arXiv subjects

James Anderson

Publications and source records attributed to James Anderson.

At least 19 recordsLinked to original sources

arXiv2026

Mind Control of LLMs via Closed-Loop Stimulation: Out-of-Distribution Robustness

Brains and large language models need not be considered equivalent systems to reveal an interpretable commonality: both exhibit high-dimensional, nonlinear dynamics whose behavior can only be modeled imperfectly. This creates a shared challenge whenever we seek to intervene in their dynamics. A controller may either rely on a model identified around a particular operating regime and risk failure as the system moves away from that regime, or explicitly account for uncertainty and a changing internal state. Neurostimulation has confronted an analogous problem for decades. The limitations of fixed, open-loop stimulation have motivated closed-loop and state-dependent approaches that condition intervention on the ongoing state of the neural system. Inspired by this principle, we formulate LLM steering as a feedback-control problem in which the network's internal state, rather than a fixed intervention alone, determines how the system is perturbed. We further account for the mismatch between tractable dynamical models and the nonlinear transformer they approximate through robust control. As one principled realization of this framework, we develop an $H_\infty$-based steering controller that limits sensitivity to disturbances and linearization mismatches. Across multiple steering benchmarks, the controller improves performance over existing baselines, with particularly pronounced gains under out-of-distribution conditions and varying length complexities. Beyond controller performance, we introduce robust steerability, $S_{\mathrm{rob}}$, a pre-deployment measure of tolerance to dynamics mismatch; across model-task pairs, it exhibits task-specific structure and varies systematically with model scale. Beyond robust LLM steering, our measure asks not merely whether control is possible, but how much uncertainty it can survive; a principle that may span artificial and biological neural systems.

q-bio.NC↗

arXiv2026

On the Gradient Domination of the LQG Problem

We consider solutions to the linear quadratic Gaussian (LQG) regulator problem via policy gradient (PG) methods. Although PG methods have demonstrated strong theoretical guarantees in solving the linear quadratic regulator (LQR) problem, despite its nonconvex landscape, their theoretical understanding in the LQG setting remains limited. Notably, the LQG problem lacks gradient dominance in the classical parameterization, i.e., with a dynamic controller, which hinders global convergence guarantees. In this work, we study a PG method for the LQG problem by adopting an alternative parameterization of the set of stabilizing controllers and employing a lifting argument. We refer to this parameterization as a history representation of the control input as it is parameterized by past input and output data from the previous p time-steps. Under this parameterization, the infinite-history LQG optimization reduces to an equivalent static state-feedback LQR problem, allowing us to recover gradient dominance and smoothness. For finite history length p, we establish model-based and model-free convergence guarantees up to a geometrically decaying history-truncation error.

math.OC↗

arXiv2026

ConicFlow: constrained Inference-time optimal control for flow matching models

We propose ConicFlow, which frames constrained sampling from a flow matching model at inference time as an optimal control problem that balances deviation from the pretrained trajectory against reward, subject to hard terminal constraints. We discretize this problem and adapt receding-horizon control, optimizing only a short window of the trajectory at each step for computational tractability. We address the resulting sequence of receding-horizon subproblems with a receding-horizon primal-dual algorithm. Its dual multipliers capture the difficulty of satisfying each constraint and are refined throughout sampling, steering generation toward feasible final samples. We further propose a terminal-estimate variant that avoids accumulating local truncation errors by evaluating the reward and constraints at the predicted terminal point rather than at the end of the current horizon. Under standard regularity assumptions, we establish finite-horizon guarantees on suboptimality. Under convex-affine structure, we derive a sharper bound that scales linearly with omitted horizon length, and we show that the terminal-estimate variant is provably tighter when the flow dynamics change slowly. Experiments in both low- and high-dimensional settings with a recent large-scale flow matching model show that ConicFlow achieves high reward and strong constraint satisfaction while deviating less from the pretrained flow than recent baselines.

cs.AI↗

arXiv2026

Preserving Unstable Modes Through Inverse Dynamics in JEPA World Models

Robotic systems often exhibit unstable modes, along which small perturbations and disturbances can cause unbounded growth unless corrected through feedback. Controlling such systems from high-dimensional visual observations requires representations that preserve these modes. Joint-embedding predictive architectures (JEPAs) provide a natural framework for learning such representations and their dynamics from visual data. However, we demonstrate that next step prediction combined with anti-collapse regularization does not guarantee that controllable unstable modes are preserved: the training loss can be minimized while these modes are collapsed, making stabilization from the learned representation impossible. To address this, we augment world-model training with an action reconstruction objective (i.e., an inverse dynamics loss) that encourages control-aware representations, namely, visual representations that preserve crucial features for control. We prove that exact action reconstruction makes the encoder injective on the finite-horizon reachable subspace. Thus, the encoder cannot discard any state direction reachable by an action sequence within $H$ steps. Moreover, we show that, as $H$ grows, the dominant eigenspace of the finite-horizon controllability Gramian converges to the controllable unstable subspace. We establish our theoretical results for linear systems and demonstrate empirically that our findings extend to nonlinear visual control tasks (CartPole, Walker2D, and PointMaze), highlighting the benefits of control-aware representation learning.

cs.LG↗

arXiv2026

JEPA-Bisim: Learning Robust Visual Representations for Planning with Joint-Embedding Predictive World Models

World models learned from high-dimensional visual observations allow agents to make decisions and plan directly in latent space, avoiding pixel-level reconstruction. However, recent latent predictive architectures (JEPAs), including the DINO world model (DINO-WM), display a degradation in test time robustness due to their sensitivity to ``slow features". These include visual variations such as background changes and distractors that are irrelevant to the task being solved. We address this limitation by augmenting the predictive objective with a bisimulation encoder that enforces control-relevant state equivalence, mapping states with similar transition dynamics to nearby latent states while limiting contributions from slow features. We evaluate our model on a navigation task (PointMaze) and on a manipulation task (PushT) under different test-time background changes and visual distractors. Across all benchmarks, our model consistently improves robustness to slow features while operating in a reduced latent space, up to $10\times$ smaller than that of DINO-WM. Moreover, our model is agnostic to the choice of pre-trained visual encoder and maintains robustness when paired with DINOv2, SimDINOv2, and iBOT features.

cs.LG↗

arXiv2026

Byzantine-Robust Federated Representation Learning

We study federated learning (FL) with adversarial clients, where the goal is to minimize the average loss of the honest (non-adversarial) clients without knowing their identity. Under heterogeneity, a single shared model parameter is statistically inappropriate: it cannot capture the distinct data-generating processes across clients, incurring an irreducible model-heterogeneity bias and severely limiting robustness to adversarial clients (a.k.a. Byzantine-robustness). We address this problem through representation learning, where each client learns a personalized linear head, while collaboratively estimating a shared nonlinear representation through Byzantine-robust aggregation. We demonstrate that the heterogeneity among honest representation gradients is controlled by the representation error and statistical errors that decay either with the number of data samples per client ($τ$) or the number of iterations ($T$). In particular, our non-asymptotic parameter recovery error bound reveals three terms: (i) an initialization-dependent error that goes away with $T$, (ii) finite-sample noise terms that decreases with $τ$ and the number of honest clients, and (iii) a stochastic gradient variance term that also reduces with $T$. Importantly, with no irreducible model-heterogeneity bias in our bounds. We extend the regression analysis to multiclass classification, and empirically validate it on CIFAR-10, FEMNIST, and School Exam Score datasets.

cs.LG↗

arXiv2026

FedSysID: A Federated Approach to Sample-Efficient System Identification

We study the problem of learning a linear system model from the observations of $M$ clients. The catch: Each client is observing data from a different dynamical system. This work addresses the question of how multiple clients collaboratively learn dynamical models in the presence of heterogeneity. We pose this problem as a federated learning problem and characterize the tension between achievable performance and system heterogeneity. Furthermore, our federated sample complexity result provides a constant factor improvement over the single agent setting. Finally, we describe a meta federated learning algorithm, FedSysID, that leverages existing federated algorithms at the client level.

cs.LG↗

arXiv2026

Model-free Learning with Heterogeneous Dynamical Systems: A Federated LQR Approach

We study a model-free federated linear quadratic regulator (LQR) problem where M agents with unknown, distinct yet similar dynamics collaboratively learn an optimal policy to minimize an average quadratic cost while keeping their data private. To exploit the similarity of the agents' dynamics, we propose to use federated learning (FL) to allow the agents to periodically communicate with a central server to train policies by leveraging a larger dataset from all the agents. With this setup, we seek to understand the following questions: (i) Is the learned common policy stabilizing for all agents? (ii) How close is the learned common policy to each agent's own optimal policy? (iii) Can each agent learn its own optimal policy faster by leveraging data from all agents? To answer these questions, we propose a federated and model-free algorithm named FedLQR. Our analysis overcomes numerous technical challenges, such as heterogeneity in the agents' dynamics, multiple local updates, and stability concerns. We show that FedLQR produces a common policy that, at each iteration, is stabilizing for all agents. We provide bounds on the distance between the common policy and each agent's local optimal policy. Furthermore, we prove that when learning each agent's optimal policy, FedLQR achieves a sample complexity reduction proportional to the number of agents M in a low-heterogeneity regime, compared to the single-agent setting.

math.OC↗

arXiv2026

Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning

We study task selection to enhance sample efficiency in model-agnostic meta-reinforcement learning (MAML-RL). Traditional meta-RL typically assumes that all available tasks are equally important, which can lead to task redundancy when they share significant similarities. To address this, we propose a coreset-based task selection approach that selects a weighted subset of tasks based on how diverse they are in gradient space, prioritizing the most informative and diverse tasks. Such task selection reduces the number of samples needed to find an $ε$-close stationary solution by a factor of O(1/$ε$). Consequently, it guarantees a faster adaptation to unseen tasks while focusing training on the most relevant tasks. As a case study, we incorporate task selection to MAML-LQR (Toso et al., 2024b), and prove a sample complexity reduction proportional to O(log(1/$ε$)) when the task specific cost also satisfy gradient dominance. Our theoretical guarantees underscore task selection as a key component for scalable and sample-efficient meta-RL. We numerically validate this trend across multiple RL benchmark problems, illustrating the benefits of task selection beyond the LQR baseline.

math.OC↗

arXiv2026

Multitask LQG Control: Performance and Generalization Bounds

We study multitask learning for stochastic and partially observed control systems, focusing on the linear quadratic Gaussian (LQG) problem. Our goal is to learn a common stabilizing controller that generalizes across a distribution of systems and objectives. To this end, we leverage a history-dependent lifting that recasts the multitask LQG problem into an equivalent high-dimensional multitask LQR problem, allowing for the analysis of policy gradient methods. We show that learning a common lifted controller induces a heterogeneity bias which we characterize via a "bisimulation function". We establish performance and generalization guarantees that explicitly depend on such bisimulation-based heterogeneity measures. For model-free, we demonstrate that multitask learning reduces policy gradient estimation variance proportionally to the number of tasks in the training set.

math.OC↗

arXiv2026

On the Gradient Heterogeneity Dynamics of Adversarially Robust Federated Regression

Federated learning (FL) is intrinsically heterogeneous: honest clients may have different data-generating models. On top of that, adversarial clients can make heterogeneity even more pronounced by sharing arbitrary updates. Existing analyses typically control the interaction between statistical heterogeneity and adversarial behavior through gradient-dissimilarity conditions. However, the underlying bound is imposed a priori and may yield conservative guarantees even for least-squares regression. We instead derive the gradient heterogeneity from the statistical model of linear and nonlinear regression with fresh data samples at every round. Our bounds separate heterogeneity among the honest clients' ground-truth model parameters, finite-sample label noise, and initialization. We then demonstrate that, for any $(f,κ)$-robust aggregator with coefficient $κ= O(f/n)$, where $f$ is the number of adversarial clients and $n$ the total number of clients (with $f/n < 1/2$), convergence holds after an explicit sample burn-in.

stat.ML↗

arXiv2026

TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

cs.RO↗

arXiv2026

Approximate Projections onto the Positive Semidefinite Cone Using Randomization

This paper presents two algorithms that compute approximate Positive Semidefinite (PSD) projections of real symmetric matrices using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection of an $n\times n$ matrix relies on a deterministic eigen-decomposition with computation that scales as $\mathcal{O}(n^3)$. Our approach leverages RNLA to construct low-rank matrix approximations before projection, significantly reducing the required numerical resources to $\mathcal{O}(k n^2)$, for some user defined fixed parameter $k$. The first algorithm utilizes random sampling to generate a low-rank approximation, followed by a standard eigen-decomposition on this smaller matrix. The second algorithm enhances this process by introducing a scaling approach that aligns the leading-order singular values with the positive eigenvalues, biasing the low-rank approximation to focus on capturing the essential information about the positive eigenvalues for PSD projection. Both methods offer a trade-off between accuracy and computational speed, supported by probabilistic error bounds. Numerical experiments on large-scale matrices ( $n\approx 20K$) demonstrate that the proposed randomized algorithms effectively approximate PSD projections.

math.OC↗

arXiv2026

On the Unification of Optimal Current Reference Theory for Wound Rotor Synchronous Machines

Controllers for motor drives typically require a current reference which will satisfy the requested torque subject to system constraints. This work generalizes existing current reference theory to the case of the Wound Rotor Synchronous Machine (WRSM). By incorporating the additional rotor-current degree-of-freedom, along with magnetic saturation, cross-coupling, and speed-dependent core losses, the problem of finding an optimal current reference is formulated within affine flux regions as a quadratically constrained quadratic program using a piecewise-affine approximation derived from finite-element data. The solution is characterized according to the active constraint regime, yielding closed-form or low-dimensional polynomial solutions in several cases, and a small semidefinite program in the voltage constrained regime. The proposed framework extends unified optimal current reference theory beyond the permanent-magnet setting to three degree-of-freedom WRSMs while remaining computationally tractable. Results on a physical WRSM prototype illustrate the effectiveness of the approach across the torque-speed operating envelope.

eess.SY↗

arXiv2025

Coloring locally sparse graphs

A graph $G$ is $k$-locally sparse if for each vertex $v \in V(G)$, the subgraph induced by its neighborhood contains at most $k$ edges. Alon, Krivelevich, and Sudakov showed that for $f > 0$ if a graph $G$ of maximum degree $Δ$ is $Δ^2/f$-locally-sparse, then $χ(G) = O\left(Δ/\log f\right)$. We introduce a more general notion of local sparsity by defining graphs $G$ to be $(k, F)$-locally-sparse for some graph $F$ if for each vertex $v \in V(G)$ the subgraph induced by the neighborhood of $v$ contains at most $k$ copies of $F$. Employing the Rödl nibble method, we prove the following generalization of the above result: for every bipartite graph $F$, if $G$ is $(k, F)$-locally-sparse, then $χ(G) = O\left( Δ/\log\left(Δk^{-1/|V(F)|}\right)\right)$. This improves upon results of Davies, Kang, Pirot, and Sereni who consider the case when $F$ is a path. Our results also recover the best known bound on $χ(G)$ when $G$ is $K_{1, t, t}$-free for $t \geq 4$, and hold for list and correspondence coloring in the more general so-called ''color-degree'' setting.

math.CO↗

arXiv2025

Online Energy Storage Arbitrage under Imperfect Predictions: A Conformal Risk-Aware Approach

This work proposes a conformal approach for energy storage arbitrage to control the downside risk arising from imperfect price forecasts. Energy storage arbitrage relies solely on predictions of future market prices, while inaccurate price predictions may lead to significant profit losses. Based on conformal decision theory, we describe a controller that dynamically adjusts decision conservativeness through prediction sets without distributional assumptions. To enable online calibration when online profit loss feedback is unobservable, we establish that a temporal difference error serves as a measurable proxy. Building on this insight, we develop two online calibration strategies: prediction error-based adaptation targeting forecast accuracy, and value error-based calibration focusing on decision quality. Analysis of the conformal controller proves bounded long-term risk with convergence guarantees in temporal difference error, which further effectively manages risk exposure in potential profit losses. Case studies demonstrate superior performance in balancing risk and opportunity compared to benchmarks under varying forecast conditions.

eess.SY↗

arXiv2025

Adversarially Robust Multitask Adaptive Control

We study adversarially robust multitask adaptive linear quadratic control; a setting where multiple systems collaboratively learn control policies under model uncertainty and adversarial corruption. We propose a clustered multitask approach that integrates clustering and system identification with resilient aggregation to mitigate corrupted model updates. Our analysis characterizes how clustering accuracy, intra-cluster heterogeneity, and adversarial behavior affect the expected regret of certainty-equivalent (CE) control across LQR tasks. We establish non-asymptotic bounds demonstrating that the regret decreases inversely with the number of honest systems per cluster and that this reduction is preserved under a bounded fraction of adversarial systems within each cluster.

cs.LG↗

arXiv2025

Physics-informed learning under mixing: How physical knowledge speeds up learning

A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.

cs.LG↗