@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}, } @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}, } @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}, } @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}, } @misc{14592, abstract = {Cryo-electron microscopy (cryo-EM) of cellular specimens provides insights into biological processes and structures within a native context. However, a major challenge still lies in the efficient and reproducible preparation of adherent cells for subsequent cryo-EM analysis. This is due to the sensitivity of many cellular specimens to the varying seeding and culturing conditions required for EM experiments, the often limited amount of cellular material and also the fragility of EM grids and their substrate. Here, we present low-cost and reusable 3D printed grid holders, designed to improve specimen preparation when culturing challenging cellular samples directly on grids. The described grid holders increase cell culture reproducibility and throughput, and reduce the resources required for cell culturing. We show that grid holders can be integrated into various cryo-EM workflows, including micro-patterning approaches to control cell seeding on grids, and for generating samples for cryo-focused ion beam milling and cryo-electron tomography experiments. Their adaptable design allows for the generation of specialized grid holders customized to a large variety of applications.}, author = {Schur, Florian KM}, publisher = {Institute of Science and Technology Austria}, title = {{STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy}}, doi = {10.15479/AT:ISTA:14592}, year = {2020}, } @article{14694, abstract = {We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 - a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {1431-0643}, journal = {Documenta Mathematica}, keywords = {General Mathematics}, pages = {1421--1539}, publisher = {EMS Press}, title = {{The Dyson equation with linear self-energy: Spectral bands, edges and cusps}}, doi = {10.4171/dm/780}, volume = {25}, year = {2020}, } @article{5681, abstract = {We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms.}, author = {Hikaru, Ibayashi and Wojtan, Christopher J and Thuerey, Nils and Igarashi, Takeo and Ando, Ryoichi}, issn = {19410506}, journal = {IEEE Transactions on Visualization and Computer Graphics}, number = {6}, pages = {2288--2302}, publisher = {IEEE}, title = {{Simulating liquids on dynamically warping grids}}, doi = {10.1109/TVCG.2018.2883628}, volume = {26}, year = {2020}, } @article{6184, abstract = {We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H and Schröder, Dominik J}, issn = {0091-1798}, journal = {Annals of Probability}, number = {2}, pages = {963--1001}, publisher = {Institute of Mathematical Statistics}, title = {{Correlated random matrices: Band rigidity and edge universality}}, doi = {10.1214/19-AOP1379}, volume = {48}, year = {2020}, } @article{6185, abstract = {For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).}, author = {Erdös, László and Krüger, Torben H and Schröder, Dominik J}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {1203--1278}, publisher = {Springer Nature}, title = {{Cusp universality for random matrices I: Local law and the complex Hermitian case}}, doi = {10.1007/s00220-019-03657-4}, volume = {378}, year = {2020}, } @article{6358, abstract = {We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.}, author = {Carlen, Eric A. and Maas, Jan}, issn = {15729613}, journal = {Journal of Statistical Physics}, number = {2}, pages = {319--378}, publisher = {Springer Nature}, title = {{Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems}}, doi = {10.1007/s10955-019-02434-w}, volume = {178}, year = {2020}, } @article{6359, abstract = {The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.}, author = {Dareiotis, Konstantinos and Gerencser, Mate}, issn = {1083-6489}, journal = {Electronic Journal of Probability}, publisher = {Institute of Mathematical Statistics}, title = {{On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift}}, doi = {10.1214/20-EJP479}, volume = {25}, year = {2020}, } @article{6488, abstract = {We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.}, author = {Cipolloni, Giorgio and Erdös, László}, issn = {20103271}, journal = {Random Matrices: Theory and Application}, number = {3}, publisher = {World Scientific Publishing}, title = {{Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices}}, doi = {10.1142/S2010326320500069}, volume = {9}, year = {2020}, } @article{6563, abstract = {This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.}, author = {Filakovský, Marek and Vokřínek, Lukas}, issn = {16153383}, journal = {Foundations of Computational Mathematics}, pages = {311--330}, publisher = {Springer Nature}, title = {{Are two given maps homotopic? An algorithmic viewpoint}}, doi = {10.1007/s10208-019-09419-x}, volume = {20}, year = {2020}, } @article{6593, abstract = {We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.}, author = {Shehu, Yekini and Li, Xiao-Huan and Dong, Qiao-Li}, issn = {1572-9265}, journal = {Numerical Algorithms}, pages = {365--388}, publisher = {Springer Nature}, title = {{An efficient projection-type method for monotone variational inequalities in Hilbert spaces}}, doi = {10.1007/s11075-019-00758-y}, volume = {84}, year = {2020}, } @article{6649, abstract = {While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials. }, author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {2097–2150}, publisher = {Springer Nature}, title = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}}, doi = {10.1007/s00220-019-03505-5}, volume = {374}, year = {2020}, } @article{6748, abstract = {Fitting a function by using linear combinations of a large number N of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is non-convex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here we consider the problem of learning a concave function f on a compact convex domain Ω⊆ℝd, using linear combinations of `bump-like' components (neurons). The parameters to be fitted are the centers of N bumps, and the resulting empirical risk minimization problem is highly non-convex. We prove that, in the limit in which the number of neurons diverges, the evolution of gradient descent converges to a Wasserstein gradient flow in the space of probability distributions over Ω. Further, when the bump width δ tends to 0, this gradient flow has a limit which is a viscous porous medium equation. Remarkably, the cost function optimized by this gradient flow exhibits a special property known as displacement convexity, which implies exponential convergence rates for N→∞, δ→0. Surprisingly, this asymptotic theory appears to capture well the behavior for moderate values of δ,N. Explaining this phenomenon, and understanding the dependence on δ,N in a quantitative manner remains an outstanding challenge.}, author = {Javanmard, Adel and Mondelli, Marco and Montanari, Andrea}, issn = {1941-7330}, journal = {Annals of Statistics}, number = {6}, pages = {3619--3642}, publisher = {Institute of Mathematical Statistics}, title = {{Analysis of a two-layer neural network via displacement convexity}}, doi = {10.1214/20-AOS1945}, volume = {48}, year = {2020}, } @article{6761, abstract = {In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.}, author = {Avni, Guy and Henzinger, Thomas A and Kupferman, Orna}, issn = {03043975}, journal = {Theoretical Computer Science}, pages = {42--55}, publisher = {Elsevier}, title = {{Dynamic resource allocation games}}, doi = {10.1016/j.tcs.2019.06.031}, volume = {807}, year = {2020}, } @article{6796, abstract = {Nearby grid cells have been observed to express a remarkable degree of long-rangeorder, which is often idealized as extending potentially to infinity. Yet their strict peri-odic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.}, author = {Stella, Federico and Urdapilleta, Eugenio and Luo, Yifan and Treves, Alessandro}, issn = {10981063}, journal = {Hippocampus}, number = {4}, pages = {302--313}, publisher = {Wiley}, title = {{Partial coherence and frustration in self-organizing spherical grids}}, doi = {10.1002/hipo.23144}, volume = {30}, year = {2020}, } @article{6808, abstract = {Super-resolution fluorescence microscopy has become an important catalyst for discovery in the life sciences. In STimulated Emission Depletion (STED) microscopy, a pattern of light drives fluorophores from a signal-emitting on-state to a non-signalling off-state. Only emitters residing in a sub-diffraction volume around an intensity minimum are allowed to fluoresce, rendering them distinguishable from the nearby, but dark fluorophores. STED routinely achieves resolution in the few tens of nanometers range in biological samples and is suitable for live imaging. Here, we review the working principle of STED and provide general guidelines for successful STED imaging. The strive for ever higher resolution comes at the cost of increased light burden. We discuss techniques to reduce light exposure and mitigate its detrimental effects on the specimen. These include specialized illumination strategies as well as protecting fluorophores from photobleaching mediated by high-intensity STED light. This opens up the prospect of volumetric imaging in living cells and tissues with diffraction-unlimited resolution in all three spatial dimensions.}, author = {Jahr, Wiebke and Velicky, Philipp and Danzl, Johann G}, issn = {1046-2023}, journal = {Methods}, number = {3}, pages = {27--41}, publisher = {Elsevier}, title = {{Strategies to maximize performance in STimulated Emission Depletion (STED) nanoscopy of biological specimens}}, doi = {10.1016/j.ymeth.2019.07.019}, volume = {174}, year = {2020}, } @article{6906, abstract = {We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential.}, author = {Boccato, Chiara and Brennecke, Christian and Cenatiempo, Serena and Schlein, Benjamin}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, pages = {1311--1395}, publisher = {Springer}, title = {{Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime}}, doi = {10.1007/s00220-019-03555-9}, volume = {376}, year = {2020}, }