@article{12684, abstract = {Given a place ω of a global function field K over a finite field, with associated affine function ring Rω and completion Kω , the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points (a,b)∈Rω2 in the plane Kω2 , and for renormalized solutions to the gcd equation ax+by=1 . The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in \ZZ2 .}, author = {Horesh, Tal and Paulin, Frédéric}, issn = {2118-8572}, journal = {Journal de Theorie des Nombres de Bordeaux}, number = {3}, pages = {679--703}, publisher = {Centre Mersenne}, title = {{Effective equidistribution of lattice points in positive characteristic}}, doi = {10.5802/JTNB.1222}, volume = {34}, year = {2022}, } @unpublished{12750, abstract = {Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored universality classes of dynamics and invite their further theoretical and experimental studies.}, author = {Brighi, Pietro and Ljubotina, Marko and Serbyn, Maksym}, booktitle = {arXiv}, title = {{Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models}}, doi = {10.48550/arXiv.2210.15607}, year = {2022}, } @inproceedings{12775, abstract = {We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a sequence of approximations converging to the true value in the limit, our aim is to obtain an algorithm with guarantees on the precision of the approximation. As this problem is undecidable in general, assumptions on the MDP are necessary. Our main contribution is to identify sufficient assumptions that are as weak as possible, thus approaching the "boundary" of which systems can be correctly and reliably analyzed. To this end, we also argue why each of our assumptions is necessary for algorithms based on processing finitely many observations. We present two solution variants. The first one provides converging lower bounds under weaker assumptions than typical ones from previous works concerned with guarantees. The second one then utilizes stronger assumptions to additionally provide converging upper bounds. Altogether, we obtain an anytime algorithm, i.e. yielding a sequence of approximants with known and iteratively improving precision, converging to the true value in the limit. Besides, due to the generality of our assumptions, our algorithms are very general templates, readily allowing for various heuristics from literature in contrast to, e.g., a specific discretization algorithm. Our theoretical contribution thus paves the way for future practical improvements without sacrificing correctness guarantees.}, author = {Grover, Kush and Kretinsky, Jan and Meggendorfer, Tobias and Weininger, Maimilian}, booktitle = {33rd International Conference on Concurrency Theory }, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Anytime guarantees for reachability in uncountable Markov decision processes}}, doi = {10.4230/LIPIcs.CONCUR.2022.11}, volume = {243}, year = {2022}, } @article{12776, abstract = {An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface.}, author = {Browning, Timothy D}, issn = {1076-9803}, journal = {New York Journal of Mathematics}, pages = {1193 -- 1229}, publisher = {State University of New York}, title = {{Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5}}, volume = {28}, year = {2022}, } @inproceedings{12780, abstract = {The ability to scale out training workloads has been one of the key performance enablers of deep learning. The main scaling approach is data-parallel GPU-based training, which has been boosted by hardware and software support for highly efficient point-to-point communication, and in particular via hardware bandwidth over-provisioning. Overprovisioning comes at a cost: there is an order of magnitude price difference between "cloud-grade" servers with such support, relative to their popular "consumer-grade" counterparts, although single server-grade and consumer-grade GPUs can have similar computational envelopes. In this paper, we show that the costly hardware overprovisioning approach can be supplanted via algorithmic and system design, and propose a framework called CGX, which provides efficient software support for compressed communication in ML applications, for both multi-GPU single-node training, as well as larger-scale multi-node training. CGX is based on two technical advances: At the system level, it relies on a re-developed communication stack for ML frameworks, which provides flexible, highly-efficient support for compressed communication. At the application level, it provides seamless, parameter-free integration with popular frameworks, so that end-users do not have to modify training recipes, nor significant training code. This is complemented by a layer-wise adaptive compression technique which dynamically balances compression gains with accuracy preservation. CGX integrates with popular ML frameworks, providing up to 3X speedups for multi-GPU nodes based on commodity hardware, and order-of-magnitude improvements in the multi-node setting, with negligible impact on accuracy.}, author = {Markov, Ilia and Ramezanikebrya, Hamidreza and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 23rd ACM/IFIP International Middleware Conference}, isbn = {9781450393409}, location = {Quebec, QC, Canada}, pages = {241--254}, publisher = {Association for Computing Machinery}, title = {{CGX: Adaptive system support for communication-efficient deep learning}}, doi = {10.1145/3528535.3565248}, year = {2022}, } @article{12793, abstract = {Let F be a global function field with constant field Fq. Let G be a reductive group over Fq. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line P1Fq with two points of ramifications.}, author = {Yu, Hongjie}, issn = {1945-5844}, journal = {Pacific Journal of Mathematics}, keywords = {Arthur–Selberg trace formula, cuspidal automorphic representations, global function fields}, number = {1}, pages = {193--237}, publisher = {Mathematical Sciences Publishers}, title = {{ A coarse geometric expansion of a variant of Arthur's truncated traces and some applications}}, doi = {10.2140/pjm.2022.321.193}, volume = {321}, year = {2022}, } @unpublished{12860, abstract = {Memorization of the relation between entities in a dataset can lead to privacy issues when using a trained model for question answering. We introduce Relational Memorization (RM) to understand, quantify and control this phenomenon. While bounding general memorization can have detrimental effects on the performance of a trained model, bounding RM does not prevent effective learning. The difference is most pronounced when the data distribution is long-tailed, with many queries having only few training examples: Impeding general memorization prevents effective learning, while impeding only relational memorization still allows learning general properties of the underlying concepts. We formalize the notion of Relational Privacy (RP) and, inspired by Differential Privacy (DP), we provide a possible definition of Differential Relational Privacy (DrP). These notions can be used to describe and compute bounds on the amount of RM in a trained model. We illustrate Relational Privacy concepts in experiments with large-scale models for Question Answering.}, author = {Bombari, Simone and Achille, Alessandro and Wang, Zijian and Wang, Yu-Xiang and Xie, Yusheng and Singh, Kunwar Yashraj and Appalaraju, Srikar and Mahadevan, Vijay and Soatto, Stefano}, booktitle = {arXiv}, title = {{Towards differential relational privacy and its use in question answering}}, doi = {10.48550/arXiv.2203.16701}, year = {2022}, } @inproceedings{12894, author = {Schlögl, Alois and Hornoiu, Andrei and Elefante, Stefano and Stadlbauer, Stephan}, booktitle = {ASHPC22 - Austrian-Slovenian HPC Meeting 2022}, isbn = {978-3-200-08499-5}, location = {Grundlsee, Austria}, pages = {7}, publisher = {EuroCC Austria c/o Universität Wien}, title = {{Where is the sweet spot? A procurement story of general purpose compute nodes}}, doi = {10.25365/phaidra.337}, year = {2022}, } @article{12923, abstract = {Photoredox-mediated Ni-catalyzed cross-couplings are powerful transformations to form carbon–heteroatom bonds and are generally photocatalyzed by noble metal complexes. Low-cost and easy-to-prepare carbon dots (CDs) are attractive quasi-homogeneous photocatalyst alternatives, but their applicability is limited by their short photoluminescence (PL) lifetimes. By tuning the surface and PL properties of CDs, we designed colloidal CD nano-photocatalysts for a broad range of Ni-mediated cross-couplings between aryl halides and nucleophiles. In particular, a CD decorated with amino groups permitted coupling to a wide range of aryl halides and thiols under mild, base-free conditions. Mechanistic studies suggested dynamic quenching of the CD excited state by the Ni co-catalyst and identified that pyridinium iodide (pyHI), a previously used additive in metallaphotocatalyzed cross-couplings, can also act as a photocatalyst in such transformations.}, author = {Zhao, Zhouxiang and Pieber, Bartholomäus and Delbianco, Martina}, issn = {2155-5435}, journal = {ACS Catalysis}, keywords = {Catalysis, General Chemistry}, number = {22}, pages = {13831--13837}, publisher = {American Chemical Society}, title = {{Modulating the surface and photophysical properties of carbon dots to access colloidal photocatalysts for cross-couplings}}, doi = {10.1021/acscatal.2c04025}, volume = {12}, year = {2022}, } @article{12924, abstract = {We demonstrate that several visible-light-mediated carbon−heteroatom cross-coupling reactions can be carried out using a photoactive NiII precatalyst that forms in situ from a nickel salt and a bipyridine ligand decorated with two carbazole groups (Ni(Czbpy)Cl2). The activation of this precatalyst towards cross-coupling reactions follows a hitherto undisclosed mechanism that is different from previously reported light-responsive nickel complexes that undergo metal-to-ligand charge transfer. Theoretical and spectroscopic investigations revealed that irradiation of Ni(Czbpy)Cl2 with visible light causes an initial intraligand charge transfer event that triggers productive catalysis. Ligand polymerization affords a porous, recyclable organic polymer for heterogeneous nickel catalysis of cross-coupling reactions. The heterogeneous catalyst shows stable performance in a packed-bed flow reactor during a week of continuous operation.}, author = {Cavedon, Cristian and Gisbertz, Sebastian and Reischauer, Susanne and Vogl, Sarah and Sperlich, Eric and Burke, John H. and Wallick, Rachel F. and Schrottke, Stefanie and Hsu, Wei‐Hsin and Anghileri, Lucia and Pfeifer, Yannik and Richter, Noah and Teutloff, Christian and Müller‐Werkmeister, Henrike and Cambié, Dario and Seeberger, Peter H. and Vura‐Weis, Josh and van der Veen, Renske M. and Thomas, Arne and Pieber, Bartholomäus}, issn = {1521-3773}, journal = {Angewandte Chemie International Edition}, keywords = {General Chemistry, Catalysis}, number = {46}, publisher = {Wiley}, title = {{Intraligand charge transfer enables visible‐light‐mediated Nickel‐catalyzed cross-coupling reactions}}, doi = {10.1002/anie.202211433}, volume = {61}, year = {2022}, } @article{12938, abstract = {In this work, a feed-forward artificial neural network (FF-ANN) design capable of locating eigensolutions to Schrödinger's equation via self-supervised learning is outlined. Based on the input potential determining the nature of the quantum problem, the presented FF-ANN strategy identifies valid solutions solely by minimizing Schrödinger's equation encoded in a suitably designed global loss function. In addition to benchmark calculations of prototype systems with known analytical solutions, the outlined methodology was also applied to experimentally accessible quantum systems, such as the vibrational states of molecular hydrogen H2 and its isotopologues HD and D2 as well as the torsional tunnel splitting in the phenol molecule. It is shown that in conjunction with the use of SIREN activation functions a high accuracy in the energy eigenvalues and wavefunctions is achieved without the requirement to adjust the implementation to the vastly different range of input potentials, thereby even considering problems under periodic boundary conditions.}, author = {Gamper, Jakob and Kluibenschedl, Florian and Weiss, Alexander K. H. and Hofer, Thomas S.}, issn = {1463-9076}, journal = {Physical Chemistry Chemical Physics}, keywords = {Physical and Theoretical Chemistry, General Physics and Astronomy}, number = {41}, pages = {25191--25202}, publisher = {Royal Society of Chemistry}, title = {{From vibrational spectroscopy and quantum tunnelling to periodic band structures – a self-supervised, all-purpose neural network approach to general quantum problems}}, doi = {10.1039/d2cp03921d}, volume = {24}, year = {2022}, } @article{9794, abstract = {Lymph nodes (LNs) comprise two main structural elements: fibroblastic reticular cells that form dedicated niches for immune cell interaction and capsular fibroblasts that build a shell around the organ. Immunological challenge causes LNs to increase more than tenfold in size within a few days. Here, we characterized the biomechanics of LN swelling on the cellular and organ scale. We identified lymphocyte trapping by influx and proliferation as drivers of an outward pressure force, causing fibroblastic reticular cells of the T-zone (TRCs) and their associated conduits to stretch. After an initial phase of relaxation, TRCs sensed the resulting strain through cell matrix adhesions, which coordinated local growth and remodeling of the stromal network. While the expanded TRC network readopted its typical configuration, a massive fibrotic reaction of the organ capsule set in and countered further organ expansion. Thus, different fibroblast populations mechanically control LN swelling in a multitier fashion.}, author = {Assen, Frank P and Abe, Jun and Hons, Miroslav and Hauschild, Robert and Shamipour, Shayan and Kaufmann, Walter and Costanzo, Tommaso and Krens, Gabriel and Brown, Markus and Ludewig, Burkhard and Hippenmeyer, Simon and Heisenberg, Carl-Philipp J and Weninger, Wolfgang and Hannezo, Edouard B and Luther, Sanjiv A. and Stein, Jens V. and Sixt, Michael K}, issn = {1529-2916}, journal = {Nature Immunology}, pages = {1246--1255}, publisher = {Springer Nature}, title = {{Multitier mechanics control stromal adaptations in swelling lymph nodes}}, doi = {10.1038/s41590-022-01257-4}, volume = {23}, year = {2022}, } @article{9977, abstract = {For a Seifert fibered homology sphere X we show that the q-series invariant Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki series Z0(X). We show that for every even k ∈ N there exists a full asymptotic expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit Zˆ0(X; e 2πi/k) exists and is equal to the WRT quantum invariant τk(X). We show that the poles of the Borel transform of Z0(X) coincide with the classical complex Chern-Simons values, which we further show classifies the corresponding components of the moduli space of flat SL(2, C)-connections.}, author = {Mistegaard, William and Andersen, Jørgen Ellegaard}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {2}, pages = {709--764}, publisher = {Wiley}, title = {{Resurgence analysis of quantum invariants of Seifert fibered homology spheres}}, doi = {10.1112/jlms.12506}, volume = {105}, year = {2022}, } @inproceedings{10665, abstract = {Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the network’s correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors into account. In this paper, we show that verifying the bitexact implementation of quantized neural networks with bitvector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches.}, author = {Henzinger, Thomas A and Lechner, Mathias and Zikelic, Dorde}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {5A}, pages = {3787--3795}, publisher = {AAAI Press}, title = {{Scalable verification of quantized neural networks}}, volume = {35}, year = {2021}, } @inproceedings{10666, abstract = {Adversarial training is an effective method to train deep learning models that are resilient to norm-bounded perturbations, with the cost of nominal performance drop. While adversarial training appears to enhance the robustness and safety of a deep model deployed in open-world decision-critical applications, counterintuitively, it induces undesired behaviors in robot learning settings. In this paper, we show theoretically and experimentally that neural controllers obtained via adversarial training are subjected to three types of defects, namely transient, systematic, and conditional errors. We first generalize adversarial training to a safety-domain optimization scheme allowing for more generic specifications. We then prove that such a learning process tends to cause certain error profiles. We support our theoretical results by a thorough experimental safety analysis in a robot-learning task. Our results suggest that adversarial training is not yet ready for robot learning.}, author = {Lechner, Mathias and Hasani, Ramin and Grosu, Radu and Rus, Daniela and Henzinger, Thomas A}, booktitle = {2021 IEEE International Conference on Robotics and Automation}, isbn = {978-1-7281-9078-5}, issn = {2577-087X}, location = {Xi'an, China}, pages = {4140--4147}, title = {{Adversarial training is not ready for robot learning}}, doi = {10.1109/ICRA48506.2021.9561036}, year = {2021}, } @inproceedings{10667, abstract = {Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction. We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems. Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate. In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy. We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications.}, author = {Lechner, Mathias and Žikelić, Ðorđe and Chatterjee, Krishnendu and Henzinger, Thomas A}, booktitle = {35th Conference on Neural Information Processing Systems}, location = {Virtual}, title = {{Infinite time horizon safety of Bayesian neural networks}}, doi = {10.48550/arXiv.2111.03165}, year = {2021}, } @inproceedings{10668, abstract = {Robustness to variations in lighting conditions is a key objective for any deep vision system. To this end, our paper extends the receptive field of convolutional neural networks with two residual components, ubiquitous in the visual processing system of vertebrates: On-center and off-center pathways, with an excitatory center and inhibitory surround; OOCS for short. The On-center pathway is excited by the presence of a light stimulus in its center, but not in its surround, whereas the Off-center pathway is excited by the absence of a light stimulus in its center, but not in its surround. We design OOCS pathways via a difference of Gaussians, with their variance computed analytically from the size of the receptive fields. OOCS pathways complement each other in their response to light stimuli, ensuring this way a strong edge-detection capability, and as a result an accurate and robust inference under challenging lighting conditions. We provide extensive empirical evidence showing that networks supplied with OOCS pathways gain accuracy and illumination-robustness from the novel edge representation, compared to other baselines.}, author = {Babaiee, Zahra and Hasani, Ramin and Lechner, Mathias and Rus, Daniela and Grosu, Radu}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, issn = {2640-3498}, location = {Virtual}, pages = {478--489}, publisher = {ML Research Press}, title = {{On-off center-surround receptive fields for accurate and robust image classification}}, volume = {139}, year = {2021}, } @inproceedings{10669, abstract = {We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR.}, author = {Grunbacher, Sophie and Hasani, Ramin and Lechner, Mathias and Cyranka, Jacek and Smolka, Scott A and Grosu, Radu}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {13}, pages = {11525--11535}, publisher = {AAAI Press}, title = {{On the verification of neural ODEs with stochastic guarantees}}, volume = {35}, year = {2021}, } @inproceedings{10670, abstract = {Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short- and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.}, author = {Vorbach, Charles J and Hasani, Ramin and Amini, Alexander and Lechner, Mathias and Rus, Daniela}, booktitle = {35th Conference on Neural Information Processing Systems}, location = {Virtual}, title = {{Causal navigation by continuous-time neural networks}}, year = {2021}, } @inproceedings{10671, abstract = {We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system’s dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the trajectory length measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs.}, author = {Hasani, Ramin and Lechner, Mathias and Amini, Alexander and Rus, Daniela and Grosu, Radu}, booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence}, isbn = {978-1-57735-866-4}, issn = {2374-3468}, location = {Virtual}, number = {9}, pages = {7657--7666}, publisher = {AAAI Press}, title = {{Liquid time-constant networks}}, volume = {35}, year = {2021}, }