pwc-archive/papers-with-abstracts huggingface dataset:
Transformers as Game Players: Provable In-context Game-playing Capabilities of Pre-trained Models
Authors: Chengshuai Shi, Kun Yang, Jing Yang, Cong Shen
Date: 2024-10-13 00:00:00
Tasks: In-Context Learning, Reinforcement Learning (RL)

The in-context learning (ICL) capability of pre-trained models based on the transformer architecture has received growing interest in recent years. While theoretical understanding has been obtained for ICL in reinforcement learning (RL), the previous results are largely confined to the single-agent setting. This work proposes to further explore the in-context learning capabilities of pre-trained transformer models in competitive multi-agent games, i.e., in-context game-playing (ICGP). Focusing on the classical two-player zero-sum games, theoretical guarantees are provided to demonstrate that pre-trained transformers can provably learn to approximate Nash equilibrium in an in-context manner for both decentralized and centralized learning settings. As a key part of the proof, constructional results are established to demonstrate that the transformer architecture is sufficiently rich to realize celebrated multi-agent game-playing algorithms, in particular, decentralized V-learning and centralized VI-ULCB.
Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics
Authors: Omar Chehab, Anna Korba, Austin Stromme, Adrien Vacher
Date: 2024-10-13 00:00:00

Geometric tempering is a popular approach to sampling from challenging multi-modal probability distributions by instead sampling from a sequence of distributions which interpolate, using the geometric mean, between an easier proposal distribution and the target distribution. In this paper, we theoretically investigate the soundness of this approach when the sampling algorithm is Langevin dynamics, proving both upper and lower bounds. Our upper bounds are the first analysis in the literature under functional inequalities. They assert the convergence of tempered Langevin in continuous and discrete-time, and their minimization leads to closed-form optimal tempering schedules for some pairs of proposal and target distributions. Our lower bounds demonstrate a simple case where the geometric tempering takes exponential time, and further reveal that the geometric tempering can suffer from poor functional inequalities and slow convergence, even when the target distribution is well-conditioned. Overall, our results indicate that geometric tempering may not help, and can even be harmful for convergence.
Scalable Weibull Graph Attention Autoencoder for Modeling Document Networks
Authors: Chaojie Wang, Xinyang Liu, Dongsheng Wang, Hao Zhang, Bo Chen, Mingyuan Zhou
Date: 2024-10-13 00:00:00
Tasks: Decoder, Graph Attention, Topic Models

Although existing variational graph autoencoders (VGAEs) have been widely used for modeling and generating graph-structured data, most of them are still not flexible enough to approximate the sparse and skewed latent node representations, especially those of document relational networks (DRNs) with discrete observations. To analyze a collection of interconnected documents, a typical branch of Bayesian models, specifically relational topic models (RTMs), has proven their efficacy in describing both link structures and document contents of DRNs, which motives us to incorporate RTMs with existing VGAEs to alleviate their potential issues when modeling the generation of DRNs. In this paper, moving beyond the sophisticated approximate assumptions of traditional RTMs, we develop a graph Poisson factor analysis (GPFA), which provides analytic conditional posteriors to improve the inference accuracy, and extend GPFA to a multi-stochastic-layer version named graph Poisson gamma belief network (GPGBN) to capture the hierarchical document relationships at multiple semantic levels. Then, taking GPGBN as the decoder, we combine it with various Weibull-based graph inference networks, resulting in two variants of Weibull graph auto-encoder (WGAE), equipped with model inference algorithms. Experimental results demonstrate that our models can extract high-quality hierarchical latent document representations and achieve promising performance on various graph analytic tasks.
Learning Orthogonal Multi-Index Models: A Fine-Grained Information Exponent Analysis
Authors: Yunwei Ren, Jason D. Lee
Date: 2024-10-13 00:00:00

The information exponent (Ben Arous et al. [2021]) -- which is equivalent to the lowest degree in the Hermite expansion of the link function for Gaussian single-index models -- has played an important role in predicting the sample complexity of online stochastic gradient descent (SGD) in various learning tasks. In this work, we demonstrate that, for multi-index models, focusing solely on the lowest degree can miss key structural details of the model and result in suboptimal rates. Specifically, we consider the task of learning target functions of form $f_*(\mathbf{x}) = \sum_{k=1}^{P} \phi(\mathbf{v}_k^* \cdot \mathbf{x})$, where $P \ll d$, the ground-truth directions $\{ \mathbf{v}_k^* \}_{k=1}^P$ are orthonormal, and only the second and $2L$-th Hermite coefficients of the link function $\phi$ can be nonzero. Based on the theory of information exponent, when the lowest degree is $2L$, recovering the directions requires $d^{2L-1}\mathrm{poly}(P)$ samples, and when the lowest degree is $2$, only the relevant subspace (not the exact directions) can be recovered due to the rotational invariance of the second-order terms. In contrast, we show that by considering both second- and higher-order terms, we can first learn the relevant space via the second-order terms, and then the exact directions using the higher-order terms, and the overall sample and complexity of online SGD is $d \mathrm{poly}(P)$.
Uncovering Attacks and Defenses in Secure Aggregation for Federated Deep Learning
Authors: Yiwei Zhang, Rouzbeh Behnia, Attila A. Yavuz, Reza Ebrahimi, Elisa Bertino
Date: 2024-10-13 00:00:00
Tasks: Federated Learning

Federated learning enables the collaborative learning of a global model on diverse data, preserving data locality and eliminating the need to transfer user data to a central server. However, data privacy remains vulnerable, as attacks can target user training data by exploiting the updates sent by users during each learning iteration. Secure aggregation protocols are designed to mask/encrypt user updates and enable a central server to aggregate the masked information. MicroSecAgg (PoPETS 2024) proposes a single server secure aggregation protocol that aims to mitigate the high communication complexity of the existing approaches by enabling a one-time setup of the secret to be re-used in multiple training iterations. In this paper, we identify a security flaw in the MicroSecAgg that undermines its privacy guarantees. We detail the security flaw and our attack, demonstrating how an adversary can exploit predictable masking values to compromise user privacy. Our findings highlight the critical need for enhanced security measures in secure aggregation protocols, particularly the implementation of dynamic and unpredictable masking strategies. We propose potential countermeasures to mitigate these vulnerabilities and ensure robust privacy protection in the secure aggregation frameworks.
EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants
Authors: Allan dos Santos Costa, Ilan Mitnikov, Franco Pellegrini, Ameya Daigavane, Mario Geiger, Zhonglin Cao, Karsten Kreis, Tess Smidt, Emine Kucukbenli, Joseph Jacobson
Date: 2024-10-12 00:00:00

Mapping the conformational dynamics of proteins is crucial for elucidating their functional mechanisms. While Molecular Dynamics (MD) simulation enables detailed time evolution of protein motion, its computational toll hinders its use in practice. To address this challenge, multiple deep learning models for reproducing and accelerating MD have been proposed drawing on transport-based generative methods. However, existing work focuses on generation through transport of samples from prior distributions, that can often be distant from the data manifold. The recently proposed framework of stochastic interpolants, instead, enables transport between arbitrary distribution endpoints. Building upon this work, we introduce EquiJump, a transferable SO(3)-equivariant model that bridges all-atom protein dynamics simulation time steps directly. Our approach unifies diverse sampling methods and is benchmarked against existing models on trajectory data of fast folding proteins. EquiJump achieves state-of-the-art results on dynamics simulation with a transferable model on all of the fast folding proteins.
Structured Regularization for Constrained Optimization on the SPD Manifold
Authors: Andrew Cheng, Melanie Weber
Date: 2024-10-12 00:00:00
Tasks: Riemannian optimization

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via constrained Euclidean optimization, where the domain is viewed as a Euclidean space and the structure of the matrices (e.g., positive definiteness) enters as constraints. More recently, geometric approaches that leverage parametrizations of the problem as unconstrained tasks on the corresponding matrix manifold have been proposed. While they exhibit algorithmic benefits in many settings, they cannot directly handle additional constraints, such as inequality or sparsity constraints. A remedy comes in the form of constrained Riemannian optimization methods, notably, Riemannian Frank-Wolfe and Projected Gradient Descent. However, both algorithms require potentially expensive subroutines that can introduce computational bottlenecks in practise. To mitigate these shortcomings, we introduce a class of structured regularizers, based on symmetric gauge functions, which allow for solving constrained optimization on the SPD manifold with faster unconstrained methods. We show that our structured regularizers can be chosen to preserve or induce desirable structure, in particular convexity and "difference of convex" structure. We demonstrate the effectiveness of our approach in numerical experiments.
Many-body Expansion Based Machine Learning Models for Octahedral Transition Metal Complexes
Authors: Ralf Meyer, Daniel Benjamin Kasman Chu, Heather J. Kulik
Date: 2024-10-12 00:00:00
Tasks: Systematic Generalization

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.
Interpolated-MLPs: Controllable Inductive Bias
Authors: Sean Wu, Jordan Hong, Keyu Bai, Gregor Bachmann
Date: 2024-10-12 00:00:00
Tasks: Inductive Bias

Due to their weak inductive bias, Multi-Layer Perceptrons (MLPs) have subpar performance at low-compute levels compared to standard architectures such as convolution-based networks (CNN). Recent work, however, has shown that the performance gap drastically reduces as the amount of compute is increased without changing the amount of inductive bias. In this work, we study the converse: in the low-compute regime, how does the incremental increase of inductive bias affect performance? To quantify inductive bias, we propose a "soft MLP" approach, which we coin Interpolated MLP (I-MLP). We control the amount of inductive bias in the standard MLP by introducing a novel algorithm based on interpolation between fixed weights from a prior model with high inductive bias. We showcase our method using various prior models, including CNNs and the MLP-Mixer architecture. This interpolation scheme allows fractional control of inductive bias, which may be attractive when full inductive bias is not desired (e.g. in the mid-compute regime). We find experimentally that for Vision Tasks in the low-compute regime, there is a continuous and two-sided logarithmic relationship between inductive bias and performance when using CNN and MLP-Mixer prior models.
Provable Acceleration of Nesterov's Accelerated Gradient for Rectangular Matrix Factorization and Linear Neural Networks
Authors: Zhenghao Xu, Yuqing Wang, Tuo Zhao, Rachel Ward, Molei Tao
Date: 2024-10-12 00:00:00

We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that gradient descent (GD) can find a pair of $\epsilon$-optimal solutions $\mathbf{X}_T\in\mathbb{R}^{m\times d}$ and $\mathbf{Y}_T\in\mathbb{R}^{n\times d}$, where $d\geq r$, satisfying $\lVert\mathbf{X}_T\mathbf{Y}_T^\top-\mathbf{A}\rVert_\mathrm{F}\leq\epsilon\lVert\mathbf{A}\rVert_\mathrm{F}$ in $T=O(\kappa^2\log\frac{1}{\epsilon})$ iterations with high probability, where $\kappa$ denotes the condition number of $\mathbf{A}$. Furthermore, we prove that Nesterov's accelerated gradient (NAG) attains an iteration complexity of $O(\kappa\log\frac{1}{\epsilon})$, which is the best-known bound of first-order methods for rectangular matrix factorization. Different from small balanced random initialization in the existing literature, we adopt an unbalanced initialization, where $\mathbf{X}_0$ is large and $\mathbf{Y}_0$ is $0$. Moreover, our initialization and analysis can be further extended to linear neural networks, where we prove that NAG can also attain an accelerated linear convergence rate. In particular, we only require the width of the network to be greater than or equal to the rank of the output label matrix. In contrast, previous results achieving the same rate require excessive widths that additionally depend on the condition number and the rank of the input data matrix.
An Ensemble Scheme for Proactive Dominant Data Migration of Pervasive Tasks at the Edge
Authors: Georgios Boulougaris, Kostas Kolomvatsos
Date: 2024-10-12 00:00:00
Tasks: Edge-computing

Nowadays, a significant focus within the research community on the intelligent management of data at the confluence of the Internet of Things (IoT) and Edge Computing (EC) is observed. In this manuscript, we propose a scheme to be implemented by autonomous edge nodes concerning their identifications of the appropriate data to be migrated to particular locations within the infrastructure, thereby facilitating the effective processing of requests. Our objective is to equip nodes with the capability to comprehend the access patterns relating to offloaded data-driven tasks and to predict which data ought to be returned to the original nodes associated with those tasks. It is evident that these tasks depend on the processing of data that is absent from the original hosting nodes, thereby underscoring the essential data assets that necessitate access. To infer these data intervals, we utilize an ensemble approach that integrates a statistically oriented model and a machine learning framework. As a result, we are able to identify the dominant data assets in addition to detecting the density of the requests. A detailed analysis of the suggested method is provided by presenting the related formulations, which is also assessed and compared with models found in the relevant literature.
Training Dynamics of Transformers to Recognize Word Co-occurrence via Gradient Flow Analysis
Authors: Hongru Yang, Bhavya Kailkhura, Zhangyang Wang, Yingbin Liang
Date: 2024-10-12 00:00:00

Understanding the training dynamics of transformers is important to explain the impressive capabilities behind large language models. In this work, we study the dynamics of training a shallow transformer on a task of recognizing co-occurrence of two designated words. In the literature of studying training dynamics of transformers, several simplifications are commonly adopted such as weight reparameterization, attention linearization, special initialization, and lazy regime. In contrast, we analyze the gradient flow dynamics of simultaneously training three attention matrices and a linear MLP layer from random initialization, and provide a framework of analyzing such dynamics via a coupled dynamical system. We establish near minimum loss and characterize the attention model after training. We discover that gradient flow serves as an inherent mechanism that naturally divide the training process into two phases. In Phase 1, the linear MLP quickly aligns with the two target signals for correct classification, whereas the softmax attention remains almost unchanged. In Phase 2, the attention matrices and the MLP evolve jointly to enlarge the classification margin and reduce the loss to a near minimum value. Technically, we prove a novel property of the gradient flow, termed \textit{automatic balancing of gradients}, which enables the loss values of different samples to decrease almost at the same rate and further facilitates the proof of near minimum training loss. We also conduct experiments to verify our theoretical results.
The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning
Authors: Jake Fawkes, Nic Fishman, Mel Andrews, Zachary C. Lipton
Date: 2024-10-12 00:00:00
Tasks: Fairness, Informativeness, Sensitivity

Fairness metrics are a core tool in the fair machine learning literature (FairML), used to determine that ML models are, in some sense, "fair". Real-world data, however, are typically plagued by various measurement biases and other violated assumptions, which can render fairness assessments meaningless. We adapt tools from causal sensitivity analysis to the FairML context, providing a general framework which (1) accommodates effectively any combination of fairness metric and bias that can be posed in the "oblivious setting"; (2) allows researchers to investigate combinations of biases, resulting in non-linear sensitivity; and (3) enables flexible encoding of domain-specific constraints and assumptions. Employing this framework, we analyze the sensitivity of the most common parity metrics under 3 varieties of classifier across 14 canonical fairness datasets. Our analysis reveals the striking fragility of fairness assessments to even minor dataset biases. We show that causal sensitivity analysis provides a powerful and necessary toolkit for gauging the informativeness of parity metric evaluations. Our repository is available here: https://github.com/Jakefawkes/fragile_fair.
Mastering AI: Big Data, Deep Learning, and the Evolution of Large Language Models -- AutoML from Basics to State-of-the-Art Techniques
Authors: Pohsun Feng, Ziqian Bi, Yizhu Wen, Benji Peng, Junyu Liu, Caitlyn Heqi Yin, Tianyang Wang, Keyu Chen, Sen Zhang, Ming Li, Jiawei Xu, Ming Liu, Xuanhe Pan, Jinlang Wang, Qian Niu
Date: 2024-10-12 00:00:00
Tasks: AutoML, Neural Architecture Search

A comprehensive guide to Automated Machine Learning (AutoML) is presented, covering fundamental principles, practical implementations, and future trends. The paper is structured to assist both beginners and experienced practitioners, with detailed discussions on popular AutoML tools such as TPOT, AutoGluon, and Auto-Keras. Emerging topics like Neural Architecture Search (NAS) and AutoML's applications in deep learning are also addressed. It is anticipated that this work will contribute to ongoing research and development in the field of AI and machine learning.
Bayesian Sheaf Neural Networks
Authors: Patrick Gillespie, Vasileios Maroulas, Ioannis Schizas
Date: 2024-10-12 00:00:00

Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn it as part of the network as a function of the node features. However, this leaves the network potentially overly sensitive to the learned sheaf. As a counter-measure, we propose a variational approach to learning cellular sheaves within sheaf neural networks, yielding an architecture we refer to as a Bayesian sheaf neural network. As part of this work, we define a novel family of reparameterizable probability distributions on the rotation group $SO(n)$ using the Cayley transform. We evaluate the Bayesian sheaf neural network on several graph datasets, and show that our Bayesian sheaf models outperform deterministic sheaf models when training data is limited, and are less sensitive to the choice of hyperparameters.
GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks
Authors: Dingyi Zhuang, Chonghe Jiang, Yunhan Zheng, Shenhao Wang, Jinhua Zhao
Date: 2024-10-12 00:00:00
Tasks: Mixture-of-Experts

Graph Neural Networks deliver strong classification results but often suffer from poor calibration performance, leading to overconfidence or underconfidence. This is particularly problematic in high stakes applications where accurate uncertainty estimates are essential. Existing post hoc methods, such as temperature scaling, fail to effectively utilize graph structures, while current GNN calibration methods often overlook the potential of leveraging diverse input information and model ensembles jointly. In the paper, we propose Graph Ensemble Temperature Scaling, a novel calibration framework that combines input and model ensemble strategies within a Graph Mixture of Experts archi SOTA calibration techniques, reducing expected calibration error by 25 percent across 10 GNN benchmark datasets. Additionally, GETS is computationally efficient, scalable, and capable of selecting effective input combinations for improved calibration performance.