, year = {2020}, } @article{7573, abstract = {This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport.}, author = {Gladbach, Peter and Kopfer, Eva and Maas, Jan and Portinale, Lorenzo}, issn = {00217824}, journal = {Journal de Mathematiques Pures et Appliquees}, number = {7}, pages = {204--234}, publisher = {Elsevier}, title = {{Homogenisation of one-dimensional discrete optimal transport}}, doi = {10.1016/j.matpur.2020.02.008}, volume = {139}, year = {2020}, } @unpublished{10022, abstract = {We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in R^d and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck equation via the method of Evolutionary Γ-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalising the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.}, author = {Forkert, Dominik L and Maas, Jan and Portinale, Lorenzo}, booktitle = {arXiv}, pages = {33}, title = {{Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions}}, year = {2020}, } @inproceedings{8724, abstract = {We study the problem of learning from multiple untrusted data sources, a scenario of increasing practical relevance given the recent emergence of crowdsourcing and collaborative learning paradigms. Specifically, we analyze the situation in which a learning system obtains datasets from multiple sources, some of which might be biased or even adversarially perturbed. It is known that in the single-source case, an adversary with the power to corrupt a fixed fraction of the training data can prevent PAC-learnability, that is, even in the limit of infinitely much training data, no learning system can approach the optimal test error. In this work we show that, surprisingly, the same is not true in the multi-source setting, where the adversary can arbitrarily corrupt a fixed fraction of the data sources. Our main results are a generalization bound that provides finite-sample guarantees for this learning setting, as well as corresponding lower bounds. Besides establishing PAC-learnability our results also show that in a cooperative learning setting sharing data with other parties has provable benefits, even if some participants are malicious. }, author = {Konstantinov, Nikola H and Frantar, Elias and Alistarh, Dan-Adrian and Lampert, Christoph}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, issn = {2640-3498}, location = {Online}, pages = {5416--5425}, publisher = {ML Research Press}, title = {{On the sample complexity of adversarial multi-source PAC learning}}, volume = {119}, year = {2020}, } @article{8644, abstract = {Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning and a suitable quasidistance between different points of the phase diagram to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which we refer as layers) are coupled to each other via an interlayer coupling. In such systems, in general, composite order parameters involving spins of different layers may emerge as a consequence of the interlayer coupling. We focus on the layered Ising and Ashkin–Teller models as a paradigmatic case study, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. We correctly retrieve the three known phases of the Ashkin–Teller model with ferromagnetic couplings, including the phase described by a composite order parameter. For the bilayer and trilayer Ising models the phases we find are only the ferromagnetic and the paramagnetic ones. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find and can be applied to other models and structures.}, author = {Rzadkowski, Wojciech and Defenu, N and Chiacchiera, S and Trombettoni, A and Bighin, Giacomo}, issn = {13672630}, journal = {New Journal of Physics}, number = {9}, publisher = {IOP Publishing}, title = {{Detecting composite orders in layered models via machine learning}}, doi = {10.1088/1367-2630/abae44}, volume = {22}, year = {2020}, } @article{8705, abstract = {We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model.}, author = {Mysliwy, Krzysztof and Seiringer, Robert}, issn = {1424-0637}, journal = {Annales Henri Poincare}, number = {12}, pages = {4003--4025}, publisher = {Springer Nature}, title = {{Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit}}, doi = {10.1007/s00023-020-00969-3}, volume = {21}, year = {2020}, } @article{10861, abstract = {We introduce in this paper AMT2.0, a tool for qualitative and quantitative analysis of hybrid continuous and Boolean signals that combine numerical values and discrete events. The evaluation of the signals is based on rich temporal specifications expressed in extended signal temporal logic, which integrates timed regular expressions within signal temporal logic. The tool features qualitative monitoring (property satisfaction checking), trace diagnostics for explaining and justifying property violations and specification-driven measurement of quantitative features of the signal. We demonstrate the tool functionality on several running examples and case studies, and evaluate its performance.}, author = {Nickovic, Dejan and Lebeltel, Olivier and Maler, Oded and Ferrere, Thomas and Ulus, Dogan}, issn = {1433-2787}, journal = {International Journal on Software Tools for Technology Transfer}, keywords = {Information Systems, Software}, number = {6}, pages = {741--758}, publisher = {Springer Nature}, title = {{AMT 2.0: Qualitative and quantitative trace analysis with extended signal temporal logic}}, doi = {10.1007/s10009-020-00582-z}, volume = {22}, year = {2020}, } @article{14125, abstract = {Motivation: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed. Results: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively.}, author = {Stark, Stefan G and Ficek, Joanna and Locatello, Francesco and Bonilla, Ximena and Chevrier, Stéphane and Singer, Franziska and Aebersold, Rudolf and Al-Quaddoomi, Faisal S and Albinus, Jonas and Alborelli, Ilaria and Andani, Sonali and Attinger, Per-Olof and Bacac, Marina and Baumhoer, Daniel and Beck-Schimmer, Beatrice and Beerenwinkel, Niko and Beisel, Christian and Bernasconi, Lara and Bertolini, Anne and Bodenmiller, Bernd and Bonilla, Ximena and Casanova, Ruben and Chevrier, Stéphane and Chicherova, Natalia and D'Costa, Maya and Danenberg, Esther and Davidson, Natalie and gan, Monica-Andreea Dră and Dummer, Reinhard and Engler, Stefanie and Erkens, Martin and Eschbach, Katja and Esposito, Cinzia and Fedier, André and Ferreira, Pedro and Ficek, Joanna and Frei, Anja L and Frey, Bruno and Goetze, Sandra and Grob, Linda and Gut, Gabriele and Günther, Detlef and Haberecker, Martina and Haeuptle, Pirmin and Heinzelmann-Schwarz, Viola and Herter, Sylvia and Holtackers, Rene and Huesser, Tamara and Irmisch, Anja and Jacob, Francis and Jacobs, Andrea and Jaeger, Tim M and Jahn, Katharina and James, Alva R and Jermann, Philip M and Kahles, André and Kahraman, Abdullah and Koelzer, Viktor H and Kuebler, Werner and Kuipers, Jack and Kunze, Christian P and Kurzeder, Christian and Lehmann, Kjong-Van and Levesque, Mitchell and Lugert, Sebastian and Maass, Gerd and Manz, Markus and Markolin, Philipp and Mena, Julien and Menzel, Ulrike and Metzler, Julian M and Miglino, Nicola and Milani, Emanuela S and Moch, Holger and Muenst, Simone and Murri, Riccardo and Ng, Charlotte KY and Nicolet, Stefan and Nowak, Marta and Pedrioli, Patrick GA and Pelkmans, Lucas and Piscuoglio, Salvatore and Prummer, Michael and Ritter, Mathilde and Rommel, Christian and Rosano-González, María L and Rätsch, Gunnar and Santacroce, Natascha and Castillo, Jacobo Sarabia del and Schlenker, Ramona and Schwalie, Petra C and Schwan, Severin and Schär, Tobias and Senti, Gabriela and Singer, Franziska and Sivapatham, Sujana and Snijder, Berend and Sobottka, Bettina and Sreedharan, Vipin T and Stark, Stefan and Stekhoven, Daniel J and Theocharides, Alexandre PA and Thomas, Tinu M and Tolnay, Markus and Tosevski, Vinko and Toussaint, Nora C and Tuncel, Mustafa A and Tusup, Marina and Drogen, Audrey Van and Vetter, Marcus and Vlajnic, Tatjana and Weber, Sandra and Weber, Walter P and Wegmann, Rebekka and Weller, Michael and Wendt, Fabian and Wey, Norbert and Wicki, Andreas and Wollscheid, Bernd and Yu, Shuqing and Ziegler, Johanna and Zimmermann, Marc and Zoche, Martin and Zuend, Gregor and Rätsch, Gunnar and Lehmann, Kjong-Van}, issn = {1367-4811}, journal = {Bioinformatics}, keywords = {Computational Mathematics, Computational Theory and Mathematics, Computer Science Applications, Molecular Biology, Biochemistry, Statistics and Probability}, number = {Supplement_2}, pages = {i919--i927}, publisher = {Oxford University Press}, title = {{SCIM: Universal single-cell matching with unpaired feature sets}}, doi = {10.1093/bioinformatics/btaa843}, volume = {36}, year = {2020}, } @inproceedings{14186, abstract = {The goal of the unsupervised learning of disentangled representations is to separate the independent explanatory factors of variation in the data without access to supervision. In this paper, we summarize the results of Locatello et al., 2019, and focus on their implications for practitioners. We discuss the theoretical result showing that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases and the practical challenges it entails. Finally, we comment on our experimental findings, highlighting the limitations of state-of-the-art approaches and directions for future research.}, author = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Rätsch, Gunnar and Gelly, Sylvain and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {The 34th AAAI Conference on Artificial Intelligence}, isbn = {9781577358350}, issn = {2374-3468}, location = {New York, NY, United States}, number = {9}, pages = {13681--13684}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{A commentary on the unsupervised learning of disentangled representations}}, doi = {10.1609/aaai.v34i09.7120}, volume = {34}, year = {2020}, } @inproceedings{14188, abstract = {Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios.}, author = {Locatello, Francesco and Poole, Ben and Rätsch, Gunnar and Schölkopf, Bernhard and Bachem, Olivier and Tschannen, Michael}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, location = {Virtual}, pages = {6348–6359}, title = {{Weakly-supervised disentanglement without compromises}}, volume = {119}, year = {2020}, } @inproceedings{14187, abstract = {We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.}, author = {Négiar, Geoffrey and Dresdner, Gideon and Tsai, Alicia and Ghaoui, Laurent El and Locatello, Francesco and Freund, Robert M. and Pedregosa, Fabian}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, location = {Virtual}, pages = {7253--7262}, title = {{Stochastic Frank-Wolfe for constrained finite-sum minimization}}, volume = {119}, year = {2020}, } @article{14195, abstract = {The idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train over 14000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.}, author = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Rätsch, Gunnar and Gelly, Sylvain and Schölkopf, Bernhard and Bachem, Olivier}, journal = {Journal of Machine Learning Research}, publisher = {MIT Press}, title = {{A sober look at the unsupervised learning of disentangled representations and their evaluation}}, volume = {21}, year = {2020}, } @article{7569, abstract = {Genes differ in the frequency at which they are expressed and in the form of regulation used to control their activity. In particular, positive or negative regulation can lead to activation of a gene in response to an external signal. Previous works proposed that the form of regulation of a gene correlates with its frequency of usage: positive regulation when the gene is frequently expressed and negative regulation when infrequently expressed. Such network design means that, in the absence of their regulators, the genes are found in their least required activity state, hence regulatory intervention is often necessary. Due to the multitude of genes and regulators, spurious binding and unbinding events, called “crosstalk”, could occur. To determine how the form of regulation affects the global crosstalk in the network, we used a mathematical model that includes multiple regulators and multiple target genes. We found that crosstalk depends non-monotonically on the availability of regulators. Our analysis showed that excess use of regulation entailed by the formerly suggested network design caused high crosstalk levels in a large part of the parameter space. We therefore considered the opposite ‘idle’ design, where the default unregulated state of genes is their frequently required activity state. We found, that ‘idle’ design minimized the use of regulation and thus minimized crosstalk. In addition, we estimated global crosstalk of S. cerevisiae using transcription factors binding data. We demonstrated that even partial network data could suffice to estimate its global crosstalk, suggesting its applicability to additional organisms. We found that S. cerevisiae estimated crosstalk is lower than that of a random network, suggesting that natural selection reduces crosstalk. In summary, our study highlights a new type of protein production cost which is typically overlooked: that of regulatory interference caused by the presence of excess regulators in the cell. It demonstrates the importance of whole-network descriptions, which could show effects missed by single-gene models.}, author = {Grah, Rok and Friedlander, Tamar}, issn = {1553-7358}, journal = {PLOS Computational Biology}, number = {2}, publisher = {Public Library of Science}, title = {{The relation between crosstalk and gene regulation form revisited}}, doi = {10.1371/journal.pcbi.1007642}, volume = {16}, year = {2020}, } @unpublished{8813, abstract = {In mammals, chromatin marks at imprinted genes are asymmetrically inherited to control parentally-biased gene expression. This control is thought predominantly to involve parent-specific differentially methylated regions (DMR) in genomic DNA. However, neither parent-of-origin-specific transcription nor DMRs have been comprehensively mapped. We here address this by integrating transcriptomic and epigenomic approaches in mouse preimplantation embryos (blastocysts). Transcriptome-analysis identified 71 genes expressed with previously unknown parent-of-origin-specific expression in blastocysts (nBiX: novel blastocyst-imprinted expression). Uniparental expression of nBiX genes disappeared soon after implantation. Micro-whole-genome bisulfite sequencing (μWGBS) of individual uniparental blastocysts detected 859 DMRs. Only 18% of nBiXs were associated with a DMR, whereas 60% were associated with parentally-biased H3K27me3. This suggests a major role for Polycomb-mediated imprinting in blastocysts. Five nBiX-clusters contained at least one known imprinted gene, and five novel clusters contained exclusively nBiX-genes. These data suggest a complex program of stage-specific imprinting involving different tiers of regulation.}, author = {Santini, Laura and Halbritter, Florian and Titz-Teixeira, Fabian and Suzuki, Toru and Asami, Maki and Ramesmayer, Julia and Ma, Xiaoyan and Lackner, Andreas and Warr, Nick and Pauler, Florian and Hippenmeyer, Simon and Laue, Ernest and Farlik, Matthias and Bock, Christoph and Beyer, Andreas and Perry, Anthony C. F. and Leeb, Martin}, booktitle = {bioRxiv}, publisher = {Cold Spring Harbor Laboratory}, title = {{Novel imprints in mouse blastocysts are predominantly DNA methylation independent}}, doi = {10.1101/2020.11.03.366948}, year = {2020}, } @misc{9777, author = {Grah, Rok and Friedlander, Tamar}, publisher = {Public Library of Science}, title = {{Maximizing crosstalk}}, doi = {10.1371/journal.pcbi.1007642.s002}, year = {2020}, } @phdthesis{8332, abstract = {Designing and verifying concurrent programs is a notoriously challenging, time consuming, and error prone task, even for experts. This is due to the sheer number of possible interleavings of a concurrent program, all of which have to be tracked and accounted for in a formal proof. Inventing an inductive invariant that captures all interleavings of a low-level implementation is theoretically possible, but practically intractable. We develop a refinement-based verification framework that provides mechanisms to simplify proof construction by decomposing the verification task into smaller subtasks. In a first line of work, we present a foundation for refinement reasoning over structured concurrent programs. We introduce layered concurrent programs as a compact notation to represent multi-layer refinement proofs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. Each program in this sequence is expressed as structured concurrent program, i.e., a program over (potentially recursive) procedures, imperative control flow, gated atomic actions, structured parallelism, and asynchronous concurrency. This is in contrast to existing refinement-based verifiers, which represent concurrent systems as flat transition relations. We present a powerful refinement proof rule that decomposes refinement checking over structured programs into modular verification conditions. Refinement checking is supported by a new form of modular, parameterized invariants, called yield invariants, and a linear permission system to enhance local reasoning. In a second line of work, we present two new reduction-based program transformations that target asynchronous programs. These transformations reduce the number of interleavings that need to be considered, thus reducing the complexity of invariants. Synchronization simplifies the verification of asynchronous programs by introducing the fiction, for proof purposes, that asynchronous operations complete synchronously. Synchronization summarizes an asynchronous computation as immediate atomic effect. Inductive sequentialization establishes sequential reductions that captures every behavior of the original program up to reordering of coarse-grained commutative actions. A sequential reduction of a concurrent program is easy to reason about since it corresponds to a simple execution of the program in an idealized synchronous environment, where processes act in a fixed order and at the same speed. Our approach is implemented the CIVL verifier, which has been successfully used for the verification of several complex concurrent programs. In our methodology, the overall correctness of a program is established piecemeal by focusing on the invariant required for each refinement step separately. While the programmer does the creative work of specifying the chain of programs and the inductive invariant justifying each link in the chain, the tool automatically constructs the verification conditions underlying each refinement step.}, author = {Kragl, Bernhard}, issn = {2663-337X}, pages = {120}, publisher = {Institute of Science and Technology Austria}, title = {{Verifying concurrent programs: Refinement, synchronization, sequentialization}}, doi = {10.15479/AT:ISTA:8332}, year = {2020}, } @inproceedings{14326, abstract = {Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-level perceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes. In this paper, we present the Slot Attention module, an architectural component that interfaces with perceptual representations such as the output of a convolutional neural network and produces a set of task-dependent abstract representations which we call slots. These slots are exchangeable and can bind to any object in the input by specializing through a competitive procedure over multiple rounds of attention. We empirically demonstrate that Slot Attention can extract object-centric representations that enable generalization to unseen compositions when trained on unsupervised object discovery and supervised property prediction tasks. }, author = {Locatello, Francesco and Weissenborn, Dirk and Unterthiner, Thomas and Mahendran, Aravindh and Heigold, Georg and Uszkoreit, Jakob and Dosovitskiy, Alexey and Kipf, Thomas}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713829546}, location = {Virtual}, pages = {11525--11538}, publisher = {Curran Associates}, title = {{Object-centric learning with slot attention}}, volume = {33}, year = {2020}, } @article{71, abstract = {We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric.}, author = {Gladbach, Peter and Kopfer, Eva and Maas, Jan}, issn = {10957154}, journal = {SIAM Journal on Mathematical Analysis}, number = {3}, pages = {2759--2802}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Scaling limits of discrete optimal transport}}, doi = {10.1137/19M1243440}, volume = {52}, year = {2020}, }