Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges posed by optimization problems arising in data science. However, such gradient methods face diverging optimality gaps or exploding objective evaluations when applied to optimization problems with realistic properties for data science applications. In this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent optimality gap divergence and avoid explosions in objective evaluations. Our methodology allows for a variety of step size routines and search direction strategies. Furthermore, we develop a particular, novel step size selection methodology that is well-suited to our framework. We show that our specific procedure is highly competitive with standard optimization methods on CUTEst test problems. We then show our specific procedure is highly favorable relative to standard optimization methods on a particularly tough data science problem: learning the parameters in a generalized estimating equation model. Thus, we provide a novel gradient methodology that is better suited to optimization problems from this important class of data science applications.
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Continual learning methods are known to suffer from catastrophic forgetting, a phenomenon that is particularly hard to counter for methods that do not store exemplars of previous tasks. Therefore, to reduce potential drift in the feature extractor, existing exemplar-free methods are typically evaluated in settings where the first task is significantly larger than subsequent tasks. Their performance drops drastically in more challenging settings starting with a smaller first task. To address this problem of feature drift estimation for exemplar-free methods, we propose to adversarially perturb the current samples such that their embeddings are close to the old class prototypes in the old model embedding space. We then estimate the drift in the embedding space from the old to the new model using the perturbed images and compensate the prototypes accordingly. We exploit the fact that adversarial samples are transferable from the old to the new feature space in a continual learning setting. The generation of these images is simple and computationally cheap. We demonstrate in our experiments that the proposed approach better tracks the movement of prototypes in embedding space and outperforms existing methods on several standard continual learning benchmarks as well as on fine-grained datasets. Code is available at //github.com/dipamgoswami/ADC.
Stochastic optimization algorithms implemented on distributed computing architectures are increasingly used to tackle large-scale machine learning applications. A key bottleneck in such distributed systems is the communication overhead for exchanging information such as stochastic gradients between different workers. Sparse communication with memory and the adaptive aggregation methodology are two successful frameworks among the various techniques proposed to address this issue. In this paper, we exploit the advantages of Sparse communication and Adaptive aggregated Stochastic Gradients to design a communication-efficient distributed algorithm named SASG. Specifically, we determine the workers who need to communicate with the parameter server based on the adaptive aggregation rule and then sparsify the transmitted information. Therefore, our algorithm reduces both the overhead of communication rounds and the number of communication bits in the distributed system. We define an auxiliary sequence and provide convergence results of the algorithm with the help of Lyapunov function analysis. Experiments on training deep neural networks show that our algorithm can significantly reduce the communication overhead compared to the previous methods, with little impact on training and testing accuracy.
Annotated datasets are an essential ingredient to train, evaluate, compare and productionalize supervised machine learning models. It is therefore imperative that annotations are of high quality. For their creation, good quality management and thereby reliable quality estimates are needed. Then, if quality is insufficient during the annotation process, rectifying measures can be taken to improve it. Quality estimation is often performed by having experts manually label instances as correct or incorrect. But checking all annotated instances tends to be expensive. Therefore, in practice, usually only subsets are inspected; sizes are chosen mostly without justification or regard to statistical power and more often than not, are relatively small. Basing estimates on small sample sizes, however, can lead to imprecise values for the error rate. Using unnecessarily large sample sizes costs money that could be better spent, for instance on more annotations. Therefore, we first describe in detail how to use confidence intervals for finding the minimal sample size needed to estimate the annotation error rate. Then, we propose applying acceptance sampling as an alternative to error rate estimation We show that acceptance sampling can reduce the required sample sizes up to 50% while providing the same statistical guarantees.
We introduce a framework for intrinsic latent diffusion models operating directly on the surfaces of 3D shapes, with the goal of synthesizing high-quality textures. Our approach is underpinned by two contributions: field latents, a latent representation encoding textures as discrete vector fields on the mesh vertices, and field latent diffusion models, which learn to denoise a diffusion process in the learned latent space on the surface. We consider a single-textured-mesh paradigm, where our models are trained to generate variations of a given texture on a mesh. We show the synthesized textures are of superior fidelity compared those from existing single-textured-mesh generative models. Our models can also be adapted for user-controlled editing tasks such as inpainting and label-guided generation. The efficacy of our approach is due in part to the equivariance of our proposed framework under isometries, allowing our models to seamlessly reproduce details across locally similar regions and opening the door to a notion of generative texture transfer.
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm. We exploit our result on the dynamics of these algorithms to derive the optimal choices for the matrix and iterate denoisers. We show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.
Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(\Omega))$. The estimator consists of discrete complementarity terms and standard residual. As an application, the residual-type error estimates are presented.
Spiking neural networks (SNNs) are investigated as biologically inspired models of neural computation, distinguished by their computational capability and energy efficiency due to precise spiking times and sparse spikes with event-driven computation. A significant question is how SNNs can emulate human-like graph-based reasoning of concepts and relations, especially leveraging the temporal domain optimally. This paper reveals that SNNs, when amalgamated with synaptic delay and temporal coding, are proficient in executing (knowledge) graph reasoning. It is elucidated that spiking time can function as an additional dimension to encode relation properties via a neural-generalized path formulation. Empirical results highlight the efficacy of temporal delay in relation processing and showcase exemplary performance in diverse graph reasoning tasks. The spiking model is theoretically estimated to achieve $20\times$ energy savings compared to non-spiking counterparts, deepening insights into the capabilities and potential of biologically inspired SNNs for efficient reasoning. The code is available at //github.com/pkuxmq/GRSNN.
Citation practices are crucial in shaping the structure of scientific knowledge, yet they are often influenced by contemporary norms and biases. The emergence of Large Language Models (LLMs) like GPT-4 introduces a new dynamic to these practices. Interestingly, the characteristics and potential biases of references recommended by LLMs that entirely rely on their parametric knowledge, and not on search or retrieval-augmented generation, remain unexplored. Here, we analyze these characteristics in an experiment using a dataset of 166 papers from AAAI, NeurIPS, ICML, and ICLR, published after GPT-4's knowledge cut-off date, encompassing 3,066 references in total. In our experiment, GPT-4 was tasked with suggesting scholarly references for the anonymized in-text citations within these papers. Our findings reveal a remarkable similarity between human and LLM citation patterns, but with a more pronounced high citation bias in GPT-4, which persists even after controlling for publication year, title length, number of authors, and venue. Additionally, we observe a large consistency between the characteristics of GPT-4's existing and non-existent generated references, indicating the model's internalization of citation patterns. By analyzing citation graphs, we show that the references recommended by GPT-4 are embedded in the relevant citation context, suggesting an even deeper conceptual internalization of the citation networks. While LLMs can aid in citation generation, they may also amplify existing biases and introduce new ones, potentially skewing scientific knowledge dissemination. Our results underscore the need for identifying the model's biases and for developing balanced methods to interact with LLMs in general.
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
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