arXiv subjects

Jennifer Tang

Publications and source records attributed to Jennifer Tang.

10 recordsLinked to original sources

arXiv2026

A Model-Driven Lossless Compression Algorithm Resistant to Mismatch

Due to the fundamental connection between next-symbol prediction and compression, modern predictive models, such as large language models (LLMs), can be combined with entropy coding to achieve compression rates that surpass those of standard compression algorithms. However, this approach relies on the assumption that the predictive model produces identical output distributions at both the encoder and decoder, since even small mismatches can cause the decoding to fail. This assumption often fails with complex predictive models, particularly those based on neural networks, a phenomenon referred to as non-determinism. In this work, we propose a new compression algorithm based on next-token prediction that is robust to arbitrarily large, but structured, prediction mismatches. We prove the correctness of the proposed scheme under a formal mismatch certification, characterize its theoretical performance, and validate it experimentally on real datasets. Our results demonstrate reliable operation within the certified mismatch regime while achieving compression ratios that exceed those of commonly used compression methods.

cs.IT↗

arXiv2026

Synchronizing Probabilities in Model-Driven Lossless Compression

It is well-known in the field of lossless data compression that probabilistic next-symbol prediction can be used to compress sequences of symbols. Deep neural networks are able to capture rich dependencies in data, offering a powerful means of estimating these probabilities and hence an avenue towards more effective compression algorithms. However, both compressor and decompressor must have exactly matching predictions; even small differences from non-determinism (which often happen with learned models due to hardware, software, or computation order) can lead to cascading decoding failures. In this paper, we formalize the problem of prediction mismatch in model-driven compression, and introduce Probability Matching Interval Coding (PMATIC), a model-agnostic algorithm that tolerates bounded prediction mismatch with low overhead. PMATIC works with the predicted probabilities, making it compatible as a drop-in replacement for the arithmetic encoder in model-driven compression tools. We show theoretical correctness and performance bounds for PMATIC, and validate these results on text data. These results confirm that, when paired an advanced prediction model, PMATIC is robust to prediction mismatch while achieving compression rates that out-perform standard modern compression tools.

cs.IT↗

arXiv2023

Estimating True Beliefs in Opinion Dynamics with Social Pressure

Social networks often exert social pressure, causing individuals to adapt their expressed opinions to conform to their peers. An agent in such systems can be modeled as having a (true and unchanging) inherent belief while broadcasting a declared opinion at each time step based on her inherent belief and the past declared opinions of her neighbors. An important question in this setting is parameter estimation: how to disentangle the effects of social pressure to estimate inherent beliefs from declared opinions. This is useful for forecasting when agents' declared opinions are influenced by social pressure while real-world behavior only depends on their inherent beliefs. To address this, Jadbabaie et al. formulated the Interacting P\'olya Urn model of opinion dynamics under social pressure and studied it on complete-graph social networks using an aggregate estimator, and found that their estimator converges to the inherent beliefs unless majority pressure pushes the network to consensus. In this work, we studythis model on arbitrary networks, providing an estimator which converges to the inherent beliefs even in consensus situations. Finally, we bound the convergence rate of our estimator in both consensus and non-consensus scenarios; to get the bound for consensus scenarios (which converge slower than non-consensus) we additionally found how quickly the system converges to consensus.

eess.SY↗

arXiv2023

Stochastic Opinion Dynamics under Social Pressure in Arbitrary Networks

Social pressure is a key factor affecting the evolution of opinions on networks in many types of settings, pushing people to conform to their neighbors' opinions. To study this, the interacting Polya urn model was introduced by Jadbabaie et al., in which each agent has two kinds of opinion: inherent beliefs, which are hidden from the other agents and fixed; and declared opinions, which are randomly sampled at each step from a distribution which depends on the agent's inherent belief and her neighbors' past declared opinions (the social pressure component), and which is then communicated to her neighbors. Each agent also has a bias parameter denoting her level of resistance to social pressure. At every step, each agent updates her declared opinion (simultaneously with all other agents) according to her neighbors' aggregate past declared opinions, her inherent belief, and her bias parameter. We study the asymptotic behavior of this opinion dynamics model and show that the agents' declaration probabilities approaches a set of equilibrium points of the expected dynamics using Lyapunov theory and stochastic approximation techniques. We also derive necessary and sufficient conditions for the agents to approach consensus on their declared opinions. Our work provides further insight into the difficulty of inferring the inherent beliefs of agents when they are under social pressure.

eess.SY↗

arXiv2022

Data-Driven Blind Synchronization and Interference Rejection for Digital Communication Signals

We study the potential of data-driven deep learning methods for separation of two communication signals from an observation of their mixture. In particular, we assume knowledge on the generation process of one of the signals, dubbed signal of interest (SOI), and no knowledge on the generation process of the second signal, referred to as interference. This form of the single-channel source separation problem is also referred to as interference rejection. We show that capturing high-resolution temporal structures (nonstationarities), which enables accurate synchronization to both the SOI and the interference, leads to substantial performance gains. With this key insight, we propose a domain-informed neural network (NN) design that is able to improve upon both "off-the-shelf" NNs and classical detection and interference rejection methods, as demonstrated in our simulations. Our findings highlight the key role communication-specific domain knowledge plays in the development of data-driven approaches that hold the promise of unprecedented gains.

eess.SP↗

arXiv2022

Exploiting Temporal Structures of Cyclostationary Signals for Data-Driven Single-Channel Source Separation

We study the problem of single-channel source separation (SCSS), and focus on cyclostationary signals, which are particularly suitable in a variety of application domains. Unlike classical SCSS approaches, we consider a setting where only examples of the sources are available rather than their models, inspiring a data-driven approach. For source models with underlying cyclostationary Gaussian constituents, we establish a lower bound on the attainable mean squared error (MSE) for any separation method, model-based or data-driven. Our analysis further reveals the operation for optimal separation and the associated implementation challenges. As a computationally attractive alternative, we propose a deep learning approach using a U-Net architecture, which is competitive with the minimum MSE estimator. We demonstrate in simulation that, with suitable domain-informed architectural choices, our U-Net method can approach the optimal performance with substantially reduced computational burden.

eess.SP↗

arXiv2022

Efficient Representation of Large-Alphabet Probability Distributions

A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent such a vector with only $b$ bits per entry. A natural choice is to partition the interval $[0,1]$ into $2^b$ uniform bins and quantize entries to each bin independently. We show that a minor modification of this procedure -- applying an entrywise non-linear function (compander) $f(x)$ prior to quantization -- yields an extremely effective quantization method. For example, for $b=8 (16)$ and $10^5$-sized alphabets, the quality of representation improves from a loss (under KL divergence) of $0.5 (0.1)$ bits/entry to $10^{-4} (10^{-9})$ bits/entry. Compared to floating point representations, our compander method improves the loss from $10^{-1}(10^{-6})$ to $10^{-4}(10^{-9})$ bits/entry. These numbers hold for both real-world data (word frequencies in books and DNA $k$-mer counts) and for synthetic randomly generated distributions. Theoretically, we set up a minimax optimality criterion and show that the compander $f(x) ~\propto~ \mathrm{ArcSinh}(\sqrt{(1/2) (K \log K) x})$ achieves near-optimal performance, attaining a KL-quantization loss of $\asymp 2^{-2b} \log^2 K$ for a $K$-letter alphabet and $b\to \infty$. Interestingly, a similar minimax criterion for the quadratic loss on the hypercube shows optimality of the standard uniform quantizer. This suggests that the $\mathrm{ArcSinh}$ quantizer is as fundamental for KL-distortion as the uniform quantizer for quadratic distortion.

cs.IT↗

arXiv2021

Capacity of Noisy Permutation Channels

We establish the capacity of a class of communication channels introduced in [1]. The $n$-letter input from a finite alphabet is passed through a discrete memoryless channel $P_{Z|X}$ and then the output $n$-letter sequence is uniformly permuted. We show that the maximal communication rate (normalized by $\log n$) equals $1/2 (rank(P_{Z|X})-1)$ whenever $P_{Z|X}$ is strictly positive. This is done by establishing a converse bound matching the achievability of [1]. The two main ingredients of our proof are (1) a sharp bound on the entropy of a uniformly sampled vector from a type class and observed through a DMC; and (2) the covering $\epsilon$-net of a probability simplex with Kullback-Leibler divergence as a metric. In addition to strictly positive DMC we also find the noisy permutation capacity for $q$-ary erasure channels, the Z-channel and others.

cs.IT↗

arXiv2018

Generative Visual Rationales

Interpretability and small labelled datasets are key issues in the practical application of deep learning, particularly in areas such as medicine. In this paper, we present a semi-supervised technique that addresses both these issues by leveraging large unlabelled datasets to encode and decode images into a dense latent representation. Using chest radiography as an example, we apply this encoder to other labelled datasets and apply simple models to the latent vectors to learn algorithms to identify heart failure. For each prediction, we generate visual rationales by optimizing a latent representation to minimize the prediction of disease while constrained by a similarity measure in image space. Decoding the resultant latent representation produces an image without apparent disease. The difference between the original decoding and the altered image forms an interpretable visual rationale for the algorithm's prediction on that image. We also apply our method to the MNIST dataset and compare the generated rationales to other techniques described in the literature.

cs.CV↗

arXiv2016

Defect tolerance: fundamental limits and examples

This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems in which defective objects are replaced by judiciously connected redundant objects. The fundamental limits of this model are characterized under various asymptotic settings and both asymptotic and finite-size systems that approach these limits are constructed. Among other results, we show that simple modular redundancy is in general suboptimal. As we develop, this combinatorial problem of defect tolerant system design has a natural interpretation as one of graph coloring, and the analysis is significantly different from that traditionally used in information redundancy for error-control codes.

cs.IT↗