Cryptographic algorithms rely on the secrecy of their corresponding keys. On embedded systems with standard CMOS chips, where secure permanent memory such as flash is not available as a key storage, the secret key can be derived from Physical Unclonable Functions (PUFs) that make use of minuscule manufacturing variations of, for instance, SRAM cells. Since PUFs are affected by environmental changes, the reliable reproduction of the PUF key requires error correction. For silicon PUFs with binary output, errors occur in the form of bitflips within the PUFs response. Modelling the channel as a Binary Symmetric Channel (BSC) with fixed crossover probability $p$ is only a first-order approximation of the real behavior of the PUF response. We propose a more realistic channel model, refered to as the Varying Binary Symmetric Channel (VBSC), which takes into account that the reliability of different PUF response bits may not be equal. We investigate its channel capacity for various scenarios which differ in the channel state information (CSI) present at encoder and decoder. We compare the capacity results for the VBSC for the different CSI cases with reference to the distribution of the bitflip probability according a work by Maes et al.
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Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random weights. To address this issue, we study the mapping between probability distributions implemented by a deep feed-forward network. We characterize this mapping as an iterated transformation of distributions, where the non-linearity in each layer transfers information between different orders of correlation functions. This allows us to identify essential statistics in the data, as well as different information representations that can be used by neural networks. Applied to an XOR task and to MNIST, we show that correlations up to second order predominantly capture the information processing in the internal layers, while the input layer also extracts higher-order correlations from the data. This analysis provides a quantitative and explainable perspective on classification.
We study a novel setting in offline reinforcement learning (RL) where a number of distributed machines jointly cooperate to solve the problem but only one single round of communication is allowed and there is a budget constraint on the total number of information (in terms of bits) that each machine can send out. For value function prediction in contextual bandits, and both episodic and non-episodic MDPs, we establish information-theoretic lower bounds on the minimax risk for distributed statistical estimators; this reveals the minimum amount of communication required by any offline RL algorithms. Specifically, for contextual bandits, we show that the number of bits must scale at least as $\Omega(AC)$ to match the centralised minimax optimal rate, where $A$ is the number of actions and $C$ is the context dimension; meanwhile, we reach similar results in the MDP settings. Furthermore, we develop learning algorithms based on least-squares estimates and Monte-Carlo return estimates and provide a sharp analysis showing that they can achieve optimal risk up to logarithmic factors. Additionally, we also show that temporal difference is unable to efficiently utilise information from all available devices under the single-round communication setting due to the initial bias of this method. To our best knowledge, this paper presents the first minimax lower bounds for distributed offline RL problems.
In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with $M$ transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a distributed manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large $M$, we prove that when the arrival rate is small (below $\frac{1}{eM}$), slotted ALOHA-type algorithms are asymptotically optimal. As the arrival rate increases beyond $\frac{1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates $\theta$, $\theta=\frac{1}{o(M)}$, the proposed algorithms provide a multiplicative factor of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that, as opposed to the common practice, it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain.
In this paper, we propose a strategy for making DNA-based data storage information-theoretically secure through the use of wiretap channel coding. This motivates us to extend the shuffling-sampling channel model of Shomorony and Heckel (2021) to include a wiretapper. Our main result is a characterization of the secure storage capacity of our DNA wiretap channel model, which is the maximum rate at which data can be stored within a pool of DNA molecules so as to be reliably retrieved by an authorized party (Bob), while ensuring that an unauthorized party (Eve) gets almost no information from her observations. Furthermore, our proof of achievability shows that index-based wiretap channel coding schemes are optimal.
In this paper, a comprehensive performance analysis of a distributed intelligent reflective surfaces (IRSs)-aided communication system is presented. First, the optimal signal-to-noise ratio (SNR), which is attainable through the direct and reflected channels, is quantified by controlling the phase shifts of the distributed IRS. Next, this optimal SNR is statistically characterized by deriving tight approximations to the exact probability density function (PDF) and cumulative distribution function (CDF) for Nakagami-$m$ fading. The accuracy/tightness of this statistical characterization is investigated by deriving the Kullback-Leibler divergence. Our PDF/CDF analysis is used to derive tight approximations/bounds for the outage probability, achievable rate, and average symbol error rate (SER) in closed-form. To obtain useful insights, the asymptotic outage probability and average SER are derived for the high SNR regime. Thereby, the achievable diversity order and array gains are quantified. Our asymptotic performance analysis reveals that the diversity order can be boosted by using distributed passive IRSs without generating additional electromagnetic (EM) waves via active radio frequency chains. Our asymptotic rate analysis shows that the lower and upper rate bounds converge to an asymptotic limit in large reflective element regime. Our analysis is validated via Monte-Carlo simulations. We present a rigorous set of numerical results to investigate the performance gains of the proposed system model. Our analytical and numerical results reveal that the performance of single-input single-output wireless systems can be boosted by recycling the EM waves generated by a transmitter through distributed passive IRS reflections to enable constructive signal combining at a receiver.
Tensors, i.e., multi-linear functions, are a fundamental building block of machine learning algorithms. In order to train on large data-sets, it is common practice to distribute the computation amongst workers. However, stragglers and other faults can severely impact the performance and overall training time. A novel strategy to mitigate these failures is the use of coded computation. We introduce a new metric for analysis called the typical recovery threshold, which focuses on the most likely event and provide a novel construction of distributed coded tensor operations which are optimal with this measure. We show that our general framework encompasses many other computational schemes and metrics as a special case. In particular, we prove that the recovery threshold and the tensor rank can be recovered as a special case of the typical recovery threshold when the probability of noise, i.e., a fault, is equal to zero, thereby providing a noisy generalization of noiseless computation as a serendipitous result. Far from being a purely theoretical construction, these definitions lead us to practical random code constructions, i.e., locally random p-adic alloy codes, which are optimal with respect to the measures. We analyze experiments conducted on Amazon EC2 and establish that they are faster and more numerically stable than many other benchmark computation schemes in practice, as is predicted by theory.
Tensors, i.e., multi-linear functions, are a fundamental building block of machine learning algorithms. In order to train on large data-sets, it is common practice to distribute the computation amongst workers. However, stragglers and other faults can severely impact the performance and overall training time. A novel strategy to mitigate these failures is the use of coded computation. We introduce a new metric for analysis called the typical recovery threshold, which focuses on the most likely event and provide a novel construction of distributed coded tensor operations which are optimal with this measure. We show that our general framework encompasses many other computational schemes and metrics as a special case. In particular, we prove that the recovery threshold and the tensor rank can be recovered as a special case of the typical recovery threshold when the probability of noise, i.e., a fault, is equal to zero, thereby providing a noisy generalization of noiseless computation as a serendipitous result. Far from being a purely theoretical construction, these definitions lead us to practical random code constructions, i.e., locally random p-adic alloy codes, which are optimal with respect to the measures. We analyze experiments conducted on Amazon EC2 and establish that they are faster and more numerically stable than many other benchmark computation schemes in practice, as is predicted by theory.
We present Neural A*, a novel data-driven search method for path planning problems. Despite the recent increasing attention to data-driven path planning, a machine learning approach to search-based planning is still challenging due to the discrete nature of search algorithms. In this work, we reformulate a canonical A* search algorithm to be differentiable and couple it with a convolutional encoder to form an end-to-end trainable neural network planner. Neural A* solves a path planning problem by encoding a problem instance to a guidance map and then performing the differentiable A* search with the guidance map. By learning to match the search results with ground-truth paths provided by experts, Neural A* can produce a path consistent with the ground truth accurately and efficiently. Our extensive experiments confirmed that Neural A* outperformed state-of-the-art data-driven planners in terms of the search optimality and efficiency trade-off, and furthermore, successfully predicted realistic human trajectories by directly performing search-based planning on natural image inputs.
The field of Multi-Agent System (MAS) is an active area of research within Artificial Intelligence, with an increasingly important impact in industrial and other real-world applications. Within a MAS, autonomous agents interact to pursue personal interests and/or to achieve common objectives. Distributed Constraint Optimization Problems (DCOPs) have emerged as one of the prominent agent architectures to govern the agents' autonomous behavior, where both algorithms and communication models are driven by the structure of the specific problem. During the last decade, several extensions to the DCOP model have enabled them to support MAS in complex, real-time, and uncertain environments. This survey aims at providing an overview of the DCOP model, giving a classification of its multiple extensions and addressing both resolution methods and applications that find a natural mapping within each class of DCOPs. The proposed classification suggests several future perspectives for DCOP extensions, and identifies challenges in the design of efficient resolution algorithms, possibly through the adaptation of strategies from different areas.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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