Related papers: Beyond Identification: Computing Boolean Functions…
We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise polynomial activation functions from two perspectives: 1) the…
The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete…
Channel capacity estimation plays a crucial role in beyond 5G intelligent communications. Despite its significance, this task is challenging for a majority of channels, especially for the complex channels not modeled as the well-known…
Large language models (LLMs) have demonstrated remarkable reasoning capabilities in math and coding, often bolstered by post-training on the chain-of-thoughts (CoTs) generated by stronger models. However, existing strategies for curating…
We prove the Courtade-Kumar conjecture, for several classes of n-dimensional Boolean functions, for all $n \geq 2$ and for all values of the error probability of the binary symmetric channel, $0 \leq p \leq 1/2$. This conjecture states that…
When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
Motivated by the resurgence of neural networks in being able to solve complex learning tasks we undertake a study of high depth networks using ReLU gates which implement the function $x \mapsto \max\{0,x\}$. We try to understand the role of…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
Channel estimation is very challenging when the receiver is equipped with a limited number of radio-frequency (RF) chains in beamspace millimeter-wave (mmWave) massive multiple-input and multiple-output systems. To solve this problem, we…
Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals…
Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…
This paper proposes a parametric-based network architecture for joint channel estimation and data detection in communications systems with hardware impairments. This architecture is composed of a data-augmented layer, a custom soft…
Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al, 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation…
The study of non-linearity (linearity) of Boolean function was initiated by Rothaus in 1976. The classical non-linearity of a Boolean function is the minimum Hamming distance of its truth table to that of affine functions. In this note we…
In this paper we present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma. The new method is a generalization to quantum communication channels of Ahlswede's…
Gaussian channels with memory and with noiseless feedback have been widely studied in the information theory literature. However, a coding scheme to achieve the feedback capacity is not available. In this paper, a coding scheme is proposed…
A coding theorem is proved for a class of stationary channels with feedback in which the output Y_n = f(X_{n-m}^n, Z_{n-m}^n) is the function of the current and past m symbols from the channel input X_n and the stationary ergodic channel…
Randomly initialized wide neural networks transition to linear functions of weights as the width grows, in a ball of radius $O(1)$ around initialization. A necessary condition for this result is that all layers of the network are wide…