Related papers: On The Communication Complexity of High-Dimensiona…
Federated Learning (FL) is a promising paradigm that offers significant advancements in privacy-preserving, decentralized machine learning by enabling collaborative training of models across distributed devices without centralizing data.…
This work tackles the challenges of data heterogeneity and communication limitations in decentralized federated learning. We focus on creating a collaboration graph that guides each client in selecting suitable collaborators for training…
Transformers, a cornerstone of deep-learning architectures for sequential data, have achieved state-of-the-art results in tasks like Natural Language Processing (NLP). Models such as BERT and GPT-3 exemplify their success and have driven…
In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
In this report, we study the multiparty communication complexity problem of the multiparty equality function (MEQ): EQ(x_1,...,x_n) = 1 if x_1=...=x_n, and 0 otherwise. The input vector (x_1,...,x_n) is distributed among n>=2 nodes, with…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices…
Superposition, the ability of neural networks to represent more features than neurons, is increasingly seen as key to the efficiency of large models. This paper investigates the theoretical foundations of computing in superposition,…
Communication efficiency is a widely recognised research problem in Federated Learning (FL), with recent work focused on developing techniques for efficient compression, distribution and aggregation of model parameters between clients and…
In federated learning (FL), a machine learning model is trained on multiple nodes in a decentralized manner, while keeping the data local and not shared with other nodes. However, FL requires the nodes to also send information on the model…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…
Federated learning (FL) is a promising learning paradigm that can tackle the increasingly prominent isolated data islands problem while keeping users' data locally with privacy and security guarantees. However, FL could result in…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
We continue the study of the communication complexity of gap cycle counting problems. These problems have been introduced by Verbin and Yu [SODA 2011] and have found numerous applications in proving streaming lower bounds. In the noisy gap…
Federated learning (FL) rests on the notion of training a global model in a decentralized manner. Under this setting, mobile devices perform computations on their local data before uploading the required updates to improve the global model.…
Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y)=f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for…
In this paper we revisit the problem of constructing randomized composable coresets for bipartite matching. In this problem the input graph is randomly partitioned across $k$ players, each of which sends a single message to a coordinator,…
We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Tor\'an and W\"orz (TOCL 2023) showed that there is a resolution refutation of narrow width $k$ for two graphs if and only if they can be…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…