He, Di, Xia, Yingce, Qin, Tao, Wang, Liwei, Yu, Nenghai, Liu, Tie-Yan, Ma, Wei-Ying

While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training. However, human labeling is very costly. To tackle this training data bottleneck, we develop a dual-learning mechanism, which can enable an NMT system to automatically learn from unlabeled data through a dual-learning game. This mechanism is inspired by the following observation: any machine translation task has a dual task, e.g., English-to-French translation (primal) versus French-to-English translation (dual); the primal and dual tasks can form a closed loop, and generate informative feedback signals to train the translation models, even if without the involvement of a human labeler. In the dual-learning mechanism, we use one agent to represent the model for the primal task and the other agent to represent the model for the dual task, then ask them to teach each other through a reinforcement learning process. Based on the feedback signals generated during this process (e.g., the language-model likelihood of the output of a model, and the reconstruction error of the original sentence after the primal and dual translations), we can iteratively update the two models until convergence (e.g., using the policy gradient methods). We call the corresponding approach to neural machine translation \emph{dual-NMT}. Experiments show that dual-NMT works very well on English$\leftrightarrow$French translation; especially, by learning from monolingual data (with 10\% bilingual data for warm start), it achieves a comparable accuracy to NMT trained from the full bilingual data for the French-to-English translation task.

Wang, Gang, Giannakis, Georgios

This paper puts forth a novel algorithm, termed \emph{truncated generalized gradient flow} (TGGF), to solve for $\mathbf{x}\in {\mathbb{R}}^n/{\mathbb{C}}^n$ a system of $m$ quadratic equations $y_i=|⟨{\mathbf{a}}_i,\mathbf{x}⟩{|}^2$, $i=1,2,\dots ,m$, which even for ${\left\{{\mathbf{a}}_i\in {\mathbb{R}}^n/{\mathbb{C}}^n\right\}}_{i=1}^m$ random is known to be \emph{NP-hard} in general. We prove that as soon as the number of equations $m$ is on the order of the number of unknowns $n$, TGGF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with the time required to read the data ${\left\{\left({\mathbf{a}}_i;y_i\right)\right\}}_{i=1}^m$. Specifically, TGGF proceeds in two stages: s1) A novel \emph{orthogonality-promoting} initialization that is obtained with simple power iterations; and, s2) a refinement of the initial estimate by successive updates of scalable \emph{truncated generalized gradient iterations}. The former is in sharp contrast to the existing spectral initializations, while the latter handles the rather challenging nonconvex and nonsmooth \emph{amplitude-based} cost function. Numerical tests demonstrate that: i) The novel orthogonality-promoting initialization method returns more accurate and robust estimates relative to its spectral counterparts; and ii) even with the same initialization, our refinement/truncation outperforms Wirtinger-based alternatives, all corroborating the superior performance of TGGF over state-of-the-art algorithms.

Wang, Ziyu, Shou, Mike Zheng, Zhang, Mengmi

Learning object-centric representations from complex natural environments enables both humans and machines with reasoning abilities from low-level perceptual features. To capture compositional entities of the scene, we proposed cyclic walks between perceptual features extracted from vision transformers and object entities. First, a slot-attention module interfaces with these perceptual features and produces a finite set of slot representations. These slots can bind to any object entities in the scene via inter-slot competitions for attention. Next, we establish entity-feature correspondence with cyclic walks along high transition probability based on the pairwise similarity between perceptual features (aka "parts") and slot-binded object representations (aka "whole"). The whole is greater than its parts and the parts constitute the whole. The part-whole interactions form cycle consistencies, as supervisory signals, to train the slot-attention module. Our rigorous experiments on \textit{seven} image datasets in \textit{three} \textit{unsupervised} tasks demonstrate that the networks trained with our cyclic walks can disentangle foregrounds and backgrounds, discover objects, and segment semantic objects in complex scenes. In contrast to object-centric models attached with a decoder for the pixel-level or feature-level reconstructions, our cyclic walks provide strong learning signals, avoiding computation overheads and enhancing memory efficiency. Our source code and data are available at: \href{https://github.com/ZhangLab-DeepNeuroCogLab/Parts-Whole-Object-Centric-Learning/}{link}.

No authors listed

In many applications such as advertisement placement or automated dialog systems, an intelligent system optimizes performance over a sequence of interactions with each user. Such tasks often involve many states and potentially time-dependent transition dynamics, and can be modeled well as episodic Markov decision processes (MDPs). In this paper, we present a PAC algorithm for reinforcement learning in episodic finite MDPs with time-dependent transitions that acts epsilon-optimal in all but O(S A H^3 / epsilon^2 log(1 / delta)) episodes. Our algorithm has a polynomial computational complexity, and our sample complexity bound accounts for the fact that we may only be able to approximately solve the internal planning problems. In addition, our PAC sample complexity bound has only linear dependency on the number of states S and actions A and strictly improves previous bounds with S^2 dependency in this setting. Compared against other methods for infinite horizon reinforcement learning with linear state space sample complexity our method has much lower dependency on the (effective) horizon. Indeed, our bound is optimal up to a factor of H.

Thomas Kerdreux, Alexandre d’Aspremont, Sebastian Pokutta

Conditional Gradients (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection step, and competitive numerical performance. While the vanilla Frank-Wolfe algorithm only ensures a worst-case rate of $O(1/ϵ)$, various recent results have shown that for strongly convex functions, the method can be slightly modified to achieve linear convergence. However, this still leaves a huge gap between sublinear $O(1/ϵ)$ convergence and linear $O(\log 1/ϵ)$ convergence to reach an $ϵ$-approximate solution. Here, we present a new variant of Conditional Gradients, that can dynamically adapt to the function’s geometric properties using restarts and thus smoothly interpolates between the sublinear and linear regimes. Furthermore, our results apply to generic compact convex constraint sets.

Kandasamy, Kirthevasan, Dasarathy, Gautam, Oliva, Junier B., Schneider, Jeff, Poczos, Barnabas

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function $\text{func}$. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to $\text{func}$ may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of $\text{func}$ in a small but promising region and speedily identify the optimum. We formalise this task as a \emph{multi-fidelity} bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop \mfgpucb, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. \mfgpucbs outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

Li, Yongbo, Dong, Weisheng, Xie, Xuemei, Shi, GUANGMING, Li, Xin, Xu, Donglai

Learning accurate prior knowledge of natural images is of great importance for single image super-resolution (SR). Existing SR methods either learn the prior from the low/high-resolution patch pairs or estimate the prior models from the input low-resolution (LR) image. Specifically, high-frequency details are learned in the former methods. Though effective, they are heuristic and have limitations in dealing with blurred LR images; while the latter suffers from the limitations of frequency aliasing. In this paper, we propose to combine those two lines of ideas for image super-resolution. More specifically, the parametric sparse prior of the desirable high-resolution (HR) image patches are learned from both the input low-resolution (LR) image and a training image dataset. With the learned sparse priors, the sparse codes and thus the HR image patches can be accurately recovered by solving a sparse coding problem. Experimental results show that the proposed SR method outperforms existing state-of-the-art methods in terms of both subjective and objective image qualities.

barbier, jean, Dia, Mohamad, Macris, Nicolas, Krzakala, Florent, Lesieur, Thibault, Zdeborová, Lenka

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available.

Romain Brault, Alex Lambert, Zoltan Szabo, Maxime Sangnier, Florence d’Alche-Buc

Machine learning has witnessed tremendous success in solving tasks depending on a single hyperparameter. When considering simultaneously a finite number of tasks, multi-task learning enables one to account for the similarities of the tasks via appropriate regularizers. A step further consists of learning a continuum of tasks for various loss functions. A promising approach, called Parametric Task Learning, has paved the way in the continuum setting for affine models and piecewise-linear loss functions. In this work, we introduce a novel approach called Infinite Task Learning whose goal is to learn a function whose output is a function over the hyperparameter space. We leverage tools from operator-valued kernels and the associated vector-valued RKHSs that provide an explicit control over the role of the hyperparameters, and also allows us to consider new type of constraints. We provide generalization guarantees to the suggested scheme and illustrate its efficiency in cost-sensitive classification, quantile regression and density level set estimation.

Wang, Peng, Shen, Xiaohui, Russell, Bryan, Cohen, Scott, Price, Brian, Yuille, Alan L.

This paper introduces an approach to regularize 2.5D surface normal and depth predictions at each pixel given a single input image. The approach infers and reasons about the underlying 3D planar surfaces depicted in the image to snap predicted normals and depths to inferred planar surfaces, all while maintaining fine detail within objects. Our approach comprises two components: (i) a fourstream convolutional neural network (CNN) where depths, surface normals, and likelihoods of planar region and planar boundary are predicted at each pixel, followed by (ii) a dense conditional random field (DCRF) that integrates the four predictions such that the normals and depths are compatible with each other and regularized by the planar region and planar boundary information. The DCRF is formulated such that gradients can be passed to the surface normal and depth CNNs via backpropagation. In addition, we propose new planar wise metrics to evaluate geometry consistency within planar surfaces, which are more tightly related to dependent 3D editing applications. We show that our regularization yields a 30% relative improvement in planar consistency on the NYU v2 dataset.

Saberian, Mohammad, Costa Pereira, Jose, Xu, Can, Yang, Jian, Nvasconcelos, Nuno

In this paper we establish a duality between boosting and SVM, and use this to derive a novel discriminant dimensionality reduction algorithm. In particular, using the multiclass formulation of boosting and SVM we note that both use a combination of mapping and linear classification to maximize the multiclass margin. In SVM this is implemented using a pre-defined mapping (induced by the kernel) and optimizing the linear classifiers. In boosting the linear classifiers are pre-defined and the mapping (predictor) is learned through combination of weak learners. We argue that the intermediate mapping, e.g. boosting predictor, is preserving the discriminant aspects of the data and by controlling the dimension of this mapping it is possible to achieve discriminant low dimensional representations for the data. We use the aforementioned duality and propose a new method, Large Margin Discriminant Dimensionality Reduction (LADDER) that jointly learns the mapping and the linear classifiers in an efficient manner. This leads to a data-driven mapping which can embed data into any number of dimensions. Experimental results show that this embedding can significantly improve performance on tasks such as hashing and image/scene classification.

Xu, Liangbei, Davenport, Mark

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the {\em matrix sensing} and {\em matrix completion} observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.

Woodworth, Blake E., Srebro, Nati

We provide tight upper and lower bounds on the complexity of minimizing the average of m convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs randomized optimization. For smooth functions, we show that accelerated gradient descent (AGD) and an accelerated variant of SVRG are optimal in the deterministic and randomized settings respectively, and that a gradient oracle is sufficient for the optimal rate. For non-smooth functions, having access to prox oracles reduces the complexity and we present optimal methods based on smoothing that improve over methods using just gradient accesses.

Quentin Berthet, Jordan Ellenberg

We study the detection problem of finding planted solutions in random instances of flat satisfiability problems, a generalization of boolean satisfiability formulas. We describe the properties of random instances of flat satisfiability, as well of the optimal rates of detection of the associated hypothesis testing problem. We also study the performance of an algorithmically efficient testing procedure. We introduce a modification of our model, the light planting of solutions, and show that it is as hard as the problem of learning parity with noise. This hints strongly at the difficulty of detecting planted flat satisfiability for a wide class of tests.

Karnin, Zohar S.

We consider the problem of finding the best arm in a stochastic Mutli-armed Bandit (MAB) game and propose a general framework based on verification that applies to multiple well-motivated generalizations of the classic MAB problem. In these generalizations, additional structure is known in advance, causing the task of verifying the optimality of a candidate to be easier than discovering the best arm. Our results are focused on the scenario where the failure probability $\delta$ must be very low; we essentially show that in this high confidence regime, identifying the best arm is as easy as the task of verification. We demonstrate the effectiveness of our framework by applying it, and improving the state-of-the art results in the problems of: Linear bandits, Dueling bandits with the Condorcet assumption, Copeland dueling bandits, Unimodal bandits and Graphical bandits.

Truyen, Tran, Phung, Dinh, Bui, Hung, Venkatesh, Svetha

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms for learning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.

Zhou, Allan, Yang, Kaien, Burns, Kaylee, Cardace, Adriano, Jiang, Yiding, Sokota, Samuel, Kolter, J. Zico, Finn, Chelsea

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned optimization, processing implicit neural representations, network editing, and policy evaluation, there are few unifying principles for designing effective architectures that process the weights of other networks. We approach the design of neural functionals through the lens of symmetry, in particular by focusing on the permutation symmetries that arise in the weights of deep feedforward networks because hidden layer neurons have no inherent order. We introduce a framework for building permutation equivariant neural functionals, whose architectures encode these symmetries as an inductive bias. The key building blocks of this framework are NF-Layers (neural functional layers) that we constrain to be permutation equivariant through an appropriate parameter sharing scheme. In our experiments, we find that permutation equivariant neural functionals are effective on a diverse set of tasks that require processing the weights of MLPs and CNNs, such as predicting classifier generalization, producing "winning ticket" sparsity masks for initializations, and classifying or editing implicit neural representations (INRs). In addition, we provide code for our models and experiments at https://github.com/AllanYangZhou/nfn.

Bautista, Miguel A., Sanakoyeu, Artsiom, Tikhoncheva, Ekaterina, Ommer, Bjorn

Exemplar learning is a powerful paradigm for discovering visual similarities in an unsupervised manner. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With only a single positive sample, a great imbalance between one positive and many negatives, and unreliable relationships between most samples, training of convolutional neural networks is impaired. Given weak estimates of local distance we propose a single optimization problem to extract batches of samples with mutually consistent relations. Conflicting relations are distributed over different batches and similar samples are grouped into compact cliques. Learning exemplar similarities is framed as a sequence of clique categorization tasks. The CNN then consolidates transitivity relations within and between cliques and learns a single representation for all samples without the need for labels. The proposed unsupervised approach has shown competitive performance on detailed posture analysis and object classification.

Cao, Wei, Wang, Dong, Li, Jian, Zhou, Hao, Li, Lei, Li, Yitan

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirectional recurrent dynamical system, without any specific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during the backpropagation. BRITS has three advantages: (a) it can handle multiple correlated missing values in time series; (b) it generalizes to time series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data. We evaluate our model on three real-world datasets, including an air quality dataset, a health-care data, and a localization data for human activity. Experiments show that our model outperforms the state-of-the-art methods in both imputation and classification/regression accuracies.

Wang, Wenhao, Sun, Yifan, Li, Wei, Yang, Yi

This paper explores a hierarchical prompting mechanism for the hierarchical image classification (HIC) task. Different from prior HIC methods, our hierarchical prompting is the first to explicitly inject ancestor-class information as a tokenized hint that benefits the descendant-class discrimination. We think it well imitates human visual recognition, i.e., humans may use the ancestor class as a prompt to draw focus on the subtle differences among descendant classes. We model this prompting mechanism into a Transformer with Hierarchical Prompting (TransHP). TransHP consists of three steps: 1) learning a set of prompt tokens to represent the coarse (ancestor) classes, 2) on-the-fly predicting the coarse class of the input image at an intermediate block, and 3) injecting the prompt token of the predicted coarse class into the intermediate feature. Though the parameters of TransHP maintain the same for all input images, the injected coarse-class prompt conditions (modifies) the subsequent feature extraction and encourages a dynamic focus on relatively subtle differences among the descendant classes. Extensive experiments show that TransHP improves image classification on accuracy (e.g., improving ViT-B/16 by +2.83% ImageNet classification accuracy), training data efficiency (e.g., +12.69% improvement under 10% ImageNet training data), and model explainability. Moreover, TransHP also performs favorably against prior HIC methods, showing that TransHP well exploits the hierarchical information. The code is available at: https://github.com/WangWenhao0716/TransHP.

Khim, Justin T., Jog, Varun, Loh, Po-Ling

We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a (1 - 1/e)-factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently. This leads to an attractive, highly scalable algorithm for influence maximization with rigorous theoretical guarantees.

Wojciech M. Czarnecki, Razvan Pascanu, Simon Osindero, Siddhant Jayakumar, Grzegorz Swirszcz, Max Jaderberg

The transfer of knowledge from one policy to another is an important tool in Deep Reinforcement Learning. This process, referred to as distillation, has been used to great success, for example, by enhancing the optimisation of agents, leading to stronger performance faster, on harder domains. Despite the widespread use and conceptual simplicity of distillation, many different formulations are used in practice, and the subtle variations between them can often drastically change the performance and the resulting objective that is being optimised. In this work, we rigorously explore the entire landscape of policy distillation, comparing the motivations and strengths of each variant through theoretical and empirical analysis. Our results point to three distillation techniques, that are preferred depending on specifics of the task. Specifically a newly proposed expected entropy regularised distillation allows for quicker learning in a wide range of situations, while still guaranteeing convergence.

Ratner, Alexander J., De Sa, Christopher M., Wu, Sen, Selsam, Daniel, Ré, Christopher

Large labeled training sets are the critical building blocks of supervised learning methods and are key enablers of deep learning techniques. For some applications, creating labeled training sets is the most time-consuming and expensive part of applying machine learning. We therefore propose a paradigm for the programmatic creation of training sets called data programming in which users provide a set of labeling functions, which are programs that heuristically label subsets of the data, but that are noisy and may conflict. By viewing these labeling functions as implicitly describing a generative model for this noise, we show that we can recover the parameters of this model to "denoise" the generated training set, and establish theoretically that we can recover the parameters of these generative models in a handful of settings. We then show how to modify a discriminative loss function to make it noise-aware, and demonstrate our method over a range of discriminative models including logistic regression and LSTMs. Experimentally, on the 2014 TAC-KBP Slot Filling challenge, we show that data programming would have led to a new winning score, and also show that applying data programming to an LSTM model leads to a TAC-KBP score almost 6 F1 points over a state-of-the-art LSTM baseline (and into second place in the competition). Additionally, in initial user studies we observed that data programming may be an easier way for non-experts to create machine learning models when training data is limited or unavailable.

Acerbi, Luigi

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to the gradient or a large number of likelihood evaluations. We introduce here a novel sample-efficient inference framework, Variational Bayesian Monte Carlo (VBMC). VBMC combines variational inference with Gaussian-process based, active-sampling Bayesian quadrature, using the latter to efficiently approximate the intractable integral in the variational objective. Our method produces both a nonparametric approximation of the posterior distribution and an approximate lower bound of the model evidence, useful for model selection. We demonstrate VBMC both on several synthetic likelihoods and on a neuronal model with data from real neurons. Across all tested problems and dimensions (up to D = 10), VBMC performs consistently well in reconstructing the posterior and the model evidence with a limited budget of likelihood evaluations, unlike other methods that work only in very low dimensions. Our framework shows great promise as a novel tool for posterior and model inference with expensive, black-box likelihoods.

Betancourt, Brenda, Zanella, Giacomo, Miller, Jeffrey W., Wallach, Hanna, Zaidi, Abbas, Steorts, Rebecca C.

Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.

Chen, Jiecao, Sun, He, Woodruff, David, Zhang, Qin

Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would like the quality of the clustering in the distributed setting to match that in the centralized setting for which all the data resides on a single site. In this work, we study both graph and geometric clustering problems in two distributed models: (1) a point-to-point model, and (2) a model with a broadcast channel. We give protocols in both models which we show are nearly optimal by proving almost matching communication lower bounds. Our work highlights the surprising power of a broadcast channel for clustering problems; roughly speaking, to cluster n points or n vertices in a graph distributed across s servers, for a worst-case partitioning the communication complexity in a point-to-point model is n*s, while in the broadcast model it is n + s. We implement our algorithms and demonstrate this phenomenon on real life datasets, showing that our algorithms are also very efficient in practice.

Song, Dogyoon, Lee, Christina E., Li, Yihua, Shah, Devavrat

We introduce the framework of {\em blind regression} motivated by {\em matrix completion} for recommendation systems: given $m$ users, $n$ movies, and a subset of user-movie ratings, the goal is to predict the unobserved user-movie ratings given the data, i.e., to complete the partially observed matrix. Following the framework of non-parametric statistics, we posit that user $u$ and movie $i$ have features $x_1(u)$ and $x_2(i)$ respectively, and their corresponding rating $y(u,i)$ is a noisy measurement of $f(x_1(u),x_2(i))$ for some unknown function $f$. In contrast with classical regression, the features $x=(x_1(u),x_2(i))$ are not observed, making it challenging to apply standard regression methods to predict the unobserved ratings. Inspired by the classical Taylor's expansion for differentiable functions, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis through our framework naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering in practice. Assuming each entry is sampled independently with probability at least $\max (m^{-1+\delta },n^{-1/2+\delta })$ with $\delta >0$, we prove that the expected fraction of our estimates with error greater than $ϵ$ is less than ${\gamma }^2/{ϵ}^2$ plus a polynomially decaying term, where ${\gamma }^2$ is the variance of the additive entry-wise noise term. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods.

Carreira-Perpinan, Miguel A., Raziperchikolaei, Ramin

Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves state-of-the-art precision and recall in experiments with image retrieval.

He, Xinran, Xu, Ke, Kempe, David, Liu, Yan

We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade (DIC) models is established by reducing incomplete observations to complete observations in a modified graph. Our improper PAC learnability result applies for the DLT and DIC models as well as the Continuous-Time Independent Cascade (CIC) model. It is based on a parametrization in terms of reachability features, and also gives rise to an efficient and practical heuristic. Experiments on synthetic and real-world datasets demonstrate the ability of our method to compensate even for a fairly large fraction of missing observations.

Haarnoja, Tuomas, Ajay, Anurag, Levine, Sergey, Abbeel, Pieter

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.

Atanackovic, Lazar, Tong, Alexander, Wang, Bo, Lee, Leo J, Bengio, Yoshua, Hartford, Jason S.

One of the grand challenges of cell biology is inferring the gene regulatory network (GRN) which describes interactions between genes and their products that control gene expression and cellular function. We can treat this as a causal discovery problem but with two non-standard challenges: (1) regulatory networks are inherently cyclic so we should not model a GRN as a directed acyclic graph (DAG), and (2) observations have significant measurement noise so for typical sample sizes, there will always be a large equivalence class of graphs that are likely given the data, and we want methods that capture this uncertainty. Existing methods either focus on challenge (1), identifying cyclic structure from dynamics, or on challenge (2) learning complex Bayesian posteriors over directed acyclic graphs, but not both. In this paper we leverage the fact that it is possible to estimate the ``velocity'' of the expression of a gene with RNA velocity techniques to develop an approach that addresses both challenges. Because we have access to velocity information, we can treat the Bayesian structure learning problem as a problem of sparse identification of a dynamical system, capturing cyclic feedback loops through time. We leverage Generative Flow Networks (GFlowNets) to estimate the posterior distribution over the combinatorial space of possible sparse dependencies. Our results indicate that our method learns posteriors that better encapsulate the distributions of cyclic structures compared to counterpart state-of-the-art Bayesian structure learning approaches.

Hou, Liang, Cao, Qi, Yuan, Yige, Zhao, Songtao, Ma, Chongyang, Pan, Siyuan, Wan, Pengfei, Wang, Zhongyuan, Shen, Huawei, Cheng, Xueqi

Training generative adversarial networks (GANs) with limited data is challenging because the discriminator is prone to overfitting. Previously proposed differentiable augmentation demonstrates improved data efficiency of training GANs. However, the augmentation implicitly introduces undesired invariance to augmentation for the discriminator since it ignores the change of semantics in the label space caused by data transformation, which may limit the representation learning ability of the discriminator and ultimately affect the generative modeling performance of the generator. To mitigate the negative impact of invariance while inheriting the benefits of data augmentation, we propose a novel augmentation-aware self-supervised discriminator that predicts the augmentation parameter of the augmented data. Particularly, the prediction targets of real data and generated data are required to be distinguished since they are different during training. We further encourage the generator to adversarially learn from the self-supervised discriminator by generating augmentation-predictable real and not fake data. This formulation connects the learning objective of the generator and the arithmetic $-$ harmonic mean divergence under certain assumptions. We compare our method with state-of-the-art (SOTA) methods using the class-conditional BigGAN and unconditional StyleGAN2 architectures on data-limited CIFAR-10, CIFAR-100, FFHQ, LSUN-Cat, and five low-shot datasets. Experimental results demonstrate significant improvements of our method over SOTA methods in training data-efficient GANs.

Chen, Xi, Chen, Xi, Cheng, Yu, Tang, Bo

The recursive teaching dimension (RTD) of a concept class $C\subseteq \{0,1{\}}^n$, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of $C$ in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension. Given a concept class $C\subseteq \{0,1{\}}^n$ with $VCD(C)=d$, we first show that $RTD(C)$ is at most $d{2}^{d+1}$. This is the first upper bound for $RTD(C)$ that depends only on $VCD(C)$, independent of the size of the concept class $|C|$ and its~domain size $n$. Before our work, the best known upper bound for $RTD(C)$ is $O(d{2}^d\log \log |C|)$, obtained by Moran et al. [MSWY15]. We remove the $\log \log |C|$ factor. We also improve the lower bound on the worst-case ratio of $RTD(C)$ to $VCD(C)$. We present a family of classes $\{C_k{\}}_{k\ge 1}$ with $VCD(C_k)=3k$ and $RTD(C_k)=5k$, which implies that the ratio of $RTD(C)$ to $VCD(C)$ in the worst case can be as large as $5/3$. Before our work, the largest ratio known was $3/2$ as obtained by Kuhlmann [Kuh99]. Since then, no finite concept class $C$ has been known to satisfy $RTD(C)>(3/2)VCD(C)$.

Cao, Yuzhou, Mozannar, Hussein, Feng, Lei, Wei, Hongxin, An, Bo

Enabling machine learning classifiers to defer their decision to a downstream expert when the expert is more accurate will ensure improved safety and performance. This objective can be achieved with the learning-to-defer framework which aims to jointly learn how to classify and how to defer to the expert. In recent studies, it has been theoretically shown that popular estimators for learning to defer parameterized with softmax provide unbounded estimates for the likelihood of deferring which makes them uncalibrated. However, it remains unknown whether this is due to the widely used softmax parameterization and if we can find a softmax-based estimator that is both statistically consistent and possesses a valid probability estimator. In this work, we first show that the cause of the miscalibrated and unbounded estimator in prior literature is due to the symmetric nature of the surrogate losses used and not due to softmax. We then propose a novel statistically consistent asymmetric softmax-based surrogate loss that can produce valid estimates without the issue of unboundedness. We further analyze the non-asymptotic properties of our proposed method and empirically validate its performance and calibration on benchmark datasets.

Rubin, Timothy, Koyejo, Oluwasanmi O., Jones, Michael N., Yarkoni, Tal

This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.

Sønderby, Casper Kaae, Raiko, Tapani, Maaløe, Lars, Sønderby, Søren Kaae, Winther, Ole

Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

Abbe, Emmanuel, Sandon, Colin

The stochastic block model (SBM) has long been studied in machine learning and network science as a canonical model for clustering and community detection. In the recent years, new developments have demonstrated the presence of threshold phenomena for this model, which have set new challenges for algorithms. For the {\it detection} problem in symmetric SBMs, Decelle et al.\ conjectured that the so-called Kesten-Stigum (KS) threshold can be achieved efficiently. This was proved for two communities, but remained open from three communities. We prove this conjecture here, obtaining a more general result that applies to arbitrary SBMs with linear size communities. The developed algorithm is a linearized acyclic belief propagation (ABP) algorithm, which mitigates the effects of cycles while provably achieving the KS threshold in $O(n\ln n)$ time. This extends prior methods by achieving universally the KS threshold while reducing or preserving the computational complexity. ABP is also connected to a power iteration method on a generalized nonbacktracking operator, formalizing the spectral-message passing interplay described in Krzakala et al., and extending results from Bordenave et al.

Chen, Shiyan, Zhang, Jiyuan, Zheng, Yajing, Huang, Tiejun, Yu, Zhaofei

Traditional cameras produce desirable vision results but struggle with motion blur in high-speed scenes due to long exposure windows. Existing frame-based deblurring algorithms face challenges in extracting useful motion cues from severely blurred images. Recently, an emerging bio-inspired vision sensor known as the spike camera has achieved an extremely high frame rate while preserving rich spatial details, owing to its novel sampling mechanism. However, typical binary spike streams are relatively low-resolution, degraded image signals devoid of color information, making them unfriendly to human vision. In this paper, we propose a novel approach that integrates the two modalities from two branches, leveraging spike streams as auxiliary visual cues for guiding deblurring in high-speed motion scenes. We propose the first spike-based motion deblurring model with bidirectional information complementarity. We introduce a content-aware motion magnitude attention module that utilizes learnable mask to extract relevant information from blurry images effectively, and we incorporate a transposed cross-attention fusion module to efficiently combine features from both spike data and blurry RGB images.Furthermore, we build two extensive synthesized datasets for training and validation purposes, encompassing high-temporal-resolution spikes, blurry images, and corresponding sharp images. The experimental results demonstrate that our method effectively recovers clear RGB images from highly blurry scenes and outperforms state-of-the-art deblurring algorithms in multiple settings.

Zhao, Han, Poupart, Pascal, Gordon, Geoffrey J.

We present a unified approach for learning the parameters of Sum-Product networks (SPNs). We prove that any complete and decomposable SPN is equivalent to a mixture of trees where each tree corresponds to a product of univariate distributions. Based on the mixture model perspective, we characterize the objective function when learning SPNs based on the maximum likelihood estimation (MLE) principle and show that the optimization problem can be formulated as a signomial program. We construct two parameter learning algorithms for SPNs by using sequential monomial approximations (SMA) and the concave-convex procedure (CCCP), respectively. The two proposed methods naturally admit multiplicative updates, hence effectively avoiding the projection operation. With the help of the unified framework, we also show that, in the case of SPNs, CCCP leads to the same algorithm as Expectation Maximization (EM) despite the fact that they are different in general.

Kondor, Risi, Pan, Horace

Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we define in this paper can account for structure at a range of different scales. At the heart of the MLG construction is another new graph kernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has the property that it can lift a base kernel defined on the vertices of two graphs to a kernel between the graphs. The MLG kernel applies such FLG kernels to subgraphs recursively. To make the MLG kernel computationally feasible, we also introduce a randomized projection procedure, similar to the Nystro ̈m method, but for RKHS operators.

Alvarez, Jose M., Salzmann, Mathieu

Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them impractical for constrained platforms. These networks, however, are known to have many redundant parameters, and could thus, in principle, be replaced by more compact architectures. In this paper, we introduce an approach to automatically determining the number of neurons in each layer of a deep network during learning. To this end, we propose to make use of a group sparsity regularizer on the parameters of the network, where each group is defined to act on a single neuron. Starting from an overcomplete network, we show that our approach can reduce the number of parameters by up to 80\% while retaining or even improving the network accuracy.

Wang, Jinzhuo, Wang, Wenmin, Chen, xiongtao, Wang, Ronggang, Gao, Wen

Contexts are crucial for action recognition in video. Current methods often mine contexts after extracting hierarchical local features and focus on their high-order encodings. This paper instead explores contexts as early as possible and leverages their evolutions for action recognition. In particular, we introduce a novel architecture called deep alternative neural network (DANN) stacking alternative layers. Each alternative layer consists of a volumetric convolutional layer followed by a recurrent layer. The former acts as local feature learner while the latter is used to collect contexts. Compared with feed-forward neural networks, DANN learns contexts of local features from the very beginning. This setting helps to preserve hierarchical context evolutions which we show are essential to recognize similar actions. Besides, we present an adaptive method to determine the temporal size for network input based on optical flow energy, and develop a volumetric pyramid pooling layer to deal with input clips of arbitrary sizes. We demonstrate the advantages of DANN on two benchmarks HMDB51 and UCF101 and report competitive or superior results to the state-of-the-art.

Li, Chris Junchi, Wang, Zhaoran, Liu, Han

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm based on diffusion processes to characterize the global dynamics of nonconvex statistical optimization. As a concrete example, we study stochastic gradient descent (SGD) for the tensor decomposition formulation of independent component analysis. In particular, we cast different phases of SGD into diffusion processes, i.e., solutions to stochastic differential equations. Initialized from an unstable equilibrium, the global dynamics of SGD transit over three consecutive phases: (i) an unstable Ornstein-Uhlenbeck process slowly departing from the initialization, (ii) the solution to an ordinary differential equation, which quickly evolves towards the desirable local minimum, and (iii) a stable Ornstein-Uhlenbeck process oscillating around the desirable local minimum. Our proof techniques are based upon Stroock and Varadhan’s weak convergence of Markov chains to diffusion processes, which are of independent interest.

Chu, Xiao, Ouyang, Wanli, Li, hongsheng, Wang, Xiaogang

Deep convolutional neural networks (CNN) have achieved great success. On the other hand, modeling structural information has been proved critical in many vision problems. It is of great interest to integrate them effectively. In a classical neural network, there is no message passing between neurons in the same layer. In this paper, we propose a CRF-CNN framework which can simultaneously model structural information in both output and hidden feature layers in a probabilistic way, and it is applied to human pose estimation. A message passing scheme is proposed, so that in various layers each body joint receives messages from all the others in an efficient way. Such message passing can be implemented with convolution between features maps in the same layer, and it is also integrated with feedforward propagation in neural networks. Finally, a neural network implementation of end-to-end learning CRF-CNN is provided. Its effectiveness is demonstrated through experiments on two benchmark datasets.

Linderman, Scott, Adams, Ryan P., Pillow, Jonathan W.

Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

Neyshabur, Behnam, Wu, Yuhuai, Salakhutdinov, Russ R., Srebro, Nati

We investigate the parameter-space geometry of recurrent neural networks (RNNs), and develop an adaptation of path-SGD optimization method, attuned to this geometry, that can learn plain RNNs with ReLU activations. On several datasets that require capturing long-term dependency structure, we show that path-SGD can significantly improve trainability of ReLU RNNs compared to RNNs trained with SGD, even with various recently suggested initialization schemes.

Cortes, Corinna, DeSalvo, Giulia, Mohri, Mehryar

We present a new boosting algorithm for the key scenario of binary classification with abstention where the algorithm can abstain from predicting the label of a point, at the price of a fixed cost. At each round, our algorithm selects a pair of functions, a base predictor and a base abstention function. We define convex upper bounds for the natural loss function associated to this problem, which we prove to be calibrated with respect to the Bayes solution. Our algorithm benefits from general margin-based learning guarantees which we derive for ensembles of pairs of base predictor and abstention functions, in terms of the Rademacher complexities of the corresponding function classes. We give convergence guarantees for our algorithm along with a linear-time weak-learning algorithm for abstention stumps. We also report the results of several experiments suggesting that our algorithm provides a significant improvement in practice over two confidence-based algorithms.

Lu, Pan, Peng, Baolin, Cheng, Hao, Galley, Michel, Chang, Kai-Wei, Wu, Ying Nian, Zhu, Song-Chun, Gao, Jianfeng

Large language models (LLMs) have achieved remarkable progress in solving various natural language processing tasks due to emergent reasoning abilities. However, LLMs have inherent limitations as they are incapable of accessing up-to-date information (stored on the Web or in task-specific knowledge bases), using external tools, and performing precise mathematical and logical reasoning. In this paper, we present Chameleon, an AI system that mitigates these limitations by augmenting LLMs with plug-and-play modules for compositional reasoning. Chameleon synthesizes programs by composing various tools (e.g., LLMs, off-the-shelf vision models, web search engines, Python functions, and heuristic-based modules) for accomplishing complex reasoning tasks. At the heart of Chameleon is an LLM-based planner that assembles a sequence of tools to execute to generate the final response. We showcase the effectiveness of Chameleon on two multi-modal knowledge-intensive reasoning tasks: ScienceQA and TabMWP. Chameleon, powered by GPT-4, achieves an 86.54% overall accuracy on ScienceQA, improving the best published few-shot result by 11.37%. On TabMWP, GPT-4-powered Chameleon improves the accuracy by 17.0%, lifting the state of the art to 98.78%. Our analysis also shows that the GPT-4-powered planner exhibits more consistent and rational tool selection via inferring potential constraints from instructions, compared to a ChatGPT-powered planner.

Angelo Porrello, Davide Abati, Simone Calderara, Rita Cucchiara

We present a novel and hierarchical approach for supervised classification of signals spanning over a fixed graph, reflecting shared properties of the dataset. To this end, we introduce a Convolutional Cluster Pooling layer exploiting a multi-scale clustering in order to highlight, at different resolutions, locally connected regions on the input graph. Our proposal generalises well-established neural models such as Convolutional Neural Networks (CNNs) on irregular and complex domains, by means of the exploitation of the weight sharing property in a graph-oriented architecture. In this work, such property is based on the centrality of each vertex within its soft-assigned cluster. Extensive experiments on NTU RGB+D, CIFAR-10 and 20NEWS demonstrate the effectiveness of the proposed technique in capturing both local and global patterns in graph-structured data out of different domains.

Chien, Eli, Chen, Wei-Ning, Pan, Chao, Li, Pan, Ozgur, Ayfer, Milenkovic, Olgica

Graph Neural Networks (GNNs) have proven to be highly effective in solving real-world learning problems that involve graph-structured data. However, GNNs can also inadvertently expose sensitive user information and interactions through their model predictions. To address these privacy concerns, Differential Privacy (DP) protocols are employed to control the trade-off between provable privacy protection and model utility. Applying standard DP approaches to GNNs directly is not advisable due to two main reasons. First, the prediction of node labels, which relies on neighboring node attributes through graph convolutions, can lead to privacy leakage. Second, in practical applications, the privacy requirements for node attributes and graph topology may differ. In the latter setting, existing DP-GNN models fail to provide multigranular trade-offs between graph topology privacy, node attribute privacy, and GNN utility. To address both limitations, we propose a new framework termed Graph Differential Privacy (GDP), specifically tailored to graph learning. GDP ensures both provably private model parameters as well as private predictions. Additionally, we describe a novel unified notion of graph dataset adjacency to analyze the properties of GDP for different levels of graph topology privacy. Our findings reveal that DP-GNNs, which rely on graph convolutions, not only fail to meet the requirements for multigranular graph topology privacy but also necessitate the injection of DP noise that scales at least linearly with the maximum node degree. In contrast, our proposed Differentially Private Decoupled Graph Convolutions (DPDGCs) represent a more flexible and efficient alternative to graph convolutions that still provides the necessary guarantees of GDP. To validate our approach, we conducted extensive experiments on seven node classification benchmarking and illustrative synthetic datasets. The results demonstrate that DPDGCs significantly outperform existing DP-GNNs in terms of privacy-utility trade-offs.