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Finite-width one hidden layer networks with multiple neurons in the readout layer display non-trivial output-output correlations that vanish in the lazy-training infinite-width limit. In this manuscript we leverage recent progress in the…
The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the…
We consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height, under the assumption of conditionally independent, identically distributed observations. We…
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Let f be a Boolean function with…
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
The Maximum Betweenness Centrality problem (MBC) can be defined as follows. Given a graph find a $k$-element node set $C$ that maximizes the probability of detecting communication between a pair of nodes $s$ and $t$ chosen uniformly at…
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of…
In this paper, we propose a fully differentiable pipeline for estimating accurate dense correspondences between 3D point clouds. The proposed pipeline is an extension and a generalization of the functional maps framework. However, instead…
We present a tractable, incremental framework for topological dialogue semantics based on finite, discrete semantic spaces. Building on the intuition that utterances correspond to open sets and their combinatorial relations form a…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and…
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.…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge…
We propose a new theoretical model for passively mobile Wireless Sensor Networks. We call it the PALOMA model, standing for PAssively mobile LOgarithmic space MAchines. The main modification w.r.t. the Population Protocol model is that…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…