arXiv subjects

Babak H. Khalaj

Publications and source records attributed to Babak H. Khalaj.

15 recordsLinked to original sources

arXiv2026

\texttt{Range-Arithmetic}: Verifiable Deep Learning Inference on an Untrusted Party

Verifiable computing (VC) has gained prominence in decentralized machine learning systems, where resource-intensive tasks like deep neural network (DNN) inference are offloaded to external participants due to blockchain limitations. This creates a need to verify the correctness of outsourced computations without re-execution. We propose \texttt{Range-Arithmetic}, a novel framework for efficient and verifiable DNN inference that transforms non-arithmetic operations, such as rounding after fixed-point matrix multiplication and ReLU, into arithmetic steps verifiable using sum-check protocols and concatenated range proofs. Our approach avoids the complexity of Boolean encoding, high-degree polynomials, and large lookup tables while remaining compatible with finite-field-based proof systems. Experimental results show that our method not only matches the performance of existing approaches, but also reduces the computational cost of verifying the results, the computational effort required from the untrusted party performing the DNN inference, and the communication overhead between the two sides.

cs.CR↗

arXiv2024

Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a gradual shift, where each pair of consecutive measures $P_i,P_{i+1}$ are close to each other in Wasserstein distance. We have a supervised dataset of size $n$ sampled from $P_0$, while for the subsequent distributions in the sequence, only unlabeled i.i.d. samples are available. Moreover, we assume that all distributions exhibit a known favorable attribute, such as (but not limited to) having intra-class soft/hard margins. In this context, we propose a methodology rooted in Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius. We theoretically show that this method guarantees the classification error across all $P_i$s can be suitably bounded. Our bounds rely on a newly introduced {\it {compatibility}} measure, which fully characterizes the error propagation dynamics along the sequence. Specifically, for inadequately constrained distributions, the error can exponentially escalate as we progress through the gradual shifts. Conversely, for appropriately constrained distributions, the error can be demonstrated to be linear or even entirely eradicated. We have substantiated our theoretical findings through several experimental results.

stat.ML↗

arXiv2024

Edge AI as a Service with Coordinated Deep Neural Networks

As artificial intelligence (AI) applications continue to expand in next-generation networks, there is a growing need for deep neural network (DNN) models. Although DNN models deployed at the edge are promising for providing AI as a service with low latency, their cooperation is yet to be explored. In this paper, we consider that DNN service providers share their computing resources as well as their models' parameters and allow other DNNs to offload their computations without mirroring. We propose a novel algorithm called coordinated DNNs on edge (\textbf{CoDE}) that facilitates coordination among DNN services by establishing new inference paths. CoDE aims to find the optimal path, which is the path with the highest possible reward, by creating multi-task DNNs from individual models. The reward reflects the inference throughput and model accuracy. With CoDE, DNN models can make new paths for inference by using their own or other models' parameters. We then evaluate the performance of CoDE through numerical experiments. The results demonstrate a $40\%$ increase in the inference throughput while degrading the average accuracy by only $2.3\%$. Experiments show that CoDE enhances the inference throughput and, achieves higher precision compared to a state-of-the-art existing method.

cs.NI↗

arXiv2024

Out-Of-Domain Unlabeled Data Improves Generalization

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in $\mathbb{R}^d$, where in addition to the $m$ independent and labeled samples from the true distribution, a set of $n$ (usually with $n\gg m$) out of domain and unlabeled samples are given as well. Using only the labeled data, it is known that the generalization error can be bounded by $\propto\left(d/m\right)^{1/2}$. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared to ERM. Our results underscore two significant insights: 1) out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the ``cluster assumption", and 2) the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

stat.ML↗

arXiv2023

Sample Complexity Bounds for Learning High-dimensional Simplices in Noisy Regimes

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a $\ell_2$ distance of at most $\varepsilon$ from the true simplex (for any $\varepsilon>0$). Also, we theoretically show that in order to achieve this bound, it is sufficient to have $n\ge\left(K^2/\varepsilon^2\right)e^{Ω\left(K/\mathrm{SNR}^2\right)}$ samples, where $\mathrm{SNR}$ stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as $\mathrm{SNR}\geΩ\left(K^{1/2}\right)$, the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in \citep{ashtiani2018nearly}, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

stat.ML↗

arXiv2020

On Statistical Learning of Simplices: Unmixing Problem Revisited

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretically show that a sufficient sample complexity for reliable learning of a $K$-dimensional simplex up to a total-variation error of $ε$ is $O\left(\frac{K^2}ε\log\frac{K}ε\right)$, which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets demonstrate a comparable performance for our method on noiseless samples, while we outperform the state-of-the-art in noisy cases.

cs.LG↗

arXiv2019

Minimizing Uplink Delay in Delay-Sensitive 5G CRAN platforms

In this paper, we consider the problem of minimizing the uplink delays of users in a 5G cellular network. Such cellular network is based on a Cloud Radio Access Network (CRAN) architecture with limited fronthaul capacity, where our goal is to minimize delays of all users through an optimal resource allocation. Earlier works minimize average delay of each user assuming same transmit power for all users. Combining Pareto optimization and Markov Decision Process (MDP), we show that every desired balance in the trade-off among infinite-horizon average-reward delays, is achievable by minimizing a properly weighted sum delays. In addition, we solve the problem in two realistic scenarios; considering both power control and different (random) service times for the users. In the latter scenario, we are able to define and minimize the more preferred criterion of total delay vs. average delay for each user. We will show that the resulting problem is equivalent to a discounted-reward infinite-horizon MDP. Simulations show significant improvement in terms of wider stability region for arrival rates in power-controlled scenario and considerably reduced sum of users total delays in the case of random service times.

eess.SP↗

arXiv2016

Fundamental Limits of Pooled-DNA Sequencing

In this paper, fundamental limits in sequencing of a set of closely related DNA molecules are addressed. This problem is called pooled-DNA sequencing which encompasses many interesting problems such as haplotype phasing, metageomics, and conventional pooled-DNA sequencing in the absence of tagging. From an information theoretic point of view, we have proposed fundamental limits on the number and length of DNA reads in order to achieve a reliable assembly of all the pooled DNA sequences. In particular, pooled-DNA sequencing from both noiseless and noisy reads are investigated in this paper. In the noiseless case, necessary and sufficient conditions on perfect assembly are derived. Moreover, asymptotically tight lower and upper bounds on the error probability of correct assembly are obtained under a biologically plausible probabilistic model. For the noisy case, we have proposed two novel DNA read denoising methods, as well as corresponding upper bounds on assembly error probabilities. It has been shown that, under mild circumstances, the performance of the reliable assembly converges to that of the noiseless regime when, for a given read length, the number of DNA reads is sufficiently large. Interestingly, the emergence of long DNA read technologies in recent years envisions the applicability of our results in real-world applications.

cs.IT↗

arXiv2010

State-Based Random Access: A Cross-Layer Approach

In this paper, we propose novel state-based algorithms which dynamically control the random access network based on its current state such as channel states of wireless links and backlog states of the queues. After formulating the problem, corresponding algorithms with diverse control functions are proposed. Consequently, it will be shown that the proposed state-based schemes for control of the random access networks, results in significant performance gains in comparison with previously proposed control algorithms. In order to select an appropriate control function, performances of the state-based control algorithms are compared for a wide range of traffic scenarios. It is also shown that even an approximate knowledge of network statistics helps in selecting the proper state dependent control function.

cs.IT↗

arXiv2010

Optimal Utility-Energy tradeoff in Delay Constrained Random Access Networks

Rate, energy and delay are three main parameters of interest in ad-hoc networks. In this paper, we discuss the problem of maximizing network utility and minimizing energy consumption while satisfying a given transmission delay constraint for each packet. We formulate this problem in the standard convex optimization form and subsequently discuss the tradeoff between utility, energy and delay in such framework. Also, in order to adapt for the distributed nature of the network, a distributed algorithm where nodes decide on choosing transmission rates and probabilities based on their local information is introduced.

cs.IT↗

arXiv2010

Energy and Utility Optimization in Wireless Networks with Random Access

Energy consumption is a main issue of concern in wireless networks. Energy minimization increases the time that networks' nodes work properly without recharging or substituting batteries. Another criterion for network performance is data transmission rate which is usually quantified by a network utility function. There exists an inherent tradeoff between these criteria and enhancing one of them can deteriorate the other one. In this paper, we consider both Network Utility Maximization (NUM) and energy minimization in a bi-criterion optimization problem. The problem is formulated for Random Access (RA) Medium Access Control (MAC) for ad-hoc networks. First, we optimize performance of the MAC and define utility as a monotonically increasing function of link throughputs. We investigate the optimal tradeoff between energy and utility in this part. In the second part, we define utility as a function of end to end rates and optimize MAC and transport layers simultaneously. We calculate optimal persistence probabilities and end-to-end rates. Finally, by means of duality theorem, we decompose the problem into smaller subproblems, which are solved at node and network layers separately. This decomposition avoids need for a central unit while sustaining benefits of layering.

cs.IT↗

arXiv2010

Utility Constrained Energy Minimization In Aloha Networks

In this paper we consider the issue of energy efficiency in random access networks and show that optimizing transmission probabilities of nodes can enhance network performance in terms of energy consumption and fairness. First, we propose a heuristic power control method that improves throughput, and then we model the Utility Constrained Energy Minimization (UCEM) problem in which the utility constraint takes into account single and multi node performance. UCEM is modeled as a convex optimization problem and Sequential Quadratic Programming (SQP) is used to find optimal transmission probabilities. Numerical results show that our method can achieve fairness, reduce energy consumption and enhance lifetime of such networks.

cs.IT↗

arXiv2010

Delay Constrained Utility Maximization in Multihop Random Access Networks

Multi-hop random access networks have received much attention due to their distributed nature which facilitates deploying many new applications over the sensor and computer networks. Recently, utility maximization framework is applied in order to optimize performance of such networks, however proposed algorithms result in large transmission delays. In this paper, we will analyze delay in random access multi-hop networks and solve the delay-constrained utility maximization problem. We define the network utility as a combination of rate utility and energy cost functions and solve the following two problems: 'optimal medium access control with link delay constraint' and, 'optimal congestion and contention control with end-to-end delay constraint'. The optimal tradeoff between delay, rate, and energy is achieved for different values of delay constraint and the scaling factors between rate and energy. Eventually linear and super-linear distributed optimization solutions are proposed for each problem and their performance are compared in terms of convergence and complexity.

cs.IT↗

arXiv2009

Delay-Constrained Utility Maximization in Multihop Random Access Networks

Multi-hop random access networks have received much attention due to their distributed nature which facilitates deploying many new applications over the sensor and computer networks. Recently, utility maximization framework is applied in order to optimize performance of such networks however delay is not limited and proposed algorithms result in very large transmission delays. In this paper, we will analyze delay in random access multi-hop networks and solve the delay-constrained utility maximization problem. We define the network utility as a combination of rate utility and energy cost functions and solve the following two problems: 'optimal medium access control with link delay constraint' and, 'optimal congestion and contention control with end-to-end delay constraint'. The optimal tradeoff between delay, rate, and energy is achieved for different values of delay constraint and the scaling factors between rate and energy. Different distributed solutions will be proposed for each problem and their performance will be compared in terms of convergence and complexity.

cs.NI↗

arXiv2009

Cooperative Transmission for Wireless Relay Networks Using Limited Feedback

To achieve the available performance gains in half-duplex wireless relay networks, several cooperative schemes have been earlier proposed using either distributed space-time coding or distributed beamforming for the transmitter without and with channel state information (CSI), respectively. However, these schemes typically have rather high implementation and/or decoding complexities, especially when the number of relays is high. In this paper, we propose a simple low-rate feedback-based approach to achieve maximum diversity with a low decoding and implementation complexity. To further improve the performance of the proposed scheme, the knowledge of the second-order channel statistics is exploited to design long-term power loading through maximizing the receiver signal-to-noise ratio (SNR) with appropriate constraints. This maximization problem is approximated by a convex feasibility problem whose solution is shown to be close to the optimal one in terms of the error probability. Subsequently, to provide robustness against feedback errors and further decrease the feedback rate, an extended version of the distributed Alamouti code is proposed. It is also shown that our scheme can be generalized to the differential transmission case, where it can be applied to wireless relay networks with no CSI available at the receiver.

cs.IT↗