arXiv subjects

Ali Jadbabaie

Publications and source records attributed to Ali Jadbabaie.

At least 19 recordsLinked to original sources

arXiv2026

How Data Shapes RoPE Frequency Usage: From Positional Scale Matching to Length Generalization

Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width $W$, the optimal frequency scales as $1/W$. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.

cs.LG↗

arXiv2026

Online Learning for Supervisory Switching Control

We study supervisory switching control for partially-observed linear dynamical systems. The objective is to identify and deploy a suitable controller for the unknown system by periodically selecting among a collection of $N$ candidate controllers, some of which may destabilize the underlying system. While classical estimator-based supervisory control guarantees asymptotic stability, it lacks quantitative finite-time performance bounds. Conversely, current non-asymptotic methods in both online learning and system identification require restrictive assumptions that are incompatible in a control setting, such as system stability, which preclude testing potentially unstable controllers. To bridge this gap, we propose a novel, non-asymptotic analysis of supervisory control that adapts multi-armed bandit algorithms to a control-theoretic setting. The proposed data-driven algorithm evaluates candidate controllers via scoring criteria that leverage system observability to isolate the effects of state history, enabling both detection of destabilizing controllers and accurate system identification. We present two algorithmic variants with dimension-free, finite-time guarantees, where each identifies the matching controller in $O(N \log^2 N)$ steps, while simultaneously achieving finite $L_2$-gain with respect to system disturbances.

math.OC↗

arXiv2025

Is Your Conditional Diffusion Model Actually Denoising?

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that when these models are queried conditionally, their generations consistently deviate from the idealized "denoising" process upon which diffusion models are formulated, inducing disagreement between popular sampling algorithms (e.g. DDPM, DDIM). We introduce Schedule Deviation, a rigorous measure which captures the rate of deviation from a standard denoising process, and provide a methodology to compute it. Crucially, we demonstrate that the deviation from an idealized denoising process occurs irrespective of the model capacity or amount of training data. We posit that this phenomenon occurs due to the difficulty of bridging distinct denoising flows across different parts of the conditioning space and show theoretically how such a phenomenon can arise through an inductive bias towards smoothness.

cs.LG↗

arXiv2025

Network and Risk Analysis of Surety Bonds

Surety bonds are financial agreements between a contractor (principal) and obligee (project owner) to complete a project. However, most large-scale projects involve multiple contractors, creating a network and introducing the possibility of incomplete obligations to propagate and result in project failures. Typical models for risk assessment assume independent failure probabilities within each contractor. However, we take a network approach, modeling the contractor network as a directed graph where nodes represent contractors and project owners and edges represent contractual obligations with associated financial records. To understand risk propagation throughout the contractor network, we extend the celebrated Friedkin-Johnsen model and introduce a stochastic process to simulate principal failures across the network. From a theoretical perspective, we show that under natural monotonicity conditions on the contractor network, incorporating network effects leads to increases in the average risk for the surety organization. We further use data from a partnering insurance company to validate our findings, estimating an approximately 2% higher exposure when accounting for network effects.

q-fin.RM↗

arXiv2025

Unbiased Regression-Adjusted Estimation of Average Treatment Effects in Randomized Controlled Trials

This article introduces a leave-one-out regression adjustment (LOORA) for estimating average treatment effects in randomized controlled trials. In finite samples, LOORA removes the bias of conventional regression adjustment and yields exact variance formulas for regression-adjusted Horvitz-Thompson and difference-in-means estimators. Ridge regularization curbs the influence of high-leverage observations, improving stability and precision in small samples. In large samples, LOORA matches the variance of the regression-adjusted estimator in Lin (2013) while remaining exactly unbiased. Two within-subject experimental applications, each providing a realistic joint distribution of potential outcomes as ground truth, show that LOORA removes substantial bias and achieves confidence interval coverage close to the nominal level.

econ.EM↗

arXiv2025

Non-submodular Visual Attention for Robot Navigation

This paper presents a task-oriented computational framework to enhance Visual-Inertial Navigation (VIN) in robots, addressing challenges such as limited time and energy resources. The framework strategically selects visual features using a Mean Squared Error (MSE)-based, non-submodular objective function and a simplified dynamic anticipation model. To address the NP-hardness of this problem, we introduce four polynomial-time approximation algorithms: a classic greedy method with constant-factor guarantees; a low-rank greedy variant that significantly reduces computational complexity; a randomized greedy sampler that balances efficiency and solution quality; and a linearization-based selector based on a first-order Taylor expansion for near-constant-time execution. We establish rigorous performance bounds by leveraging submodularity ratios, curvature, and element-wise curvature analyses. Extensive experiments on both standardized benchmarks and a custom control-aware platform validate our theoretical results, demonstrating that these methods achieve strong approximation guarantees while enabling real-time deployment.

cs.RO↗

arXiv2025

Weak Identification in Peer Effects Estimation

It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared socioeconomic circumstances. The network linear-in-means model is a workhorse statistical model which incorporates these peer effects by including average neighborhood characteristics as regressors. Although the model's parameters are identifiable under mild structural conditions on the network, it remains unclear whether identification ensures reliable estimation in the "infill" asymptotic setting, where a single network grows in size. We show that when covariates are i.i.d. and the average network degree of nodes increases with the population size, standard estimators suffer from bias or slow convergence rates due to asymptotic collinearity induced by network averaging. As an alternative, we demonstrate that linear-in-sums models, which are based on aggregate rather than average neighborhood characteristics, do not exhibit such issues as long as the network degrees have some nontrivial variation, a condition satisfied by most network models.

math.ST↗

arXiv2025

A Test-Function Approach to Incremental Stability

This paper presents a novel framework for analyzing Incremental-Input-to-State Stability ($\delta$ISS) based on the idea of using rewards as "test functions." Whereas control theory traditionally deals with Lyapunov functions that satisfy a time-decrease condition, reinforcement learning (RL) value functions are constructed by exponentially decaying a Lipschitz reward function that may be non-smooth and unbounded on both sides. Thus, these RL-style value functions cannot be directly understood as Lyapunov certificates. We develop a new equivalence between a variant of incremental input-to-state stability of a closed-loop system under given a policy, and the regularity of RL-style value functions under adversarial selection of a H\"older-continuous reward function. This result highlights that the regularity of value functions, and their connection to incremental stability, can be understood in a way that is distinct from the traditional Lyapunov-based approach to certifying stability in control theory.

cs.LG↗

arXiv2025

The Pitfalls of Imitation Learning when Actions are Continuous

We study the problem of imitating an expert demonstrator in a discrete-time, continuous state-and-action control system. We show that, even if the dynamics satisfy a control-theoretic property called exponential stability (i.e. the effects of perturbations decay exponentially quickly), and the expert is smooth and deterministic, any smooth, deterministic imitator policy necessarily suffers error on execution that is exponentially larger, as a function of problem horizon, than the error under the distribution of expert training data. Our negative result applies to any algorithm which learns solely from expert data, including both behavior cloning and offline-RL algorithms, unless the algorithm produces highly "improper" imitator policies--those which are non-smooth, non-Markovian, or which exhibit highly state-dependent stochasticity--or unless the expert trajectory distribution is sufficiently "spread." We provide experimental evidence of the benefits of these more complex policy parameterizations, explicating the benefits of today's popular policy parameterizations in robot learning (e.g. action-chunking and diffusion policies). We also establish a host of complementary negative and positive results for imitation in control systems.

cs.LG↗

arXiv2025

Fast Tensor Completion via Approximate Richardson Iteration

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker, and tensor-train decompositions). However, such algebraic structure is often lost in TC regression problems, making direct extensions unclear. This work proposes a novel lifting method for approximately solving TC regression problems using structured TD regression algorithms as blackbox subroutines, enabling sublinear-time methods. We analyze the convergence rate of our approximate Richardson iteration-based algorithm, and our empirical study shows that it can be 100x faster than direct methods for CP completion on real-world tensors.

cs.DS↗

arXiv2025

GraphHash: Graph Clustering Enables Parameter Efficiency in Recommender Systems

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques are often employed to map multiple entities to the same embedding and thus reduce the size of the embedding tables. Concurrently, graph-based collaborative signals have emerged as powerful tools in recommender systems, yet their potential for optimizing embedding table reduction remains unexplored. This paper introduces GraphHash, the first graph-based approach that leverages modularity-based bipartite graph clustering on user-item interaction graphs to reduce embedding table sizes. We demonstrate that the modularity objective has a theoretical connection to message-passing, which provides a foundation for our method. By employing fast clustering algorithms, GraphHash serves as a computationally efficient proxy for message-passing during preprocessing and a plug-and-play graph-based alternative to traditional ID hashing. Extensive experiments show that GraphHash substantially outperforms diverse hashing baselines on both retrieval and click-through-rate prediction tasks. In particular, GraphHash achieves on average a 101.52% improvement in recall when reducing the embedding table size by more than 75%, highlighting the value of graph-based collaborative information for model reduction. Our code is available at https://github.com/snap-research/GraphHash.

cs.IR↗

arXiv2025

On the Emergence of Position Bias in Transformers

Recent studies have revealed various manifestations of position bias in transformer architectures, from the "lost-in-the-middle" phenomenon to attention sinks, yet a comprehensive theoretical understanding of how attention masks and positional encodings shape these biases remains elusive. This paper presents a graph-theoretic framework for analyzing position bias in multi-layer attention. Modeling attention masks as directed graphs, we quantify how tokens interact with contextual information based on their sequential positions. We uncover two key insights: First, causal masking inherently biases attention toward earlier positions, as tokens in deeper layers attend to increasingly more contextualized representations of earlier tokens. Second, we characterize the competing effects of the causal mask and relative positional encodings, such as the decay mask and rotary positional encoding (RoPE): while both mechanisms introduce distance-based decay within individual attention maps, their aggregate effect across multiple attention layers$\unicode{x2013}$coupled with the causal mask$\unicode{x2013}$leads to a trade-off between the long-term decay effects and the cumulative importance of early sequence positions. Through controlled numerical experiments, we not only validate our theoretical findings but also reproduce position biases observed in real-world LLMs. Our framework offers a principled foundation for understanding positional biases in transformers, shedding light on the complex interplay of attention mechanism components and guiding more informed architectural design.

cs.LG↗

arXiv2025

On the Role of Transformer Feed-Forward Layers in Nonlinear In-Context Learning

Transformer-based models demonstrate a remarkable ability for in-context learning (ICL), where they can adapt to unseen tasks from a few prompt examples without parameter updates. Recent research has illuminated how Transformers perform ICL, showing that the optimal linear self-attention (LSA) mechanism can implement one step of gradient descent for linear least-squares objectives when trained on random linear regression tasks. Building on this, we investigate ICL for nonlinear function classes. We first prove that LSA is inherently incapable of outperforming linear predictors on nonlinear tasks, underscoring why prior solutions cannot readily extend to these problems. To overcome this limitation, we analyze a Transformer block consisting of LSA and feed-forward layers inspired by the gated linear units (GLU), which is a standard component of modern Transformers. We show that this block achieves nonlinear ICL by implementing one step of gradient descent on a polynomial kernel regression loss. Furthermore, our analysis reveals that the expressivity of a single block is inherently limited by its dimensions. We then show that a deep Transformer can overcome this bottleneck by distributing the computation of richer kernel functions across multiple blocks, performing block-coordinate descent in a high-dimensional feature space that a single block cannot represent. Our findings highlight that the feed-forward layers provide a crucial and scalable mechanism by which Transformers can express nonlinear representations for ICL.

cs.LG↗

arXiv2024

Optimal estimation in spatially distributed systems: how far to share measurements from?

We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to have a degree of spatial localization in the sense that the estimator gains decay in space, with the spatial decay rates serving as a proxy for how far measurements need to be shared in an optimal distributed estimator. In particular, we examine the dependence of spatial decay rates on problem specifications such as system dynamics, measurement and process noise variances, as well as their spatial autocorrelations. We propose non-dimensional parameters that characterize the decay rates as a function of problem specifications. In particular, we find an interesting matching condition between the characteristic lengthscale of the dynamics and the measurement noise correlation lengthscale for which the optimal centralized estimator is completely decentralized. A new technique - termed the Branch Point Locus - is introduced to quantify spatial decay rates in terms of analyticity regions in the complex spatial frequency plane. Our results are illustrated through two case studies of systems with dynamics modeled by diffusion and the Swift-Hohenberg equation, respectively.

eess.SY↗

arXiv2024

On the Role of Attention Masks and LayerNorm in Transformers

Self-attention is the key mechanism of transformers, which are the essential building blocks of modern foundation models. Recent studies have shown that pure self-attention suffers from an increasing degree of rank collapse as depth increases, limiting model expressivity and further utilization of model depth. The existing literature on rank collapse, however, has mostly overlooked other critical components in transformers that may alleviate the rank collapse issue. In this paper, we provide a general analysis of rank collapse under self-attention, taking into account the effects of attention masks and layer normalization (LayerNorm). In particular, we find that although pure masked attention still suffers from exponential collapse to a rank one subspace, sparse or local masked attention can provably slow down the collapse rate. In the case of self-attention with LayerNorm, we first show that for certain classes of value matrices, collapse to a rank one subspace still happens exponentially. However, through construction of nontrivial counterexamples, we then establish that with proper choice of value matrices, a general class of sequences may not converge to a rank one subspace, and the self-attention dynamics with LayerNorm can simultaneously possess a rich set of equilibria with any possible rank between one and full. Our result refutes the previous hypothesis that LayerNorm plays no role in the rank collapse of self-attention and suggests that self-attention with LayerNorm constitutes a much more expressive, versatile nonlinear dynamical system than what was originally thought.

cs.LG↗

arXiv2024

Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control

Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert controllers for arbitrary systems remains challenging, especially in the presence of input and state constraints. As our primary contribution, we show how such a smoothed expert can be designed for a general class of systems using a log-barrier-based relaxation of a standard Model Predictive Control (MPC) optimization problem. Improving upon our previous work, we show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction. At the core of this theoretical guarantee on smoothness is an improved lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we believe could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing.

eess.SY↗

arXiv2024

Stochastic Opinion Dynamics under Social Pressure in Arbitrary Networks

Social pressure is a key factor affecting the evolution of opinions on networks in many types of settings, pushing people to conform to their neighbors' opinions. To study this, the interacting Polya urn model was introduced by Jadbabaie et al., in which each agent has two kinds of opinion: inherent beliefs, which are hidden from the other agents and fixed; and declared opinions, which are randomly sampled at each step from a distribution which depends on the agent's inherent belief and her neighbors' past declared opinions (the social pressure component), and which is then communicated to her neighbors. Each agent also has a bias parameter denoting her level of resistance to social pressure. At every step, each agent updates her declared opinion (simultaneously with all other agents) according to her neighbors' aggregate past declared opinions, her inherent belief, and her bias parameter. We study the asymptotic behavior of this opinion dynamics model and show that the agents' declaration probabilities approaches a set of equilibrium points of the expected dynamics using Lyapunov theory and stochastic approximation techniques. We also derive necessary and sufficient conditions for the agents to approach consensus on their declared opinions. Our work provides further insight into the difficulty of inferring the inherent beliefs of agents when they are under social pressure.

eess.SY↗

arXiv2024

Capturing Tie Strength with Algebraic Topology

The association between tie strength and social structure is a fundamental topic in the social sciences. We study this association by analyzing tie strength in higher-order networks, an increasingly relevant model which can encode group interactions between three or more individuals. First, we introduce three measures based on algebraic topology which characterize the network context and influence of an edge. Our experimental results across 15 datasets indicate that these measures outperform standard network proxies in estimating tie strength. We further find that these measures can replicate and explain a puzzle wherein certain bridging ties are surprisingly strong. We then consider a single centrality measure which combines the three initial measures, is highly inversely related to tie strength, and can be interpreted through an information exchange process which highlights ties that have access to useful information. In this sense, we are able to illuminate the information advantages of weak ties due to their network position.

cs.SI↗