arXiv subjects

Rebekka Burkholz

Publications and source records attributed to Rebekka Burkholz.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Agent Systems are Mixtures of Experts: Who Becomes an Influencer?

The effectiveness of multi-agent LLM deliberation depends not only on the agents' individual predictions, but also on how they communicate and collaborate. We study this mechanism through the lens of Friedkin-Johnsen (FJ) opinion dynamics, a tractable model for analyzing stubbornness, influence, and opinion change in multi-agent systems that captures empirically observed deliberation patterns. We show that the FJ parameters are input-dependent, turning multi-agent deliberation into a mixture of experts. This perspective implies that multi-agent systems can outperform single agents and static ensembles when routing reflects agent competence. Since competence is latent in practice, we analyze how influence is established through observable proxies: agents' self-assessed confidence, their perceived confidence, and initial alignment with other agents' views.

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arXiv2026

Robustness of Mixtures of Experts to Feature Noise

Despite their practical success, it remains unclear why Mixture of Experts (MoE) models can outperform dense networks beyond sheer parameter scaling. We study an iso-parameter regime where inputs exhibit latent modular structure but are corrupted by feature noise, a proxy for noisy internal activations. We show that sparse expert activation acts as a noise filter: compared to a dense estimator, MoEs achieve lower generalization error under feature noise, improved robustness to perturbations, and faster convergence speed. Empirical results on synthetic data and real-world language tasks corroborate the theoretical insights, demonstrating consistent robustness and efficiency gains from sparse modular computation.

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arXiv2026

Fixed Aggregation Features Can Rival GNNs

Graph neural networks (GNNs) are widely believed to excel at node representation learning through trainable neighborhood aggregations. We challenge this view by introducing Fixed Aggregation Features (FAFs), a training-free approach that transforms graph learning tasks into tabular problems. This simple shift enables the use of well-established tabular methods, offering strong interpretability and the flexibility to deploy diverse classifiers. Across 14 benchmarks, well-tuned multilayer perceptrons trained on FAFs rival or outperform state-of-the-art GNNs and graph transformers on 12 tasks -- often using only mean aggregation. The only exceptions are the Roman Empire and Minesweeper datasets, which typically require unusually deep GNNs. To explain the theoretical possibility of non-trainable aggregations, we connect our findings to Kolmogorov-Arnold representations and discuss when mean aggregation can be sufficient. In conclusion, our results call for (i) richer benchmarks benefiting from learning diverse neighborhood aggregations, (ii) strong tabular baselines as standard, and (iii) employing and advancing tabular models for graph data to gain new insights into related tasks.

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arXiv2026

SparseOpt: Addressing Normalization-induced Gradient Skew in Sparse Training

Dynamic Sparse Training (DST) methods train neural networks by maintaining sparsity while dynamically adapting the network topology. Despite the promise of reduced computation, DST methods converge significantly slower than dense training, often requiring comparable training time to achieve similar accuracy. We demonstrate both analytically and empirically that Batch Normalization (BN) adversely affects sparse training, and propose SparseOpt, a sparsity-aware optimizer, to address this. Experiments on ResNet models across CIFAR-100 and ImageNet demonstrate consistently faster convergence and improved generalization with our proposed method. Our work highlights the limitations of current normalization layers in sparse training and provides the first systematic study of the interaction between Batch Normalization, sparse layers, and DST, taking a significant step toward making DST practically competitive with dense training.

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arXiv2026

HORST: Composing Optimizer Geometries for Sparse Transformer Training

Sparsifying transformers remains a fundamental challenge, as standard optimizers fail to simultaneously encourage sparsity and maintain training stability. Effective adaptive optimizers exhibit an implicit $L_{\infty}$ bias favoring stability, yet, sparsity requires an $L_1$ bias. To integrate sparsity, we propose a composition of optimizer steps, which we cast as non-commutative operators to analyze and combine their optimization geometry in a principled way. This yields HORST (Hyperbolic Operator for Robust Sparse Training), a modular optimizer that inherits stability from adaptive methods while inducing $L_1$ sparsity bias through a hyperbolic mirror map. Our experiments demonstrate its utility for sparse training of transformers on both vision and language tasks. HORST consistently and significantly outperforms AdamW baselines across all sparsity levels, with large gains at higher sparsity.

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arXiv2026

Don't Trust Stubborn Neighbors: A Security Framework for Agentic Networks

Large Language Model (LLM)-based Multi-Agent Systems (MASs) are increasingly deployed for agentic tasks, such as web automation, itinerary planning, and collaborative problem solving. Yet, their interactive nature introduces new security risks: malicious or compromised agents can exploit communication channels to propagate misinformation and manipulate collective outcomes. In this paper, we study how such manipulation can arise and spread by borrowing the Friedkin-Johnsen opinion formation model from social sciences to propose a general theoretical framework to study LLM-MAS. Remarkably, this model closely captures LLM-MAS behavior, as we verify in extensive experiments across different network topologies and attack and defense scenarios. Theoretically and empirically, we find that a single highly stubborn and persuasive agent can take over MAS dynamics, underscoring the systems' high susceptibility to attacks by triggering a persuasion cascade that reshapes collective opinion. Our theoretical analysis reveals three mechanisms to increase system security: a) increasing the number of benign agents, b) increasing the innate stubbornness or peer-resistance of agents, or c) reducing trust in potential adversaries. Because scaling is computationally expensive and high stubbornness degrades the network's ability to reach consensus, we propose a new mechanism to mitigate threats by a trust-adaptive defense that dynamically adjusts inter-agent trust to limit adversarial influence while maintaining cooperative performance. Extensive experiments confirm that this mechanism effectively defends against manipulation.

cs.MA↗

arXiv2026

Bridging Domains through Subspace-Aware Model Merging

Model merging integrates multiple task-specific models into a single consolidated one. Recent research has made progress in improving merging performance for in-distribution or multi-task scenarios, but domain generalization in model merging remains underexplored. We investigate how merging models fine-tuned on distinct domains affects generalization to unseen domains. Through an analysis of parameter competition in the task matrix using singular value decomposition, we show that merging models trained under different distribution shifts induces stronger conflicts between their subspaces compared to traditional multi-task settings. To mitigate this issue, we propose SCORE (Subspace COnflict-Resolving mErging), a method designed to alleviate such singular subspace conflicts. SCORE finds a shared orthogonal basis by computing the principal components of the concatenated leading singular vectors of all models. It then projects each task matrix into the shared basis, pruning off-diagonal components to remove conflicting singular directions. SCORE consistently outperforms, on average, existing model merging approaches in domain generalization settings across a variety of architectures and model scales, demonstrating its effectiveness and scalability.

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arXiv2026

Hyperbolic Aware Minimization: Implicit Bias for Sparsity

Understanding the implicit bias of optimization algorithms is key to explaining and improving the generalization of deep models. The hyperbolic implicit bias induced by pointwise overparameterization promotes sparsity, but also yields a small inverse Riemannian metric near zero, slowing down parameter movement and impeding meaningful parameter sign flips. To overcome this obstacle, we propose Hyperbolic Aware Minimization (HAM), which alternates a standard optimizer step with a lightweight hyperbolic mirror step. The mirror step incurs less compute and memory than pointwise overparameterization, reproduces its beneficial hyperbolic geometry for feature learning, and mitigates the small-inverse-metric bottleneck. Our characterization of the implicit bias in the context of underdetermined linear regression provides insights into the mechanism how HAM consistently increases performance --even in the case of dense training, as we demonstrate in experiments with standard vision benchmarks. HAM is especially effective in combination with different sparsification methods, advancing the state of the art.

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arXiv2026

Never Saddle for Reparameterized Steepest Descent as Mirror Flow

How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows as a unifying theoretical framework. This framework reveals how optimization geometry governs learning dynamics, implicit bias, and sparsity and it provides two explanations for why Adam and AdamW often outperform SGD in fine-tuning. Focusing on diagonal linear networks and deep diagonal linear reparameterizations (a simplified proxy for attention), we show that steeper descent facilitates both saddle-point escape and feature learning. In contrast, gradient descent requires unrealistically large learning rates to escape saddles, an uncommon regime in fine-tuning. Empirically, we confirm that saddle-point escape is a central challenge in fine-tuning. Furthermore, we demonstrate that decoupled weight decay, as in AdamW, stabilizes feature learning by enforcing novel balance equations. Together, these results highlight two mechanisms how steepest descent can aid modern optimization.

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arXiv2026

Frequency-Based Hyperparameter Selection in Games

Learning in smooth games fundamentally differs from standard minimization due to rotational dynamics, which invalidate classical hyperparameter tuning strategies. Despite their practical importance, effective methods for tuning in games remain underexplored. A notable example is LookAhead (LA), which achieves strong empirical performance but introduces additional parameters that critically influence performance. We propose a principled approach to hyperparameter selection in games by leveraging frequency estimation of oscillatory dynamics. Specifically, we analyze oscillations both in continuous-time trajectories and through the spectrum of the discrete dynamics in the associated frequency-based space. Building on this analysis, we introduce \emph{Modal LookAhead (MoLA)}, an extension of LA that selects the hyperparameters adaptively to a given problem. We provide convergence guarantees and demonstrate in experiments that MoLA accelerates training in both purely rotational games and mixed regimes, all with minimal computational overhead.

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arXiv2025

Sign-In to the Lottery: Reparameterizing Sparse Training From Scratch

The performance gap between training sparse neural networks from scratch (PaI) and dense-to-sparse training presents a major roadblock for efficient deep learning. According to the Lottery Ticket Hypothesis, PaI hinges on finding a problem specific parameter initialization. As we show, to this end, determining correct parameter signs is sufficient. Yet, they remain elusive to PaI. To address this issue, we propose Sign-In, which employs a dynamic reparameterization that provably induces sign flips. Such sign flips are complementary to the ones that dense-to-sparse training can accomplish, rendering Sign-In as an orthogonal method. While our experiments and theory suggest performance improvements of PaI, they also carve out the main open challenge to close the gap between PaI and dense-to-sparse training.

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arXiv2025

Pay Attention to Small Weights

Finetuning large pretrained neural networks is known to be resource-intensive, both in terms of memory and computational cost. To mitigate this, a common approach is to restrict training to a subset of the model parameters. By analyzing the relationship between gradients and weights during finetuning, we observe a notable pattern: large gradients are often associated with small-magnitude weights. This correlation is more pronounced in finetuning settings than in training from scratch. Motivated by this observation, we propose NANOADAM, which dynamically updates only the small-magnitude weights during finetuning and offers several practical advantages: first, this criterion is gradient-free -- the parameter subset can be determined without gradient computation; second, it preserves large-magnitude weights, which are likely to encode critical features learned during pretraining, thereby reducing the risk of catastrophic forgetting; thirdly, it permits the use of larger learning rates and consistently leads to better generalization performance in experiments. We demonstrate this for both NLP and vision tasks.

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arXiv2025

The Graphon Limit Hypothesis: Understanding Neural Network Pruning via Infinite Width Analysis

Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterizes sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. We postulate the Graphon Limit Hypothesis and provide empirical evidence to support it. Leveraging this graphon representation, we derive a Graphon Neural Tangent Kernel (Graphon NTK) to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. Our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures.

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arXiv2025

Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?

Implicit bias plays an important role in explaining how overparameterized models generalize well. Explicit regularization like weight decay is often employed in addition to prevent overfitting. While both concepts have been studied separately, in practice, they often act in tandem. Understanding their interplay is key to controlling the shape and strength of implicit bias, as it can be modified by explicit regularization. To this end, we incorporate explicit regularization into the mirror flow framework and analyze its lasting effects on the geometry of the training dynamics, covering three distinct effects: positional bias, type of bias, and range shrinking. Our analytical approach encompasses a broad class of problems, including sparse coding, matrix sensing, single-layer attention, and LoRA, for which we demonstrate the utility of our insights. To exploit the lasting effect of regularization and highlight the potential benefit of dynamic weight decay schedules, we propose to switch off weight decay during training, which can improve generalization, as we demonstrate in experiments.

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arXiv2025

When Shift Happens - Confounding Is to Blame

Distribution shifts introduce uncertainty that undermines the robustness and generalization capabilities of machine learning models. While conventional wisdom suggests that learning causal-invariant representations enhances robustness to such shifts, recent empirical studies present a counterintuitive finding: (i) empirical risk minimization (ERM) can rival or even outperform state-of-the-art out-of-distribution (OOD) generalization methods, and (ii) its OOD generalization performance improves when all available covariates, not just causal ones, are utilized. Drawing on both empirical and theoretical evidence, we attribute this phenomenon to hidden confounding. Shifts in hidden confounding induce changes in data distributions that violate assumptions commonly made by existing OOD generalization approaches. Under such conditions, we prove that effective generalization requires learning environment-specific relationships, rather than relying solely on invariant ones. Furthermore, we show that models augmented with proxies for hidden confounders can mitigate the challenges posed by hidden confounding shifts. These findings offer new theoretical insights and practical guidance for designing robust OOD generalization algorithms and principled covariate selection strategies.

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arXiv2025

Mask in the Mirror: Implicit Sparsification

Continuous sparsification strategies are among the most effective methods for reducing the inference costs and memory demands of large-scale neural networks. A key factor in their success is the implicit $L_1$ regularization induced by jointly learning both mask and weight variables, which has been shown experimentally to outperform explicit $L_1$ regularization. We provide a theoretical explanation for this observation by analyzing the learning dynamics, revealing that early continuous sparsification is governed by an implicit $L_2$ regularization that gradually transitions to an $L_1$ penalty over time. Leveraging this insight, we propose a method to dynamically control the strength of this implicit bias. Through an extension of the mirror flow framework, we establish convergence and optimality guarantees in the context of underdetermined linear regression. Our theoretical findings may be of independent interest, as we demonstrate how to enter the rich regime and show that the implicit bias can be controlled via a time-dependent Bregman potential. To validate these insights, we introduce PILoT, a continuous sparsification approach with novel initialization and dynamic regularization, which consistently outperforms baselines in standard experiments.

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arXiv2025

GNNs Getting ComFy: Community and Feature Similarity Guided Rewiring

Maximizing the spectral gap through graph rewiring has been proposed to enhance the performance of message-passing graph neural networks (GNNs) by addressing over-squashing. However, as we show, minimizing the spectral gap can also improve generalization. To explain this, we analyze how rewiring can benefit GNNs within the context of stochastic block models. Since spectral gap optimization primarily influences community strength, it improves performance when the community structure aligns with node labels. Building on this insight, we propose three distinct rewiring strategies that explicitly target community structure, node labels, and their alignment: (a) community structure-based rewiring (ComMa), a more computationally efficient alternative to spectral gap optimization that achieves similar goals; (b) feature similarity-based rewiring (FeaSt), which focuses on maximizing global homophily; and (c) a hybrid approach (ComFy), which enhances local feature similarity while preserving community structure to optimize label-community alignment. Extensive experiments confirm the effectiveness of these strategies and support our theoretical insights.

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arXiv2024

Spectral Graph Pruning Against Over-Squashing and Over-Smoothing

Message Passing Graph Neural Networks are known to suffer from two problems that are sometimes believed to be diametrically opposed: over-squashing and over-smoothing. The former results from topological bottlenecks that hamper the information flow from distant nodes and are mitigated by spectral gap maximization, primarily, by means of edge additions. However, such additions often promote over-smoothing that renders nodes of different classes less distinguishable. Inspired by the Braess phenomenon, we argue that deleting edges can address over-squashing and over-smoothing simultaneously. This insight explains how edge deletions can improve generalization, thus connecting spectral gap optimization to a seemingly disconnected objective of reducing computational resources by pruning graphs for lottery tickets. To this end, we propose a more effective spectral gap optimization framework to add or delete edges and demonstrate its effectiveness on large heterophilic datasets.

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