@article{12333, abstract = {Together, copy-number and point mutations form the basis for most evolutionary novelty, through the process of gene duplication and divergence. While a plethora of genomic data reveals the long-term fate of diverging coding sequences and their cis-regulatory elements, little is known about the early dynamics around the duplication event itself. In microorganisms, selection for increased gene expression often drives the expansion of gene copy-number mutations, which serves as a crude adaptation, prior to divergence through refining point mutations. Using a simple synthetic genetic reporter system that can distinguish between copy-number and point mutations, we study their early and transient adaptive dynamics in real time in Escherichia coli. We find two qualitatively different routes of adaptation, depending on the level of functional improvement needed. In conditions of high gene expression demand, the two mutation types occur as a combination. However, under low gene expression demand, copy-number and point mutations are mutually exclusive; here, owing to their higher frequency, adaptation is dominated by copy-number mutations, in a process we term amplification hindrance. Ultimately, due to high reversal rates and pleiotropic cost, copy-number mutations may not only serve as a crude and transient adaptation, but also constrain sequence divergence over evolutionary time scales.}, author = {Tomanek, Isabella and Guet, Calin C}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Adaptation dynamics between copynumber and point mutations}}, doi = {10.7554/ELIFE.82240}, volume = {11}, year = {2022}, } @misc{12339, abstract = {Copy-number and point mutations form the basis for most evolutionary novelty through the process of gene duplication and divergence. While a plethora of genomic sequence data reveals the long-term fate of diverging coding sequences and their cis-regulatory elements, little is known about the early dynamics around the duplication event itself. In microorganisms, selection for increased gene expression often drives the expansion of gene copy-number mutations, which serves as a crude adaptation, prior to divergence through refining point mutations. Using a simple synthetic genetic system that allows us to distinguish copy-number and point mutations, we study their early and transient adaptive dynamics in real-time in Escherichia coli. We find two qualitatively different routes of adaptation depending on the level of functional improvement selected for: In conditions of high gene expression demand, the two types of mutations occur as a combination. Under low gene expression demand, negative epistasis between the two types of mutations renders them mutually exclusive. Thus, owing to their higher frequency, adaptation is dominated by copy-number mutations. Ultimately, due to high rates of reversal and pleiotropic cost, copy-number mutations may not only serve as a crude and transient adaptation but also constrain sequence divergence over evolutionary time scales.}, author = {Tomanek, Isabella and Guet, Calin C}, publisher = {Dryad}, title = {{Flow cytometry YFP and CFP data and deep sequencing data of populations evolving in galactose}}, doi = {10.5061/dryad.rfj6q57ds}, year = {2022}, } @inproceedings{12432, abstract = {We present CertifyHAM, a deterministic algorithm that takes a graph G as input and either finds a Hamilton cycle of G or outputs that such a cycle does not exist. If G ∼ G(n, p) and p ≥ 100 log n/n then the expected running time of CertifyHAM is O(n/p) which is best possible. This improves upon previous results due to Gurevich and Shelah, Thomason and Alon, and Krivelevich, who proved analogous results for p being constant, p ≥ 12n −1/3 and p ≥ 70n −1/2 respectively.}, author = {Anastos, Michael}, booktitle = {63rd Annual IEEE Symposium on Foundations of Computer Science}, isbn = {9781665455190}, issn = {0272-5428}, location = {Denver, CO, United States}, pages = {919--930}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Solving the Hamilton cycle problem fast on average}}, doi = {10.1109/FOCS54457.2022.00091}, volume = {2022-October}, year = {2022}, } @inproceedings{12452, abstract = {Portrait viewpoint and illumination editing is an important problem with several applications in VR/AR, movies, and photography. Comprehensive knowledge of geometry and illumination is critical for obtaining photorealistic results. Current methods are unable to explicitly model in 3D while handing both viewpoint and illumination editing from a single image. In this paper, we propose VoRF, a novel approach that can take even a single portrait image as input and relight human heads under novel illuminations that can be viewed from arbitrary viewpoints. VoRF represents a human head as a continuous volumetric field and learns a prior model of human heads using a coordinate-based MLP with separate latent spaces for identity and illumination. The prior model is learnt in an auto-decoder manner over a diverse class of head shapes and appearances, allowing VoRF to generalize to novel test identities from a single input image. Additionally, VoRF has a reflectance MLP that uses the intermediate features of the prior model for rendering One-Light-at-A-Time (OLAT) images under novel views. We synthesize novel illuminations by combining these OLAT images with target environment maps. Qualitative and quantitative evaluations demonstrate the effectiveness of VoRF for relighting and novel view synthesis even when applied to unseen subjects under uncontrolled illuminations.}, author = {Rao, Pramod and B R, Mallikarjun and Fox, Gereon and Weyrich, Tim and Bickel, Bernd and Seidel, Hans-Peter and Pfister, Hanspeter and Matusik, Wojciech and Tewari, Ayush and Theobalt, Christian and Elgharib, Mohamed}, booktitle = {33rd British Machine Vision Conference}, location = {London, United Kingdom}, publisher = {British Machine Vision Association and Society for Pattern Recognition}, title = {{VoRF: Volumetric Relightable Faces}}, year = {2022}, } @article{12480, abstract = {We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms. However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix. Assuming that such an initialization is available is typically not realistic. In this paper, we solve this problem by proposing an AMP algorithm initialized with a spectral estimator. With such an initialization, the standard AMP analysis fails since the spectral estimator depends in a complicated way on the design matrix. Our main contribution is a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. The key technical idea is to define and analyze a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP. We also provide numerical results that demonstrate the validity of the proposed approach.}, author = {Mondelli, Marco and Venkataramanan, Ramji}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics}, number = {11}, publisher = {IOP Publishing}, title = {{Approximate message passing with spectral initialization for generalized linear models}}, doi = {10.1088/1742-5468/ac9828}, volume = {2022}, year = {2022}, } @article{12495, abstract = {Fairness-aware learning aims at constructing classifiers that not only make accurate predictions, but also do not discriminate against specific groups. It is a fast-growing area of machine learning with far-reaching societal impact. However, existing fair learning methods are vulnerable to accidental or malicious artifacts in the training data, which can cause them to unknowingly produce unfair classifiers. In this work we address the problem of fair learning from unreliable training data in the robust multisource setting, where the available training data comes from multiple sources, a fraction of which might not be representative of the true data distribution. We introduce FLEA, a filtering-based algorithm that identifies and suppresses those data sources that would have a negative impact on fairness or accuracy if they were used for training. As such, FLEA is not a replacement of prior fairness-aware learning methods but rather an augmentation that makes any of them robust against unreliable training data. We show the effectiveness of our approach by a diverse range of experiments on multiple datasets. Additionally, we prove formally that –given enough data– FLEA protects the learner against corruptions as long as the fraction of affected data sources is less than half. Our source code and documentation are available at https://github.com/ISTAustria-CVML/FLEA.}, author = {Iofinova, Eugenia B and Konstantinov, Nikola H and Lampert, Christoph}, issn = {2835-8856}, journal = {Transactions on Machine Learning Research}, publisher = {ML Research Press}, title = {{FLEA: Provably robust fair multisource learning from unreliable training data}}, year = {2022}, } @inproceedings{12508, abstract = {We explore the notion of history-determinism in the context of timed automata (TA). History-deterministic automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and history-deterministic specifications allow for game-based verification without an expensive determinization step. We show yet another characterisation of history-determinism in terms of fair simulation, at the general level of labelled transition systems: a system is history-deterministic precisely if and only if it fairly simulates all language smaller systems. For timed automata over infinite timed words it is known that universality is undecidable for Büchi TA. We show that for history-deterministic TA with arbitrary parity acceptance, timed universality, inclusion, and synthesis all remain decidable and are ExpTime-complete. For the subclass of TA with safety or reachability acceptance, we show that checking whether such an automaton is history-deterministic is decidable (in ExpTime), and history-deterministic TA with safety acceptance are effectively determinizable without introducing new automata states.}, author = {Henzinger, Thomas A and Lehtinen, Karoliina and Totzke, Patrick}, booktitle = {33rd International Conference on Concurrency Theory}, isbn = {9783959772464}, issn = {1868-8969}, location = {Warsaw, Poland}, pages = {14:1--14:21}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{History-deterministic timed automata}}, doi = {10.4230/LIPIcs.CONCUR.2022.14}, volume = {243}, year = {2022}, } @inproceedings{12509, abstract = {A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We summarize how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games.}, author = {Avni, Guy and Henzinger, Thomas A}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959772563}, issn = {1868-8969}, location = {Vienna, Austria}, pages = {3:1--3:6}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{An updated survey of bidding games on graphs}}, doi = {10.4230/LIPIcs.MFCS.2022.3}, volume = {241}, year = {2022}, } @article{12510, abstract = {We introduce a new statistical verification algorithm that formally quantifies the behavioral robustness of any time-continuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness. GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments. GoTube is stable and sets the state-of-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible.}, author = {Gruenbacher, Sophie A. and Lechner, Mathias and Hasani, Ramin and Rus, Daniela and Henzinger, Thomas A and Smolka, Scott A. and Grosu, Radu}, isbn = {978577358350}, issn = {2374-3468}, journal = {Proceedings of the AAAI Conference on Artificial Intelligence}, keywords = {General Medicine}, number = {6}, pages = {6755--6764}, publisher = {Association for the Advancement of Artificial Intelligence}, title = {{GoTube: Scalable statistical verification of continuous-depth models}}, doi = {10.1609/aaai.v36i6.20631}, volume = {36}, year = {2022}, } @inproceedings{12516, abstract = {The homogeneous continuous LWE (hCLWE) problem is to distinguish samples of a specific high-dimensional Gaussian mixture from standard normal samples. It was shown to be at least as hard as Learning with Errors, but no reduction in the other direction is currently known. We present four new public-key encryption schemes based on the hardness of hCLWE, with varying tradeoffs between decryption and security errors, and different discretization techniques. Our schemes yield a polynomial-time algorithm for solving hCLWE using a Statistical Zero-Knowledge oracle.}, author = {Bogdanov, Andrej and Cueto Noval, Miguel and Hoffmann, Charlotte and Rosen, Alon}, booktitle = {Theory of Cryptography}, isbn = {9783031223648}, issn = {1611-3349}, location = {Chicago, IL, United States}, pages = {565--592}, publisher = {Springer Nature}, title = {{Public-Key Encryption from Homogeneous CLWE}}, doi = {10.1007/978-3-031-22365-5_20}, volume = {13748}, year = {2022}, } @inproceedings{12529, abstract = {We consider turn-based stochastic 2-player games on graphs with ω-regular winning conditions. We provide a direct symbolic algorithm for solving such games when the winning condition is formulated as a Rabin condition. For a stochastic Rabin game with k pairs over a game graph with n vertices, our algorithm runs in O(nk+2k!) symbolic steps, which improves the state of the art. We have implemented our symbolic algorithm, along with performance optimizations including parallellization and acceleration, in a BDD-based synthesis tool called Fairsyn. We demonstrate the superiority of Fairsyn compared to the state of the art on a set of synthetic benchmarks derived from the VLTS benchmark suite and on a control system benchmark from the literature. In our experiments, Fairsyn performed significantly faster with up to two orders of magnitude improvement in computation time.}, author = {Banerjee, Tamajit and Majumdar, Rupak and Mallik, Kaushik and Schmuck, Anne-Kathrin and Soudjani, Sadegh}, booktitle = {28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems}, location = {Munich, Germany}, pages = {81--98}, publisher = {Springer Nature}, title = {{A direct symbolic algorithm for solving stochastic rabin games}}, doi = {10.1007/978-3-030-99527-0_5}, volume = {13244}, year = {2022}, } @inproceedings{12530, abstract = {We present BOCoSy, a tool for Bounded symbolic Output-feedback Controller Synthesis. Given a specification, BOCoSy synthesizes symbolic output-feedback controllers which interact with a given plant via a pre-defined finite symbolic interface. BOCoSy solves this problem by a new lazy abstraction-refinement technique which starts with a very coarse abstraction of the external trace semantics of the given plant and iteratively removes non-admissible behavior from this abstract model until a controller is found. BOCoSy steers the search for controllers towards small and concise state space representations by utilizing ideas from bounded synthesis. As a result, BOCoSy returns small and explainable controllers that are still powerful enough to solve the given synthesis problem. We show that BOCoSy is able to synthesize small, human readable symbolic controllers quickly on a set of benchmarks.}, author = {Finkbeiner, Bernd and Mallik, Kaushik and Passing, Noemi and Schledjewski, Malte and Schmuck, Anne-Kathrin}, booktitle = {25th ACM International Conference on Hybrid Systems: Computation and Control}, isbn = {9781450391962}, location = {Milan, Italy}, pages = {24:1--24:11}, publisher = {ACM}, title = {{BOCoSy: Small but powerful symbolic output-feedback control}}, doi = {10.1145/3501710.3519535}, year = {2022}, } @inproceedings{12536, abstract = {We consider the problem of estimating a rank-1 signal corrupted by structured rotationally invariant noise, and address the following question: how well do inference algorithms perform when the noise statistics is unknown and hence Gaussian noise is assumed? While the matched Bayes-optimal setting with unstructured noise is well understood, the analysis of this mismatched problem is only at its premises. In this paper, we make a step towards understanding the effect of the strong source of mismatch which is the noise statistics. Our main technical contribution is the rigorous analysis of a Bayes estimator and of an approximate message passing (AMP) algorithm, both of which incorrectly assume a Gaussian setup. The first result exploits the theory of spherical integrals and of low-rank matrix perturbations; the idea behind the second one is to design and analyze an artificial AMP which, by taking advantage of the flexibility in the denoisers, is able to "correct" the mismatch. Armed with these sharp asymptotic characterizations, we unveil a rich and often unexpected phenomenology. For example, despite AMP is in principle designed to efficiently compute the Bayes estimator, the former is outperformed by the latter in terms of mean-square error. We show that this performance gap is due to an incorrect estimation of the signal norm. In fact, when the SNR is large enough, the overlaps of the AMP and the Bayes estimator coincide, and they even match those of optimal estimators taking into account the structure of the noise.}, author = {Barbier, Jean and Hou, TianQi and Mondelli, Marco and Saenz, Manuel}, booktitle = {36th Annual Conference on Neural Information Processing Systems}, isbn = {9781713871088}, location = {New Orleans, LA, United States}, title = {{The price of ignorance: How much does it cost to forget noise structure in low-rank matrix estimation?}}, volume = {35}, year = {2022}, } @inproceedings{12537, abstract = {The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide memorization, optimization and generalization guarantees in deep neural networks. A line of work has studied the NTK spectrum for two-layer and deep networks with at least a layer with Ω(N) neurons, N being the number of training samples. Furthermore, there is increasing evidence suggesting that deep networks with sub-linear layer widths are powerful memorizers and optimizers, as long as the number of parameters exceeds the number of samples. Thus, a natural open question is whether the NTK is well conditioned in such a challenging sub-linear setup. In this paper, we answer this question in the affirmative. Our key technical contribution is a lower bound on the smallest NTK eigenvalue for deep networks with the minimum possible over-parameterization: the number of parameters is roughly Ω(N) and, hence, the number of neurons is as little as Ω(N−−√). To showcase the applicability of our NTK bounds, we provide two results concerning memorization capacity and optimization guarantees for gradient descent training.}, author = {Bombari, Simone and Amani, Mohammad Hossein and Mondelli, Marco}, booktitle = {36th Conference on Neural Information Processing Systems}, isbn = {9781713871088}, issn = {1049-5258}, location = {New Orleans, LA, United States}, pages = {7628--7640}, publisher = {Neural Information Processing Systems Foundation}, title = {{Memorization and optimization in deep neural networks with minimum over-parameterization}}, volume = {35}, year = {2022}, } @article{12538, abstract = {In this paper, we study the compression of a target two-layer neural network with N nodes into a compressed network with M