arXiv subjects

Rebekka Burkholz

Publications and source records attributed to Rebekka Burkholz.

At least 37 records · Page 2Linked to original sources

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.

cs.LG↗

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.

cs.LG↗

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.

cs.LG↗

arXiv2024

Pruning neural network models for gene regulatory dynamics using data and domain knowledge

The practical utility of machine learning models in the sciences often hinges on their interpretability. It is common to assess a model's merit for scientific discovery, and thus novel insights, by how well it aligns with already available domain knowledge--a dimension that is currently largely disregarded in the comparison of neural network models. While pruning can simplify deep neural network architectures and excels in identifying sparse models, as we show in the context of gene regulatory network inference, state-of-the-art techniques struggle with biologically meaningful structure learning. To address this issue, we propose DASH, a generalizable framework that guides network pruning by using domain-specific structural information in model fitting and leads to sparser, better interpretable models that are more robust to noise. Using both synthetic data with ground truth information, as well as real-world gene expression data, we show that DASH, using knowledge about gene interaction partners within the putative regulatory network, outperforms general pruning methods by a large margin and yields deeper insights into the biological systems being studied.

cs.LG↗

arXiv2024

GATE: How to Keep Out Intrusive Neighbors

Graph Attention Networks (GATs) are designed to provide flexible neighborhood aggregation that assigns weights to neighbors according to their importance. In practice, however, GATs are often unable to switch off task-irrelevant neighborhood aggregation, as we show experimentally and analytically. To address this challenge, we propose GATE, a GAT extension that holds three major advantages: i) It alleviates over-smoothing by addressing its root cause of unnecessary neighborhood aggregation. ii) Similarly to perceptrons, it benefits from higher depth as it can still utilize additional layers for (non-)linear feature transformations in case of (nearly) switched-off neighborhood aggregation. iii) By down-weighting connections to unrelated neighbors, it often outperforms GATs on real-world heterophilic datasets. To further validate our claims, we construct a synthetic test bed to analyze a model's ability to utilize the appropriate amount of neighborhood aggregation, which could be of independent interest.

cs.LG↗

arXiv2024

Cyclic Sparse Training: Is it Enough?

The success of iterative pruning methods in achieving state-of-the-art sparse networks has largely been attributed to improved mask identification and an implicit regularization induced by pruning. We challenge this hypothesis and instead posit that their repeated cyclic training schedules enable improved optimization. To verify this, we show that pruning at initialization is significantly boosted by repeated cyclic training, even outperforming standard iterative pruning methods. The dominant mechanism how this is achieved, as we conjecture, can be attributed to a better exploration of the loss landscape leading to a lower training loss. However, at high sparsity, repeated cyclic training alone is not enough for competitive performance. A strong coupling between learnt parameter initialization and mask seems to be required. Standard methods obtain this coupling via expensive pruning-training iterations, starting from a dense network. To achieve this with sparse training instead, we propose SCULPT-ing, i.e., repeated cyclic training of any sparse mask followed by a single pruning step to couple the parameters and the mask, which is able to match the performance of state-of-the-art iterative pruning methods in the high sparsity regime at reduced computational cost.

cs.LG↗

arXiv2024

CAVACHON: a hierarchical variational autoencoder to integrate multi-modal single-cell data

Paired single-cell sequencing technologies enable the simultaneous measurement of complementary modalities of molecular data at single-cell resolution. Along with the advances in these technologies, many methods based on variational autoencoders have been developed to integrate these data. However, these methods do not explicitly incorporate prior biological relationships between the data modalities, which could significantly enhance modeling and interpretation. We propose a novel probabilistic learning framework that explicitly incorporates conditional independence relationships between multi-modal data as a directed acyclic graph using a generalized hierarchical variational autoencoder. We demonstrate the versatility of our framework across various applications pertinent to single-cell multi-omics data integration. These include the isolation of common and distinct information from different modalities, modality-specific differential analysis, and integrated cell clustering. We anticipate that the proposed framework can facilitate the construction of highly flexible graphical models that can capture the complexities of biological hypotheses and unravel the connections between different biological data types, such as different modalities of paired single-cell multi-omics data. The implementation of the proposed framework can be found in the repository https://github.com/kuijjerlab/CAVACHON.

cs.LG↗

arXiv2024

Masks, Signs, And Learning Rate Rewinding

Learning Rate Rewinding (LRR) has been established as a strong variant of Iterative Magnitude Pruning (IMP) to find lottery tickets in deep overparameterized neural networks. While both iterative pruning schemes couple structure and parameter learning, understanding how LRR excels in both aspects can bring us closer to the design of more flexible deep learning algorithms that can optimize diverse sets of sparse architectures. To this end, we conduct experiments that disentangle the effect of mask learning and parameter optimization and how both benefit from overparameterization. The ability of LRR to flip parameter signs early and stay robust to sign perturbations seems to make it not only more effective in mask identification but also in optimizing diverse sets of masks, including random ones. In support of this hypothesis, we prove in a simplified single hidden neuron setting that LRR succeeds in more cases than IMP, as it can escape initially problematic sign configurations.

cs.LG↗

arXiv2023

Are GATs Out of Balance?

While the expressive power and computational capabilities of graph neural networks (GNNs) have been theoretically studied, their optimization and learning dynamics, in general, remain largely unexplored. Our study undertakes the Graph Attention Network (GAT), a popular GNN architecture in which a node's neighborhood aggregation is weighted by parameterized attention coefficients. We derive a conservation law of GAT gradient flow dynamics, which explains why a high portion of parameters in GATs with standard initialization struggle to change during training. This effect is amplified in deeper GATs, which perform significantly worse than their shallow counterparts. To alleviate this problem, we devise an initialization scheme that balances the GAT network. Our approach i) allows more effective propagation of gradients and in turn enables trainability of deeper networks, and ii) attains a considerable speedup in training and convergence time in comparison to the standard initialization. Our main theorem serves as a stepping stone to studying the learning dynamics of positive homogeneous models with attention mechanisms.

cs.LG↗

arXiv2023

Why Random Pruning Is All We Need to Start Sparse

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity $1 / \log(1/\text{sparsity})$. This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

cs.LG↗

arXiv2023

Preserving local densities in low-dimensional embeddings

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are therefore routinely applied in standard analysis pipelines in biology. We show, however, that these methods fail to reconstruct local properties, such as relative differences in densities (Fig. 1) and that apparent differences in cluster size can arise from computational artifact caused by differing sample sizes (Fig. 2). Providing a theoretical analysis of this issue, we then suggest dtSNE, which approximately conserves local densities. In an extensive study on synthetic benchmark and real world data comparing against five state-of-the-art methods, we empirically show that dtSNE provides similar global reconstruction, but yields much more accurate depictions of local distances and relative densities.

cs.LG↗

arXiv2023

Most Activation Functions Can Win the Lottery Without Excessive Depth

The strong lottery ticket hypothesis has highlighted the potential for training deep neural networks by pruning, which has inspired interesting practical and theoretical insights into how neural networks can represent functions. For networks with ReLU activation functions, it has been proven that a target network with depth $L$ can be approximated by the subnetwork of a randomly initialized neural network that has double the target's depth $2L$ and is wider by a logarithmic factor. We show that a depth $L+1$ network is sufficient. This result indicates that we can expect to find lottery tickets at realistic, commonly used depths while only requiring logarithmic overparametrization. Our novel construction approach applies to a large class of activation functions and is not limited to ReLUs.

cs.LG↗

arXiv2022

Dynamical Isometry for Residual Networks

The training success, training speed and generalization ability of neural networks rely crucially on the choice of random parameter initialization. It has been shown for multiple architectures that initial dynamical isometry is particularly advantageous. Known initialization schemes for residual blocks, however, miss this property and suffer from degrading separability of different inputs for increasing depth and instability without Batch Normalization or lack feature diversity. We propose a random initialization scheme, RISOTTO, that achieves perfect dynamical isometry for residual networks with ReLU activation functions even for finite depth and width. It balances the contributions of the residual and skip branches unlike other schemes, which initially bias towards the skip connections. In experiments, we demonstrate that in most cases our approach outperforms initialization schemes proposed to make Batch Normalization obsolete, including Fixup and SkipInit, and facilitates stable training. Also in combination with Batch Normalization, we find that RISOTTO often achieves the overall best result.

cs.LG↗

arXiv2022

DRAGON: Determining Regulatory Associations using Graphical models on multi-Omic Networks

The increasing quantity of multi-omics data, such as methylomic and transcriptomic profiles, collected on the same specimen, or even on the same cell, provide a unique opportunity to explore the complex interactions that define cell phenotype and govern cellular responses to perturbations. We propose a network approach based on Gaussian Graphical Models (GGMs) that facilitates the joint analysis of paired omics data. This method, called DRAGON (Determining Regulatory Associations using Graphical models on multi-Omic Networks), calibrates its parameters to achieve an optimal trade-off between the network's complexity and estimation accuracy, while explicitly accounting for the characteristics of each of the assessed omics "layers." In simulation studies, we show that DRAGON adapts to edge density and feature size differences between omics layers, improving model inference and edge recovery compared to state-of-the-art methods. We further demonstrate in an analysis of joint transcriptome - methylome data from TCGA breast cancer specimens that DRAGON can identify key molecular mechanisms such as gene regulation via promoter methylation. In particular, we identify Transcription Factor AP-2 Beta (TFAP2B) as a potential multi-omic biomarker for basal-type breast cancer. DRAGON is available as open-source code in Python through the Network Zoo package (netZooPy v0.8; netzoo.github.io).

q-bio.MN↗

arXiv2022

Lottery Tickets with Nonzero Biases

The strong lottery ticket hypothesis holds the promise that pruning randomly initialized deep neural networks could offer a computationally efficient alternative to deep learning with stochastic gradient descent. Common parameter initialization schemes and existence proofs, however, are focused on networks with zero biases, thus foregoing the potential universal approximation property of pruning. To fill this gap, we extend multiple initialization schemes and existence proofs to nonzero biases, including explicit 'looks-linear' approaches for ReLU activation functions. These do not only enable truly orthogonal parameter initialization but also reduce potential pruning errors. In experiments on standard benchmark data, we further highlight the practical benefits of nonzero bias initialization schemes, and present theoretically inspired extensions for state-of-the-art strong lottery ticket pruning.

cs.LG↗

arXiv2022

Plant 'n' Seek: Can You Find the Winning Ticket?

The lottery ticket hypothesis has sparked the rapid development of pruning algorithms that aim to reduce the computational costs associated with deep learning during training and model deployment. Currently, such algorithms are primarily evaluated on imaging data, for which we lack ground truth information and thus the understanding of how sparse lottery tickets could be. To fill this gap, we develop a framework that allows us to plant and hide winning tickets with desirable properties in randomly initialized neural networks. To analyze the ability of state-of-the-art pruning to identify tickets of extreme sparsity, we design and hide such tickets solving four challenging tasks. In extensive experiments, we observe similar trends as in imaging studies, indicating that our framework can provide transferable insights into realistic problems. Additionally, we can now see beyond such relative trends and highlight limitations of current pruning methods. Based on our results, we conclude that the current limitations in ticket sparsity are likely of algorithmic rather than fundamental nature. We anticipate that comparisons to planted tickets will facilitate future developments of efficient pruning algorithms.

cs.LG↗

arXiv2022

Convolutional and Residual Networks Provably Contain Lottery Tickets

The Lottery Ticket Hypothesis continues to have a profound practical impact on the quest for small scale deep neural networks that solve modern deep learning tasks at competitive performance. These lottery tickets are identified by pruning large randomly initialized neural networks with architectures that are as diverse as their applications. Yet, theoretical insights that attest their existence have been mostly focused on deep fully-connected feed forward networks with ReLU activation functions. We prove that also modern architectures consisting of convolutional and residual layers that can be equipped with almost arbitrary activation functions can contain lottery tickets with high probability.

cs.LG↗

arXiv2022

On the Existence of Universal Lottery Tickets

The lottery ticket hypothesis conjectures the existence of sparse subnetworks of large randomly initialized deep neural networks that can be successfully trained in isolation. Recent work has experimentally observed that some of these tickets can be practically reused across a variety of tasks, hinting at some form of universality. We formalize this concept and theoretically prove that not only do such universal tickets exist but they also do not require further training. Our proofs introduce a couple of technical innovations related to pruning for strong lottery tickets, including extensions of subset sum results and a strategy to leverage higher amounts of depth. Our explicit sparse constructions of universal function families might be of independent interest, as they highlight representational benefits induced by univariate convolutional architectures.

cs.LG↗