arXiv subjects

Mehrdad Mahdavi

Publications and source records attributed to Mehrdad Mahdavi.

At least 19 recordsLinked to original sources

arXiv2026

Conditional Optimal Bridge for Riemannian Activation Steering

Activation steering offers a lightweight alternative to fine-tuning for controlling large language models at inference time. While many existing methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions, they do so heuristically rather than deriving it from a principled optimization problem. Moreover, these methods produce query-independent steering directions that can degrade performance on both in-distribution and out-of-distribution (OOD) inputs. We introduce \textsc{Cobras} (Conditional Optimal Bridge for Riemannian Activation Steering), which addresses both limitations by casting activation steering as a Schr\"{o}dinger Bridge on the residual-stream hypersphere. This formulation yields, to our knowledge, the first principled derivation of the log-density-ratio steering objective from a well-posed optimization problem. Solving the bridge via entropic optimal transport and extracting the probability flow ODE recovers the widely used density-ratio gradient as a special case when the Sinkhorn potentials are uniform. Crucially, the Schr\"{o}dinger potentials are evaluated at the current activation, making the resulting steering direction inherently query-adaptive. Empirically, across four models and three alignment axes (helpfulness, truthfulness, and detoxification), \textsc{Cobras} consistently outperforms prior activation steering baselines while avoiding the OOD degradation commonly observed in existing methods. The code can be found at https://github.com/arshandalili/cobras.

cs.LG↗

arXiv2026

Correlation-Aware Contextual Bandits with Surrogate Rewards for LLM Routing

We study contextual bandit problems with correlated arms and access to surrogate reward signals produced by a machine learning model, motivated by applications such as large language model (LLM) routing. Unlike classical contextual bandits that rely solely on bandit feedback and assume conditional independence across arms, our setting allows context-dependent inter-arm correlations and auxiliary reward information that may be noisy or misspecified. We propose algorithms that leverage such surrogate rewards through two complementary designs. A coupled reward-mixing approach pools true and surrogate rewards to accelerate learning when surrogate signals are reliable, while a decoupled prediction-mixing approach maintains separate estimators for bandit feedback and surrogate rewards and adaptively combines their predictions. This decoupling yields robustness to surrogate misspecification, recovering regret guarantees comparable to reward-only bandit methods in the worst case, while achieving improved regret when surrogate predictions are sufficiently informative. We provide theoretical regret analyses for both approaches and evaluate them on LLM routing benchmarks under varying accuracy versus cost trade-offs. The results demonstrate improved sample efficiency and consistently better accuracy-cost trade-offs compared to standard contextual bandit baselines and strong static routing methods.

cs.LG↗

arXiv2026

Curvature-Guided Module Localization for Low-Rank Detoxification of Backdoored Large Language Models

Backdoor attacks pose a serious threat to large language models (LLMs) by causing otherwise benign systems to produce attacker-specified malicious behavior when a hidden trigger is present. In this work, we study post hoc detoxification of backdoored LLMs in a practical setting where the defender has access to the poisoned model but does not wish to retrain the full network from scratch. We propose a mechanistically guided weight-space repair framework that first localizes modules involved in propagating trigger-induced behavior using activation patching and Fisher/K-FAC curvature analysis, and then applies targeted low-rank repair to only the most influential modules. We evaluate the method on poisoned variants of \texttt{Llama-3.2-1B-Instruct} with triggers inserted at the beginning, middle, and end of otherwise benign prompts. Results show that the proposed approach substantially suppresses trigger-conditioned malicious responses while preserving benign model behavior. These findings suggest that backdoor removal in LLMs can be formulated as a localized structural repair problem rather than only a broad behavioral alignment problem.

cs.CR↗

arXiv2026

Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretability

Sparse Autoencoders (SAEs) are widely used for mechanistic interpretability in large language models, yet their formulation assigns each latent feature a single decoder direction, implicitly assuming features to be one-dimensional. We show that this assumption mismatches with the multi-dimensional structure of model features, provably inducing feature splitting through two distinct mechanisms. Geometrically, reconstructing a feature of intrinsic dimension $d_i \ge 2$ to error $\varepsilon$ with single-direction decoders forces a number of atoms that is exponential in $d_i$. From an end-to-end optimization perspective, this splitting is not merely possible but actively preferred. We prove that there exists a continuous path from the true $d_i$-dimensional basis to a strictly lower risk of the $\ell_1$-regularized SAE objective, whose descent directions drive any trained dictionary into that exponential regime. A single coherent feature is therefore fragmented across many near-collinear latents, producing spurious multiplicity and obscuring the intrinsic geometry. Motivated by this, we introduce Subspace-Aware Sparse Autoencoders (SASA), which replace single-vector decoders with learned decoder subspaces, enforce block sparsity via Top-$s$ group gating, and adapt each group's effective rank with a nuclear-norm regularizer. We then show that once the block size satisfies $r \ge d_i$, a single group not only can represent the entire feature slice but is the global minimizer of the SASA objective. This consolidation yields a sample complexity polynomial in $d_i$ rather than exponential -- a decisive advantage given that every training activation costs an LLM forward pass. Empirically, on GPT-2 and Mistral-7B, SASA reduces feature splitting and absorption, improves monosemanticity and interpretability, and matches or exceeds standard SAEs while training on roughly half the token budget.

cs.LG↗

arXiv2025

Merge before Forget: A Single LoRA Continual Learning via Continual Merging

Parameter-efficient continual learning has emerged as a promising approach for large language models (LLMs) to mitigate catastrophic forgetting while enabling adaptation to new tasks. Current Low-Rank Adaptation (LoRA) continual learning techniques often retain and freeze previously learned LoRAs or generate data representations to overcome forgetting, typically utilizing these to support new LoRAs learn new tasks. However, these methods not only ignore growing computational memory with tasks and limited storage space but also suffer from potential task interference due to the lack of effective LoRA merging mechanisms. In this paper, we propose a novel continual learning method that orthogonally initializes and sequentially merges LoRAs updates into a single unified LoRA. Our method leverages orthogonal basis extraction from previously learned LoRA to initialize the learning of new tasks, further exploits the intrinsic asymmetry property of LoRA components by using a time-aware scaling mechanism to balance new and old knowledge during continual merging. Our approach maintains constant memory complexity with respect to the number of tasks, minimizes interference between past and new tasks via orthogonal basis initialization, and improves performance over asymmetric LoRA merging via adaptive scaling. We provide theoretical analysis to justify our design and conduct extensive experiments across diverse continual learning benchmarks using various Llama models, demonstrating the effectiveness and efficiency of our method.

cs.LG↗

arXiv2025

Model Merging via Multi-Teacher Knowledge Distillation

Model merging has emerged as a lightweight alternative to joint multi-task learning (MTL), yet the generalization properties of merged models remain largely unexplored. Establishing such theoretical guarantees is non-trivial, as the merging process typically forbids access to the original training data and involves combining fine-tuned models trained on fundamentally heterogeneous data distributions. Without a principled understanding of these dynamics, current methods often rely on heuristics to approximate the optimal combination of parameters. This dependence is most critical in coefficient scaling, the weighting factors that modulate the magnitude of each fine-tuned model's contribution to the shared parameter. However, without a principled objective to guide their selection, these methods lead to brittle performance and are highly sensitive to scaling initialization. We address this gap by (i) establishing a novel flatness-aware PAC-Bayes generalization bound specifically for the model merging setting. This analysis introduces a "cross-task heterogeneity" term that formally captures the mismatch between diverse fine-tuned model priors and the target multi-task distributions. Guided by this theoretical insight, (ii) we frame model merging as multi-teacher knowledge distillation on scarce, unlabeled data. We formally demonstrate that minimizing the student-teacher Kullback-Leibler divergence directly tightens the upper bound on the merged model's excess risk. Guided by the flatness-aware bound derived, (iii) we operationalize this objective via SAMerging, a method that employs Sharpness-Aware Minimization (SAM) to find flat minima. Empirically, SAMerging establishes a new state of the art across vision and NLP benchmarks, achieving remarkable performance. The code is available at https://github.com/arshandalili/SAMerging.

cs.LG↗

arXiv2025

On the Convergence and Stability of Distributed Sub-model Training

As learning models continue to grow in size, enabling on-device local training of these models has emerged as a critical challenge in federated learning. A popular solution is sub-model training, where the server only distributes randomly sampled sub-models to the edge clients, and clients only update these small models. However, those random sampling of sub-models may not give satisfying convergence performance. In this paper, observing the success of SGD with shuffling, we propose a distributed shuffled sub-model training, where the full model is partitioned into several sub-models in advance, and the server shuffles those sub-models, sends each of them to clients at each round, and by the end of local updating period, clients send back the updated sub-models, and server averages them. We establish the convergence rate of this algorithm. We also study the generalization of distributed sub-model training via stability analysis, and find that the sub-model training can improve the generalization via amplifying the stability of training process. The extensive experiments also validate our theoretical findings.

cs.LG↗

arXiv2025

NaviSense: A Multimodal Assistive Mobile application for Object Retrieval by Persons with Visual Impairment

People with visual impairments often face significant challenges in locating and retrieving objects in their surroundings. Existing assistive technologies present a trade-off: systems that offer precise guidance typically require pre-scanning or support only fixed object categories, while those with open-world object recognition lack spatial feedback for reaching the object. To address this gap, we introduce 'NaviSense', a mobile assistive system that combines conversational AI, vision-language models, augmented reality (AR), and LiDAR to support open-world object detection with real-time audio-haptic guidance. Users specify objects via natural language and receive continuous spatial feedback to navigate toward the target without needing prior setup. Designed with insights from a formative study and evaluated with 12 blind and low-vision participants, NaviSense significantly reduced object retrieval time and was preferred over existing tools, demonstrating the value of integrating open-world perception with precise, accessible guidance.

cs.HC↗

arXiv2025

Harnessing Optimization Dynamics for Curvature-Informed Model Merging

Model merging is an effective post-training strategy for composing capabilities in large language models without joint retraining. We study this in the supervised fine-tuning (SFT) stage, where multiple capability-based SFT checkpoints -- spanning math, code, precise instruction following, general instruction following, and knowledge recall -- must be consolidated into a single model. We introduce Optimization Trajectory Aware (OTA) Merging, a curvature-aware aggregation that leverages optimizer second-moment statistics as a diagonal curvature proxy to reweight parameter edits and mitigate interference. Complementing OTA, we propose Fast Fisher Grafting (FFG), a curvature-driven task-localization step that sparsifies conflicting or low-importance edits. FFG induces extremely low-rank masks concentrated in early attention query/key projections and token embeddings, exploiting shared curvature across capabilities. We further develop a memory-light compression of the second moments that preserves OTA's effect. Across diverse capability-based SFT checkpoints, OTA+FFG improves merged-model quality over strong weight-space baselines, reduces negative transfer, and remains robust across sparsity levels. Analyses reveal substantial curvature overlap between checkpoints, offering a novel lens on why simple linear merging can be effective in practice. Ablations confirm that FFG is critical for reducing task interference and that the compressed second moments retain the gains of the full formulation. To facilitate reproducibility, we open-source all code, training and evaluation scripts, visualization artifacts, and capability-specific SFT checkpoints at https://github.com/pmahdavi/ota-merge.

cs.LG↗

arXiv2025

Low-rank Momentum Factorization for Memory Efficient Training

Fine-tuning large foundation models presents significant memory challenges due to stateful optimizers like AdamW, often requiring several times more GPU memory than inference. While memory-efficient methods like parameter-efficient fine-tuning (e.g., LoRA) and optimizer state compression exist, recent approaches like GaLore bridge these by using low-rank gradient projections and subspace moment accumulation. However, such methods may struggle with fixed subspaces or computationally costly offline resampling (e.g., requiring full-matrix SVDs). We propose Momentum Factorized SGD (MoFaSGD), which maintains a dynamically updated low-rank SVD representation of the first-order momentum, closely approximating its full-rank counterpart throughout training. This factorization enables a memory-efficient fine-tuning method that adaptively updates the optimization subspace at each iteration. Crucially, MoFaSGD leverages the computed low-rank momentum factors to perform efficient spectrally normalized updates, offering an alternative to subspace moment accumulation. We establish theoretical convergence guarantees for MoFaSGD, proving it achieves an optimal rate for non-convex stochastic optimization under standard assumptions. Empirically, we demonstrate MoFaSGD's effectiveness on large language model alignment benchmarks, achieving a competitive trade-off between memory reduction (comparable to LoRA) and performance compared to state-of-the-art low-rank optimization methods. Our implementation is available at https://github.com/pmahdavi/MoFaSGD.

cs.LG↗

arXiv2025

Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oracles

We present quantum speedups for sampling from distributions of the form $\pi\propto e^{-f}$ on $\mathbb{R}^d$. We consider two stochastic oracle models: a stochastic gradient oracle, where $f=\frac{1}{n}\sum_{i=1}^n f_i $ and component gradients $\{\nabla f_i\}_{i \in [n]}$ are available, and a stochastic evaluation oracle, where only noisy values of $f$ are available. Our framework accelerates classical stochastic Langevin Monte Carlo (LMC) and Hamiltonian Monte Carlo (HMC) algorithms by replacing stochastic gradient estimators with variance-controlled quantum mean estimation and gradient estimation subroutines. Unlike quantum walk based approaches, our algorithms do not require reversibility or exact gradients, and they preserve the structure of the underlying Markov chain. In the finite-sum setting, quantum mean estimation combined with classical variance-reduction techniques improves the stochastic gradient-query complexity for the approximate sampling task. In the stochastic zeroth-order setting, we develop gradient estimators robust to noisy function evaluations, yielding improved evaluation complexity for LMC and HMC. These results apply to strongly log-concave and/or non-log-concave distributions satisfying a log-Sobolev inequality, with convergence guarantees in Wasserstein distance and Kullback--Leibler divergence. We also show that faster sampling methods lead to quantum speedups for optimization, including for non-smooth and approximately convex objectives.

quant-ph↗

arXiv2024

Stochastic Compositional Minimax Optimization with Provable Convergence Guarantees

Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional minimax problem, which involves optimizing a minimax loss with a compositional structure either in primal , dual, or both primal and dual variables. We introduce a simple yet effective algorithm, stochastically Corrected stOchastic gradient Descent Ascent (CODA), which is a descent ascent type algorithm with compositional correction steps, and establish its convergence rate in aforementioned three settings. In the presence of the compositional structure in primal, the objective function typically becomes nonconvex in primal due to function composition. Thus, we consider the nonconvex-strongly-concave and nonconvex-concave settings and show that CODA can efficiently converge to a stationary point. In the case of composition on the dual, the objective function becomes nonconcave in the dual variable, and we demonstrate convergence in the strongly-convex-nonconcave and convex-nonconcave setting. In the case of composition on both variables, the primal and dual variables may lose convexity and concavity, respectively. Therefore, we anaylze the convergence in weakly-convex-weakly-concave setting. We also give a variance reduction version algorithm, CODA+, which achieves the best known rate on nonconvex-strongly-concave and nonconvex-concave compositional minimax problem. This work initiates the theoretical study of the stochastic compositional minimax problem on various settings and may inform modern machine learning scenarios such as domain adaptation or robust model-agnostic meta-learning.

math.OC↗

arXiv2024

On the Generalization Ability of Unsupervised Pretraining

Recent advances in unsupervised learning have shown that unsupervised pre-training, followed by fine-tuning, can improve model generalization. However, a rigorous understanding of how the representation function learned on an unlabeled dataset affects the generalization of the fine-tuned model is lacking. Existing theoretical research does not adequately account for the heterogeneity of the distribution and tasks in pre-training and fine-tuning stage. To bridge this gap, this paper introduces a novel theoretical framework that illuminates the critical factor influencing the transferability of knowledge acquired during unsupervised pre-training to the subsequent fine-tuning phase, ultimately affecting the generalization capabilities of the fine-tuned model on downstream tasks. We apply our theoretical framework to analyze generalization bound of two distinct scenarios: Context Encoder pre-training with deep neural networks and Masked Autoencoder pre-training with deep transformers, followed by fine-tuning on a binary classification task. Finally, inspired by our findings, we propose a novel regularization method during pre-training to further enhances the generalization of fine-tuned model. Overall, our results contribute to a better understanding of unsupervised pre-training and fine-tuning paradigm, and can shed light on the design of more effective pre-training algorithms.

cs.LG↗

arXiv2024

On the Generalization Capability of Temporal Graph Learning Algorithms: Theoretical Insights and a Simpler Method

Temporal Graph Learning (TGL) has become a prevalent technique across diverse real-world applications, especially in domains where data can be represented as a graph and evolves over time. Although TGL has recently seen notable progress in algorithmic solutions, its theoretical foundations remain largely unexplored. This paper aims at bridging this gap by investigating the generalization ability of different TGL algorithms (e.g., GNN-based, RNN-based, and memory-based methods) under the finite-wide over-parameterized regime. We establish the connection between the generalization error of TGL algorithms and "the number of layers/steps" in the GNN-/RNN-based TGL methods and "the feature-label alignment (FLA) score", where FLA can be used as a proxy for the expressive power and explains the performance of memory-based methods. Guided by our theoretical analysis, we propose Simplified-Temporal-Graph-Network, which enjoys a small generalization error, improved overall performance, and lower model complexity. Extensive experiments on real-world datasets demonstrate the effectiveness of our method. Our theoretical findings and proposed algorithm offer essential insights into TGL from a theoretical standpoint, laying the groundwork for the designing practical TGL algorithms in future studies.

cs.LG↗

arXiv2024

Understanding Deep Gradient Leakage via Inversion Influence Functions

Deep Gradient Leakage (DGL) is a highly effective attack that recovers private training images from gradient vectors. This attack casts significant privacy challenges on distributed learning from clients with sensitive data, where clients are required to share gradients. Defending against such attacks requires but lacks an understanding of when and how privacy leakage happens, mostly because of the black-box nature of deep networks. In this paper, we propose a novel Inversion Influence Function (I$^2$F) that establishes a closed-form connection between the recovered images and the private gradients by implicitly solving the DGL problem. Compared to directly solving DGL, I$^2$F is scalable for analyzing deep networks, requiring only oracle access to gradients and Jacobian-vector products. We empirically demonstrate that I$^2$F effectively approximated the DGL generally on different model architectures, datasets, modalities, attack implementations, and perturbation-based defenses. With this novel tool, we provide insights into effective gradient perturbation directions, the unfairness of privacy protection, and privacy-preferred model initialization. Our codes are provided in https://github.com/illidanlab/inversion-influence-function.

cs.LG↗

arXiv2023

Mixture Weight Estimation and Model Prediction in Multi-source Multi-target Domain Adaptation

We consider the problem of learning a model from multiple heterogeneous sources with the goal of performing well on a new target distribution. The goal of learner is to mix these data sources in a target-distribution aware way and simultaneously minimize the empirical risk on the mixed source. The literature has made some tangible advancements in establishing theory of learning on mixture domain. However, there are still two unsolved problems. Firstly, how to estimate the optimal mixture of sources, given a target domain; Secondly, when there are numerous target domains, how to solve empirical risk minimization (ERM) for each target using possibly unique mixture of data sources in a computationally efficient manner. In this paper we address both problems efficiently and with guarantees. We cast the first problem, mixture weight estimation, as a convex-nonconcave compositional minimax problem, and propose an efficient stochastic algorithm with provable stationarity guarantees. Next, for the second problem, we identify that for certain regimes, solving ERM for each target domain individually can be avoided, and instead parameters for a target optimal model can be viewed as a non-linear function on a space of the mixture coefficients. Building upon this, we show that in the offline setting, a GD-trained overparameterized neural network can provably learn such function to predict the model of target domain instead of solving a designated ERM problem. Finally, we also consider an online setting and propose a label efficient online algorithm, which predicts parameters for new targets given an arbitrary sequence of mixing coefficients, while enjoying regret guarantees.

cs.LG↗

arXiv2023

Distributed Personalized Empirical Risk Minimization

This paper advocates a new paradigm Personalized Empirical Risk Minimization (PERM) to facilitate learning from heterogeneous data sources without imposing stringent constraints on computational resources shared by participating devices. In PERM, we aim to learn a distinct model for each client by learning who to learn with and personalizing the aggregation of local empirical losses by effectively estimating the statistical discrepancy among data distributions, which entails optimal statistical accuracy for all local distributions and overcomes the data heterogeneity issue. To learn personalized models at scale, we propose a distributed algorithm that replaces the standard model averaging with model shuffling to simultaneously optimize PERM objectives for all devices. This also allows us to learn distinct model architectures (e.g., neural networks with different numbers of parameters) for different clients, thus confining underlying memory and compute resources of individual clients. We rigorously analyze the convergence of the proposed algorithm and conduct experiments that corroborate the effectiveness of the proposed paradigm.

cs.LG↗

arXiv2023

Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functions

We present quantum algorithms for sampling from non-logconcave probability distributions in the form of $π(x) \propto \exp(-βf(x))$. Here, $f$ can be written as a finite sum $f(x):= \frac{1}{N}\sum_{k=1}^N f_k(x)$. Our approach is based on quantum simulated annealing on slowly varying Markov chains derived from unadjusted Langevin algorithms, removing the necessity for function evaluations which can be computationally expensive for large data sets in mixture modeling and multi-stable systems. We also incorporate a stochastic gradient oracle that implements the quantum walk operators inexactly by only using mini-batch gradients. As a result, our stochastic gradient based algorithm only accesses small subsets of data points in implementing the quantum walk. One challenge of quantizing the resulting Markov chains is that they do not satisfy the detailed balance condition in general. Consequently, the mixing time of the algorithm cannot be expressed in terms of the spectral gap of the transition density, making the quantum algorithms nontrivial to analyze. To overcome these challenges, we first build a hypothetical Markov chain that is reversible, and also converges to the target distribution. Then, we quantified the distance between our algorithm's output and the target distribution by using this hypothetical chain as a bridge to establish the total complexity. Our quantum algorithms exhibit polynomial speedups in terms of both dimension and precision dependencies when compared to the best-known classical algorithms.

quant-ph↗