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Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Yilang Zhang, Georgios B Giannakis

Relying on prior knowledge accumulated from related tasks, meta-learning offers a powerful approach to learning a novel task from a limited number of training data. Recent approaches use a family of prior probability density functions or recurrent neural network models, whose parameters can be optimized by utilizing labeled data from the observed tasks. While these approaches have appealing empirical performance, expressiveness of their prior is relatively low, which limits generalization and interpretation of meta-learning. Aiming at expressive yet meaningful priors, this contribution puts forth a novel prior representation model that leverages the notion of algorithm unrolling. The key idea is to unroll the proximal gradient descent steps, where learnable piecewise linear functions are developed to approximate the desired proximal operators within *tight* theoretical error bounds established for both smooth and non-smooth proximal functions. The resultant multi-block neural network not only broadens the scope of learnable priors, but also enhances interpretability from an optimization viewpoint. Numerical tests conducted on few-shot learning datasets demonstrate markedly improved performance with flexible, visualizable, and understandable priors.

Deep Learning · Graph Neural Networks

Tianyu Fan, Lirong Wu, Yufei Huang, Haitao Lin, Cheng Tan, Zhangyang Gao, Stan Z Li

Recent years have witnessed the great success of graph pre-training for graph representation learning. With hundreds of graph pre-training tasks proposed, integrating knowledge acquired from multiple pre-training tasks has become a popular research topic. In this paper, we identify two important collaborative processes for this topic: (1) select: how to select an optimal task combination from a given task pool based on their compatibility, and (2) weigh: how to weigh the selected tasks based on their importance. While there currently has been a lot of work focused on weighing, comparatively little effort has been devoted to selecting. This paper proposes a novel instance-level framework for integrating multiple graph pre-training tasks,Weigh And Select (WAS), where the two collaborative processes, weighing and selecting, are combined by decoupled siamese networks. Specifically, it first adaptively learns an optimal combination of tasks for each instance from a given task pool, based on which a customized instance-level task weighing strategy is learned. Extensive experiments on 16 graph datasets across node-level and graph-level downstream tasks have demonstrated that by combining a few simple but classical tasks, WAS can achieve comparable performance to other leading counterparts.The code is available at https://github.com/TianyuFan0504/WAS.

Optimization · Non-Convex

Aaron Zweig, Joan Bruna

Few neural architectures lend themselves to provable learning with gradient based methods. One popular model is the single-index model, in which labels are produced by composing an unknown linear projection with a possibly unknown scalar link function. Learning this model with SGD is relatively well-understood, whereby the so-called information exponent of the link function governs a polynomial sample complexity rate. However, extending this analysis to deeper or more complicated architectures remains challenging.In this work, we consider single index learning in the setting of symmetric neural networks. Under analytic assumptions on the activation and maximum degree assumptions on the link function, we prove that gradient flow recovers the hidden planted direction, represented as a finitely supported vector in the feature space of power sum polynomials. We characterize a notion of information exponent adapted to our setting that controls the efficiency of learning.

Deep Learning · Robustness

Kai Hu, Klas Leino, Zifan Wang, Matt Fredrikson

Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks.A key challenge, supported both theoretically and empirically, is that robustness demands greater network capacity and more data than standard training. However, effectively adding capacity under stringent Lipschitz constraints has proven more difficult than it may seem, evident by the fact that state-of-the-art approach tend more towards \emph{underfitting} than overfitting.Moreover, we posit that a lack of careful exploration of the design space for Lipshitz-based approaches has left potential performance gains on the table.In this work, we provide a more comprehensive evaluation to better uncover the potential of Lipschitz-based certification methods.Using a combination of novel techniques, design optimizations, and synthesis of prior work, we are able to significantly improve the state-of-the-art VRA for deterministic certification on a variety of benchmark datasets, and over a range of perturbation sizes.Of particular note, we discover that the addition of large ``Cholesky-orthogonalized residual dense'' layers to the end of existing state-of-the-art Lipschitz-controlled ResNet architectures is especially effective for increasing network capacity and performance.Combined with filtered generative data augmentation, our final results further the state of the art deterministic VRA by up to 8.5 percentage points.

Deep Learning · Everything Else

Moritz Imfeld, Jacopo Graldi, Marco Giordano, Thomas Hofmann, Sotiris Anagnostidis, Sidak Pal Singh

Fusion is a technique for merging multiple independently-trained neural networks in order to combine their capabilities. Past attempts have been restricted to the case of fully-connected, convolutional, and residual networks. This paper presents a systematic approach for fusing two or more transformer-based networks exploiting Optimal Transport to (soft-)align the various architectural components. We flesh out an abstraction for layer alignment, that can generalize to arbitrary architectures -- in principle -- and we apply this to the key ingredients of Transformers such as multi-head self-attention, layer-normalization, and residual connections, and we discuss how to handle them via various ablation studies. Furthermore, our method allows the fusion of models of different sizes (heterogeneous fusion), providing a new and efficient way to compress Transformers. The proposed approach is evaluated on both image classification tasks via Vision Transformer and natural language modeling tasks using BERT. Our approach consistently outperforms vanilla fusion, and, after a surprisingly short finetuning, also outperforms the individual converged parent models.In our analysis, we uncover intriguing insights about the significant role of soft alignment in the case of Transformers. Our results showcase the potential of fusing multiple Transformers, thus compounding their expertise, in the budding paradigm of model fusion and recombination. Code is available at https://github.com/graldij/transformer-fusion.

Alexander Theus, Olin Geimer, Friedrich Wicke, Thomas Hofmann, Sotiris Anagnostidis, Sidak Pal Singh

Structural pruning of neural networks conventionally relies on identifying and discarding less important neurons, a practice often resulting in significant accuracy loss that necessitates subsequent fine-tuning efforts. This paper introduces a novel approach named Intra-Fusion, challenging this prevailing pruning paradigm.Unlike existing methods that focus on designing meaningful neuron importance metrics, Intra-Fusion redefines the overlying pruning procedure.Through utilizing the concepts of model fusion and Optimal Transport, we leverage an agnostically given importance metric to arrive at a more effective sparse model representation.Notably, our approach achieves substantial accuracy recovery without the need for resource-intensive fine-tuning, making it an efficient and promising tool for neural network compression.Additionally, we explore how fusion can be added to the pruning process to significantly decrease the training time while maintaining competitive performance. We benchmark our results for various networks on commonly used datasets such as CIFAR-10, CIFAR-100, and ImageNet. More broadly, we hope that the proposed Intra-Fusion approach invigorates exploration into a fresh alternative to the predominant compression approaches.Our code is available [here](https://github.com/alexandertheus/Intra-Fusion).

Social Aspects · Trustworthy Machine Learning

Yuhao Mao, Mark N Müller, Marc Fischer, Martin Vechev

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounds. Still, we lack a theoretical understanding of the mechanisms making IBP so successful. In this work, we investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models (DLNs), tightness decreases with width and depth at initialization, but improves with IBP training. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, providing an explanation for the observed robustness-accuracy trade-off. Finally, we show how these results on DLNs transfer to ReLU networks, before conducting an extensive empirical study, (i) confirming this transferability and yielding state-of-the-art certified accuracy, (ii) finding that while all IBP-based training methods lead to high tightness, this increase is dominated by the size of the propagated input regions rather than the robustness specification, and finally (iii) observing that non-IBP-based methods do not increase tightness. Together, these results help explain the success of recent certified training methods and may guide the development of new ones.

Applications · Physics

Peiyan Hu, Yue Wang, Zhi-Ming Ma

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Ampère equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.

Deep Learning · Graph Neural Networks

Yuxing Tian, Yiyan Qi, Fan Guo

Link prediction is a crucial task in dynamic graph learning. Recent advancements in continuous-time dynamic graph models, primarily by leveraging richer temporal details, have significantly improved link prediction performance. However, due to their complex modules, they still face several challenges, such as overfitting and optimization difficulties. More importantly, it is challenging for these methods to capture the 'shift' phenomenon, where node interaction patterns change over time. To address these issues, we propose a simple yet novel method called \textbf{Fre}quency \textbf{E}nhanced Continuous-Time \textbf{Dy}namic \textbf{G}raph ({\bf FreeDyG}) model for link prediction. Specifically, we propose a node interaction frequency encoding module that both explicitly captures the proportion of common neighbors and the frequency of the interaction of the node pair. Unlike previous works that primarily focus on the time domain, we delve into the frequency domain, allowing a deeper and more nuanced extraction of interaction patterns, revealing periodic and "shift" behaviors. Extensive experiments conducted on seven real-world continuous-time dynamic graph datasets validate the effectiveness of FreeDyG. The results consistently demonstrate that FreeDyG outperforms existing methods in both transductive and inductive settings. Our code is available at this repository: \href{https://github.com/Tianxzzz/FreeDyG}{https://github.com/Tianxzzz/FreeDyG}

Deep Learning · Theory

Quinn Fisher, Haoming Meng, Vardan Papyan

Mixup is a data augmentation strategy that employs convex combinations of training instances and their respective labels to improve the robustness and calibration of deep neural networks. Despite its widespread adoption, the nuanced mechanisms that underpin its success are not entirely understood. The observed phenomenon of Neural Collapse, where the last-layer activations and classifier of deep networks converge to a simplex equiangular tight frame (ETF), provides a compelling motivation to explore whether mixup induces alternative geometric configurations and whether those could explain its success. In this study, we delve into the last-layer activations of training data for deep networks subjected to mixup, aiming to uncover insights into its operational efficacy. Our investigation, spanning various architectures and dataset pairs, reveals that mixup's last-layer activations predominantly converge to a distinctive configuration different than one might expect. In this configuration, activations from mixed-up examples of identical classes align with the classifier, while those from different classes delineate channels along the decision boundary. These findings are unexpected, as mixed-up features are not simple convex combinations of feature class means (as one might get, for example, by training mixup with the mean squared error loss). By analyzing this distinctive geometric configuration, we elucidate the mechanisms by which mixup enhances model calibration. To further validate our empirical observations, we conduct a theoretical analysis under the assumption of an unconstrained features model, utilizing the mixup loss. Through this, we characterize and derive the optimal last-layer features under the assumption that the classifier forms a simplex ETF.

Deep Learning

Gabryel Mason-Williams, Fredrik Dahlqvist

Pruning is an effective method to reduce the size of deep neural network models, maintain accuracy, and, in some cases, improve the network's overall performance. However, the mechanisms underpinning pruning remain unclear. Why can different methods prune by different percentages yet achieve similar performance? Why can we not prune at the start of training? Why are some models more amenable to being pruned than others? Given a model, what is the maximum amount it can be pruned before significantly affecting the performance? This paper explores and answers these questions from the global unstructured magnitude pruning perspective with one epoch of fine-tuning. We develop the idea that cosine similarity is an effective proxy measure for functional similarity between the parent and the pruned network. We prove that the L1 pruning method is optimal when pruning by cosine similarity. We show that the higher the kurtosis of a model's parameter distribution, the more it can be pruned while maintaining performance. Finally, we present a simple method to determine the optimal amount by which a network can be L1-pruned based on its parameter distribution. The code demonstrating the method is available at https://github.com/gmw99/what_makes_a_good_prune

Applications · Computer Vision

yiwei zhang, Guo Lu, Yunuo Chen, Shen Wang, Yibo Shi, Jing Wang, Li Song

The learning-based video compression method has made significant progress in recent years, exhibiting promising compression performance compared with traditional video codecs. However, prior works have primarily focused on advanced compression architectures while neglecting the rate control technique. Rate control can precisely control the coding bitrate with optimal compression performance, which is a critical technique in practical deployment. To address this issue, we present a fully neural network-based rate control system for learned video compression methods. Our system accurately encodes videos at a given bitrate while enhancing the rate-distortion performance. Specifically, we first design a rate allocation model to assign optimal bitrates to each frame based on their varying spatial and temporal characteristics. Then, we propose a deep learning-based rate implementation network to perform the rate-parameter mapping, precisely predicting coding parameters for a given rate. Our proposed rate control system can be easily integrated into existing learning-based video compression methods. The extensive experimental results show that the proposed method achieves accurate rate control on several baseline methods while also improving overall rate-distortion performance.

Applications · Time Series

Liu Xiaoyi, Duxin Chen, Wenjia Wei, Xia Zhu, Wenwu Yu

With the continuous advancement of neural network methodologies, time series prediction has attracted substantial interest over the past decades. Nonetheless, the interpretability of neural networks is insufficient and the utilization of deep learning techniques for prediction necessitates significant computational expenditures, rendering its application arduous in numerous scenarios. In order to tackle this challenge, an interpretable sparse system identification method which does not require a time-consuming training through back-propagation is proposed in this study. This method integrates advantages from both knowledge-based and data-driven approaches, and constructs dictionary functions by leveraging Fourier basis and taking into account both the long-term trends and the short-term fluctuations behind data. By using the $l_1$ norm for sparse optimization, prediction results can be gained with an explicit sparse expression function and an extremely high accuracy. The performance evaluation of the proposed method is conducted on comprehensive benchmark datasets, including ETT, Exchange, and ILI. Results reveal that our proposed method attains a significant overall improvement of more than 20\% in accordance with the most recent state-of-the-art deep learning methodologies. Additionally, our method demonstrates the efficient training capability on only CPUs. Therefore, this study may shed some light onto the realm of time series reconstruction and prediction.

Reinforcement Learning · Online

Zichen Liu, Chao Du, Wee Sun Lee, Min Lin

Acquiring an accurate world model $\textit{online}$ for model-based reinforcement learning (MBRL) is challenging due to data nonstationarity, which typically causes catastrophic forgetting for neural networks (NNs). From the online learning perspective, a Follow-The-Leader (FTL) world model is desirable, which optimally fits all previous experiences at each round. Unfortunately, NN-based models need re-training on all accumulated data at every interaction step to achieve FTL, which is computationally expensive for lifelong agents. In this paper, we revisit models that can achieve FTL with incremental updates. Specifically, our world model is a linear regression model supported by nonlinear random features. The linear part ensures efficient FTL update while the nonlinear random feature empowers the fitting of complex environments. To best trade off model capacity and computation efficiency, we introduce a locality sensitive sparse encoding, which allows us to conduct efficient sparse updates even with very high dimensional nonlinear features. We validate the representation power of our encoding and verify that it allows efficient online learning under data covariate shift. We also show, in the Dyna MBRL setting, that our world models learned online using a $\textit{single pass}$ of trajectory data either surpass or match the performance of deep world models trained with replay and other continual learning methods.

Zhenfeng He, Yao Shu, Zhongxiang Dai, Bryan Kian Hsiang Low

Neural architecture search (NAS) has become a key component of AutoML and a standard tool to automate the design of deep neural networks. Recently, training-free NAS as an emerging paradigm has successfully reduced the search costs of standard training-based NAS by estimating the true architecture performance with only training-free metrics. Nevertheless, the estimation ability of these metrics typically varies across different tasks, making it challenging to achieve robust and consistently good search performance on diverse tasks with only a single training-free metric. Meanwhile, the estimation gap between training-free metrics and the true architecture performances limits training-free NAS to achieve superior performance. To address these challenges, we propose the robustifying and boosting training-free NAS (RoBoT) algorithm which (a) employs the optimized combination of existing training-free metrics explored from Bayesian optimization to develop a robust and consistently better-performing metric on diverse tasks, and (b) applies greedy search, i.e., the exploitation, on the newly developed metric to bridge the aforementioned gap and consequently to boost the search performance of standard training-free NAS further. Remarkably, the expected performance of our RoBoT can be theoretically guaranteed, which improves over the existing training-free NAS under mild conditions with additional interesting insights. Our extensive experiments on various NAS benchmark tasks yield substantial empirical evidence to support our theoretical results.

Deep Learning

AOCHUAN CHEN, Yimeng Zhang, Jinghan Jia, James Diffenderfer, Konstantinos Parasyris, Jiancheng Liu, Yihua Zhang, Zheng Zhang, Bhavya Kailkhura, Sijia Liu

Zeroth-order (ZO) optimization has become a popular technique for solving machine learning (ML) problems when first-order (FO) information is difficult or impossible to obtain. However, the scalability of ZO optimization remains an open problem: Its use has primarily been limited to relatively small-scale ML problems, such as sample-wise adversarial attack generation. To our best knowledge, no prior work has demonstrated the effectiveness of ZO optimization in training deep neural networks (DNNs) without a significant decrease in performance. To overcome this roadblock, we develop DeepZero, a principled and practical ZO deep learning (DL) framework that can scale ZO optimization to DNN training from scratch through three primary innovations. First, we demonstrate the advantages of coordinate-wise gradient estimation (CGE) over randomized vector-wise gradient estimation in training accuracy and computational efficiency. Second, we propose a sparsity-induced ZO training protocol that extends the model pruning methodology using only finite differences to explore and exploit the sparse DL prior in CGE. Third, we develop the methods of feature reuse and forward parallelization to advance the practical implementations of ZO training. Our extensive experiments show that DeepZero achieves state-of-the-art (SOTA) accuracy on ResNet-20 trained on CIFAR-10, approaching FO training performance for the first time. Furthermore, we show the practical utility of DeepZero in applications of certified adversarial defense and DL-based partial differential equation error correction, achieving 10-20% improvement over SOTA. We believe our results will inspire future research on scalable ZO optimization and contribute to advancing deep learning.

Optimization · Learning for Optimization

Wenxi Wang, Yang Hu, Mohit Tiwari, Sarfraz Khurshid, Kenneth McMillan, Risto Miikkulainen

Propositional satisfiability (SAT) is an NP-complete problem that impacts manyresearch fields, such as planning, verification, and security. Mainstream modernSAT solvers are based on the Conflict-Driven Clause Learning (CDCL) algorithm.Recent work aimed to enhance CDCL SAT solvers using Graph Neural Networks(GNNs). However, so far this approach either has not made solving more effective,or required substantial GPU resources for frequent online model inferences. Aimingto make GNN improvements practical, this paper proposes an approach calledNeuroBack, which builds on two insights: (1) predicting phases (i.e., values) ofvariables appearing in the majority (or even all) of the satisfying assignments areessential for CDCL SAT solving, and (2) it is sufficient to query the neural modelonly once for the predictions before the SAT solving starts. Once trained, theoffline model inference allows NeuroBack to execute exclusively on the CPU,removing its reliance on GPU resources. To train NeuroBack, a new dataset calledDataBack containing 120,286 data samples is created. Finally, NeuroBack is implementedas an enhancement to a state-of-the-art SAT solver called Kissat. As a result,it allowed Kissat to solve 5.2% more problems on the recent SAT competitionproblem set, SATCOMP-2022. NeuroBack therefore shows how machine learningcan be harnessed to improve SAT solving in an effective and practical manner.

Deep Learning · Generative Models and Autoencoders

Tianrong Chen, Jiatao Gu, Laurent Dinh, Evangelos Theodorou, Joshua Susskind, Shuangfei Zhai

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in \textbf{phase space dynamics}, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Deep Learning · Robustness

Guang Lin, Chao Li, Jianhai Zhang, Toshihisa Tanaka, Qibin Zhao

The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot generalize well to unseen attacks. Another effective defense technique based on adversarial purification (AP) can enhance generalization but cannot achieve optimal robustness. Meanwhile, both methods share one common limitation on the degraded standard accuracy. To mitigate these issues, we propose a novel pipeline to acquire the robust purifier model, named Adversarial Training on Purification (AToP), which comprises two components: perturbation destruction by random transforms (RT) and purifier model fine-tuned (FT) by adversarial loss. RT is essential to avoid overlearning to known attacks, resulting in the robustness generalization to unseen attacks, and FT is essential for the improvement of robustness. To evaluate our method in an efficient and scalable way, we conduct extensive experiments on CIFAR-10, CIFAR-100, and ImageNette to demonstrate that our method achieves optimal robustness and exhibits generalization ability against unseen attacks.

Deep Learning · Graph Neural Networks

Anson Simon Bastos, Kuldeep Singh, Abhishek Nadgeri, Manish Singh, Toyotaro Suzumura

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with \eft for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.