NeurIPS 2024 Papers

In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA). Specifically, we demonstrate that a clipped version of Adam with model EMA achieves the optimal convergence rates in various nonconvex optimization settings, both smooth and nonsmooth. Moreover, when the scale varies significantly across different coordinates, we demonstrate that the coordinate-wise adaptivity of Adam is provably advantageous. Notably, unlike previous analyses of Adam, our analysis crucially relies on its core elements---momentum and discounting factors---as well as model EMA, motivating their wide applications in practice.

We address the challenges of Byzantine-robust training in asynchronous distributed machine learning systems, aiming to enhance efficiency amid massive parallelization and heterogeneous compute resources. Asynchronous systems, marked by independently operating workers and intermittent updates, uniquely struggle with maintaining integrity against Byzantine failures, which encompass malicious or erroneous actions that disrupt learning. The inherent delays in such settings not only introduce additional bias to the system but also obscure the disruptions caused by Byzantine faults. To tackle these issues, we adapt the Byzantine framework to asynchronous dynamics by introducing a novel weighted robust aggregation framework. This allows for the extension of robust aggregators and a recent meta-aggregator to their weighted versions, mitigating the effects of delayed updates. By further incorporating a recent variance-reduction technique, we achieve an optimal convergence rate for the first time in an asynchronous Byzantine environment. Our methodology is rigorously validated through empirical and theoretical analysis, demonstrating its effectiveness in enhancing fault tolerance and optimizing performance in asynchronous ML systems.

Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise computation of derivatives, often resulting in prohibitively high iteration costs. In this work, we study the impact of Jacobian inaccuracy on second-order methods. For the smooth and monotone case, we establish a lower bound with explicit dependence on the level of Jacobian inaccuracy and propose an optimal algorithm for this key setting. When derivatives are exact, our method converges at the same rate as exact optimal second-order methods. To reduce the cost of solving the auxiliary problem, which arises in all high-order methods with global convergence, we introduce several Quasi-Newton approximations. Our method with Quasi-Newton updates achieves a global sublinear convergence rate. We extend our approach with a tensor generalization for inexact high-order derivatives and support the theory with experiments.

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic primal-dual algorithm which combines cyclic and randomized components with a carefully regularized primal update to achieve dual variance reduction. Owing to its design, Drago enjoys a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems witha fine-grained dependency on primal and dual condition numbers. The theoretical results are supported with numerical benchmarks on regression and classification tasks.

Human Mesh Recovery (HMR) is the task of estimating a parameterized 3D human mesh from an image. There is a kind of methods first training a regression model for this problem, then further optimizing the pretrained regression model for any specific sample individually at test time. However, the pretrained model may not provide an ideal optimization starting point for the test-time optimization. Inspired by meta-learning, we incorporate the test-time optimization into training, performing a step of test-time optimization for each sample in the training batch before really conducting the training optimization over all the training samples. In this way, we obtain a meta-model, the meta-parameter of which is friendly to the test-time optimization. At test time, after several test-time optimization steps starting from the meta-parameter, we obtain much higher HMR accuracy than the test-time optimization starting from the simply pretrained regression model. Furthermore, we find test-time HMR objectives are different from training-time objectives, which reduces the effectiveness of the learning of the meta-model. To solve this problem, we propose a dual-network architecture that unifies the training-time and test-time objectives. Our method, armed with meta-learning and the dual networks, outperforms state-of-the-art regression-based and optimization-based HMR approaches, as validated by the extensive experiments. The codes are available at https://github.com/fmx789/Meta-HMR.

Split federated learning (SFL) is a recent distributed approach for collaborative model training among multiple clients. In SFL, a global model is typically split into two parts, where clients train one part in a parallel federated manner, and a main server trains the other. Despite the recent research on SFL algorithm development, the convergence analysis of SFL is missing in the literature, and this paper aims to fill this gap. The analysis of SFL can be more challenging than that of federated learning (FL), due to the potential dual-paced updates at the clients and the main server. We provide convergence analysis of SFL for strongly convex and general convex objectives on heterogeneous data. The convergence rates are $O(1/T)$ and $O(1/\sqrt[3]{T})$, respectively, where $T$ denotes the total number of rounds for SFL training. We further extend the analysis to non-convex objectives and where some clients may be unavailable during training. Numerical experiments validate our theoretical results and show that SFL outperforms FL and split learning (SL) when data is highly heterogeneous across a large number of clients.

Sign stochastic gradient descent (signSGD) is a communication-efficient method that transmits only the sign of stochastic gradients for parameter updating. Existing literature has demonstrated that signSGD can achieve a convergence rate of $\mathcal{O}(d^{1/2}T^{-1/4})$, where $d$ represents the dimension and $T$ is the iteration number. In this paper, we improve this convergence rate to $\mathcal{O}(d^{1/2}T^{-1/3})$ by introducing the Sign-based Stochastic Variance Reduction (SSVR) method, which employs variance reduction estimators to track gradients and leverages their signs to update. For finite-sum problems, our method can be further enhanced to achieve a convergence rate of $\mathcal{O}(m^{1/4}d^{1/2}T^{-1/2})$, where $m$ denotes the number of component functions. Furthermore, we investigate the heterogeneous majority vote in distributed settings and introduce two novel algorithms that attain improved convergence rates of $\mathcal{O}(d^{1/2}T^{-1/2} + dn^{-1/2})$ and $\mathcal{O}(d^{1/4}T^{-1/4})$ respectively, outperforming the previous results of $\mathcal{O}(dT^{-1/4} + dn^{-1/2})$ and $\mathcal{O}(d^{3/8}T^{-1/8})$, where $n$ represents the number of nodes. Numerical experiments across different tasks validate the effectiveness of our proposed methods.

Interest in bilevel optimization has grown in recent years, partially due to its relevance for challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - support vector machine (SVM) - based model training and infrastructure planning in transportation networks.

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for manifold optimization in the centralized setting, there are currently very few works addressing the federated setting. In this paper, we consider nonconvex federated learning over a compact smooth submanifold in the setting of heterogeneous client data. We propose an algorithm that leverages stochastic Riemannian gradients and a manifold projection operator to improve computational efficiency, uses local updates to improve communication efficiency, and avoids client drift. Theoretically, we show that our proposed algorithm converges sub-linearly to a neighborhood of a first-order optimal solution by using a novel analysis that jointly exploits the manifold structure and properties of the loss functions. Numerical experiments demonstrate that our algorithm has significantly smaller computational and communication overhead than existing methods.

Gradient-based bilevel programming leverages unrolling differentiation (UD) or implicit function theorem (IFT) to solve hyperparameter optimization (HO) problems, and is proven effective and scalable in practice. To understand their generalization behavior, existing works establish upper bounds on the uniform stability of these algorithms, while their tightness is still unclear. To this end, this paper attempts to establish stability lower bounds for UD-based and IFT-based algorithms. A central technical challenge arises from the dependency of each outer-level update on the concurrent stage of inner optimization in bilevel programming. To address this problem, we introduce lower-bounded expansion properties to characterize the instability in update rules which can serve as general tools for lower-bound analysis. These properties guarantee the hyperparameter divergence at the outer level and the Lipschitz constant of inner output at the inner level in the context of HO. Guided by these insights, we construct a quadratic example that yields tight lower bounds for the UD-based algorithm and meaningful bounds for a representative IFT-based algorithm. Our tight result indicates that uniform stability has reached its limit in stability analysis for the UD-based algorithm.

This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer an additional $\mathcal{O}(\log T)$ term in the convergence rate. To address these limitations, we introduce a novel adaptive STORM method that achieves an optimal convergence rate of $\mathcal{O}(T^{-1/3})$ for non-convex functions with our newly designed learning rate strategy. Compared with existing approaches, our method requires weaker assumptions and attains the optimal convergence rate without the additional $\mathcal{O}(\log T)$ term. We also extend the proposed technique to stochastic compositional optimization, obtaining the same optimal rate of $\mathcal{O}(T^{-1/3})$. Furthermore, we investigate the non-convex finite-sum problem and develop another innovative adaptive variance reduction method that achieves an optimal convergence rate of $\mathcal{O}(n^{1/4} T^{-1/2} )$, where $n$ represents the number of component functions. Numerical experiments across various tasks validate the effectiveness of our method.

Equivariant neural networks have been widely used in a variety of applications due to their ability to generalize well in tasks where the underlying data symmetries are known. Despite their successes, such networks can be difficult to optimize and require careful hyperparameter tuning to train successfully. In this work, we propose a novel framework for improving the optimization of such models by relaxing the hard equivariance constraint during training: We relax the equivariance constraint of the network's intermediate layers by introducing an additional non-equivariant term that we progressively constrain until we arrive at an equivariant solution. By controlling the magnitude of the activation of the additional relaxation term, we allow the model to optimize over a larger hypothesis space containing approximate equivariant networks and converge back to an equivariant solution at the end of training. We provide experimental results on different state-of-the-art network architectures, demonstrating how this training framework can result in equivariant models with improved generalization performance. Our code is available at https://github.com/StefanosPert/Equivariant_Optimization_CR

Achieving robust and precise pose estimation in dynamic scenes is a significant research challenge in Visual Simultaneous Localization and Mapping (SLAM). Recent advancements integrating Gaussian Splatting into SLAM systems have proven effective in creating high-quality renderings using explicit 3D Gaussian models, significantly improving environmental reconstruction fidelity. However, these approaches depend on a static environment assumption and face challenges in dynamic environments due to inconsistent observations of geometry and photometry. To address this problem, we propose DG-SLAM, the first robust dynamic visual SLAM system grounded in 3D Gaussians, which provides precise camera pose estimation alongside high-fidelity reconstructions. Specifically, we propose effective strategies, including motion mask generation, adaptive Gaussian point management, and a hybrid camera tracking algorithm to improve the accuracy and robustness of pose estimation. Extensive experiments demonstrate that DG-SLAM delivers state-of-the-art performance in camera pose estimation, map reconstruction, and novel-view synthesis in dynamic scenes, outperforming existing methods meanwhile preserving real-time rendering ability.

Analytics on structured data is a mature field with many successful methods. However, most real world data exists in unstructured form, such as images and conversations. We investigate the potential of Large Language Models (LLMs) to enable unstructured data analytics. In particular, we propose a new Universal Query Engine (UQE) that directly interrogates and draws insights from unstructured data collections. This engine accepts queries in a Universal Query Language (UQL), a dialect of SQL that provides full natural language flexibility in specifying conditions and operators. The new engine leverages the ability of LLMs to conduct analysis of unstructured data, while also allowing us to exploit advances in sampling and optimization techniques to achieve efficient and accurate query execution. In addition, we borrow techniques from classical compiler theory to better orchestrate the workflow between sampling methods and foundation model calls. We demonstrate the efficiency of UQE on data analytics across different modalities, including images, dialogs and reviews, across a range of useful query types, including conditional aggregation, semantic retrieval and abstraction aggregation.

In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often exhibits patterns, we ask the following question: can predictions be used to accelerate the update time of dynamic submodular maximization algorithms? We consider the model for dynamic algorithms with predictions where predictions regarding the insertion and deletion times of elements can be used for preprocessing. Our main result is an algorithm with an $O(\text{poly}(\log \eta, \log w, \log k))$ amortized update time over the sequence of updates that achieves a $1/2 - \epsilon$ approximation for dynamic monotone submodular maximization under a cardinality constraint $k$, where the prediction error $\eta$ is the number of elements that are not inserted and deleted within $w$ time steps of their predicted insertion and deletion times. This amortized update time is independent of the length of the stream and instead depends on the prediction error.

The rising footprint of machine learning has led to a focus on imposing model sparsity as a means of reducing computational and memory costs. For deep neural networks (DNNs), the state-of-the-art accuracy-vs-sparsity is achieved by heuristics inspired by the classical Optimal Brain Surgeon (OBS) framework [LeCun et al., 1989, Hassibi and Stork, 1992, Hassibi et al., 1993], which leverages loss curvature information to make better pruning decisions. Yet, these results still lack a solid theoretical understanding, and it is unclear whether they can be improved by leveraging connections to the wealth of work on sparse recovery algorithms. In this paper, we draw new connections between these two areas and present new sparse recovery algorithms inspired by the OBS framework that come with theoretical guarantees under reasonable assumptions and have strong practical performance. Specifically, our work starts from the observation that we can leverage curvature information in OBS-like fashion upon the projection step of classic iterative sparse recovery algorithms such as IHT. We show for the first time that this leads both to improved convergence bounds in well-behaved settings and to stronger practical convergence. Furthermore, we present extensions of this approach to training accurate sparse DNNs, and validate it experimentally at scale.

Diffusion models have achieved remarkable progress in the field of image generation due to their outstanding capabilities. However, these models require substantial computing resources because of the multi-step denoising process during inference. While traditional pruning methods have been employed to optimize these models, the retraining process necessitates large-scale training datasets and extensive computational costs to maintain generalization ability, making it neither convenient nor efficient. Recent studies attempt to utilize the similarity of features across adjacent denoising stages to reduce computational costs through simple and static strategies. However, these strategies cannot fully harness the potential of the similar feature patterns across adjacent timesteps. In this work, we propose a novel pruning method that derives an efficient diffusion model via a more intelligent and differentiable pruner. At the core of our approach is casting the model pruning process into a SubNet search process. Specifically, we first introduce a SuperNet based on standard diffusion via adding some backup connections built upon the similar features. We then construct a plugin pruner network and design optimization losses to identify redundant computation. Finally, our method can identify an optimal SubNet through few-step gradient optimization and a simple post-processing procedure. We conduct extensive experiments on various diffusion models including Stable Diffusion series and DiTs. Our DiP-GO approach achieves 4.4 x speedup for SD-1.5 without any loss of accuracy, significantly outperforming the previous state-of-the-art methods.

We present adaptive gradient methods (both basic and accelerated) for solving convex composite optimization problems in which the main part is approximately smooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a (potentially biased) stochastic gradient oracle. This setting covers many interesting examples including Hölder smooth problems and various inexact computations of the stochastic gradient. Our methods use AdaGrad stepsizes and are adaptive in the sense that they do not require knowing any problem-dependent constants except an estimate of the diameter of the feasible set but nevertheless achieve the best possible convergence rates as if they knew the corresponding constants. We demonstrate that AdaGrad stepsizes work in a variety of situations by proving, in a unified manner, three types of new results. First, we establish efficiency guarantees for our methods in the classical setting where the oracle's variance is uniformly bounded. We then show that, under more refined assumptions on the variance, the same methods without any modifications enjoy implicit variance reduction properties allowing us to express their complexity estimates in terms of the variance only at the minimizer. Finally, we show how to incorporate explicit SVRG-type variance reduction into our methods and obtain even faster algorithms. In all three cases, we present both basic and accelerated algorithms achieving state-of-the-art complexity bounds. As a direct corollary of our results, we obtain universal stochastic gradient methods for Hölder smooth problems which can be used in all situations.

Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit ($\mu$P and its depth extension), then some hyperparameters --- such as the learning rate --- exhibit transfer from small to very large models. From an optimization perspective, this phenomenon is puzzling, as it implies that the loss landscape is consistently similar across very different model sizes. In this work, we study the landscape through the lens of the Hessian, with a focus on its largest eigenvalue (i.e. the sharpness), and find that certain spectral properties under $\mu$P are largely independent of the width and depth of the network along the training trajectory. We name this property *super consistency* of the landscape. On the other hand, we show that in the Neural Tangent Kernel (NTK) and other scaling regimes, the sharpness exhibits very different dynamics at different scales. But what causes these differences in the sharpness dynamics? Through a connection between the Hessian's and the NTK's spectrum, we argue that the cause lies in the presence (for $\mu$P) or progressive absence (for the NTK scaling) of feature learning. We corroborate our claims with a substantial suite of experiments, covering a wide range of datasets and architectures: from ResNets and Vision Transformers trained on benchmark vision datasets to Transformers-based language models trained on WikiText.