arXiv subjects

Sennur Ulukus

Publications and source records attributed to Sennur Ulukus.

At least 19 recordsLinked to original sources

arXiv2026

Private Information Retrieval With Arbitrary Privacy Requirements: Introduction and Capacity Results

In this paper, we introduce the problem of private information retrieval (PIR) under arbitrary privacy requirements, in a graph-based storage system. This formulation is motivated by the server storage limitations, abundance of data (messages) and heterogeneous data privacy requirements. Under the arbitrary privacy requirement, each message has to be retrieved privately from a pre-specified subset of servers, where the subset always includes the servers storing it. Thus, each server is associated with a privacy set, which pre-specifies the message indices that should be privately retrieved from it. This setting is a generalization of the classical PIR setting, where the required message index needs to be kept private from all servers, i.e., there, the privacy set of each server comprises all message indices. Our setting is also a bridge between the newly formulated local PIR (LPIR) setting and the classical PIR setting, where in the former, the privacy set is exactly the set of stored message indices. In this paper, we derive general lower and upper bounds on the PIR capacity for general graphs, under certain privacy requirements, that capture the essence of both LPIR and classical PIR. Then, we focus on path and cyclic storage graphs under these and more fine-grained settings, for which we derive capacity results for certain cases, and establish lower and upper bounds for others. Their low degree allows for a more in-depth understanding of the new privacy formulation and admits more privacy requirement settings compared to other simple graphs. Finally, we introduce a new graph structure, the pyramid storage graph, to model server storage. Although this graph has never been investigated in the literature in any PIR context, it enjoys a nice symmetric structure for message storage and replication patterns.

cs.IT↗

arXiv2026

The Rate-Distortion-Deception Tradeoff

The problem of finding the optimal compression rate for a given random variable has been traditionally studied under two main constraints: distortion and perception. The distortion constraint enforces the fidelity of our reconstruction with respect to the observed realization of the random variable, while the perception constraint ensures that the reconstruction is close to a sample from the distribution of the random variable of interest. In this work, we explore the possibility of reconstruction, such that the reconstructed sample is still within a desired fidelity level with our original realization of the random variable, but at the same time, it resembles a sample from a different target distribution. We term this criterion as the deception constraint and find the fundamental tradeoffs of rate-distortion and deception.

cs.IT↗

arXiv2026

Quantum Private Distributed Matrix Multiplication: Extending the Classical Codes and Limitations

In this paper, we explore how quantum resources can be used to increase the rate of private distributed matrix multiplication (PDMM). In PDMM, a user who has two high-dimensional matrices, A and B, and lacks the computational capabilities to apply matrix multiplication locally, divides the matrices A and B into K and L sub-blocks, respectively. Then, the user sends them to N servers to apply the required multiplication \emph{privately}, i.e., any $T$ colluding servers cannot get any information about the user's matrices. The goal is to reduce the number of servers needed to perform the required matrix multiplication, thereby decreasing the communication cost. First, in the high-privacy regime, the state-of-the-art classical code is called the gap additive secure polynomial (GASP) code. We define a feasibility requirement in the quantum setting for the GASP code such that the highest performance is achieved when the requirement is satisfied. Thus, super-dense coding gain is achieved when the feasibility condition is satisfied. We show that when $T \geq KL-K+1$, the feasibility condition is always satisfied and the GASP code can be extended to the quantum version. In the case of $T < KL-K+1$, the feasibility can still be satisfied. To further examine this behavior, we numerically study how the minimum privacy requirement depends on the matrix dimensions and provide a quadratic estimate for this relation. The results suggest that feasibility can be achieved when $T \sim 0.5 KL$. Second, in the low-privacy regime, the recently developed cyclic-addition degree tables (CAT) and discretely optimized GASP (DOG) codes are among the most efficient known classical constructions for PDMM. We show that the feasibility condition developed for GASP can be adopted for both CAT and DOG codes as well, thus unifying the feasibility framework for multiple classical PDMM coding schemes.

cs.IT↗

arXiv2026

Local Private Information Retrieval for Graph-Based Replicated Systems

We rethink the definition of privacy in multi-server, graph-replicated private information retrieval (PIR) systems, by introducing a novel setting where the user's privacy is governed by the servers' storage structure. In classical graph-replicated PIR, the user retrieves a single message stored at the servers, while hiding the message index from each server. In our proposed privacy setting, the user is concerned with hiding the message index from a particular server, only if that server stores the message being retrieved, and privacy is not imposed otherwise. We coin this relaxed privacy requirement as local user privacy and the resulting PIR problem as local PIR on the graph. Our focus is on two-replicated PIR systems, where every message is replicated twice and stored on two distinct servers. Specifically, we study local PIR systems where the storage is represented by simple graphs, i.e., every pair of vertices is associated with at most one edge, and by their multigraph extension, i.e., $r$ parallel edges replace every edge. For these settings, we establish bounds on the local PIR capacity, defined as the maximum number of message symbols retrieved, per downloaded symbol. The local privacy requirement yields significant capacity gain over the classical PIR capacity under the same storage structure. For instance, in settings where the graph is a disjoint union of multiple identical sub-graphs, the gain in the local PIR capacity over classical PIR capacity is multiplicative in the number of sub-graphs. Further, for connected graphs, we derive capacity lower bounds for edge-transitive and bipartite graphs, which are greater than the best-known PIR capacity bounds. From these and by establishing matching upper bounds, we exactly characterize the capacity for star graphs, cyclic graphs, and path graphs with odd number of vertices. We introduce two local PIR schemes for general graphs.

cs.IT↗

arXiv2026

All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme

Classical Block Withholding (BWH) attacks have been extensively studied in block-dependent reward schemes, where pool members are compensated upon a block discovery within the pool. However, most contemporary mining pools operate under share-based schemes, wherein participants are paid immediately upon submission of valid shares. In this paper, we analyze BWH under Pay-Per-Share (PPS) for Nakamoto-style blockchains and prove that these mechanisms are not incentive compatible, contrary to claims in prior literature. Under PPS, the optimal strategy for a BWH attacker is the All-out Attack (AoA): the adversary allocates its entire hashpower toward the victim pool, submitting only partial Proof-of-Work shares (pPoW) while withholding all valid blocks, i.e., full Proof-of-Work (fPoW). Prior to the first difficulty adjustment, the adversary incurs negligible loss from withheld fPoWs. After the adjustment reduces block difficulty, the adversary either generates more pPoWs per unit time when the pPoW difficulty is reduced accordingly or, if the pPoW difficulty is held fixed, earns a higher reward per share. In both cases, it achieves a post-adjustment reward rate of $\fracα{1-α}$ per target epoch, compared with the honest baseline rate of $α$. Remarkably, this gain matches the theoretical upper bound achieved by optimal selfish mining in Nakamoto consensus under perfect network influence. The results further indicate that BWH is substantially more profitable under PPS than under mainstream block-dependent payout schemes, even when compared with advanced BWH variants. Honest miners benefit at the same rate as the adversary per unit hashpower, while the victim pool operator bears all losses, paying out-of-pocket for pPoW submissions without receiving fPoW compensation in return.

cs.CR↗

arXiv2026

Age of Gossip in Ring Networks With Non-Poisson Updates

We consider a network consisting of $n$ nodes connected in a ring formation and a source that generates updates according to a renewal process and disseminates them to the ring network according to a Poisson process. The nodes in the network gossip with each other according to a push-based gossiping protocol, and disseminate version updates. Gossip between two neighbors happens at the arrivals of renewal processes with finite mean and variance. All renewal processes and Poisson processes in the network are independent but not identically distributed. We consider both uni-directional ring networks and bi-directional ring networks. We use version age of information to quantify the freshness of information at each node. Prior work has used the stochastic hybrid systems (SHS) approach or a first passage percolation (FPP) approach to analyze ring networks with edges following identical Poisson processes. In this work, we use a sample-path backtracking approach to characterize the probabilistic scaling of the version age of information of an arbitrary node in the gossip network, where each edge follows an independent but not identically distributed renewal process. We show that the version age of information of any node in the network is stochastically equivalent to $\sqrt{n}$ at any time instant after the node has received its first update from the source.

cs.IT↗

arXiv2026

Chained Recursive Language Models for Multi-Iteration Reasoning

Long context reasoning in large language models (LLMs) is usually constrained by the fact that a single inference trajectory has to simultaneously explore the context, store intermediate state, verify evidence, and produce the final answer. This becomes particularly difficult in tasks that require extraction, counting, ordering, or multi-hop reasoning, where an early mistake can propagate until the final response. In this work, we propose Chained Recursive Language Models (Chained RLM), an inference-time architecture, in which the same underlying model is called repeatedly as a sequence of fresh reasoning roots. Each root receives the original problem and context, but does not inherit the full conversational history. Instead, it receives a compact plain-text summary, a plain-text blackboard, and some durable task-specific artifacts written by predecessor roots. The motivation is to manage the context by chopping into partial tasks rather than one large inference response; in each staged computation, intermediate artifacts can be inspected, corrected, and extended by a later fresh inference by the same model. We describe the system model, handoff mechanism, artifact workspace, and evaluation protocol for this system. We study when fresh-context artifact continuation gives a measurable gain in accuracy over direct LLM answering even with recursive tool-calling.

cs.CL↗

arXiv2026

Dependency Triad: A Metric to Quantify the Dependencies Between Attributes for Local Differential Privacy

Collecting multidimensional user data is essential for extracting rich insights across various applications. Local Differential Privacy (LDP) has emerged as a de facto standard for mitigating privacy risks in such scenarios. A key challenge in privacy-preserving multidimensional data collection lies in inter-attribute dependencies, as they can inadvertently reveal correlated information and increase privacy vulnerabilities. Therefore, accurately measuring correlation-induced privacy leakage (CPL) is essential for privacy analysis and privacy-utility trade-off. However, existing CPL analysis solutions either require accurate prior knowledge or face scalability challenges for large numbers of attributes and high-cardinality attributes. These limit their practical applicability in real data. To address this research gap, we propose a novel metric, ``Dependency Triad'' (DT), which summarizes the pairwise dependency information relevant to CPL using three parameters and yields a \emph{constant-time} conservative estimator of pairwise CPL. DT explicitly models uncertainty in prior distributional knowledge through its parameters, delivering robust leakage estimates. Moreover, its robustness to sparse distributions makes it particularly suitable for high-cardinality attributes, while the pairwise formulation serves as a tractable building block for assessing total leakage in multidimensional settings. Extensive experiments on both synthetic and real datasets demonstrate that DT consistently estimates CPL across diverse dependency regimes and prior uncertainties.

cs.CR↗

arXiv2026

Squeezing the Most Out of Preemption for AoI Minimization: Single-source Case

In this work, we study a single-source single-server continuous-time status update system where the updates arrive according to a Poisson process and update service times are generally distributed. In our proposed setting, a preemption policy refers to one where a new update preempts the ongoing one with a probability depending on the age of the update in service. We first propose an analytical method to derive the average age of information (AoI) and average peak AoI (PAoI) for any such preemption policy. This analysis is then utilized to tune two particular preemption policies: (i) probabilistic preemption (PP), in which preemption takes place according to a fixed probability regardless of the update age, (ii) threshold-based preemption (TP), for which preemption is incurred when the update age exceeds a certain threshold, both using one-dimensional line search. The effectiveness of policy tuning for the PP and TP policies is validated using lognormal-distributed update service times.

cs.IT↗

arXiv2026

On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers

We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers. We show that in embedding dimension two, for any key, query, and value matrices, the dynamics can be reformulated as a generalized Kuramoto-type model with pure second-harmonic coupling. This formulation is amenable to Watanabe--Strogatz theory which reveals the dynamics are intrinsically low-dimensional regardless of the parameter matrices. For a class of token initializations associated with the Ott--Antonsen (OA) manifold, we show that the parameter matrices induce a diverse variety of long-time behaviors in linear transformers, including clustering, oscillations, and bifurcations. The oscillations and bifurcations are characterized by uncovering a hidden Hamiltonian structure in the dynamics. By establishing a structural stability result, we further show that dynamics initialized near the OA manifold exhibit the same long-time behavior as those initialized exactly on the manifold. Motivated by our theory in dimension two, we conduct numerical experiments for analogous parameter regimes in higher-dimensional transformers. Our numerical experiments suggest that the long-time behaviors characterized in our theoretical results persist in higher dimensions.

cs.LG↗

arXiv2026

Semantic Leakage and Privacy Preservation in Relay-Assisted Semantic Communications

Semantic communication (SemCom) has emerged as a promising paradigm in which the transmission of task-relevant information is prioritized over raw data, enabling efficient and robust communication under resource and channel constraints. In this paper, the privacy implications of relay-assisted SemCom systems are studied, where the intermediate relay node operates directly on learned latent representations. It is shown that the relay, even without access to source data, can reliably infer semantic meaning and reconstruct signals with performance comparable to that of the legitimate receiver, revealing a fundamental privacy vulnerability of semantic representations. To address this issue, an iterative adversarial training framework is proposed in which a strong, adaptively trained eavesdropper at the relay is explicitly accounted for. The proposed approach alternates between optimizing the relay's eavesdropping function and the legitimate system, resulting in representations that preserve semantic decoding performance at the intended receiver while degrading semantic inference at the relay. The semantic accuracy gap between the legitimate receiver and the eavesdropper is significantly enlarged across channel conditions. Importantly, this protection is achieved in a stealthy manner, with high reconstruction fidelity maintained while semantic leakage is selectively suppressed.

cs.NI↗

arXiv2026

Dual-Regime Absorbing Markov Chain Theory in Remote Estimation: Age-Minimizing Push Policies

For a remote estimation system, we study the optimization of age of incorrect information (AoII), which is a recently proposed semantic-aware information freshness metric. In particular, we assume an information source that observes a discrete-time finite-state Markov chain (DTMC), and occasionally transmits status update packets to a remote monitor which is tasked with remote estimation of the source. For the forward channel from the source to the monitor, we assume the channel delay to be modeled by a general discrete-time phase-type (DPH) distribution, whereas the reverse channel from the monitor to the source is assumed to be perfect, ensuring that the source has perfect information on the AoII and the remote estimate at the monitor, at all times. Push-based transmissions are initiated when AoII exceeds a threshold depending on the current estimation value, i.e., multi-threshold policy. In this very general setting, our goal is to minimize a weighted sum of the time average of a polynomial function of AoII, depending on the remote estimate, and energy consumption from transmissions. We formulate the problem as a semi-Markov decision process (SMDP) with the same state-space of the original DTMC to obtain the optimal multi-threshold policy, whereas the parameters of the SMDP are obtained by using a novel stochastic tool called dual-regime absorbing Markov chain (DR-AMC), and its corresponding absorption time distribution named as dual-regime DPH (DR-DPH). The proposed method is validated with numerical examples using comparisons against other policies obtained by exhaustive search, and also various benchmark policies.

cs.IT↗

arXiv2026

Wireless Backdoor Attack and Defense for Semantic Communications over Multiple Access Channel

Semantic communication (SemCom) aims to preserve semantic meaning and task-oriented information beyond conventional message recovery over wireless channels. The adoption of SemCom in shared-access wireless networks introduces new vulnerabilities for multi-user semantic inference. This paper considers a SemCom system for two transmitters communicating with a common receiver over a multiple access channel. Each transmitter maps source information into latent semantic representations, while the receiver jointly reconstructs and classifies the semantic information for both transmitters. A selective over-the-air backdoor (Trojan) attack is presented in which an adversary transmits a low-power trigger waveform over the air and injects it into the shared received signal during training. By transmitting the trigger again during testing, this stealthy, low-power attack selectively manipulates the semantic inference for one transmitter while minimally affecting the inference of the other transmitter. To mitigate this vulnerability, a trigger-aware defense mechanism is developed to preserve correct semantic labels under trigger-contaminated wireless observations. The results demonstrate both the vulnerability of shared-access SemCom systems to selective over-the-air backdoor attacks and the effectiveness of trigger-aware robust training for semantic protection.

cs.NI↗

arXiv2026

When and Which Sensor to Observe? Timely Tracking of a Joint Markov Source

We investigate the problem of remote estimation (at a monitor) of a discrete-time joint Markov process with individual components which can be observed with dedicated sensors. At a given time slot, the monitor has the option of staying idle or sending a pull request to one of the sensors to obtain a partial state value, while the sensors are assumed to have heterogeneous sampling costs. Our goal is to develop a monitor pull policy, i.e., determining when and towards which sensor to send a pull request, in order to minimize a weighted sum of average age of incorrect information (AoII), or in short age, and sampling costs. As the communication model, we assume an erasure channel with a fixed one-slot delay from each sensor to the monitor. In this setting, the monitor does not perfectly know either the state of the process or the age, at any given time. We first obtain a sufficient statistic, namely belief, representing the joint distribution of the age and the current state of the observed process, by using the history of all pull requests and observations. Then, we formulate the optimization problem as a continuous state-space Markov decision process (MDP), namely belief-MDP, for the solution of which we propose two model predictive control (MPC) methods, namely MPC without terminal costs (MPC-WTC), and reinforcement learning MPC (RL-MPC). The effectiveness of the proposed methods is validated by numerical examples.

cs.IT↗

arXiv2026

Storage-Rate Trade-off in A-XPIR

We consider the storage problem in an asymmetric $X$-secure private information retrieval (A-XPIR) setting. The A-XPIR setting considers the $X$-secure PIR problem (XPIR) when a given arbitrary set of servers is communicating. We focus on the trade-off region between the average storage at the servers and the average download cost. In the case of $N=4$ servers and two non-overlapping sets of communicating servers with $K=2$ messages, we characterize the achievable region and show that the three main inequalities compared to the no-security case collapse to two inequalities in the asymmetric security case. In the general case, we derive bounds that need to be satisfied for the general achievable region for an arbitrary number of servers and messages. In addition, we provide the storage and retrieval scheme for the case of $N=4$ servers with $K=2$ messages and two non-overlapping sets of communicating servers, such that the messages are not replicated (in the sense of a coded version of each symbol) and at the same time achieve the optimal achievable rate for the case of replication. Finally, we derive the exact capacity for the case of asymmetric security and asymmetric collusion for $N=4$ servers, with the communication links $\{1,2\}$ and $\{3,4\}$, which splits the servers into two groups, i.e., $g=2$, and with the collusion links $\{1,3\}$, $\{2,4\}$, as $C=\frac{1}{3}$. More generally, we derive a capacity result for a certain family of asymmetric collusion and asymmetric security cases.

cs.IT↗

arXiv2026

SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work

The security and decentralization of Proof-of-Work (PoW) have been well-tested in existing blockchain systems. However, its tremendous energy waste has raised concerns about sustainability. Proof-of-Useful-Work (PoUW) aims to redirect the meaningless computation to meaningful tasks such as solving machine learning (ML) problems, giving rise to the branch of Proof-of-Learning (PoL). While previous studies have proposed various PoLs, they all, to some degree, suffer from security, decentralization, or efficiency issues. In this paper, we propose a PoL framework that trains ML models efficiently while maintaining blockchain security in a fully distributed manner. We name the framework SEDULity, which stands for a Secure, Efficient, Distributed, and Useful Learning-based blockchain system. Specifically, we encode the template block into the training process and design a useful function that is difficult to solve but relatively easy to verify, as a substitute for the PoW puzzle. We show that our framework is distributed, secure, and efficiently trains ML models. We further demonstrate that the proposed PoL framework can be extended to other types of useful work and design an incentive mechanism to incentivize task verification. We show theoretically that a rational miner is incentivized to train fully honestly with well-designed system parameters. Finally, we present simulation results to demonstrate the performance of our framework and validate our analysis.

cs.CR↗

arXiv2026

Temporary Power Adjusting Withholding Attack

We consider the block withholding attacks on pools, more specifically the state-of-the-art Power Adjusting Withholding (PAW) attack. We propose a generalization called Temporary PAW (T-PAW) where the adversary withholds a fPoW from pool mining at most $T$-time even when no other block is mined. We show that PAW attack corresponds to $T\to\infty$ and is not optimal. In fact, the extra reward of T-PAW compared to PAW improves by an unbounded factor as adversarial hash fraction $α$, pool size $β$ and adversarial network influence $γ$ decreases. For example, the extra reward of T-PAW is 22 times that of PAW when an adversary targets a pool with $(α,β,γ)=(0.05,0.05,0)$. We show that honest mining is sub-optimal to T-PAW even when there is no difficulty adjustment and the adversarial revenue increase is non-trivial, e.g., for most $(α,β)$ at least $1\%$ within $2$ weeks in Bitcoin even when $γ=0$ (for PAW it was at most $0.01\%$). Hence, T-PAW exposes a significant structural weakness in pooled mining-its primary participants, small miners, are not only contributors but can easily turn into potential adversaries with immediate non-trivial benefits.

cs.CR↗

arXiv2026

How Far Back in Time a Digital Twin Reflects the State of the Physical Object: Age of Staleness

The groundbreaking metric age of information (AoI) has been introduced to measure information freshness in communication networks. As transformational as it is, AoI metric falls short in some applications, such as remote monitoring, since it is a semantic-agnostic metric which does not consider the dynamics of the random process. There is a need to quantify the performance of a remote estimator via a metric that combines freshness and semantic aspects. To this end, in this paper, we introduce a novel metric coined age of staleness (AoS) that measures when the last time that the current estimation was correct. First, we analyze a simple scenario where an $n$-ary symmetric Markov source is observed by a monitor via a constant sampling rate, obtain a closed-form expression for the AoS, and show that it is a monotonically decreasing function of the sampling rate. Next, we consider multiple distinct Markov sources, and formulate an optimization problem, where the remote monitor allocates the total sampling rate to tracking the sources. Although the optimization problem is non-convex, its structure is suitable for obtaining a near-optimal solution using the polyblock algorithm, which leverages the monotonicity of the objective function. While the new AoS metric could be applicable in many scenarios, we believe it is particularly well-suited for a digital twin network (DTN) where multiple physical objects (POs) are monitored with a total sampling rate constraint to maintain a digital representation of them, namely, their digital twin (DT).

cs.IT↗