34 accepted papers
Aligning large language models (LLMs) is a central objective of post-training, often achieved through reward modeling and reinforcement learning methods. Among these, direct preference optimization (DPO) has emerged as a widely adopted technique that fine-tunes LLMs on preferred completions over les…
Recent work on large language models (LLMs) has increasingly focused on post-training and alignment with datasets curated to enhance instruction following, world knowledge, and specialized skills. However, most post-training datasets used in leading open- and closed-source LLMs remain inaccessible t…
Physical law learning is the ambiguous attempt at automating the derivation of governing equations with the use of machine learning techniques. This paper shall serve as a first step to build a comprehensive theoretical framework for learning physical laws, aiming to provide reliability to according…
Wireless channels are considered that change over time but remain constant for a certain (coherence) period. This behavior is perfectly captured by block fading channels and affects the performance of the corresponding wireless communication systems. Desired closed-form characterizations of optimal…
In this work, we study the system of two interacting non-cooperative Q-learning agents, where one agent has the privilege of observing the other's actions. We show that this information asymmetry can lead to a stable outcome of population learning, which does not occur in an environment of general i…
Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Of particular interest are so- called denial-of-service (DoS) attacks in which the jammer is able to completely disrupt the commun…
We study the time-domain concentration of bandlimited signals form a computational point of view. To this end we employ the concept of Turing computability that exactly describes what can be theoretically computed on a digital machine. A previous definition of computability for bandlimited signals i…
A Turing machine is a model describing the fundamental limits of any realizable computer, digital signal processor (DSP), or field programmable gate array (FPGA). This paper shows that there exist very simple linear time-invariant (LTI) systems which can not be simulated on a Turing machine. In part…
In this paper we study the peak value problem, i.e., the task of computing the peak value of a bandlimited signal from its samples. The peak value problem is important, for example, in communications, where the peak value of the transmit signal has to be controlled in order that the amplifier is not…
Although the Hilbert transform and the spectral factorization are of central importance in signal processing, both operations can generally not be calculated in closed form. Therefore, algorithmic solutions are prevalent which provide an approximation of the true solution. Then it is important to ef…
Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the comp…
The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the ac…
Online-learning literature has focused on designing algorithms that ensure sub-linear growth of the cumulative long-term constraint violations. The drawback of this guarantee is that strictly feasible actions may cancel out constraint violations on other time slots. For this reason, we introduce a n…
We consider the problem of resource congestion control for competing online learning agents under privacy and security constraints. Based on the non-cooperative game as the model for agents' interaction and the noisy online mirror ascent as the model for the rationality of the agents, we propose a n…
The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes are well studied and often closed-form solutions are known. On the other hand, the case of imper…
New applications in modern communications are demanding robust and ultra-reliable low latency information exchange such as machine-to-machine and human-to-machine communications. For many of these applications, the identification approach of Ahlswede and Dueck is much more efficient than the classic…
In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that th…
Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Accordingly it is of crucial interest for the legitimate users to detect such adversarial attacks. This paper develops a detection…
This paper considers the problem of approximating continuous functions of finite Dirichlet energy from samples of these functions. It will be shown that there exists no sampling-based method which is able to approximate every function in this space from its samples. Specifically, we are going to sho…
Secret key generation refers to the problem of generating a common secret key without revealing any information about it to an eaves-dropper. All users observe correlated components of a common source and can further use a rate-limited public channel for discussion which is open to eavesdroppers. Th…
In this paper we study whether it is possible to decide algorithmically if the Fourier series of a continuous function converges uniformly. We show that this decision cannot be made algorithmically, because there exists no Turing machine that can decide for each and every continuous functions whethe…
Our work is based on a recently introduced mathematical theory of deep convolutional neural networks (DCNNs). It was shown that DCNN s are stable with respect to deformations of bandlimited input functions. In the present paper, we generalize this result: We prove deformation stability on Sobolev sp…
Approximating the transfer function of stable causal linear systems by a basis expansion is a common task in signal- and system theory. This paper characterizes a scale of signal spaces, containing stable causal transfer functions, with a very simple basis (the Fourier basis) but which is not comput…
In this paper we study the tone reservation technique for the reduction of the peak to average power ratio (PAPR) in code division multiple access (CDMA) systems that employ the Walsh functions. In the tone reservation method, the available carriers are partitioned into two sets, the information set…
We investigate secure communication over a channel that undergoes two different classes of attacks at the same time: passive eavesdropping and active jamming. This scenario is perfectly modeled by the concept of arbitrarily varying wiretap channels (AVWCs). We derive a full characterization of the s…
Large peak to average power ratios (PAPRs) are problematic for communication systems. One possible approach to control the PAPR is the tone reservation method. We analyze the tone reservation method for general complete orthonormal systems, and consider two solvability concepts: strong solvability a…
In this paper we analyze the convergence behavior of a sampling based system approximation process, where the time variable is in the argument of the signal and not in the argument of the bandlimited impulse response. We consider the Paley-Wiener space PW <sub xmlns:mml="http://www.w3.org/1998/Math/…
High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and degradation of several transmission performances. We continue the theoretical contributions made by B. and Farell [1, 2] towards the understanding of peak value reduction, using the str…
It is known that there exist signals in Paley-Wiener space PW <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> of bandlimited signals with abso…
In this work, we show by means of the technique inspired by the Banach-Steinhaus Thm., that typically the Fourier transform of an integrable signal decays arbitrarily slowly toward the infinity, and has an arbitrary weak worst continuity/smoothness behaviour. However, the corresponding characterizat…
Many important non-adaptive approximation methods are know to diverge for almost all functions from certain Banach space X. One can show that a corresponding adaptive method will improve this behavior in the sense that it converges to the desired result for almost all functions in X. However, even t…
The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. However, the convergence of the approximation series is not guaranteed: there exist stable LTI systems and bandlimited input signals such that the approximation series diverges, re…
Many divergence results for sampling series are in terms of the limit superior and not the limit. This leaves the possibility of a convergent subsequence. If there exists a convergent subsequence, adaptive signal processing techniques can be used. In this paper we study sampling-based signal reconst…
This paper considers the problem of recovering a k-sparse, N-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very high probability whenever M ≳ 4k log <sub xmlns:mml="http://www.…