arXiv subjects

Javad Lavaei

Publications and source records attributed to Javad Lavaei.

At least 19 recordsLinked to original sources

arXiv2026

Structural Correspondence and Universal Approximation in Diagonal plus Low-Rank Neural Networks

The massive computational costs of scaling modern deep learning architectures have driven the widespread use of parameter-efficient low-rank structures, such as LoRA and low-rank factorization. However, theoretical guarantees for their expressive power are less explored, often relying on restrictive priors like a pretrained base matrix, ReLU activations or non-verifiable singularity conditions. We first investigate the limits of neural networks constrained strictly to low-rank manifolds without pretrained dense priors. We demonstrate a theoretical paradox: while purely rank-1 layers can exactly interpolate arbitrary scalar datasets, they collapse for function approximations. To overcome this bottleneck without surrendering parameter efficiency, we introduce a unified \textit{Structural Correspondence} framework. We prove that augmenting low-rank layers with only a minimal sparse diagonal component, say a Diagonal plus Low-Rank (DLoR) structure, is sufficient to reach Universal Approximation. We show that any full-rank transformation can be exactly reconstructed using these DLoR components by trading off network width (additive decomposition) or depth (multiplicative decomposition). By tracking asymptotic Taylor remainders, we prove that DLoR neural networks fully restore the Universal Approximation Theorem for general activation functions. Finally, we establish that multiplicative depth provides superior parameter-to-expressivity scaling compared to additive width. Our results show that dense matrices and specific activation functions are not topological prerequisites for universal expressivity.

cs.LG↗

arXiv2026

LLMs Should Express Uncertainty Explicitly

Large language models (LLMs) often produce confident yet incorrect answers, which can lead to risky failures in real-world applications. We study whether post-training can make a model's self-assessment explicit: when the model is uncertain, can it be trained to signal so within its own response? A central design question is where in the response this signal should be exposed -- during reasoning, while the answer is still being formed, or at the end, once the answer has been produced. We study both. For end-of-reasoning self-assessment, we train the model to verbalize a confidence score for its response, with the aim of high confidence on correct answers and low confidence on incorrect ones. For during-reasoning self-assessment, we train the model to emit the marker whenever its current reasoning state appears unreliable. Across factual reasoning tasks, both forms sharply reduce overconfident errors while improving answer quality, and both can be used as triggers for retrieval augmented generation (RAG) to improve the final response. We further analyze their internal mechanisms: end-of-reasoning verbalized confidence sharpens a confidence-related structure already present in the pretrained model, whereas during-reasoning emission teaches the model to mark high-risk reasoning steps, with parameter changes concentrated in the model's late layers.

cs.LG↗

arXiv2026

Huber-based Robust System Identification with Near-Optimal Guarantees Across Independent and Adversarial Regimes

Dynamical systems can confront one of two extreme types of disturbances: persistent zero-mean independent noise, and sparse nonzero-mean adversarial attacks, depending on the specific scenario being modeled. While mean-based estimators like least-squares are well-suited for the former, a median-based approach such as the $\ell_1$-norm estimator is required for the latter. In this paper, we propose a Huber-based estimator, characterized by a threshold constant $\mu$, to identify the governing matrix of a linearly parameterized nonlinear system from a single trajectory of length $T$. This formulation bridges the gap between mean- and median-based estimation, achieving provably robust error in both extreme disturbance scenarios under mild assumptions. In particular, for persistent zero-mean noise with a positive probability density around zero, the proposed estimator achieves an $\mathcal{O}(1/\sqrt{T})$ error rate if the disturbance is symmetric or the basis functions are linear. For arbitrary nonzero-mean attacks that occur at each time with probability smaller than 0.5, the error is bounded by $\mathcal{O}(\mu)$. We validate our theoretical results with experiments illustrating that integrating our approach into frameworks like SINDy yields robust identification of discrete-time systems.

math.OC↗

arXiv2026

A Trust-Region Interior-Point Stochastic Sequential Quadratic Programming Method

In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality constraints. In this setting, exact evaluations of the objective function and its gradient are unavailable, but their stochastic estimates can be constructed. In particular, at each iteration our method builds stochastic oracles, which estimate the objective value and gradient to satisfy proper adaptive accuracy conditions with a fixed probability. To handle inequality constraints, we adopt an interior-point method (IPM), in which the barrier parameter follows a prescribed decaying sequence. Under standard assumptions, we establish global almost-sure convergence of the proposed method to first-order stationary points. We implement the method on a subset of problems from the CUTEst test set, as well as on logistic regression problems, to demonstrate its practical performance.

math.OC↗

arXiv2026

Why is Normalization Preferred? A Worst-Case Complexity Theory for Stochastically Preconditioned SGD under Heavy-Tailed Noise

We develop a worst-case complexity theory for stochastically preconditioned stochastic gradient descent (SPSGD) and its accelerated variants under heavy-tailed noise, a setting that encompasses widely used adaptive methods such as Adam, RMSProp, and Shampoo. We assume the stochastic gradient noise has a finite $p$-th moment for some $p \in (1,2]$, and measure convergence after $T$ iterations. While clipping and normalization are parallel tools for stabilizing training of SGD under heavy-tailed noise, there is a fundamental separation in their worst-case properties in stochastically preconditioned settings. We demonstrate that normalization guarantees convergence to a first-order stationary point at rate $\mathcal{O}(T^{-\frac{p-1}{3p-2}})$ when problem parameters are known, and $\mathcal{O}(T^{-\frac{p-1}{2p}})$ when problem parameters are unknown, matching the optimal rates for normalized SGD, respectively. In contrast, we prove that clipping may fail to converge in the worst case due to the statistical dependence between the stochastic preconditioner and the gradient estimates. To enable the analysis, we develop a novel vector-valued Burkholder-type inequality that may be of independent interest. These results provide a theoretical explanation for the empirical preference for normalization over clipping in large-scale model training.

cs.LG↗

arXiv2026

System Identification under Noise and Attack Regimes: Agnostic and Composite Robustness

Dynamical systems often confront persistent zero-mean independent noise and/or sparse nonzero-mean adversarial attacks. While mean-based estimators like least-squares handle the former, the median-based $\ell_1$-norm estimator is effective for the latter. In this paper, we develop robust system identification frameworks to identify a linearly-parametrized nonlinear system from a single trajectory of length $T$. We tackle two types of robustness: (1) $\textit{agnostic robustness}$ under either pure noise or pure attacks without knowing which regime is active; and (2) $\textit{composite robustness}$ under concurrent noise and attacks. We first show that the Huber estimator attains agnostic robustness by achieving an $\mathcal{O}(1/\sqrt{T})$ error rate for the noise regime and a bounded error for the attack regime, serving as a one-stage estimator interpolating between mean- and median-based methods. We then prove that no convex one-stage estimator is consistent under both noise and attacks, which motivates a two-stage estimation that sequentially applies median- and mean-based estimators for composite robustness. These dual notions of robustness require a corresponding duality in estimator design, providing a solid foundation for robust control in safety-critical systems.

math.OC↗

arXiv2026

3DGS$^2$-TR: Scalable Second-Order Trust-Region Method for 3D Gaussian Splatting

We propose 3DGS$^2$-TR,a second-order optimizer for accelerating the scene training problem in 3D Gaussian Splatting (3DGS). Unlike existing second-order approaches that rely on explicit or dense curvature representations, such as 3DGS-LM (H\"ollein et al., 2025) or 3DGS2 (Lan et al., 2025), our method approximates curvature using only the diagonal of the Hessian matrix, efficiently via Hutchinson's method. Our approach is fully matrix-free and has the same complexity as ADAM (Kingma, 2024), $O(n)$ in both computation and memory costs. To ensure stable optimization in the presence of strong nonlinearity in the 3DGS rasterization process, we introduce a parameter-wise trust-region technique based on the squared Hellinger distance, regularizing updates to Gaussian parameters. Under identical parameter initialization and without densification, 3DGS$^2$-TR is able to achieve better reconstruction quality on standard datasets, using 50% fewer training iterations compared to ADAM, while incurring less than 1GB of peak GPU memory overhead (17% more than ADAM and 85% less than 3DGS-LM), enabling scalability to very large scenes and potentially to distributed training settings.

cs.CV↗

arXiv2026

TRSVR: An Adaptive Stochastic Trust-Region Method with Variance Reduction

We propose a stochastic trust-region method for unconstrained nonconvex optimization that incorporates stochastic variance-reduced gradients (SVRG) to accelerate convergence. Unlike classical trust-region methods, the proposed algorithm relies solely on stochastic gradient information and does not require function value evaluations. The trust-region radius is adaptively adjusted based on a radius-control parameter and the stochastic gradient estimate. Under mild assumptions, we establish that the algorithm converges in expectation to a first-order stationary point. Moreover, the method achieves iteration and sample complexity bounds that match those of SVRG-based first-order methods, while allowing stochastic and potentially gradient-dependent second-order information. Extensive numerical experiments demonstrate that incorporating SVRG accelerates convergence, and that the use of trust-region methods and Hessian information further improves performance. We also highlight the impact of batch size and inner-loop length on efficiency, and show that the proposed method outperforms SGD and Adam on several machine learning tasks.

math.OC↗

arXiv2026

All-Pass Fractional OPF: A Solver-Friendly, Physics-Preserving Approximation of AC OPF

This paper presents a fractional approximation of the AC optimal power flow (AC OPF) problem based on an all-pass approximation of the exponential power flow kernel. The classical AC OPF relies on trigonometric coupling between bus voltage phasors, which yields a nonconvex program with oscillatory derivatives that can slow, or in some cases destabilize, interior-point methods. We replace the trigonometric terms with an all-pass fractional (APF) approximation whose real and imaginary components act as smooth surrogates for the cosine and sine functions, and we introduce a pre-rotation to shift the argument of the approximation toward its most accurate region, ensuring that the reformulated power flow model preserves physical loss behavior, maintains the symmetry of the classical kernels, and improves the conditioning of the Jacobian and Hessian matrices. The proposed APF OPF formulation remains nonconvex, as in the classical model, but it eliminates trigonometric evaluations and empirically produces larger and more stable Newton steps under standard interior-point solvers. Numerical results on more than 25 IEEE and PGLib test systems ranging from 9 to 10{,}000 buses demonstrate that the APF OPF model achieves solutions with accuracy comparable to that of the classical formulation while reducing solver times, indicating a more solver-friendly nonconvex representation of AC OPF. All code, functions, verification scripts, and generated results are publicly available on \href{https://github.com/LSU-RAISE-LAB/APF-OPF}{GitHub}, along with a README describing how to run and reproduce the experiments.

eess.SY↗

arXiv2025

StyleBench: Evaluating thinking styles in Large Language Models

Structured reasoning can improve the inference performance of large language models (LLMs), but it also introduces computational cost and control constraints. When additional reasoning structure helps, and when it instead reduces efficiency or robustness, remains poorly understood. We propose StyleBench, where we study reasoning structure as a capacity-constrained design choice rather than a fixed inference recipe. We evaluate five representative reasoning styles: Chain-of-Thought, Tree-of-Thought, Algorithm-of-Thought, Sketch-of-Thought, and Chain-of-Draft across five reasoning tasks and 15 open-source LLMs ranging from 270M to 120B parameters. We find that greater structural complexity improves accuracy only in limited regimes defined by task demands and model capacity. Search-based styles help on open-ended combinatorial problems but fail on smaller models, while concise styles achieve large efficiency gains on structured tasks without sacrificing performance. We also identify systematic failure modes in smaller models, including premature guessing and weak adherence to reasoning-control instructions. To study adaptive reasoning control, we further compare supervised and reinforcement-based strategy selection on Qwen-7B-Instruct. Supervised fine-tuning collapses to shallow style preferences, whereas GRPO learns stronger adaptive control and improves downstream performance. Together, these results clarify when structured reasoning is useful, when it is wasteful, and why learning to choose a reasoning strategy is itself a challenging inference problem, we open source the benchmark in https://github.com/JamesJunyuGuo/Style_Bench.

cs.LG↗

arXiv2025

Bridging Batch and Streaming Estimations to System Identification under Adversarial Attacks

System identification in modern engineering systems faces emerging challenges from unanticipated adversarial attacks beyond existing detection mechanisms. In this work, we obtain a provably accurate estimate of the Markov parameter matrix of order $k$ to identify partially observed linear systems, in which the probability of having an attack at each time is $O(1/k)$. We show that given the batch data accumulated up to time $T^*$, the $\ell_2$-norm estimator achieves an error decaying exponentially as $k$ grows. We then propose a stochastic projected subgradient descent algorithm on streaming data that produces an estimate at each time $t<T^*$, in which case the expected estimation error proves to be the larger of $O(k/\sqrt{t})$ and an exponentially decaying term in $k$. This stochastic approach illustrates how non-smooth estimators can leverage first-order methods despite lacking recursive formulas. Finally, we integrate batch and streaming estimations to recover the Hankel matrix using the appropriate estimates of the Markov parameter matrix, which enables the synthesis of a robust adaptive controller based on the estimated balanced truncated model under adversarial attacks.

math.OC↗

arXiv2025

Few-Shot Test-Time Optimization Without Retraining for Semiconductor Recipe Generation and Beyond

We introduce Model Feedback Learning (MFL), a novel test-time optimization framework for optimizing inputs to pre-trained AI models or deployed hardware systems without requiring any retraining of the models or modifications to the hardware. In contrast to existing methods that rely on adjusting model parameters, MFL leverages a lightweight reverse model to iteratively search for optimal inputs, enabling efficient adaptation to new objectives under deployment constraints. This framework is particularly advantageous in real-world settings, such as semiconductor manufacturing recipe generation, where modifying deployed systems is often infeasible or cost-prohibitive. We validate MFL on semiconductor plasma etching tasks, where it achieves target recipe generation in just five iterations, significantly outperforming both Bayesian optimization and human experts. Beyond semiconductor applications, MFL also demonstrates strong performance in chemical processes (e.g., chemical vapor deposition) and electronic systems (e.g., wire bonding), highlighting its broad applicability. Additionally, MFL incorporates stability-aware optimization, enhancing robustness to process variations and surpassing conventional supervised learning and random search methods in high-dimensional control settings. By enabling few-shot adaptation, MFL provides a scalable and efficient paradigm for deploying intelligent control in real-world environments.

cs.LG↗

arXiv2025

On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks

This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges posed by an adversary with access to the full information history, provided that the attack times are sparse, i.e., the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under probabilistic adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works.

math.OC↗

arXiv2025

Coordinating Distributed Energy Resources with Nodal Pricing in Distribution Networks: a Game-Theoretic Approach

We propose a real-time nodal pricing mechanism for cost minimization and voltage control in a distribution network with autonomous distributed energy resources and analyze the resulting market using stochastic game theory. Unlike existing methods, the proposed pricing scheme does not require device-aware centralized coordination or communication between prosumers. By developing new sufficient conditions under which a stochastic game is a Markov potential game, we show that the problem of computing an equilibrium for the proposed model is equivalent to solving a single-agent Markov Decision Process. These new conditions are general and may apply to other applications. We compute the equilibrium for an IEEE test system to empirically demonstrate the effectiveness of the pricing policy.

eess.SY↗

arXiv2025

System Identification from Partial Observations under Adversarial Attacks

This paper is concerned with the partially observed linear system identification, where the goal is to obtain reasonably accurate estimation of the balanced truncation of the true system up to order $k$ from output measurements. We consider the challenging case of system identification under adversarial attacks, where the probability of having an attack at each time is $\Theta(1/k)$ while the value of the attack is arbitrary. We first show that the $\ell_1$-norm estimator exactly identifies the true Markov parameter matrix for nilpotent systems under any type of attack. We then build on this result to extend it to general systems and show that the estimation error exponentially decays as $k$ grows. The estimated balanced truncation model accordingly shows an exponentially decaying error for the identification of the true system up to a similarity transformation. This work is the first to provide the input-output analysis of the system with partial observations under arbitrary attacks.

math.OC↗

arXiv2025

High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise

In this paper, we consider nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method and establish its high-probability iteration complexity bounds for identifying first- and second-order $\epsilon$-stationary points. In our algorithm, we assume that exact objective values, gradients, and Hessians are not directly accessible but can be estimated via zeroth-, first-, and second-order probabilistic oracles. Compared to existing complexity studies of SSQP methods that rely on a zeroth-order oracle with sub-exponential tail noise (i.e., light-tailed) and focus mostly on first-order stationarity, our analysis accommodates biased (also referred to as irreducible in the literature) and heavy-tailed noise in the zeroth-order oracle, and significantly extends the analysis to second-order stationarity. We show that under heavy-tailed noise conditions, our SSQP method achieves the same high-probability first-order iteration complexity bounds as in the light-tailed noise setting, while further exhibiting promising second-order iteration complexity bounds. Specifically, the method identifies a first-order $\epsilon$-stationary point in $\mathcal{O}(\epsilon^{-2})$ iterations and a second-order $\epsilon$-stationary point in $\mathcal{O}(\epsilon^{-3})$ iterations with high probability, provided that $\epsilon$ is lower bounded by a constant determined by the bias magnitude (i.e., the irreducible noise) in the estimation. We validate our theoretical findings and evaluate practical performance of our method on CUTEst benchmark test set.

math.OC↗

arXiv2025

Subgradient Method for System Identification with Non-Smooth Objectives

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting, where the optimization problems to be solved evolve over time as new measurements are collected, and we establish linear convergence to the ground-truth system for both the best and Polyak step sizes after a burn-in period. We further characterize sublinear convergence of the iterates under constant and diminishing step sizes, which require only minimal information and thus offer broad applicability. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.

math.OC↗

arXiv2025

Don't Trade Off Safety: Diffusion Regularization for Constrained Offline RL

Constrained reinforcement learning (RL) seeks high-performance policies under safety constraints. We focus on an offline setting where the agent has only a fixed dataset -- common in realistic tasks to prevent unsafe exploration. To address this, we propose Diffusion-Regularized Constrained Offline Reinforcement Learning (DRCORL), which first uses a diffusion model to capture the behavioral policy from offline data and then extracts a simplified policy to enable efficient inference. We further apply gradient manipulation for safety adaptation, balancing the reward objective and constraint satisfaction. This approach leverages high-quality offline data while incorporating safety requirements. Empirical results show that DRCORL achieves reliable safety performance, fast inference, and strong reward outcomes across robot learning tasks. Compared to existing safe offline RL methods, it consistently meets cost limits and performs well with the same hyperparameters, indicating practical applicability in real-world scenarios.

cs.LG↗