arXiv subjects

Ali Khalesi

Publications and source records attributed to Ali Khalesi.

16 recordsLinked to original sources

arXiv2026

Densification Converses for Walker Constellations

We establish densification converses for Walker LEO constellations under nearest-visible association in the full-frequency-reuse setting. Performance is evaluated under the invariant (stationary) measure induced by the constellation/Earth dynamics on the user--constellation ``phase state.'' A key Walker-specific feature, absent from unbounded planar models, is that association is restricted to a bounded visible cap determined by Earth geometry. Under power-law path-loss, a two-level antenna-gain model, i.i.d.\ nonnegative fading with unit mean and finite second moment, and nonzero noise, we prove that increasing the total satellite count $N=N_oN_s$ forces the aggregate interference to grow at least linearly in $N$, while the useful signal remains uniformly bounded above. Consequently, the downlink SINR coverage probability at any fixed threshold and the ergodic spectral efficiency both vanish as $N\to\infty$. These collapse statements concern link-level performance on one shared time--frequency resource block and do not imply that the aggregate capacity of the overall multi-resource network vanishes. The key technical ingredient is a deterministic visibility-annulus block lemma, uniform over all sufficiently large constellations and all ``phase states,'' showing that a fixed fraction of visible satellites lies in a distance annulus strictly inside the horizon; this yields explicit finite-$N$ collapse bounds. In particular, we derive nonasymptotic $O(1/N)$ upper bounds on both coverage and ergodic spectral efficiency. Finally, in the case of frequency reuse through independent thinning, with activity probability $q$, we show that avoiding densification collapse necessarily requires $qN=O(1)$, equivalently a reuse factor $Ω(N)$, and we obtain a corresponding explicit $O(1/(qN))$ upper bound.

cs.IT↗

arXiv2026

Fundamental Limits of Decentralized Self-Regulating Random Walks

We study self-regulating random walks (SRRWs), a decentralized mechanism for maintaining a stable population of mobile tokens on a graph. Tokens move by random walks, may be lost at faulty or malicious trap nodes, and may be locally forked or terminated according to node visit ages. The goal is to prevent both extinction and runaway growth without a central coordinator. We develop a graph-aware, controller-agnostic theory for SRRWs on finite connected graphs with lazy reversible random-walk dynamics. The main technical tool is a set of node-dependent return-time tail bounds, which yield population-dependent envelope functions describing how often local ages are large enough to trigger control actions. These envelopes translate graph structure into drift certificates: when the population is small, the achieved fork rate must compensate trap-induced absorption; when the population is large, trap losses and deliberate terminations must dominate forks. Using these certificates, we characterize population corridors for which the full system-state process is positive recurrent. We also identify two fundamental limits: stable finite-communication operation requires sufficient graph-limited forking capacity to offset absorption, and recovery from burst deletions or insertions is limited by the graph-dependent frequency of eligible local visits. Finally, we describe a minimal hysteresis controller with two age thresholds, one for replenishment and one for suppression, and show that its recovery behavior follows from the same certified margin conditions. Worked examples and numerical experiments on heterogeneous graphs illustrate how the stationary distribution, return-time envelopes, drift margins, finite-cost balance, reaction-time limits, and operating corridors can be computed and validated in concrete SRRW systems.

math.PR↗

arXiv2026

Wireless Broadcast Gossip for Decentralized Drone Swarms: Success Probability, Contraction, and Optimal Aloha

We study a tractable baseline for average-preserving broadcast gossip in decentralized drone swarms under a quasi-static planar Poisson model and a matching-based abstraction. With slotted Aloha, Rayleigh fading, and threshold decoding, we derive: 1) a closed-form SIR success law; 2) a mean-square contraction bound that separates ideal mixing from wireless successful updates via a conservative lower bound; and 3) a closed-form proxy access rule with interpretable density scaling. Explicit-interference simulations, together with robustness checks for receiver selection, noise, fading, and spatial regularity, confirm a stable intermediate operating region for the Aloha probability.

cs.IT↗

arXiv2026

Expert Routing for Communication-Efficient MoE via Finite Expert Banks

Resource-efficient machine learning increasingly uses sparse Mixture-of-Experts (MoE) architectures, where the gate acts as both a learning component and a routing interface controlling computation, communication, and accuracy. Motivated by finite-rate interpretations of MoE gating, we treat the gate as a stochastic channel and use $I(X;T)$ to quantify the routing information available to the selected expert. To make the associated information quantities tractable beyond synthetic examples, we develop a finite-bank MNIST construction using pretrained CNN experts and a discrete, data-dependent selection rule. Since the selected model belongs to a finite candidate set, the algorithmic mutual information $I(S;W)$ admits a closed-form discrete-entropy estimator from the empirical posterior $q(W|S)$. Sweeping a data-dependence parameter $α$, we observe that $\widehat I(S;W)$ monotonically tracks the generalization gap, while the Xu-Raginsky bound exhibits the expected looseness. We also compare with a uniform union-bound baseline and introduce an empirical estimator of $I(X;T)$ together with a Blahut-Arimoto procedure for tracing an accuracy-rate curve over the expert bank. The proposed framework provides a practical tool for analyzing resource-aware MoE inference systems and for interpreting $I(X;T)$ and $D(R_g)$ as design proxies for efficient expert routing.

cs.LG↗

arXiv2026

Multi-User Non-Linearly Separable Distributed Computing

This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output is raised to a bounded power. Our aim is to seek efficient task allocation and data communication techniques that reduce computation and communication costs. To this end, we take a tensor-theoretic approach, in which we represent the requested non-linearly decomposable functions using a properly designed tensor $\bar{\mathcal{F}}$, whose sparse decomposition into a tensor $\bar{\mathcal{E}}$ and a matrix $\mathbf{D}$ directly defines the task assignment, connectivity, and communication patterns. We design a lossless achievable scheme that integrates fixed-support SVD-based tensor factorization with multi-dimensional tiling of $\bar{\mathcal{E}}$ and $\mathbf{D}$, followed by a bipartite graph matching-based recursive assignment of tiles. This step transforms an overlapping decomposition into a disjoint one and reduces the resulting sum rank of the tiles, thereby decreasing the number of required servers. Under mild dimensionality conditions, we derive an explicit zero-error characterization of the achievable system rate $K/N$. Numerical simulations demonstrate the computational and communication savings over existing state-of-the-art matrix factorization approaches across a wide range of system parameters.

cs.IT↗

arXiv2026

Secure Multi-User Linearly-Separable Distributed Computing

The introduction of the new multi-user linearly-separable distributed computing framework, has recently revealed how a parallel treatment of users can yield large parallelization gains with relatively low computation and communication costs. These gains stem from a new approach that converts the computing problem into a sparse matrix factorization problem; a matrix $\mathbf{F}$ that describes the users' requests, is decomposed as $\mathbf{F} = \mathbf{DE}$, where a $γ$-sparse $\mathbf{E}$ defines the task allocation across $N$ servers, and a $δ$-sparse $\mathbf{D}$ defines the connectivity between $N$ servers and $K$ users as well as the decoding process. While this approach provides near-optimal performance, its linear nature has raised data secrecy concerns. We adopt an information-theoretic secrecy framework requiring that each user learns nothing more than its own requested function. Our main results provide (i) a necessary condition stating that for each user $k$ observing $α_k$ server responses, the common randomness visible to that user must span a subspace of dimension greater than $α_k-1$, and (ii) a necessary and sufficient condition requiring that removing from $\mathbf{D}$ the columns corresponding to the servers observed by a user leaves a matrix of rank at least $K-1$. Based on these conditions, we design a general, cost-preserving secrecy-enforcing transformation valid over both finite and real fields, obtained by appending to $\mathbf{E}$ a basis of $\mathrm{Null}(\mathbf{D})$ and carefully injecting shared randomness. This scheme preserves communication and computation costs, guarantees perfect information-theoretic secrecy over finite fields, and in the real case yields an explicit mutual-information bound that can be made arbitrarily small by increasing the variance of Gaussian common randomness.

cs.IT↗

arXiv2026

General Multi-User Distributed Computing: A Learning-Theoretic RKHS Framework for Generic Nonlinear Target Functions with Topology-Aware Risk Analysis

This paper studies multi-user distributed computation over shared real-valued subfunctions under computation and communication constraints. We consider a \emph{General Multi-User Distributed Computing (GMUDC)} model in which different users request heterogeneous target functions represented in the reproducing-kernel Hilbert space of a shift-invariant kernel, thereby covering generic nonlinear target mappings beyond linearly separable tasks. Unlike tessellated distributed computing frameworks that rely on disjoint-support topologies in their native setting, the GMUDC model allows arbitrary task-assignment and connectivity topologies subject to per-server computation and communication budgets~$Γ$ and~$Δ$. We analyze two complementary regimes. In the \emph{quenched} regime, the assignment and communication topology are fixed, and we derive upper and lower bounds on the resulting reconstruction risk that separate a spectral approximation term from a topology-dependent coverage term. In the \emph{annealed} regime, the assignment and links are drawn uniformly at random from a prescribed ensemble, and we characterize the corresponding average-risk scaling together with a topology-dependent coverage threshold. These results provide a topology-aware characterization of the computation--communication--accuracy trade-off for approximate multi-user distributed computation. They identify fundamental limits, up to constants and logarithmic factors, under the model assumptions adopted in the paper. In the shared linear/isotropic comparison regime, the framework also recovers the relevant tessellated distributed computing benchmark, while the broader GMUDC formulation applies to generic nonlinear target functions in kernel RKHSs and accommodates a wider range of task-assignment and communication topologies than disjoint-support constructions alone.

cs.IT↗

arXiv2026

Mixture-of-Experts under Finite-Rate Gating: Communication--Generalization Trade-offs

Mixture-of-Experts (MoE) architectures decompose prediction tasks into specialized expert sub-networks selected by a gating mechanism. This letter adopts a communication-theoretic view of MoE gating, modeling the gate as a stochastic channel operating under a finite information rate. Within an information-theoretic learning framework, {we specialize a mutual-information generalization bound and develop a rate-distortion characterization $D(R_g)$ of finite-rate gating, where $R_g:=I(X; T)$, yielding (under a standard empirical rate-distortion optimality condition) $\mathbb{E}[R(W)] \le D(R_g)+δ_m+\sqrt{(2/m)\, I(S; W)}$. }The analysis yields capacity-aware limits for communication-constrained MoE systems, and numerical simulations on synthetic multi-expert models empirically confirm the predicted trade-offs between gating rate, expressivity, and generalization.

stat.ML↗

arXiv2025

Hyper-Minrank: A Unified Hypergraph Characterization of Multi-Sender Index Coding

This work introduces a hypergraph formulation that generalizes the classical paradigm of Bar-Yossef et al. to the multi-sender index coding (MSIC) setting. Central to the model is a 4-regular side-information hypergraph G, a new adjacency representation A_G = [A_1 ... A_N], and a simple fitting criterion for sub-hypergraph validity, in the presence of specially designed hyperedges that capture both side information and cross-sender signal cancellation. This formulation establishes a tight achievability-converse equivalence for the general N-sender, K-receiver problem: every valid fitting induces a valid linear multi-sender index code, every linear code induces a valid fitting, and the optimal scalar linear broadcast length equals the hyper-minrank l**lin(G) = hyperminrank(G) = min*{A fits G} sum_{n=1}^N rank(A_n). Beyond this exact characterization, the approach yields hypergraph analogues of Haemers-type bounds on the broadcast length, including a clique-cover upper bound and a lower bound via the clique number of a carefully defined complement hypergraph. Algorithmically, we provide an exact procedure to compute hyperminrank(G), and show that in certain regimes its complexity is asymptotically better than approximate LT-CMAR solutions. The framework captures well-known settings such as embedded index coding, and applies directly to multi-sender cache-aided communications, coded computation, distributed storage, and edge/satellite systems, where hyperminrank can serve as a unified design target.

cs.IT↗

arXiv2025

Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing

We solve, in the typical-case sense, the multi-sender linearly-decomposable distributed computing problem introduced by tessellated distributed computing. We model real-valued encoders/decoders and demand matrices, and assess structural fidelity via a thresholded graph edit distance between the demand support and the two-hop support of the computed product. Our analysis yields: a closed-form second-moment (Frobenius) risk under spike-and-slab ensembles; deterministic links between thresholded GED and norm error; a Gaussian surrogate with sub-exponential tails that exposes explicit recall lines; concentration of GED and operator-norm control; and a compute-capped design with a visible knee. We map the rules to aeronautical and satellite networks.

cs.IT↗

arXiv2025

The Distributed Multi-User Point Function

In this paper, we study the problem of information-theoretic distributed multi-user point function, involving a trusted master node, $N \in \mathbb{N}$ server nodes, and $K\in \mathbb{N}$ users, where each user has access to the contents of a subset of the storages of server nodes. Each user is associated with an independent point function $f_{X_k,Z_k}: \{1,2,\hdots,T\} \rightarrow{GF(q^{m R_k})},T,mR_k \in \mathbb{N}$. Using these point functions, the trusted master node encodes and places functional shares $G_1,G_2,\hdots,G_N \in GF(q^{M}), M \in \mathbb{N}$ in the storage nodes such that each user can correctly recover its point function result from the response transmitted to itself and gains no information about the point functions of any other user, even with knowledge of all responses transmitted from its connected servers. For the first time, we propose a multi-user scheme that satisfies the correctness and information-theoretic privacy constraints, ensuring recovery for all point functions. We also characterize the inner and outer bounds on the capacity -- the maximum achievable rate defined as the size of the range of each point function $mR_k$ relative to the storage size of the servers $M$ -- of the distributed multi-user point function scheme by presenting a novel converse argument.

cs.IT↗

arXiv2024

Tessellated Distributed Computing

The work considers the $N$-server distributed computing scenario with $K$ users requesting functions that are linearly-decomposable over an arbitrary basis of $L$ real (potentially non-linear) subfunctions. In our problem, the aim is for each user to receive their function outputs, allowing for reduced reconstruction error (distortion) $ε$, reduced computing cost ($γ$; the fraction of subfunctions each server must compute), and reduced communication cost ($δ$; the fraction of users each server must connect to). For any given set of $K$ requested functions -- which is here represented by a coefficient matrix $\mathbf {F} \in \mathbb{R}^{K \times L}$ -- our problem is made equivalent to the open problem of sparse matrix factorization that seeks -- for a given parameter $T$, representing the number of shots for each server -- to minimize the reconstruction distortion $\frac{1}{KL}\|\mathbf {F} - \mathbf{D}\mathbf{E}\|^2_{F}$ overall $δ$-sparse and $γ$-sparse matrices $\mathbf{D}\in \mathbb{R}^{K \times NT}$ and $\mathbf{E} \in \mathbb{R}^{NT \times L}$. With these matrices respectively defining which servers compute each subfunction, and which users connect to each server, we here design our $\mathbf{D},\mathbf{E}$ by designing tessellated-based and SVD-based fixed support matrix factorization methods that first split $\mathbf{F}$ into properly sized and carefully positioned submatrices, which we then approximate and then decompose into properly designed submatrices of $\mathbf{D}$ and $\mathbf{E}$.

cs.IT↗

arXiv2024

Perfect Multi-User Distributed Computing

In this paper, we investigate the problem of multi-user linearly decomposable function computation, where $N$ servers help compute functions for $K$ users, and where each such function can be expressed as a linear combination of $L$ basis subfunctions. The process begins with each server computing some of the subfunctions, then broadcasting a linear combination of its computed outputs to a selected group of users, and finally having each user linearly combine its received data to recover its function. As it has become recently known, this problem can be translated into a matrix decomposition problem $\mathbf{F}=\mathbf{D}\mathbf{E}$, where $\mathbf{F} \in \mathbf{GF}(q)^{K \times L}$ describes the coefficients that define the users' demands, where $\mathbf{E} \in \mathbf{GF}(q)^{N \times L}$ describes which subfunction each server computes and how it combines the computed outputs, and where $\mathbf{D} \in \mathbf{GF}(q)^{K \times N}$ describes which servers each user receives data from and how it combines this data. Our interest here is in reducing the total number of subfunction computations across the servers (cumulative computational cost), as well as the worst-case load which can be a measure of computational delay. Our contribution consists of novel bounds on the two computing costs, where these bounds are linked here to the covering and packing radius of classical codes. One of our findings is that in certain cases, our distributed computing problem -- and by extension our matrix decomposition problem -- is treated optimally when $\mathbf{F}$ is decomposed into a parity check matrix $\mathbf{D}$ of a perfect code, and a matrix $\mathbf{E}$ which has as columns the coset leaders of this same code.

cs.IT↗

arXiv2023

Multi-User Distributed Computing Via Compressed Sensing

The multi-user linearly-separable distributed computing problem is considered here, in which $N$ servers help to compute the real-valued functions requested by $K$ users, where each function can be written as a linear combination of up to $L$ (generally non-linear) subfunctions. Each server computes a fraction $γ$ of the subfunctions, then communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. Our goal is to bound the ratio between the computation workload done by all servers over the number of datasets. To this end, we here reformulate the real-valued distributed computing problem into a matrix factorization problem and then into a basic sparse recovery problem, where sparsity implies computational savings. Building on this, we first give a simple probabilistic scheme for subfunction assignment, which allows us to upper bound the optimal normalized computation cost as $γ\leq \frac{K}{N}$ that a generally intractable $\ell_0$-minimization would give. To bypass the intractability of such optimal scheme, we show that if these optimal schemes enjoy $γ\leq - r\frac{K}{N}W^{-1}_{-1}(- \frac{2K}{e N r} )$ (where $W_{-1}(\cdot)$ is the Lambert function and $r$ calibrates the communication between servers and users), then they can actually be derived using a tractable Basis Pursuit $\ell_1$-minimization. This newly-revealed connection between distributed computation and compressed sensing opens up the possibility of designing practical distributed computing algorithms by employing tools and methods from compressed sensing.

cs.IT↗

arXiv2022

Multi-User Linearly-Separable Distributed Computing

In this work, we explore the problem of multi-user linearly-separable distributed computation, where $N$ servers help compute the desired functions (jobs) of $K$ users, and where each desired function can be written as a linear combination of up to $L$ (generally non-linear) subtasks (or sub-functions). Each server computes some of the subtasks, communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. We explore the computation and communication relationship between how many servers compute each subtask vs. how much data each user receives. For a matrix $\mathbf{F}$ representing the linearly-separable form of the set of requested functions, our problem becomes equivalent to the open problem of sparse matrix factorization $\mathbf{F} = \mathbf{D}\mathbf{E}$ over finite fields, where a sparse decoding matrix $\mathbf{D}$ and encoding matrix $\mathbf{E}$ imply reduced communication and computation costs respectively. This paper establishes a novel relationship between our distributed computing problem, matrix factorization, syndrome decoding and covering codes. To reduce the computation cost, the above $\mathbf{D}$ is drawn from covering codes or from a here-introduced class of so-called `partial covering' codes, whose study here yields computation cost results that we present.

cs.IT↗

arXiv2021

The Capacity Region of Distributed Multi-User Secret Sharing

In this paper, we study the problem of distributed multi-user secret sharing, including a trusted master node, $N\in \mathbb{N}$ storage nodes, and $K$ users, where each user has access to the contents of a subset of storage nodes. Each user has an independent secret message with certain rate, defined as the size of the message normalized by the size of a storage node. Having access to the secret messages, the trusted master node places encoded shares in the storage nodes, such that (i) each user can recover its own message from the content of the storage nodes that it has access to, (ii) each user cannot gain any information about the message of any other user. We characterize the capacity region of the distributed multi-user secret sharing, defined as the set of all achievable rate tuples, subject to the correctness and privacy constraints. In the achievable scheme, for each user, the master node forms a polynomial with the degree equal to the number of its accessible storage nodes minus one, where the value of this polynomial at certain points are stored as the encoded shares. The message of that user is embedded in some of the coefficients of the polynomial. The remaining coefficients are determined such that the content of each storage node serves as the encoded shares for all users that have access to that storage node.

cs.IT↗