@article{14889, abstract = {We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.}, author = {Leopold, Nikolai K and Mitrouskas, David Johannes and Rademacher, Simone Anna Elvira and Schlein, Benjamin and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {4}, pages = {653--676}, publisher = {Mathematical Sciences Publishers}, title = {{Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron}}, doi = {10.2140/paa.2021.3.653}, volume = {3}, year = {2021}, } @article{14890, abstract = {We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions.}, author = {Bossmann, Lea and Petrat, Sören P and Pickl, Peter and Soffer, Avy}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {4}, pages = {677--726}, publisher = {Mathematical Sciences Publishers}, title = {{Beyond Bogoliubov dynamics}}, doi = {10.2140/paa.2021.3.677}, volume = {3}, year = {2021}, } @inbook{14984, abstract = {Hybrid zones are narrow geographic regions where different populations, races or interbreeding species meet and mate, producing mixed ‘hybrid’ offspring. They are relatively common and can be found in a diverse range of organisms and environments. The study of hybrid zones has played an important role in our understanding of the origin of species, with hybrid zones having been described as ‘natural laboratories’. This is because they allow us to study,in situ, the conditions and evolutionary forces that enable divergent taxa to remain distinct despite some ongoing gene exchange between them.}, author = {Stankowski, Sean and Shipilina, Daria and Westram, Anja M}, booktitle = {Encyclopedia of Life Sciences}, isbn = {9780470016176}, publisher = {Wiley}, title = {{Hybrid Zones}}, doi = {10.1002/9780470015902.a0029355}, volume = {2}, year = {2021}, } @inbook{14987, abstract = {The goal of zero-shot learning is to construct a classifier that can identify object classes for which no training examples are available. When training data for some of the object classes is available but not for others, the name generalized zero-shot learning is commonly used. In a wider sense, the phrase zero-shot is also used to describe other machine learning-based approaches that require no training data from the problem of interest, such as zero-shot action recognition or zero-shot machine translation.}, author = {Lampert, Christoph}, booktitle = {Computer Vision}, editor = {Ikeuchi, Katsushi}, isbn = {9783030634155}, pages = {1395--1397}, publisher = {Springer}, title = {{Zero-Shot Learning}}, doi = {10.1007/978-3-030-63416-2_874}, year = {2021}, } @misc{14988, abstract = {Raw data generated from the publication - The TPLATE complex mediates membrane bending during plant clathrin-mediated endocytosis by Johnson et al., 2021 In PNAS}, author = {Johnson, Alexander J}, publisher = {Zenodo}, title = {{Raw data from Johnson et al, PNAS, 2021}}, doi = {10.5281/ZENODO.5747100}, year = {2021}, } @article{15013, abstract = {We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {2690-1005}, journal = {Probability and Mathematical Physics}, number = {2}, pages = {221--280}, publisher = {Mathematical Sciences Publishers}, title = {{Spectral radius of random matrices with independent entries}}, doi = {10.2140/pmp.2021.2.221}, volume = {2}, year = {2021}, } @article{14117, abstract = {The two fields of machine learning and graphical causality arose and are developed separately. However, there is, now, cross-pollination and increasing interest in both fields to benefit from the advances of the other. In this article, we review fundamental concepts of causal inference and relate them to crucial open problems of machine learning, including transfer and generalization, thereby assaying how causality can contribute to modern machine learning research. This also applies in the opposite direction: we note that most work in causality starts from the premise that the causal variables are given. A central problem for AI and causality is, thus, causal representation learning, that is, the discovery of high-level causal variables from low-level observations. Finally, we delineate some implications of causality for machine learning and propose key research areas at the intersection of both communities.}, author = {Scholkopf, Bernhard and Locatello, Francesco and Bauer, Stefan and Ke, Nan Rosemary and Kalchbrenner, Nal and Goyal, Anirudh and Bengio, Yoshua}, issn = {1558-2256}, journal = {Proceedings of the IEEE}, keywords = {Electrical and Electronic Engineering}, number = {5}, pages = {612--634}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Toward causal representation learning}}, doi = {10.1109/jproc.2021.3058954}, volume = {109}, year = {2021}, } @inproceedings{14176, abstract = {Intensive care units (ICU) are increasingly looking towards machine learning for methods to provide online monitoring of critically ill patients. In machine learning, online monitoring is often formulated as a supervised learning problem. Recently, contrastive learning approaches have demonstrated promising improvements over competitive supervised benchmarks. These methods rely on well-understood data augmentation techniques developed for image data which do not apply to online monitoring. In this work, we overcome this limitation by supplementing time-series data augmentation techniques with a novel contrastive learning objective which we call neighborhood contrastive learning (NCL). Our objective explicitly groups together contiguous time segments from each patient while maintaining state-specific information. Our experiments demonstrate a marked improvement over existing work applying contrastive methods to medical time-series.}, author = {Yèche, Hugo and Dresdner, Gideon and Locatello, Francesco and Hüser, Matthias and Rätsch, Gunnar}, booktitle = {Proceedings of 38th International Conference on Machine Learning}, location = {Virtual}, pages = {11964--11974}, publisher = {ML Research Press}, title = {{Neighborhood contrastive learning applied to online patient monitoring}}, volume = {139}, year = {2021}, } @inproceedings{14177, abstract = {The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.}, author = {Träuble, Frederik and Creager, Elliot and Kilbertus, Niki and Locatello, Francesco and Dittadi, Andrea and Goyal, Anirudh and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, location = {Virtual}, pages = {10401--10412}, publisher = {ML Research Press}, title = {{On disentangled representations learned from correlated data}}, volume = {139}, year = {2021}, } @inproceedings{14178, abstract = {Learning meaningful representations that disentangle the underlying structure of the data generating process is considered to be of key importance in machine learning. While disentangled representations were found to be useful for diverse tasks such as abstract reasoning and fair classification, their scalability and real-world impact remain questionable. We introduce a new high-resolution dataset with 1M simulated images and over 1,800 annotated real-world images of the same setup. In contrast to previous work, this new dataset exhibits correlations, a complex underlying structure, and allows to evaluate transfer to unseen simulated and real-world settings where the encoder i) remains in distribution or ii) is out of distribution. We propose new architectures in order to scale disentangled representation learning to realistic high-resolution settings and conduct a large-scale empirical study of disentangled representations on this dataset. We observe that disentanglement is a good predictor for out-of-distribution (OOD) task performance.}, author = {Dittadi, Andrea and Träuble, Frederik and Locatello, Francesco and Wüthrich, Manuel and Agrawal, Vaibhav and Winther, Ole and Bauer, Stefan and Schölkopf, Bernhard}, booktitle = {The Ninth International Conference on Learning Representations}, location = {Virtual}, title = {{On the transfer of disentangled representations in realistic settings}}, year = {2021}, } @inproceedings{14179, abstract = {Self-supervised representation learning has shown remarkable success in a number of domains. A common practice is to perform data augmentation via hand-crafted transformations intended to leave the semantics of the data invariant. We seek to understand the empirical success of this approach from a theoretical perspective. We formulate the augmentation process as a latent variable model by postulating a partition of the latent representation into a content component, which is assumed invariant to augmentation, and a style component, which is allowed to change. Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space. We study the identifiability of the latent representation based on pairs of views of the observations and prove sufficient conditions that allow us to identify the invariant content partition up to an invertible mapping in both generative and discriminative settings. We find numerical simulations with dependent latent variables are consistent with our theory. Lastly, we introduce Causal3DIdent, a dataset of high-dimensional, visually complex images with rich causal dependencies, which we use to study the effect of data augmentations performed in practice.}, author = {Kügelgen, Julius von and Sharma, Yash and Gresele, Luigi and Brendel, Wieland and Schölkopf, Bernhard and Besserve, Michel and Locatello, Francesco}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {16451--16467}, title = {{Self-supervised learning with data augmentations provably isolates content from style}}, volume = {34}, year = {2021}, } @inproceedings{14180, abstract = {Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a feat that is hypothesized to require compositional reasoning and reuse of knowledge. In this work, we present Neural Interpreters, an architecture that factorizes inference in a self-attention network as a system of modules, which we call \emph{functions}. Inputs to the model are routed through a sequence of functions in a way that is end-to-end learned. The proposed architecture can flexibly compose computation along width and depth, and lends itself well to capacity extension after training. To demonstrate the versatility of Neural Interpreters, we evaluate it in two distinct settings: image classification and visual abstract reasoning on Raven Progressive Matrices. In the former, we show that Neural Interpreters perform on par with the vision transformer using fewer parameters, while being transferrable to a new task in a sample efficient manner. In the latter, we find that Neural Interpreters are competitive with respect to the state-of-the-art in terms of systematic generalization. }, author = {Rahaman, Nasim and Gondal, Muhammad Waleed and Joshi, Shruti and Gehler, Peter and Bengio, Yoshua and Locatello, Francesco and Schölkopf, Bernhard}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {10985--10998}, title = {{Dynamic inference with neural interpreters}}, volume = {34}, year = {2021}, } @inproceedings{14181, abstract = {Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.}, author = {Dresdner, Gideon and Shekhar, Saurav and Pedregosa, Fabian and Locatello, Francesco and Rätsch, Gunnar}, booktitle = {Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence}, location = {Montreal, Canada}, pages = {2337--2343}, publisher = {International Joint Conferences on Artificial Intelligence}, title = {{Boosting variational inference with locally adaptive step-sizes}}, doi = {10.24963/ijcai.2021/322}, year = {2021}, } @inproceedings{14182, abstract = {When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly improving state-of-the-art models. While new improved models develop at a fast pace, downstream tasks vary more slowly or stay constant. Assume that we have a large unlabelled data set for which we want to maintain accurate predictions. Whenever a new and presumably better ML models becomes available, we encounter two problems: (i) given a limited budget, which data points should be re-evaluated using the new model?; and (ii) if the new predictions differ from the current ones, should we update? Problem (i) is about compute cost, which matters for very large data sets and models. Problem (ii) is about maintaining consistency of the predictions, which can be highly relevant for downstream applications; our demand is to avoid negative flips, i.e., changing correct to incorrect predictions. In this paper, we formalize the Prediction Update Problem and present an efficient probabilistic approach as answer to the above questions. In extensive experiments on standard classification benchmark data sets, we show that our method outperforms alternative strategies along key metrics for backward-compatible prediction updates.}, author = {Träuble, Frederik and Kügelgen, Julius von and Kleindessner, Matthäus and Locatello, Francesco and Schölkopf, Bernhard and Gehler, Peter}, booktitle = {35th Conference on Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {116--128}, title = {{Backward-compatible prediction updates: A probabilistic approach}}, volume = {34}, year = {2021}, } @unpublished{14221, abstract = {The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may translate to faster, more accurate, and more flexible models, which may directly relate to real-world impact. In this dissertation, we consider two different research areas that concern structuring a learning algorithm's solution: when the structure is known and when it has to be discovered.}, author = {Locatello, Francesco}, booktitle = {arXiv}, title = {{Enforcing and discovering structure in machine learning}}, doi = {10.48550/arXiv.2111.13693}, year = {2021}, } @inproceedings{14332, abstract = {Learning data representations that are useful for various downstream tasks is a cornerstone of artificial intelligence. While existing methods are typically evaluated on downstream tasks such as classification or generative image quality, we propose to assess representations through their usefulness in downstream control tasks, such as reaching or pushing objects. By training over 10,000 reinforcement learning policies, we extensively evaluate to what extent different representation properties affect out-of-distribution (OOD) generalization. Finally, we demonstrate zero-shot transfer of these policies from simulation to the real world, without any domain randomization or fine-tuning. This paper aims to establish the first systematic characterization of the usefulness of learned representations for real-world OOD downstream tasks.}, author = {Träuble, Frederik and Dittadi, Andrea and Wuthrich, Manuel and Widmaier, Felix and Gehler, Peter Vincent and Winther, Ole and Locatello, Francesco and Bachem, Olivier and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {ICML 2021 Workshop on Unsupervised Reinforcement Learning}, location = {Virtual}, title = {{Representation learning for out-of-distribution generalization in reinforcement learning}}, year = {2021}, } @article{10000, abstract = {Inhibition or targeted deletion of histone deacetylase 3 (HDAC3) is neuroprotective in a variety neurodegenerative conditions, including retinal ganglion cells (RGCs) after acute optic nerve damage. Consistent with this, induced HDAC3 expression in cultured cells shows selective toxicity to neurons. Despite an established role for HDAC3 in neuronal pathology, little is known regarding the mechanism of this pathology.}, author = {Schmitt, Heather M. and Fehrman, Rachel L. and Maes, Margaret E and Yang, Huan and Guo, Lian Wang and Schlamp, Cassandra L. and Pelzel, Heather R. and Nickells, Robert W.}, issn = {1552-5783}, journal = {Investigative Ophthalmology and Visual Science}, number = {10}, publisher = {Association for Research in Vision and Ophthalmology}, title = {{Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression}}, doi = {10.1167/IOVS.62.10.14}, volume = {62}, year = {2021}, } @inproceedings{10002, abstract = {We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of ω -regular objectives for MDPs. We consider the canonical parity objectives for ω -regular objectives, and for parity objectives with d -priorities we present an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .}, author = {Chatterjee, Krishnendu and Dvorak, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Computational modeling, Markov processes, Probabilistic logic, Formal verification, Game Theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Symbolic time and space tradeoffs for probabilistic verification}}, doi = {10.1109/LICS52264.2021.9470739}, year = {2021}, } @inproceedings{10004, abstract = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Heuristic algorithms, Memory management, Automata, Markov processes, Probability distribution, Complexity theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Stochastic processes with expected stopping time}}, doi = {10.1109/LICS52264.2021.9470595}, year = {2021}, } @article{10005, abstract = {We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.}, author = {Bulíček, Miroslav and Maringová, Erika and Málek, Josef}, issn = {1793-6314}, journal = {Mathematical Models and Methods in Applied Sciences}, keywords = {Nonlinear parabolic systems, implicit constitutive theory, weak solutions, existence, uniqueness}, number = {09}, publisher = {World Scientific}, title = {{On nonlinear problems of parabolic type with implicit constitutive equations involving flux}}, doi = {10.1142/S0218202521500457}, volume = {31}, year = {2021}, }