@inbook{8281, abstract = {We review the history of population genetics, starting with its origins a century ago from the synthesis between Mendel and Darwin's ideas, through to the recent development of sophisticated schemes of inference from sequence data, based on the coalescent. We explain the close relation between the coalescent and a diffusion process, which we illustrate by their application to understand spatial structure. We summarise the powerful methods available for analysis of multiple loci, when linkage equilibrium can be assumed, and then discuss approaches to the more challenging case, where associations between alleles require that we follow genotype, rather than allele, frequencies. Though we can hardly cover the whole of population genetics, we give an overview of the current state of the subject, and future challenges to it.}, author = {Barton, Nicholas H and Etheridge, Alison}, booktitle = {Handbook of statistical genomics}, editor = {Balding, David and Moltke, Ida and Marioni, John}, isbn = {9781119429142}, pages = {115--144}, publisher = {Wiley}, title = {{Mathematical models in population genetics}}, doi = {10.1002/9781119487845.ch4}, year = {2019}, } @unpublished{8184, abstract = {Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l d + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. }, author = {Avvakumov, Sergey and Karasev, R. and Skopenkov, A.}, booktitle = {arXiv}, publisher = {arXiv}, title = {{Stronger counterexamples to the topological Tverberg conjecture}}, year = {2019}, } @inproceedings{6430, abstract = {A proxy re-encryption (PRE) scheme is a public-key encryption scheme that allows the holder of a key pk to derive a re-encryption key for any other key 𝑝𝑘′. This re-encryption key lets anyone transform ciphertexts under pk into ciphertexts under 𝑝𝑘′ without having to know the underlying message, while transformations from 𝑝𝑘′ to pk should not be possible (unidirectional). Security is defined in a multi-user setting against an adversary that gets the users’ public keys and can ask for re-encryption keys and can corrupt users by requesting their secret keys. Any ciphertext that the adversary cannot trivially decrypt given the obtained secret and re-encryption keys should be secure. All existing security proofs for PRE only show selective security, where the adversary must first declare the users it wants to corrupt. This can be lifted to more meaningful adaptive security by guessing the set of corrupted users among the n users, which loses a factor exponential in Open image in new window , rendering the result meaningless already for moderate Open image in new window . Jafargholi et al. (CRYPTO’17) proposed a framework that in some cases allows to give adaptive security proofs for schemes which were previously only known to be selectively secure, while avoiding the exponential loss that results from guessing the adaptive choices made by an adversary. We apply their framework to PREs that satisfy some natural additional properties. Concretely, we give a more fine-grained reduction for several unidirectional PREs, proving adaptive security at a much smaller loss. The loss depends on the graph of users whose edges represent the re-encryption keys queried by the adversary. For trees and chains the loss is quasi-polynomial in the size and for general graphs it is exponential in their depth and indegree (instead of their size as for previous reductions). Fortunately, trees and low-depth graphs cover many, if not most, interesting applications. Our results apply e.g. to the bilinear-map based PRE schemes by Ateniese et al. (NDSS’05 and CT-RSA’09), Gentry’s FHE-based scheme (STOC’09) and the LWE-based scheme by Chandran et al. (PKC’14).}, author = {Fuchsbauer, Georg and Kamath Hosdurg, Chethan and Klein, Karen and Pietrzak, Krzysztof Z}, isbn = {9783030172589}, issn = {16113349}, location = {Beijing, China}, pages = {317--346}, publisher = {Springer Nature}, title = {{Adaptively secure proxy re-encryption}}, doi = {10.1007/978-3-030-17259-6_11}, volume = {11443}, year = {2019}, } @article{6069, abstract = {Electron transport in two-dimensional conducting materials such as graphene, with dominant electron–electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the classical Ohm’s law. The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where the constitutive pressure–speed relation is Stoke’s law. Here we report evidence of such vortices observed in a viscous flow of Newtonian fluid in a microfluidic device consisting of a rectangular cavity—analogous to the electronic system. We extend our experimental observations to elliptic cavities of different eccentricities, and validate them by numerically solving bi-harmonic equation obtained for the viscous flow with no-slip boundary conditions. We verify the existence of a predicted threshold at which vortices appear. Strikingly, we find that a two-dimensional theoretical model captures the essential features of three-dimensional Stokes flow in experiments.}, author = {Mayzel, Jonathan and Steinberg, Victor and Varshney, Atul}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Stokes flow analogous to viscous electron current in graphene}}, doi = {10.1038/s41467-019-08916-5}, volume = {10}, year = {2019}, } @article{6014, abstract = {Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.}, author = {Varshney, Atul and Steinberg, Victor}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Elastic alfven waves in elastic turbulence}}, doi = {10.1038/s41467-019-08551-0}, volume = {10}, year = {2019}, } @article{6451, abstract = {Epidermal growth factor receptor (EGFR) signaling controls skin development and homeostasis inmice and humans, and its deficiency causes severe skin inflammation, which might affect epidermalstem cell behavior. Here, we describe the inflammation-independent effects of EGFR deficiency dur-ing skin morphogenesis and in adult hair follicle stem cells. Expression and alternative splicing analysisof RNA sequencing data from interfollicular epidermis and outer root sheath indicate that EGFR con-trols genes involved in epidermal differentiation and also in centrosome function, DNA damage, cellcycle, and apoptosis. Genetic experiments employingp53deletion in EGFR-deficient epidermis revealthat EGFR signaling exhibitsp53-dependent functions in proliferative epidermal compartments, aswell asp53-independent functions in differentiated hair shaft keratinocytes. Loss of EGFR leads toabsence of LEF1 protein specifically in the innermost epithelial hair layers, resulting in disorganizationof medulla cells. Thus, our results uncover important spatial and temporal features of cell-autonomousEGFR functions in the epidermis.}, author = {Amberg, Nicole and Sotiropoulou, Panagiota A. and Heller, Gerwin and Lichtenberger, Beate M. and Holcmann, Martin and Camurdanoglu, Bahar and Baykuscheva-Gentscheva, Temenuschka and Blanpain, Cedric and Sibilia, Maria}, issn = {2589-0042}, journal = {iScience}, pages = {243--256}, publisher = {Elsevier}, title = {{EGFR controls hair shaft differentiation in a p53-independent manner}}, doi = {10.1016/j.isci.2019.04.018}, volume = {15}, year = {2019}, } @article{10879, abstract = {We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H.}, author = {Dietlein, Adrian M and Gebert, Martin and Müller, Peter}, issn = {1664-039X}, journal = {Journal of Spectral Theory}, keywords = {Random Schrödinger operators, spectral shift function, Anderson orthogonality}, number = {3}, pages = {921--965}, publisher = {European Mathematical Society Publishing House}, title = {{Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function}}, doi = {10.4171/jst/267}, volume = {9}, year = {2019}, } @article{10878, abstract = {Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles.}, author = {Flandoli, Franco and Priola, Enrico and Zanco, Giovanni A}, issn = {1553-5231}, journal = {Discrete and Continuous Dynamical Systems}, keywords = {Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis}, number = {6}, pages = {3037--3067}, publisher = {American Institute of Mathematical Sciences}, title = {{A mean-field model with discontinuous coefficients for neurons with spatial interaction}}, doi = {10.3934/dcds.2019126}, volume = {39}, year = {2019}, } @inproceedings{6935, abstract = {This paper investigates the power of preprocessing in the CONGEST model. Schmid and Suomela (ACM HotSDN 2013) introduced the SUPPORTED CONGEST model to study the application of distributed algorithms in Software-Defined Networks (SDNs). In this paper, we show that a large class of lower bounds in the CONGEST model still hold in the SUPPORTED model, highlighting the robustness of these bounds. This also raises the question how much does preprocessing help in the CONGEST model.}, author = {Foerster, Klaus-Tycho and Korhonen, Janne and Rybicki, Joel and Schmid, Stefan}, booktitle = {Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing}, isbn = {9781450362177}, location = {Toronto, ON, Canada}, pages = {259--261}, publisher = {ACM}, title = {{Does preprocessing help under congestion?}}, doi = {10.1145/3293611.3331581}, year = {2019}, } @article{138, abstract = {Autoregulation is the direct modulation of gene expression by the product of the corresponding gene. Autoregulation of bacterial gene expression has been mostly studied at the transcriptional level, when a protein acts as the cognate transcriptional repressor. A recent study investigating dynamics of the bacterial toxin–antitoxin MazEF system has shown how autoregulation at both the transcriptional and post-transcriptional levels affects the heterogeneity of Escherichia coli populations. Toxin–antitoxin systems hold a crucial but still elusive part in bacterial response to stress. This perspective highlights how these modules can also serve as a great model system for investigating basic concepts in gene regulation. However, as the genomic background and environmental conditions substantially influence toxin activation, it is important to study (auto)regulation of toxin–antitoxin systems in well-defined setups as well as in conditions that resemble the environmental niche.}, author = {Nikolic, Nela}, journal = {Current Genetics}, number = {1}, pages = {133--138}, publisher = {Springer}, title = {{Autoregulation of bacterial gene expression: lessons from the MazEF toxin–antitoxin system}}, doi = {10.1007/s00294-018-0879-8}, volume = {65}, year = {2019}, } @article{151, abstract = {We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2 we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.}, author = {Fischer, Julian L and Kneuss, Olivier}, journal = {Journal of Differential Equations}, number = {1}, pages = {257 -- 311}, publisher = {Elsevier}, title = {{Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity}}, doi = {10.1016/j.jde.2018.07.045}, volume = {266}, year = {2019}, } @article{27, abstract = {The cerebral cortex is composed of a large variety of distinct cell-types including projection neurons, interneurons and glial cells which emerge from distinct neural stem cell (NSC) lineages. The vast majority of cortical projection neurons and certain classes of glial cells are generated by radial glial progenitor cells (RGPs) in a highly orchestrated manner. Recent studies employing single cell analysis and clonal lineage tracing suggest that NSC and RGP lineage progression are regulated in a profound deterministic manner. In this review we focus on recent advances based mainly on correlative phenotypic data emerging from functional genetic studies in mice. We establish hypotheses to test in future research and outline a conceptual framework how epigenetic cues modulate the generation of cell-type diversity during cortical development. This article is protected by copyright. All rights reserved.}, author = {Amberg, Nicole and Laukoter, Susanne and Hippenmeyer, Simon}, journal = {Journal of Neurochemistry}, number = {1}, pages = {12--26}, publisher = {Wiley}, title = {{Epigenetic cues modulating the generation of cell type diversity in the cerebral cortex}}, doi = {10.1111/jnc.14601}, volume = {149}, year = {2019}, } @article{5789, abstract = {Tissue morphogenesis is driven by mechanical forces that elicit changes in cell size, shape and motion. The extent by which forces deform tissues critically depends on the rheological properties of the recipient tissue. Yet, whether and how dynamic changes in tissue rheology affect tissue morphogenesis and how they are regulated within the developing organism remain unclear. Here, we show that blastoderm spreading at the onset of zebrafish morphogenesis relies on a rapid, pronounced and spatially patterned tissue fluidization. Blastoderm fluidization is temporally controlled by mitotic cell rounding-dependent cell–cell contact disassembly during the last rounds of cell cleavages. Moreover, fluidization is spatially restricted to the central blastoderm by local activation of non-canonical Wnt signalling within the blastoderm margin, increasing cell cohesion and thereby counteracting the effect of mitotic rounding on contact disassembly. Overall, our results identify a fluidity transition mediated by loss of cell cohesion as a critical regulator of embryo morphogenesis.}, author = {Petridou, Nicoletta and Grigolon, Silvia and Salbreux, Guillaume and Hannezo, Edouard B and Heisenberg, Carl-Philipp J}, issn = {14657392}, journal = {Nature Cell Biology}, pages = {169–178}, publisher = {Nature Publishing Group}, title = {{Fluidization-mediated tissue spreading by mitotic cell rounding and non-canonical Wnt signalling}}, doi = {10.1038/s41556-018-0247-4}, volume = {21}, year = {2019}, } @article{196, abstract = {The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain. }, author = {Lang, Moritz and Shkolnikov, Mikhail}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {8}, pages = {2821--2830}, publisher = {National Academy of Sciences}, title = {{Harmonic dynamics of the Abelian sandpile}}, doi = {10.1073/pnas.1812015116}, volume = {116}, year = {2019}, } @inproceedings{14184, abstract = {Learning disentangled representations is considered a cornerstone problem in representation learning. Recently, Locatello et al. (2019) demonstrated that unsupervised disentanglement learning without inductive biases is theoretically impossible and that existing inductive biases and unsupervised methods do not allow to consistently learn disentangled representations. However, in many practical settings, one might have access to a limited amount of supervision, for example through manual labeling of (some) factors of variation in a few training examples. In this paper, we investigate the impact of such supervision on state-of-the-art disentanglement methods and perform a large scale study, training over 52000 models under well-defined and reproducible experimental conditions. We observe that a small number of labeled examples (0.01--0.5\% of the data set), with potentially imprecise and incomplete labels, is sufficient to perform model selection on state-of-the-art unsupervised models. Further, we investigate the benefit of incorporating supervision into the training process. Overall, we empirically validate that with little and imprecise supervision it is possible to reliably learn disentangled representations.}, author = {Locatello, Francesco and Tschannen, Michael and Bauer, Stefan and Rätsch, Gunnar and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {8th International Conference on Learning Representations}, location = {Virtual}, title = {{Disentangling factors of variation using few labels}}, year = {2019}, } @inproceedings{14189, abstract = {We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.}, author = {Gresele, Luigi and Rubenstein, Paul K. and Mehrjou, Arash and Locatello, Francesco and Schölkopf, Bernhard}, booktitle = {Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence}, location = {Tel Aviv, Israel}, pages = {217--227}, publisher = {ML Research Press}, title = {{The incomplete Rosetta Stone problem: Identifiability results for multi-view nonlinear ICA}}, volume = {115}, year = {2019}, } @inproceedings{14197, abstract = {Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an \emph{unobserved} sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing the representations of more than \num{12600} trained state-of-the-art disentangled models, we observe that several disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.}, author = {Locatello, Francesco and Abbati, Gabriele and Rainforth, Tom and Bauer, Stefan and Schölkopf, Bernhard and Bachem, Olivier}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, pages = {14611–14624}, title = {{On the fairness of disentangled representations}}, volume = {32}, year = {2019}, } @inproceedings{14191, abstract = {A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily available. In this setting, generalized conditional gradient methods (aka Frank-Wolfe-type methods) provide scalable solutions by leveraging the so-called linear minimization oracle instead of the projection onto the semidefinite cone. Most problems in machine learning and modern engineering applications, however, contain some degree of stochasticity. In this work, we propose the first conditional-gradient-type method for solving stochastic optimization problems under affine constraints. Our method guarantees O(k−1/3) convergence rate in expectation on the objective residual and O(k−5/12) on the feasibility gap.}, author = {Locatello, Francesco and Yurtsever, Alp and Fercoq, Olivier and Cevher, Volkan}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, pages = {14291–14301}, title = {{Stochastic Frank-Wolfe for composite convex minimization}}, volume = {32}, year = {2019}, } @inproceedings{14193, abstract = {A disentangled representation encodes information about the salient factors of variation in the data independently. Although it is often argued that this representational format is useful in learning to solve many real-world down-stream tasks, there is little empirical evidence that supports this claim. In this paper, we conduct a large-scale study that investigates whether disentangled representations are more suitable for abstract reasoning tasks. Using two new tasks similar to Raven's Progressive Matrices, we evaluate the usefulness of the representations learned by 360 state-of-the-art unsupervised disentanglement models. Based on these representations, we train 3600 abstract reasoning models and observe that disentangled representations do in fact lead to better down-stream performance. In particular, they enable quicker learning using fewer samples.}, author = {Steenkiste, Sjoerd van and Locatello, Francesco and Schmidhuber, Jürgen and Bachem, Olivier}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, title = {{Are disentangled representations helpful for abstract visual reasoning?}}, volume = {32}, year = {2019}, } @inproceedings{14200, abstract = {The key 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 more than 12000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different 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, increased disentanglement does not seem to 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}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, location = {Long Beach, CA, United States}, pages = {4114--4124}, publisher = {ML Research Press}, title = {{Challenging common assumptions in the unsupervised learning of disentangled representations}}, volume = {97}, year = {2019}, }