@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{14190, abstract = {Learning meaningful and compact representations with disentangled semantic aspects is considered to be of key importance in representation learning. Since real-world data is notoriously costly to collect, many recent state-of-the-art disentanglement models have heavily relied on synthetic toy data-sets. In this paper, we propose a novel data-set which consists of over one million images of physical 3D objects with seven factors of variation, such as object color, shape, size and position. In order to be able to control all the factors of variation precisely, we built an experimental platform where the objects are being moved by a robotic arm. In addition, we provide two more datasets which consist of simulations of the experimental setup. These datasets provide for the first time the possibility to systematically investigate how well different disentanglement methods perform on real data in comparison to simulation, and how simulated data can be leveraged to build better representations of the real world. We provide a first experimental study of these questions and our results indicate that learned models transfer poorly, but that model and hyperparameter selection is an effective means of transferring information to the real world.}, author = {Gondal, Muhammad Waleed and Wüthrich, Manuel and Miladinović, Đorđe and Locatello, Francesco and Breidt, Martin and Volchkov, Valentin and Akpo, Joel and Bachem, Olivier and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713807933}, location = {Vancouver, Canada}, title = {{On the transfer of inductive bias from simulation to the real world: a new disentanglement dataset}}, 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{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{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}, } @article{14299, abstract = {DNA origami nano-objects are usually designed around generic single-stranded “scaffolds”. Many properties of the target object are determined by details of those generic scaffold sequences. Here, we enable designers to fully specify the target structure not only in terms of desired 3D shape but also in terms of the sequences used. To this end, we built design tools to construct scaffold sequences de novo based on strand diagrams, and we developed scalable production methods for creating design-specific scaffold strands with fully user-defined sequences. We used 17 custom scaffolds having different lengths and sequence properties to study the influence of sequence redundancy and sequence composition on multilayer DNA origami assembly and to realize efficient one-pot assembly of multiscaffold DNA origami objects. Furthermore, as examples for functionalized scaffolds, we created a scaffold that enables direct, covalent cross-linking of DNA origami via UV irradiation, and we built DNAzyme-containing scaffolds that allow postfolding DNA origami domain separation.}, author = {FAS, Engelhardt and Praetorius, Florian M and Wachauf, CH and Brüggenthies, G and Kohler, F and Kick, B and Kadletz, KL and Pham, PN and Behler, KL and Gerling, T and Dietz, H}, issn = {1936-086x}, journal = {ACS Nano}, number = {5}, pages = {5015--5027}, publisher = {ACS Publications}, title = {{Custom-size, functional, and durable DNA origami with design-specific scaffolds}}, doi = {10.1021/acsnano.9b01025}, volume = {13}, 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}, } @unpublished{15147, abstract = {Circadian rhythms are generated by a transcription-based feedback loop where CLOCK:BMAL1 drive transcription of their repressors (PER1/2, CRY1/2), which bind to CLOCK:BMAL1 to close the feedback loop with ~24-hour periodicity. Here we identify a key biochemical and structural difference between CRY1 and CRY2 that underlies their differential strengths as transcriptional repressors. While both cryptochromes bind the BMAL1 transactivation domain with similar affinity to sequester it from coactivators, CRY1 is recruited with much higher affinity to the PAS domain core of CLOCK:BMAL1, allowing it to serve as a stronger repressor that lengthens circadian period. We identify a dynamic loop in the secondary pocket that regulates differential binding of cryptochromes to the PAS domain core. Notably, PER2 binding remodels this loop in CRY2 to enhance its affinity for CLOCK:BMAL1, explaining why CRY2 forms an obligate heterodimer with PER2, while CRY1 is capable of repressing CLOCK:BMAL1 both with and without PER2.}, author = {Fribourgh, Jennifer L. and Srivastava, Ashutosh and Sandate, Colby R. and Michael, Alicia and Hsu, Peter L. and Rakers, Christin and Nguyen, Leslee T. and Torgrimson, Megan R. and Parico, Gian Carlo G. and Tripathi, Sarvind and Zheng, Ning and Lander, Gabriel C. and Hirota, Tsuyoshi and Tama, Florence and Partch, Carrie L.}, booktitle = {bioRxiv}, title = {{Protein dynamics regulate distinct biochemical properties of cryptochromes in mammalian circadian rhythms}}, doi = {10.1101/740464}, year = {2019}, } @article{15230, abstract = {We have searched the Gaia DR2 catalog for previously unknown hot white dwarfs in the direction of young open star clusters. The aim of this experiment was to try and extend the initial–final mass relation (IFMR) to somewhat higher masses, potentially challenging the Chandrasekhar limit currently thought to be around 1.38 M⊙. We discovered a particularly interesting white dwarf in the direction of the young ∼150 Myr old cluster Messier 47 (NGC 2422). All Gaia indicators (proper motion, parallax, location in the Gaia color–magnitude diagram) suggest that it is a cluster member. Its spectrum, obtained from Gemini-South, yields a number of anomalies: it is a DB (helium-rich atmosphere) white dwarf, it has a large magnetic field (2.5 MG), is of high mass (∼1.06 M⊙), and its colors are very peculiar—particularly the redder ones (r, i, z and y), which suggests that it may have a late-type companion. This may be the only magnetized, detached binary white dwarf with a non-degenerate companion of any spectral type known in or out of a star cluster. If the white dwarf is a cluster member, as all indicators suggest, its progenitor had a mass just over 6 M⊙. It may, however, be telling an even more interesting story than the one related to the IFMR, one about the origin of stellar magnetic fields, SNe I, and gravitational waves from low-mass stellar systems.}, author = {Richer, Harvey B. and Kerr, Ronan and Heyl, Jeremy and Caiazzo, Ilaria and Cummings, Jeffrey and Bergeron, Pierre and Dufour, Patrick}, issn = {1538-4357}, journal = {The Astrophysical Journal}, keywords = {Space and Planetary Science, Astronomy and Astrophysics}, number = {2}, publisher = {American Astronomical Society}, title = {{A massive magnetic helium atmosphere white dwarf binary in a young star cluster}}, doi = {10.3847/1538-4357/ab2874}, volume = {880}, year = {2019}, } @article{15231, abstract = {In this paper, we analyze stellar proper motions in the core of the globular cluster 47 Tucanae to explore the possibility of an intermediate-mass black hole (IMBH) influence on the stellar dynamics. Our use of short-wavelength photometry affords us an exceedingly clear view of stellar motions into the very center of the crowded core, yielding proper motions for >50,000 stars in the central 2′. We model the velocity dispersion profile of the cluster using an isotropic Jeans model. The density distribution is taken as a central IMBH point mass added to a combination of King templates. We individually model the general low-mass cluster objects (main sequence/giant stars), as well as the concentrated populations of heavy binary systems and dark stellar remnants. Using unbinned likelihood model fitting, we find that the inclusion of the concentrated populations in our model plays a crucial role in fitting for an IMBH mass. The concentrated binaries and stellar-mass black holes (BHs) produce a sufficient velocity dispersion signal in the core so as to make an IMBH unnecessary to fit the observations. We additionally determine that a stellar-mass BH retention fraction of 8.5% becomes incompatible with our observed velocities in the core.}, author = {Mann, Christopher R. and Richer, Harvey and Heyl, Jeremy and Anderson, Jay and Kalirai, Jason and Caiazzo, Ilaria and Möhle, Swantje D. and Knee, Alan and Baumgardt, Holger}, issn = {1538-4357}, journal = {The Astrophysical Journal}, keywords = {Space and Planetary Science, Astronomy and Astrophysics}, number = {1}, publisher = {American Astronomical Society}, title = {{A multimass velocity dispersion model of 47 Tucanae indicates no evidence for an intermediate-mass black hole}}, doi = {10.3847/1538-4357/ab0e6d}, volume = {875}, year = {2019}, } @article{170, abstract = {Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over ℚ that contains a conic defined over ℚ .}, author = {Browning, Timothy D and Sofos, Efthymios}, journal = {Mathematische Annalen}, number = {3-4}, pages = {977--1016}, publisher = {Springer Nature}, title = {{Counting rational points on quartic del Pezzo surfaces with a rational conic}}, doi = {10.1007/s00208-018-1716-6}, volume = {373}, year = {2019}, } @article{19473, abstract = {Leptin informs the brain about sufficiency of fuel stores. When insufficient, leptin levels fall, triggering compensatory increases in appetite. Falling leptin is first sensed by hypothalamic neurons, which then initiate adaptive responses. With regard to hunger, it is thought that leptin-sensing neurons work entirely via circuits within the central nervous system (CNS). Very unexpectedly, however, we now show this is not the case. Instead, stimulation of hunger requires an intervening endocrine step, namely activation of the hypothalamic–pituitary–adrenocortical (HPA) axis. Increased corticosterone then activates AgRP neurons to fully increase hunger. Importantly, this is true for 2 forms of low leptin-induced hunger, fasting and poorly controlled type 1 diabetes. Hypoglycemia, which also stimulates hunger by activating CNS neurons, albeit independently of leptin, similarly recruits and requires this pathway by which HPA axis activity stimulates AgRP neurons. Thus, HPA axis regulation of AgRP neurons is a previously underappreciated step in homeostatic regulation of hunger.}, author = {Perry, Rachel J. and Resch, Jon M. and Douglass, Amelia May Barnett and Madara, Joseph C. and Rabin-Court, Aviva and Kucukdereli, Hakan and Wu, Chen and Song, Joongyu D. and Lowell, Bradford B. and Shulman, Gerald I.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {27}, pages = {13670--13679}, publisher = {National Academy of Sciences}, title = {{Leptin’s hunger-suppressing effects are mediated by the hypothalamic–pituitary–adrenocortical axis in rodents}}, doi = {10.1073/pnas.1901795116}, volume = {116}, year = {2019}, } @article{19493, abstract = {In 2016, Balakrishnan, Ho, Kaplan, Spicer, Stein and Weigandt produced a database of elliptic curves over Q ordered by height in which they computed the rank, the size of the 2-Selmer group, and other arithmetic invariants. They observed that after a certain point, the average rank seemed to decrease as the height increased. Here we consider the family of elliptic curves over Q whose rational torsion subgroup is isomorphic to Z∕2Z×Z∕8Z. Conditional on GRH and BSD, we compute the rank of 92% of the 202,461 curves with parameter height less than 103. We also compute the size of the 2-Selmer group and the Tamagawa product, and prove that their averages tend to infinity for this family.}, author = {Chan, Yik Tung and Hanselman, Jeroen and Li, Wanlin}, issn = {2329-907X}, journal = {The Open Book Series}, pages = {173--189}, publisher = {Mathematical Sciences Publishers}, title = {{Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion}}, doi = {10.2140/obs.2019.2.173}, volume = {2}, 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 of the United States of America}, 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}, } @article{441, author = {Kalinin, Nikita and Shkolnikov, Mikhail}, issn = {2199-6768}, journal = {European Journal of Mathematics}, number = {3}, pages = {909–928}, publisher = {Springer Nature}, title = {{Tropical formulae for summation over a part of SL(2,Z)}}, doi = {10.1007/s40879-018-0218-0}, volume = {5}, year = {2019}, } @article{5, abstract = {In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2.}, author = {Ganev, Iordan V}, journal = {Journal of the London Mathematical Society}, number = {3}, pages = {778--806}, publisher = {Wiley}, title = {{The wonderful compactification for quantum groups}}, doi = {10.1112/jlms.12193}, volume = {99}, 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 = {1465-7392}, 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{5790, abstract = {The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some predrawn chords that represent an induced subgraph of G. The question is whether one can extend R′ to a representation R of the entire graph G, that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of G. Our main result is an O(n3) time algorithm for partial representation extension of circle graphs, where n is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.}, author = {Chaplick, Steven and Fulek, Radoslav and Klavík, Pavel}, issn = {0364-9024}, journal = {Journal of Graph Theory}, number = {4}, pages = {365--394}, publisher = {Wiley}, title = {{Extending partial representations of circle graphs}}, doi = {10.1002/jgt.22436}, volume = {91}, year = {2019}, }