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Let $p$ denote a generative language model. Let $r$ denote a reward model that returns a scalar that captures the degree at which a draw from $p$ is preferred. The goal of language model alignment is to alter $p$ to a new distribution $\phi$ that results in a higher expected reward while keeping $\phi$ close to $p.$ A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution $\phi_\Delta$ that maximizes $E_{\phi_{\Delta}} r(y)$ subject to a relative entropy constraint $KL(\phi_\Delta || p) \leq \Delta.$ Another simple alignment method is best-of-$N$, where $N$ samples are drawn from $p$ and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-$N$ alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-$N$ is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

In the wideband regime, the performance of many of the popular modulation schemes such as code division multiple access and orthogonal frequency division multiplexing falls quickly without channel state information. Obtaining the amount of channel information required for these techniques to work is costly and difficult, which suggests the need for schemes which can perform well without channel state information. In this work, we present one such scheme, called wideband time frequency coding, which achieves rates on the order of the additive white Gaussian noise capacity without requiring any channel state information. Wideband time frequency coding combines impulsive frequency shift keying with pulse position modulation, which allows for information to be encoded in both the transmitted frequency and the transmission time period. On the detection side, we propose a non-coherent decoder based on a square-law detector, akin to the optimal decoder for frequency shift keying based signals. The impacts of various parameters on the symbol error probability and capacity of wideband time frequency coding are investigated, and the results show that it is robust to shadowing and highly fading channels. When compared to other modulation schemes such as code division multiple access, orthogonal frequency division multiplexing, pulse position modulation, and impulsive frequency shift keying without channel state information, wideband time frequency coding achieves higher rates in the wideband regime, and performs comparably in smaller bandwidths.

In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural networks which are all trained jointly for the task of communicating correlated sources through a network of noisy point-to-point links. The NNC scheme is application-specific and makes use of a training set of data, instead of making assumptions on the source statistics. In addition, it can adapt to any arbitrary network topology and power constraint. We show empirically that, for the task of transmitting MNIST images over a network, the NNC scheme shows improvement over baseline schemes, especially in the low-SNR regime.

We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it combines information-theory security with public-key cryptography. In addition, the scheme is general and can be applied to any communication network, and to any public-key cryptosystem. Our hybrid scheme is based on the information theoretic notion of individual secrecy, which traditionally relies on the assumption that an eavesdropper can only observe a subset of the communication links between the trusted parties - an assumption that is often challenging to enforce. For this setting, several code constructions have been developed, where the messages are linearly mixed before transmission over each of the paths in a way that guarantees that an adversary which observes only a subset has sufficient uncertainty about each individual message. Instead, in this paper, we take a computational viewpoint, and construct a coding scheme in which an arbitrary secure cryptosystem is utilized on a subset of the links, while a pre-processing similar to the one in individual security is utilized. Under this scheme, we demonstrate 1) a computational security guarantee for an adversary which observes the entirety of the links 2) an information theoretic security guarantee for an adversary which observes a subset of the links, and 3) information rates which approach the capacity of the network and greatly improve upon the current solutions. A perhaps surprising consequence of our scheme is that, to guarantee a computational security level b, it is sufficient to encrypt a single link using a computational post-quantum scheme. In addition, the information rate approaches 1 as the number of communication links increases.

According to recent empirical studies, a majority of users have the same, or very similar, passwords across multiple password-secured online services. This practice can have disastrous consequences, as one password being compromised puts all the other accounts at much higher risk. Generally, an adversary may use any side-information he/she possesses about the user, be it demographic information, password reuse on a previously compromised account, or any other relevant information to devise a better brute-force strategy (so called targeted attack). In this work, we consider a distributed brute-force attack scenario in which $m$ adversaries, each observing some side information, attempt breaching a password secured system. We compare two strategies: an uncoordinated attack in which the adversaries query the system based on their own side-information until they find the correct password, and a fully coordinated attack in which the adversaries pool their side-information and query the system together. For passwords $\mathbf{X}$ of length $n$, generated independently and identically from a distribution $P_X$, we establish an asymptotic closed-form expression for the uncoordinated and coordinated strategies when the side-information $\mathbf{Y}_{(m)}$ are generated independently from passing $\mathbf{X}$ through a memoryless channel $P_{Y|X}$, as the length of the password $n$ goes to infinity. We illustrate our results for binary symmetric channels and binary erasure channels, two families of side-information channels which model password reuse. We demonstrate that two coordinated agents perform asymptotically better than any finite number of uncoordinated agents for these channels, meaning that sharing side-information is very valuable in distributed attacks.

We study the relationship between randomized low influence functions and differentially private mechanisms. Our main aim is to formally determine whether differentially private mechanisms are low influence and whether low influence randomized functions can be differentially private. We show that differential privacy does not necessarily imply low influence in a formal sense. However, low influence implies approximate differential privacy. These results hold for both independent and non-independent randomized mechanisms, where an important instance of the former is the widely-used additive noise techniques in the differential privacy literature. Our study also reveals the interesting dynamics between utility, low influence, and independence of a differentially private mechanism. As the name of this paper suggests, we show that any two such features are simultaneously possible. However, in order to have a differentially private mechanism that has both utility and low influence, even under a very mild utility condition, one has to employ non-independent mechanisms.

Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some applications, a set of analog signals are acquired individually and processed jointly. Such setups are referred to as distributed quantization. In this work, we propose a distributed quantization scheme for representing a set of sparse time sequences acquired using conventional scalar ADCs. Our approach utilizes tools from secure group testing theory to exploit the sparse nature of the acquired analog signals, obtaining a compact and accurate representation while operating in a distributed fashion. We then show how our technique can be implemented when the quantized signals are transmitted over a multi-hop communication network providing a low-complexity network policy for routing and signal recovery. Our numerical evaluations demonstrate that the proposed scheme notably outperforms conventional methods based on the combination of quantization and compressed sensing tools.

Sparse signals are encountered in a broad range of applications. In order to process these signals using digital hardware, they must be first sampled and quantized using an analog-to-digital convertor (ADC), which typically operates in a serial scalar manner. In this work, we propose a method for serial quantization of sparse time sequences (SQuaTS) inspired by group testing theory, which is designed to reliably and accurately quantize sparse signals acquired in a sequential manner using serial scalar ADCs. Unlike previously proposed approaches which combine quantization and compressed sensing (CS), our SQuaTS scheme updates its representation on each incoming analog sample and does not require the complete signal to be observed and stored in analog prior to quantization. We characterize the asymptotic tradeoff between accuracy and quantization rate of SQuaTS as well as its computational burden. We also propose a variation of SQuaTS, which trades rate for computational efficiency. Next, we show how SQuaTS can be naturally extended to distributed quantization scenarios, where a set of jointly sparse time sequences are acquired individually and processed jointly. Our numerical results demonstrate that SQuaTS is capable of achieving substantially improved representation accuracy over previous CS-based schemes without requiring the complete set of analog signal samples to be observed prior to its quantization, making it an attractive approach for acquiring sparse time sequences.

We study the problem of mismatched guesswork, where we evaluate the number of symbols $y \in \mathcal{Y}$ which have higher likelihood than $X \sim \mu$ according to a mismatched distribution $\nu$. We discuss the role of the tilted/exponential families of the source distribution $\mu$ and of the mismatched distribution $\nu$. We show that the value of guesswork can be characterized using the tilted family of the mismatched distribution $\nu$, while the probability of guessing is characterized by an exponential family which passes through $\mu$. Using this characterization, we demonstrate that the mismatched guesswork follows a large deviation principle (LDP), where the rate function is described implicitly using information theoretic quantities. We apply these results to one-to-one source coding (without prefix free constraint) to obtain the cost of mismatch in terms of average codeword length. We show that the cost of mismatch in one-to-one codes is no larger than that of the prefix-free codes, i.e., $D(\mu\| \nu)$. Further, the cost of mismatch vanishes if and only if $\nu$ lies on the tilted family of the true distribution $\mu$, which is in stark contrast to the prefix-free codes. These results imply that one-to-one codes are inherently more robust to mismatch., Comment: Accepted to ITW 2019

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA do not scale to large, high-dimensional datasets. By re-interpreting the objective in CA using an information-theoretic tool called the principal inertia components, we demonstrate that performing CA is equivalent to solving a functional optimization problem over the space of finite variance functions of two random variable. We show that this optimization problem, in turn, can be efficiently approximated by neural networks. The resulting formulation, called the correspondence analysis neural network (CA-NN), enables CA to be performed at an unprecedented scale. We validate the CA-NN on synthetic data, and demonstrate how it can be used to perform CA on a variety of datasets, including food recipes, wine compositions, and images. Our results outperform traditional methods used in CA, indicating that CA-NN can serve as a new, scalable tool for interpretability and visualization of complex dependencies between random variables., Comment: Accepted to AISTATS 2019. Overlaps with arXiv:1806.08449

We analyze expenditure patterns of discretionary funds by Brazilian congress members. This analysis is based on a large dataset containing over $7$ million expenses made publicly available by the Brazilian government. This dataset has, up to now, remained widely untouched by machine learning methods. Our main contributions are two-fold: (i) we provide a novel dataset benchmark for machine learning-based efforts for government transparency to the broader research community, and (ii) introduce a neural network-based approach for analyzing and visualizing outlying expense patterns. Our hope is that the approach presented here can inspire new machine learning methodologies for government transparency applicable to other developing nations., Comment: Presented at NIPS 2018 Workshop on Machine Learning for the Developing World

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from epidemiology to social sciences; however, current methods do not scale to large, high-dimensional datasets. In this paper, we provide a novel interpretation of CA in terms of an information-theoretic quantity called the principal inertia components. We show that estimating the principal inertia components, which consists in solving a functional optimization problem over the space of finite variance functions of two random variable, is equivalent to performing CA. We then leverage this insight to design novel algorithms to perform CA at an unprecedented scale. Particularly, we demonstrate how the principal inertia components can be reliably approximated from data using deep neural networks. Finally, we show how these maximally correlated embeddings of pairs of random variables in CA further play a central role in several learning problems including visualization of classification boundary and training process, and underlying recent multi-view and multi-modal learning methods., Comment: 30 pages, 7 figures, 6 tables. arXiv admin note: text overlap with arXiv:1902.07828

In September 2017, McAffee Labs quarterly report estimated that brute force attacks represent 20\% of total network attacks, making them the most prevalent type of attack ex-aequo with browser based vulnerabilities. These attacks have sometimes catastrophic consequences, and understanding their fundamental limits may play an important role in the risk assessment of password-secured systems, and in the design of better security protocols. While some solutions exist to prevent online brute-force attacks that arise from one single IP address, attacks performed by botnets are more challenging. In this paper, we analyze these distributed attacks by using a simplified model. Our aim is to understand the impact of distribution and asynchronization on the overall computational effort necessary to breach a system. Our result is based on Guesswork, a measure of the number of queries (guesses) required of an adversary before a correct sequence, such as a password, is found in an optimal attack. Guesswork is a direct surrogate for time and computational effort of guessing a sequence from a set of sequences with associated likelihoods. We model the lack of synchronization by a worst-case optimization in which the queries made by multiple adversarial agents are received in the worst possible order for the adversary, resulting in a min-max formulation. We show that, even without synchronization, and for sequences of growing length, the asymptotic optimal performance is achievable by using randomized guesses drawn from an appropriate distribution. Therefore, randomization is key for distributed asynchronous attacks. In other words, asynchronous guessers can asymptotically perform brute-force attacks as efficiently as synchronized guessers., Comment: Accepted to IEEE Transactions on Information Forensics and Security

Given a pair of random variables $(X,Y)\sim P_{XY}$ and two convex functions $f_1$ and $f_2$, we introduce two bottleneck functionals as the lower and upper boundaries of the two-dimensional convex set that consists of the pairs $\left(I_{f_1}(W; X), I_{f_2}(W; Y)\right)$, where $I_f$ denotes $f$-information and $W$ varies over the set of all discrete random variables satisfying the Markov condition $W \to X \to Y$. Applying Witsenhausen and Wyner's approach, we provide an algorithm for computing boundaries of this set for $f_1$, $f_2$, and discrete $P_{XY}$. In the binary symmetric case, we fully characterize the set when (i) $f_1(t)=f_2(t)=t\log t$, (ii) $f_1(t)=f_2(t)=t^2-1$, and (iii) $f_1$ and $f_2$ are both $\ell^\beta$ norm function for $\beta \geq 2$. We then argue that upper and lower boundaries in (i) correspond to Mrs. Gerber's Lemma and its inverse (which we call Mr. Gerber's Lemma), in (ii) correspond to estimation-theoretic variants of Information Bottleneck and Privacy Funnel, and in (iii) correspond to Arimoto Information Bottleneck and Privacy Funnel., Comment: IEEE International Symposium on Information Theory (ISIT), 2018

This paper considers the problem of channel coding over Gaussian intersymbol interference (ISI) channels with a given metric decoding rule. Specifically, it is assumed that the mismatched decoder has an incorrect assumption on the impulse response function. The mismatch capacity is the highest achievable rate for a given decoding rule. Existing lower bounds to the mismatch capacity for channels and decoding metrics with memory (as in our model) are presented only in the form of multi-letter expressions that have not been calculated in practice. Consequently, they provide little insight on the mismatch problem. In this paper, we derive computable single-letter lower bounds to the mismatch capacity, and discuss some implications of our results. Our achievable rates are based on two ensembles, the ensemble of codewords generated by an autoregressive process, and the ensemble of codewords drawn uniformly over a "type class" of real-valued sequences. Computation of our achievable rates demonstrates non-trivial behavior of the achievable rates as a function of the mismatched parameters. As a simple application of our technique, we derive also the random coding exponent associated with a mismatched decoder which assumes that there is no ISI at all. Finally, we compare our results with universal decoders which are designed outside the true class of channels that we consider in this paper.

We study a notion of guesswork, where multiple agents intend to launch a coordinated brute-force attack to find a single binary secret string, and each agent has access to side information generated through either a BEC or a BSC. The average number of trials required to find the secret string grows exponentially with the length of the string, and the rate of the growth is called the guesswork exponent. We compute the guesswork exponent for several multi-agent attacks. We show that a multi-agent attack reduces the guesswork exponent compared to a single agent, even when the agents do not exchange information to coordinate their attack, and try to individually guess the secret string using a predetermined scheme in a decentralized fashion. Further, we show that the guesswork exponent of two agents who do coordinate their attack is strictly smaller than that of any finite number of agents individually performing decentralized guesswork., Comment: Accepted at IEEE International Symposium on Information Theory (ISIT) 2017

Consider two correlated sources $X$ and $Y$ generated from a joint distribution $p_{X,Y}$. Their G\'acs-K\"orner Common Information, a measure of common information that exploits the combinatorial structure of the distribution $p_{X,Y}$, leads to a source decomposition that exhibits the latent common parts in $X$ and $Y$. Using this source decomposition we construct an efficient distributed compression scheme, which can be efficiently used in the network setting as well. Then, we relax the combinatorial conditions on the source distribution, which results in an efficient scheme with a helper node, which can be thought of as a front-end cache. This relaxation leads to an inherent trade-off between the rate of the helper and the rate reduction at the sources, which we capture by a notion of optimal decomposition. We formulate this as an approximate G\'acs-K\"orner optimization. We then discuss properties of this optimization, and provide connections with the maximal correlation coefficient, as well as an efficient algorithm, both through the application of spectral graph theory to the induced bipartite graph of $p_{X,Y}$., Comment: Submitted to ITW 2016

Consider a multi-source network coding problem with correlated sources. While the fundamental limits are known, achieving them, in general, involves a computational burden due to the complex decoding process. Efficient solutions, on the other hand, are by large based on source and network coding separation, thus imposing strict topological constraints on the networks which can be solved. In this work, we introduce a novel notion of separation of source and network coding using G\'acs-K\"orner Common Information (CI). Unlike existing notions of separation, the sufficient condition for this separation to hold depends on the source structure rather than the network topology. Using the suggested separation scheme, we tackle three important multi-source problems. The first is the multi-source multicast. We construct efficient, zero error source codes, and via properties of the CI completely characterize the resulting rate region. The second is broadcast with side information. We establish a duality between this problem and the classical problem of degraded message set broadcast, and give two code constructions and their associated regions. Finally, we consider the Ahlswede-Korner problem in a network, and give an efficient solution which is tight under the CI constraints.

We propose a practical methodology to protect a user's private data, when he wishes to publicly release data that is correlated with his private data, in the hope of getting some utility. Our approach relies on a general statistical inference framework that captures the privacy threat under inference attacks, given utility constraints. Under this framework, data is distorted before it is released, according to a privacy-preserving probabilistic mapping. This mapping is obtained by solving a convex optimization problem, which minimizes information leakage under a distortion constraint. We address practical challenges encountered when applying this theoretical framework to real world data. On one hand, the design of optimal privacy-preserving mechanisms requires knowledge of the prior distribution linking private data and data to be released, which is often unavailable in practice. On the other hand, the optimization may become untractable and face scalability issues when data assumes values in large size alphabets, or is high dimensional. Our work makes three major contributions. First, we provide bounds on the impact on the privacy-utility tradeoff of a mismatched prior. Second, we show how to reduce the optimization size by introducing a quantization step, and how to generate privacy mappings under quantization. Third, we evaluate our method on three datasets, including a new dataset that we collected, showing correlations between political convictions and TV viewing habits. We demonstrate that good privacy properties can be achieved with limited distortion so as not to undermine the original purpose of the publicly released data, e.g. recommendations.

We focus on the privacy-utility trade-off encountered by users who wish to disclose some information to an analyst, that is correlated with their private data, in the hope of receiving some utility. We rely on a general privacy statistical inference framework, under which data is transformed before it is disclosed, according to a probabilistic privacy mapping. We show that when the log-loss is introduced in this framework in both the privacy metric and the distortion metric, the privacy leakage and the utility constraint can be reduced to the mutual information between private data and disclosed data, and between non-private data and disclosed data respectively. We justify the relevance and generality of the privacy metric under the log-loss by proving that the inference threat under any bounded cost function can be upper-bounded by an explicit function of the mutual information between private data and disclosed data. We then show that the privacy-utility tradeoff under the log-loss can be cast as the non-convex Privacy Funnel optimization, and we leverage its connection to the Information Bottleneck, to provide a greedy algorithm that is locally optimal. We evaluate its performance on the US census dataset.