Related papers: Beyond Identification: Computing Boolean Functions…
We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability.…
Arbitrarily varying channels offer a powerful framework for analyzing the robustness of quantum communication systems, especially for classical-quantum models, where the analysis displays strengths or weaknesses of specific signal…
We derive a lower and upper bound on the reliability function of discrete memoryless multiple-access channel (MAC) with noiseless feedback and variable-length codes (VLCs). For the upper-bound, we use proof techniques of Burnashev for the…
We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of…
In this paper, we present a dual representation of the influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an…
Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…
One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean…
We characterize the power of constant-depth Boolean circuits in generating uniform symmetric distributions. Let $f\colon\{0,1\}^m\to\{0,1\}^n$ be a Boolean function where each output bit of $f$ depends only on $O(1)$ input bits. Assume the…
Channel uncertainty and co-channel interference are two major challenges in the design of wireless systems such as future generation cellular networks. This paper studies receiver design for a wireless channel model with both time-varying…
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
With the increasing demands for accountability, interpretability is becoming an essential capability for real-world AI applications. However, most methods utilize post-hoc approaches rather than training the interpretable model. In this…
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of…
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
The algebraic degree of Boolean functions (or vectorial Boolean functions) is an important cryptographic parameter that should be computed by fast algorithms. They work in two main ways: (1) by computing the algebraic normal form and then…