arXiv subjects

Soummya Kar

Publications and source records attributed to Soummya Kar.

At least 19 recordsLinked to original sources

arXiv2026

An Optimization Framework for Certain Separable Problems using Neural Networks

This paper studies a class of parametric constrained optimization problems that are motivated by applications in real time applications. Under a parameter-separable problem structure that naturally arises in these applications, the paper proposes a two phase strategy, based on offline learning and online processing, to address these optimization problems on resource limited devices. Specifically, by exploiting the separable structure, an iterative Alternating Direction Method of Multipliers (ADMM) based solution procedure is developed that enables the use of certain learning based function representations (learned offline but readily computable online) to reduce the overall online on-device implementation complexity. By carefully crafting the ADMM procedure, it is shown that even as the parameters vary, the corresponding instances of the parametric optimization problem may be solved by lightweight online computations in the device with the assistance of a neural network co-processor.

eess.SP↗

arXiv2026

Tight Long-Term Tail Decay of (Clipped) SGD in Non-Convex Optimization

The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying the error rate for a fixed probability threshold, there is a lack of work directly studying the probability of failure, i.e., quantifying the tail decay rate for a fixed error threshold. Moreover, existing results are of finite-time nature, limiting their ability to capture the true long-term tail decay which is more informative for modern learning models, typically trained for millions of iterations. Our work closes these gaps, by studying the long-term tail decay of SGD-based methods through the lens of large deviations theory, establishing several strong results in the process. First, we provide an upper bound on the tails of the gradient norm-squared of the best iterate produced by (vanilla) SGD, for non-convex costs and bounded noise, with long-term decay at rate $e^{-t/\log(t)}$. Next, we relax the noise assumption by considering clipped SGD (c-SGD) under heavy-tailed noise with bounded moment of order $p \in (1,2]$, showing an upper bound with long-term decay at rate $e^{-t^{β_p}/\log(t)}$, where $β_p = \frac{4(p-1)}{3p-2}$ for $p \in (1,2)$ and $e^{-t/\log^2(t)}$ for $p = 2$. Finally, we provide lower bounds on the tail decay, at rate $e^{-t}$, showing that our rates for both SGD and c-SGD are tight, up to poly-logarithmic factors. Notably, our results demonstrate an order of magnitude faster long-term tail decay compared to existing work based on finite-time bounds, which show rates $e^{-\sqrt{t}}$ and $e^{-t^{β_p/2}}$, $p \in (1,2]$, for SGD and c-SGD, respectively. As such, we uncover regimes where the tails decay much faster than previously known, providing stronger long-term guarantees for individual runs.

cs.LG↗

arXiv2026

Decentralized Nonconvex Optimization under Heavy-Tailed Noise: Normalization and Optimal Convergence

Heavy-tailed noise in nonconvex stochastic optimization has garnered increasing research interest, as empirical studies, including those on training attention models, suggest it is a more realistic gradient noise condition. This paper studies first-order nonconvex stochastic optimization under heavy-tailed gradient noise in a decentralized setup, where each node can only communicate with its direct neighbors in a predefined graph. Specifically, we consider a class of heavy-tailed gradient noise that is zero-mean and has only $p$-th moment for $p \in (1, 2]$. We propose GT-NSGDm, Gradient Tracking based Normalized Stochastic Gradient Descent with momentum, that utilizes normalization, in conjunction with gradient tracking and momentum, to cope with heavy-tailed noise on distributed nodes. We show that, when the communication graph admits primitive and doubly stochastic weights, GT-NSGDm guarantees, for the \textit{first} time in the literature, that the expected gradient norm converges at an optimal non-asymptotic rate $O\big(1/T^{(p-1)/(3p-2)}\big)$, which matches the lower bound in the centralized setup. When tail index $p$ is unknown, GT-NSGDm attains a non-asymptotic rate $O\big( 1/T^{(p-1)/(2p)} \big)$ that is, for $p < 2$, topology independent and has a speedup factor $n^{1-1/p}$ in terms of the number of nodes $n$. Finally, experiments on nonconvex linear regression with tokenized synthetic data and decentralized training of language models on a real-world corpus demonstrate that GT-NSGDm is more robust and efficient than baselines.

math.OC↗

arXiv2026

Tackling heavy-tailed noise in distributed estimation: Asymptotic performance and tradeoffs

We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbolθ^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear, e.g., in densely deployed Internet of Things (IoT) or wireless sensor network systems. The presented algorithm falls within the class of \emph{consensus+innovation} estimators and combats the effect of the heavy-tailed noises by adding general nonlinearities in the consensus and innovations update parts. We present results on almost sure convergence and asymptotic normality of the estimator. In addition, we provide novel analytical studies that reveal interesting tradeoffs between the system noises and the underlying network topology.

cs.IT↗

arXiv2026

Distributed Gradient Clustering: Convergence and the Effect of Initialization

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.

cs.LG↗

arXiv2026

Multi-Period Sparse Optimization for Proactive Grid Blackout Diagnosis

Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are correlated or share similar patterns, it is reasonable to expect that the dominant vulnerability or failure sources behind them share the same locations but with different severity. Early warning diagnosis that proactively identifies the key vulnerabilities responsible for a number of system collapses of interest can significantly enhance resilience. This paper proposes a multi-period sparse optimization method, enabling the discovery of persistent failure sources across a sequence of collapsed systems with increasing system stress, such as rising demand or worsening contingencies. This work defines persistency and efficiently integrates persistency constraints to capture the ``hidden'' evolving vulnerabilities. Circuit-theory based power flow formulations and circuit-inspired optimization heuristics are used to facilitate the scalability of the method. Experiments on benchmark systems show that the method reliably tracks persistent vulnerability locations under increasing load stress, and solves with scalability to large systems (on average taking around 200 s per scenario on 2000+ bus systems).

eess.SY↗

arXiv2026

Sharp High-Probability Rates for Nonlinear SGD under Heavy-Tailed Noise via Symmetrization

We study convergence in high-probability of SGD-type methods in non-convex optimization and the presence of heavy-tailed noise. To combat the heavy-tailed noise, a general black-box nonlinear framework is considered, subsuming nonlinearities like sign, clipping, normalization and their smooth counterparts. Our first result shows that nonlinear SGD (N-SGD) achieves the rate $\widetilde{\mathcal{O}}(t^{-1/2})$, for any noise with unbounded moments and a symmetric probability density function (PDF). Crucially, N-SGD has exponentially decaying tails, matching the performance of linear SGD under light-tailed noise. To handle non-symmetric noise, we propose two novel estimators, based on the idea of noise symmetrization. The first, dubbed Symmetrized Gradient Estimator (SGE), assumes a noiseless gradient at any reference point is available at the start of training, while the second, dubbed Mini-batch SGE (MSGE), uses mini-batches to estimate the noiseless gradient. Combined with the nonlinear framework, we get N-SGE and N-MSGE methods, respectively, both achieving the same convergence rate and exponentially decaying tails as N-SGD, while allowing for non-symmetric noise with unbounded moments and PDF satisfying a mild technical condition, with N-MSGE additionally requiring bounded noise moment of order $p \in (1,2]$. Compared to works assuming noise with bounded $p$-th moment, our results: 1) are based on a novel symmetrization approach; 2) provide a unified framework and relaxed moment conditions; 3) imply optimal oracle complexity of N-SGD and N-SGE, strictly better than existing works when $p < 2$, while the complexity of N-MSGE is close to existing works. Compared to works assuming symmetric noise with unbounded moments, we: 1) provide a sharper analysis and improved rates; 2) facilitate state-dependent symmetric noise; 3) extend the strong guarantees to non-symmetric noise.

stat.ML↗

arXiv2025

Stability Analysis of a B-Spline Deep Neural Operator for Nonlinear Systems

This paper investigates the stability properties of neural operators through the structured representation offered by the Hybrid B-spline Deep Neural Operator (HBDNO). While existing stability-aware architectures typically enforce restrictive constraints that limit universality, HBDNO preserves full expressive power by representing outputs via B-spline control points. We show that these control points form a natural observable for post-training stability analysis. By applying Dynamic Mode Decomposition and connecting the resulting discrete dynamics to the Koopman operator framework, we provide a principled approach to spectral characterization of learned operators. Numerical results demonstrate the ability to assess stability and reveal future directions for safety-critical applications.

eess.SY↗

arXiv2025

Safe Driving in Occluded Environments

Ensuring safe autonomous driving in the presence of occlusions poses a significant challenge in its policy design. While existing model-driven control techniques based on set invariance can handle visible risks, occlusions create latent risks in which safety-critical states are not observable. Data-driven techniques also struggle to handle latent risks because direct mappings from risk-critical objects in sensor inputs to safe actions cannot be learned without visible risk-critical objects. Motivated by these challenges, in this paper, we propose a probabilistic safety certificate for latent risk. Our key technical enabler is the application of probabilistic invariance: It relaxes the strict observability requirements imposed by set-invariance methods that demand the knowledge of risk-critical states. The proposed techniques provide linear action constraints that confine the latent risk probability within tolerance. Such constraints can be integrated into model predictive controllers or embedded in data-driven policies to mitigate latent risks. The proposed method is tested using the CARLA simulator and compared with a few existing techniques. The theoretical and empirical analysis jointly demonstrate that the proposed methods assure long-term safety in real-time control in occluded environments without being overly conservative and with transparency to exposed risks.

eess.SY↗

arXiv2025

Cyber-Resilient System Identification for Power Grid through Bayesian Integration

Power grids increasingly need real-time situational awareness under the ever-evolving cyberthreat landscape. Advances in snapshot-based system identification approaches have enabled accurately estimating states and topology from a snapshot of measurement data, under random bad data and topology errors. However, modern interactive, targeted false data can stay undetectable to these methods, and significantly compromise estimation accuracy. This work advances system identification that combines snapshot-based method with time-series model via Bayesian Integration, to advance cyber resiliency against both random and targeted false data. Using a distance-based time-series model, this work can leverage historical data of different distributions induced by changes in grid topology and other settings. The normal system behavior captured from historical data is integrated into system identification through a Bayesian treatment, to make solutions robust to targeted false data. We experiment on mixed random anomalies (bad data, topology error) and targeted false data injection attack (FDIA) to demonstrate our method's 1) cyber resilience: achieving over 70% reduction in estimation error under FDIA; 2) anomalous data identification: being able to alarm and locate anomalous data; 3) almost linear scalability: achieving comparable speed with the snapshot-based baseline, both taking <1min per time tick on the large 2,383-bus system using a laptop CPU.

eess.SY↗

arXiv2025

Test-Time Scaling in Diffusion LLMs via Hidden Semi-Autoregressive Experts

Diffusion-based large language models (dLLMs) are trained flexibly to model extreme dependence in the data distribution; however, how to best utilize this information at inference time remains an open problem. In this work, we uncover an interesting property of these models: dLLMs trained on textual data implicitly learn a mixture of semi-autoregressive experts, where different generation orders reveal different specialized behaviors. We show that committing to any single, fixed inference time schedule, a common practice, collapses performance by failing to leverage this latent ensemble. To address this, we introduce HEX (Hidden semiautoregressive EXperts for test-time scaling), a training-free inference method that ensembles across heterogeneous block schedules. By doing a majority vote over diverse block-sized generation paths, HEX robustly avoids failure modes associated with any single fixed schedule. On reasoning benchmarks such as GSM8K, it boosts accuracy by up to 3.56X (from 24.72% to 88.10%), outperforming top-K margin inference and specialized fine-tuned methods like GRPO, without additional training. HEX even yields significant gains on MATH benchmark from 16.40% to 40.00%, scientific reasoning on ARC-C from 54.18% to 87.80%, and TruthfulQA from 28.36% to 57.46%. Our results establish a new paradigm for test-time scaling in diffusion-based LLMs (dLLMs), revealing that the sequence in which masking is performed plays a critical role in determining performance during inference.

cs.LG↗

arXiv2025

Decentralized Local Voltage Control for Active Distribution Networks

Distribution networks face challenges from the increasing deployment of Distributed Energy Resources (DERs) and the emergence of bidirectional power flows. We propose a decentralized Volt/VAr control method based on a saddle-point reformulation and consensus+innovation (C+I) updates. Each agent at a controllable bus computes and enforces its own set-points using only neighbor communication. Our method embeds passive buses directly, preserves network physics through a linearized Jacobian model, and avoids any supervisory nodes. Simulation results on a modified CIGRE low-voltage network show voltage stability improvement within operational limits, indicating the viability of a fully decentralized (edge-based) Volt/VAr control solution.

eess.SY↗

arXiv2025

Federated Multi-Objective Learning with Controlled Pareto Frontiers

Federated learning (FL) is a widely adopted paradigm for privacy-preserving model training, but FedAvg optimise for the majority while under-serving minority clients. Existing methods such as federated multi-objective learning (FMOL) attempts to import multi-objective optimisation (MOO) into FL. However, it merely delivers task-wise Pareto-stationary points, leaving client fairness to chance. In this paper, we introduce Conically-Regularised FMOL (CR-FMOL), the first federated MOO framework that enforces client-wise Pareto optimality through a novel preference-cone constraint. After local federated multi-gradient descent averaging (FMGDA) / federated stochastic multi-gradient descent averaging (FSMGDA) steps, each client transmits its aggregated task-loss vector as an implicit preference; the server then solves a cone-constrained Pareto-MTL sub-problem centred at the uniform vector, producing a descent direction that is Pareto-stationary for every client within its cone. Experiments on non-IID benchmarks show that CR-FMOL enhances client fairness, and although the early-stage performance is slightly inferior to FedAvg, it is expected to achieve comparable accuracy given sufficient training rounds.

cs.LG↗

arXiv2025

Distributed Truncated Predictive Control for Networked Systems under Uncertainty: Stability and Near-Optimality Guarantee

We study the problem of distributed online control of networked systems with time-varying cost functions and disturbances, where each node only has local information of the states and forecasts of the costs and disturbances. We develop a distributed truncated predictive control (DTPC) algorithm, where each node solves a ``truncated'' predictive optimal control problem with horizon $k$, but only involving nodes in a $κ$-hop neighborhood (ignoring nodes outside). We show that the DTPC algorithm satisfies input-to-state stability (ISS) bounds and has regret decaying exponentially in $k$ and $κ$, meaning a short predictive horizon $k$ and a small truncation radius $κ$ is sufficient to achieve near-optimal performance. Furthermore, we show that when the future costs and disturbances are not exactly known, the regret has exponentially decaying sensitivity to the forecast errors in terms of predictive horizon, meaning near-term forecast errors play a much more important role than longer-term forecasts.

math.OC↗

arXiv2025

Distributed gradient methods under heavy-tailed communication noise

We consider a standard distributed optimization problem in which networked nodes collaboratively minimize the sum of their locally known convex costs. For this setting, we address for the first time the fundamental problem of design and analysis of distributed methods to solve the above problem when inter-node communication is subject to \emph{heavy-tailed} noise. Heavy-tailed noise is highly relevant and frequently arises in densely deployed wireless sensor and Internet of Things (IoT) networks. Specifically, we design a distributed gradient-type method that features a carefully balanced mixed time-scale time-varying consensus and gradient contribution step sizes and a bounded nonlinear operator on the consensus update to limit the effect of heavy-tailed noise. Assuming heterogeneous strongly convex local costs with mutually different minimizers that are arbitrarily far apart, we show that the proposed method converges to a neighborhood of the network-wide problem solution in the mean squared error (MSE) sense, and we also characterize the corresponding convergence rate. We further show that the asymptotic MSE can be made arbitrarily small through consensus step-size tuning, possibly at the cost of slowing down the transient error decay. Numerical experiments corroborate our findings and demonstrate the resilience of the proposed method to heavy-tailed (and infinite variance) communication noise. They also show that existing distributed methods, designed for finite-communication-noise-variance settings, fail in the presence of infinite variance noise.

math.OC↗

arXiv2025

Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry

We study large deviation upper bounds and mean-squared error (MSE) guarantees of a general framework of nonlinear stochastic gradient methods in the online setting, in the presence of heavy-tailed noise. Unlike existing works that rely on the closed form of a nonlinearity (typically clipping), our framework treats the nonlinearity in a black-box manner, allowing us to provide unified guarantees for a broad class of bounded nonlinearities, including many popular ones, like sign, quantization, normalization, as well as component-wise and joint clipping. We provide several strong results for a broad range of step-sizes in the presence of heavy-tailed noise with symmetric probability density function, positive in a neighbourhood of zero and potentially unbounded moments. In particular, for non-convex costs we provide a large deviation upper bound for the minimum norm-squared of gradients, showing an asymptotic tail decay on an exponential scale, at a rate $\sqrt{t} / \log(t)$. We establish the accompanying rate function, showing an explicit dependence on the choice of step-size, nonlinearity, noise and problem parameters. Next, for non-convex costs and the minimum norm-squared of gradients, we derive the optimal MSE rate $\widetilde{\mathcal{O}}(t^{-1/2})$. Moreover, for strongly convex costs and the last iterate, we provide an MSE rate that can be made arbitrarily close to the optimal rate $\mathcal{O}(t^{-1})$, improving on the state-of-the-art results in the presence of heavy-tailed noise. Finally, we establish almost sure convergence of the minimum norm-squared of gradients, providing an explicit rate, which can be made arbitrarily close to $o(t^{-1/4})$.

cs.LG↗

arXiv2025

Nonlinear Stochastic Gradient Descent and Heavy-tailed Noise: A Unified Framework and High-probability Guarantees

We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign, quantization, component-wise and joint clipping. In our work the nonlinearity is treated in a black-box manner, allowing us to establish unified guarantees for a broad range of nonlinear methods. For symmetric noise and non-convex costs we establish convergence of gradient norm-squared, at a rate $\widetilde{\mathcal{O}}(t^{-1/4})$, while for the last iterate of strongly convex costs we establish convergence to the population optima, at a rate $\mathcal{O}(t^{-ζ})$, where $ζ\in (0,1)$ depends on noise and problem parameters. Further, if the noise is a (biased) mixture of symmetric and non-symmetric components, we show convergence to a neighbourhood of stationarity, whose size depends on the mixture coefficient, nonlinearity and noise. Compared to state-of-the-art, who only consider clipping and require unbiased noise with bounded $p$-th moments, $p \in (1,2]$, we provide guarantees for a broad class of nonlinearities, without any assumptions on noise moments. While the rate exponents in state-of-the-art depend on noise moments and vanish as $p \rightarrow 1$, our exponents are constant and strictly better whenever $p < 6/5$ for non-convex and $p < 8/7$ for strongly convex costs. Experiments validate our theory, showing that clipping is not always the optimal nonlinearity, further underlining the value of a general framework.

cs.LG↗

arXiv2025

Distributed Sign Momentum with Local Steps for Training Transformers

Pre-training Transformer models is resource-intensive, and recent studies have shown that sign momentum is an efficient technique for training large-scale deep learning models, particularly Transformers. However, its application in distributed training remains underexplored. This paper investigates a novel communication-efficient distributed sign momentum method with multiple local steps, to cope with the scenarios where communicating at every step is prohibitive. Our proposed method allows for a broad class of base optimizers for local steps, and uses sign momentum in the global step, where momentum is generated from differences accumulated during local steps. For generic base optimizers, by approximating the sign operator with a randomized version that acts as a continuous analog in expectation, we present a general convergence analysis, which specializes to an $O(1/\sqrt{T})$ rate for a particular instance. When local step is stochastic gradient descent, we show an optimal $O(1/T^{1/4})$ rate in terms of $\ell_1$ gradient norm for nonconvex smooth cost functions. We extensively evaluate our method on the pre-training of various sized GPT-2 models from scratch, and the empirical results show significant improvement compared to other distributed methods with multiple local steps.

cs.LG↗