2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)最新文献

{"title":"A tight (non-combinatorial) conditional lower bound for Klee’s Measure Problem in 3D","authors":"Marvin Kunnemann","doi":"10.1109/focs54457.2022.00059","DOIUrl":"https://doi.org/10.1109/focs54457.2022.00059","url":null,"abstract":"","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114773816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Incrementally Verifiable Computation via Rate-1 Batch Arguments","authors":"Omer Paneth, R. Pass","doi":"10.1109/FOCS54457.2022.00102","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00102","url":null,"abstract":"Non-interactive delegation schemes enable producing succinct proofs (that can be efficiently verified) that a machine M transitions from c1 to c2 in a certain number of deterministic steps. We here consider the problem of efficiently merging such proofs: given a proof Π1 that M transitions from c1 to c2, and a proof Π2 that M transitions from c2 to c3, can these proofs be efficiently merged into a single short proof (of roughly the same size as the original proofs) that M transitions from c1 to c3? To date, the only known constructions of such a mergeable delegation scheme rely on strong non-falsifiable “knowledge extraction” assumptions. In this work, we present a provably secure construction based on the standard LWE assumption. As an application of mergeable delegation, we obtain a construction of incrementally verifiable computation (IVC) (with polylogarithmic length proofs) for any (unbounded) polynomial number of steps based on LWE; as far as we know, this is the first such construction based on any falsifiable (as opposed to knowledge-extraction) assumption. The central building block that we rely on, and construct based on LWE, is a rate-l batch argument (BARG): this is a non-interactive argument for NP that enables proving k NP statements $x_{1},ldots, x_{k}$ with communication/verifier complexity m + o(m), where m is the length of one witness. rate-1 BARGs are particularly useful as they can be recursively composed a super-constant number of times.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130814809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Binary Codes with Resilience Beyond 1/4 via Interaction","authors":"K. Efremenko, Gillat Kol, Raghuvansh R. Saxena, Zhijun Zhang","doi":"10.1109/FOCS54457.2022.00008","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00008","url":null,"abstract":"In the reliable transmission problem, a sender, Alice, wishes to transmit a bit-string x to a remote receiver, Bob, over a binary channel with adversarial noise. The solution to this problem is to encode x using an error correcting code. As it is long known that the distance of binary codes is at most 1/2, reliable transmission is possible only if the channel corrupts (flips) at most a 1/4-fraction of the communicated bits.We revisit the reliable transmission problem in the two-way setting, where both Alice and Bob can send bits to each other. Our main result is the construction of two-way error correcting codes that are resilient to a constant fraction of corruptions strictly larger than 1/4. Moreover, our code has constant rate and requires Bob to only send one short message. We mention that our result resolves an open problem by Haeupler, Kamath, and Velingker [APPROX-RANDOM, 2015] and by Gupta, Kalai, and Zhang [STOC, 2022].Curiously, our new two-way code requires a fresh perspective on classical error correcting codes: While classical codes have only one distance guarantee for all pairs of codewords (i.e., the minimum distance), we construct codes where the distance between a pair of codewords depends on the “compatibility” of the messages they encode. We also prove that such codes are necessary for our result.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114343999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Planting Undetectable Backdoors in Machine Learning Models : [Extended Abstract]","authors":"S. Goldwasser, Michael P. Kim, V. Vaikuntanathan, Or Zamir","doi":"10.1109/FOCS54457.2022.00092","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00092","url":null,"abstract":"Given the computational cost and technical expertise required to train machine learning models, users may delegate the task of learning to a service provider. Delegation of learning has clear benefits, and at the same time raises serious concerns of trust. This work studies possible abuses of power by untrusted learners.We show how a malicious learner can plant an undetectable backdoor into a classifier. On the surface, such a backdoored classifier behaves normally, but in reality, the learner maintains a mechanism for changing the classification of any input, with only a slight perturbation. Importantly, without the appropriate “backdoor key,” the mechanism is hidden and cannot be detected by any computationally-bounded observer. We demonstrate two frameworks for planting undetectable backdoors, with incomparable guarantees.•First, we show how to plant a backdoor in any model, using digital signature schemes. The construction guarantees that given query access to the original model and the backdoored version, it is computationally infeasible to find even a single input where they differ. This property implies that the backdoored model has generalization error comparable with the original model. Moreover, even if the distinguisher can request backdoored inputs of its choice, they cannot backdoor a new input—a property we call non-replicability.•Second, we demonstrate how to insert undetectable backdoors in models trained using the Random Fourier Features (RFF) learning paradigm (Rahimi, Recht; NeurIPS 2007). In this construction, undetectability holds against powerful white-box distinguishers: given a complete description of the network and the training data, no efficient distinguisher can guess whether the model is “clean” or contains a backdoor. The backdooring algorithm executes the RFF algorithm faithfully on the given training data, tampering only with its random coins. We prove this strong guarantee under the hardness of the Continuous Learning With Errors problem (Bruna, Regev, Song, Tang; STOC 2021). We show a similar white-box undetectable backdoor for random ReLU networks based on the hardness of Sparse PCA (Berthet, Rigollet; COLT 2013).Our construction of undetectable backdoors also sheds light on the related issue of robustness to adversarial examples. In particular, by constructing undetectable backdoor for an “adversarially-robust” learning algorithm, we can produce a classifier that is indistinguishable from a robust classifier, but where every input has an adversarial example! In this way, the existence of undetectable backdoors represent a significant theoretical roadblock to certifying adversarial robustness.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127433184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Properly learning monotone functions via local correction","authors":"Jane Lange, R. Rubinfeld, A. Vasilyan","doi":"10.1109/FOCS54457.2022.00015","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00015","url":null,"abstract":"We give a $2^{tilde{O}(sqrt{n}/varepsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over ${0,1}^{n}$. Our algorithm is robust to adversarial label noise and has a running time nearly matching that of the state-of-the-art improper learning algorithm of Bshouty and Tamon (JACM 96) and an information-theoretic lower bound of Blais et al (RANDOM ’15). Prior to this work, no proper learning algorithm with running time smaller than $2^{Omega(n)}$ was known to exist. The core of our proper learner is a local computation algorithm for sorting binary labels on a poset. Our algorithm is built on a body of work on distributed greedy graph algorithms; specifically we rely on a recent work of Ghaffari (FOCS’22), which gives an efficient algorithm for computing maximal matchings in a graph in the LCA model of Rubinfeld et al and Alon et al (ICS’II, SODA’12). The applications of our local sorting algorithm extend beyond learning on the Boolean cube: we also give a tolerant tester for Boolean functions over general posets that distinguishes functions that are $varepsilon$/3-close to monotone from those that are $varepsilon-$far. Previous tolerant testers for the Boolean cube only distinguished between $varepsilon/Omega(sqrt{n}$)-close and $varepsilon-$far.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130784961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential Privacy from Locally Adjustable Graph Algorithms: k-Core Decomposition, Low Out-Degree Ordering, and Densest Subgraphs","authors":"Laxman Dhulipala, Quanquan C. Liu, Sofya Raskhodnikova, Jessica Shi, Julian Shun, Shangdi Yu","doi":"10.1109/FOCS54457.2022.00077","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00077","url":null,"abstract":"Differentially private algorithms allow large-scale data analytics while preserving user privacy. Designing such algorithms for graph data is gaining importance with the growth of large networks that model various (sensitive) relationships between individuals. While there exists a rich history of important literature in this space, to the best of our knowledge, no results formalize a relationship between certain parallel and distributed graph algorithms and differentially private graph analysis. In this paper, we define locally adjustable graph algorithms and show that algorithms of this type can be transformed into differentially private algorithms. Our formalization is motivated by a set of results that we present in the central and local models of differential privacy for a number of problems, including k-core decomposition, low out-degree ordering, and densest subgraphs. First, we design an $varepsilon$-edge differentially private (DP) algorithm that returns a subset of nodes that induce a subgraph of density at least $ frac{D^{*}}{1+eta}-O(operatorname{poly}(log n)/varepsilon)$, where $D^{*}$ is the density of the densest subgraph in the input graph (for any constant $etagt 0$). This algorithm achieves a two-fold improvement on the multiplicative approximation factor of the previously best-known private densest subgraph algorithms while maintaining a near-linear runtime. Then, we present an $varepsilon$-locally edge differentially private (LEDP) algorithm for k-core decompositions. Our LEDP algorithm provides approximates the core numbers (for any constant $etagt 0$) with $(2+eta)$ multiplicative and $O(operatorname{poly}(log n)/varepsilon)$ additive error. This is the first differentially private algorithm that outputs private k-core decomposition statistics. We also modify our algorithm to return a differentially private low out-degree ordering of the nodes, where orienting the edges from nodes earlier in the ordering to nodes later in the ordering results in out-degree at most $O(d+$ poly $(log n)/varepsilon$) (where d is the degeneracy of the graph). A small modification to the algorithm also yields a $varepsilon$-LEDP algorithm for $(4+eta,O(operatorname{poly}(log n)/varepsilon))$ approximate densest subgraph (which returns both the set of nodes in the subgraph and its density). Our algorithm uses $O(log^{2}n)$ rounds of communication between the curator and individual nodes.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"363 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122478962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Having Hope in Hops: New Spanners, Preservers and Lower Bounds for Hopsets","authors":"Shimon Kogan, M. Parter","doi":"10.1109/FOCS54457.2022.00078","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00078","url":null,"abstract":"Hopsets and spanners are fundamental graph structures, playing a key role in shortest path computation, distributed communication, and more. A (near-exact) hopset for a given graph G is a (small) subset of weighted edges H that when added to the graph G reduces the number of hops (edges) of near-exact shortest paths. Spanners and distance preservers, on the other hand, ask for removing many edges from the graph while approximately preserving shortest path distances.We provide a general reduction scheme from graph hopsets to the known metric compression schemes of spanners, emulators and distance preservers. Consequently, we get new and improved upper bound constructions for the latter, as well as, new lower bound results for hopsets. Our main results include:•For n-vertex directed weighted graphs, one can provide $(1+epsilon)$-approximate distance preservers1 for p pairs in $Vtimes V$ with $O_{epsilon}(ncdot p^{2/5}+(np)^{2/3})$ edges. For $pgeq n^{5/4}$, this matches the state-of-the art bounds for reachability preservers by [Abboud and Bodwin, SODA 2018] and the lower bound for exact-distance preservers by [Bodwin, SODA 2016].•For n-vertex undirected weighted graphs, one can provide $(1+epsilon)$ distance preserves with $overline{O}_{epsilon}(n^{1+o(1)}+pcdot n^{o(1)})$ edges. So far, such bounds could be obtained only for unweighted graphs. Consequently, we also get improved sourcewise spanners [Roditty, Thorup and Zwick, ICALP 2005] and spanners with slack [Chan, Dinitz and Gupta, ESA 2006].•Exact hopsets of linear size admit a worst-case hopbound of $beta=Omega(n^{1/3})$. This holds even for undirected weighted graphs, improving upon the $Omega(n^{1/6})$ lower bound by [Huang and Pettie, SIAM J. Discret. Math 2021]. Interestingly this matches the recent diameter bound achieved for linear directed shortcuts.1I.e., subgraphs that preserve the pairwise distances up to a multiplicative stretch of (1+$epsilon$).More conceptually, our work makes a significant progress on the tantalizing open problem concerning the formal connection between hopsets and spanners, e.g., as posed by Elkin and Neiman [Bull. EATCS 2020].","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134364016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constant Approximation of Min-Distances in Near-Linear Time","authors":"S. Chechik, Tianyi Zhang","doi":"10.1109/FOCS54457.2022.00089","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00089","url":null,"abstract":"In a weighed directed graph $G=(V, E, omega)$ with m edges and n vertices, we are interested in its basic graph parameters such as diameter, radius and eccentricities, under the nonstandard measure of min-distance which is defined for every pair of vertices $u, v in V$ as the minimum of the shortest path distances from u to v and from v to u. Similar to standard shortest paths distances, computing graph parameters exactly in terms of min-distances essentially requires $tilde{Omega}(m n)$ time under plausible hardness conjectures 1. Hence, for faster running time complexities we have to tolerate approximations. Abboud, Vassilevska Williams and Wang [SODA 2016] were the first to study min-distance problems, and they obtained constant factor approximation algorithms in acyclic graphs, with running time $tilde{O}(m)$ and $tilde{O}(m sqrt{n})$ for diameter and radius, respectively. The time complexity of radius in acyclic graphs was recently improved to $tilde{O}(m)$ by Dalirrooyfard and Kaufmann [ICALP 2021], but at the cost of an $O(log n)$ approximation ratio. For general graphs, the authors of [DWV+, ICALP 2019] gave the first constant factor approximation algorithm for diameter, radius and eccentricities which runs in time $tilde{O}(m sqrt{n})$; besides, for the diameter problem, the running time can be improved to $tilde{O}(m)$ while blowing up the approximation ratio to $O(log n)$. A natural question is whether constant approximation and near-linear time can be achieved simultaneously for diameter, radius and eccentricities; so far this is only possible for diameter in the restricted setting of acyclic graphs. In this paper, we answer this question in the affirmative by presenting near-linear time algorithms for all three parameters in general graphs.1As usual, the $tilde{O}(cdot)$ notation hides poly-logarithmic factors in n","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113989536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relaxed Locally Decodable and Correctable Codes: Beyond Tensoring","authors":"Gil Cohen, Tal Yankovitz","doi":"10.1109/FOCS54457.2022.00010","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00010","url":null,"abstract":"In their highly influential paper, Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC 2004) introduced the notion of a relaxed locally decodable code (RLDC). Similarly to a locally decodable code (Katz-Trevisan; STOC 2000), the former admits access to any desired message symbol with only a few queries to a possibly corrupted codeword. An RLDC, however, is allowed to abort when identifying corruption. The natural analog to locally correctable codes, dubbed relaxed locally correctable codes (RLCC), was introduced by Gur, Ramnarayan and Rothblum (ITCS 2018) who constructed asymptotically-good length-nRLCC and RLDC with $(log n)^{O(loglog n)}$ queries.In this work we construct asymptotically-good RLDC and RLCC with an improved query complexity of $(log n)^{O(logloglog n)}$. To achieve this, we devise a mechanism-an alternative to the tensor product-that squares the length of a given code. Compared to the tensor product that was used by Gur et al. and by many other constructions, our mechanism is significantly more efficient in terms of rate deterioration, allowing us to obtain our improved construction.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125041351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radical Sylvester-Gallai Theorem for Cubics","authors":"Rafael Oliveira, A. Sengupta","doi":"10.1109/FOCS54457.2022.00027","DOIUrl":"https://doi.org/10.1109/FOCS54457.2022.00027","url":null,"abstract":"We prove that any cubic radical Sylvester-Gallai configuration is constant dimensional. This solves a conjecture of Gupta in degree 3 and generalizes the result from Shpilka, who proved that quadratic radical Sylvester-Gallai configurations are constant dimensional. To prove our Sylvester-Gallai theorem, we develop several new tools combining techniques from algebraic geometry and elimination theory. Among our technical contributions, we prove a structure theorem characterizing non-radical ideals generated by two cubic forms, generalizing previous structure theorems for intersections of two quadrics. Moreover, building upon the groundbreaking work Ananyan and Hochster, we introduce the notion of wide Ananyan-Hochster algebras and show that these algebras allow us to transfer the local conditions of Sylvester-Gallai configurations into global conditions.","PeriodicalId":390222,"journal":{"name":"2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127224701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}