Sharpness-Aware Minimization (SAM) is an optimizer that takes a descent step based on the gradient at a perturbation $y_t = x_t + \rho \frac{\nabla f(x_t)}{\lVert \nabla f(x_t) \rVert}$ of the current point $x_t$. Existing studies prove convergence of SAM for smooth functions, but they do so by assuming decaying perturbation size $\rho$ and/or no gradient normalization in $y_t$, which is detached from practice. To address this gap, we study deterministic/stochastic versions of SAM with practical configurations (i.e., constant $\rho$ and gradient normalization in $y_t$) and explore their convergence properties on smooth functions with (non)convexity assumptions. Perhaps surprisingly, in many scenarios, we find out that SAM has limited capability to converge to global minima or stationary points. For smooth strongly convex functions, we show that while deterministic SAM enjoys tight global convergence rates of $\tilde \Theta(\frac{1}{T^2})$, the convergence bound of stochastic SAM suffers an inevitable additive term $O(\rho^2)$, indicating convergence only up to neighborhoods of optima. In fact, such $O(\rho^2)$ factors arise for stochastic SAM in all the settings we consider, and also for deterministic SAM in nonconvex cases; importantly, we prove by examples that such terms are unavoidable. Our results highlight vastly different characteristics of SAM with vs. without decaying perturbation size or gradient normalization, and suggest that the intuitions gained from one version may not apply to the other.
相關內容
Within the statistical literature, there is a lack of methods that allow for asymmetric multivariate spatial effects to model relations underlying complex spatial phenomena. Intercropping is one such phenomenon. In this ancient agricultural practice multiple crop species or varieties are cultivated together in close proximity and are subject to mutual competition. To properly analyse such a system, it is necessary to account for both within- and between-plot effects, where between-plot effects are asymmetric. Building on the multivariate spatial autoregressive model and the Gaussian graphical model, the proposed method takes asymmetric spatial relations into account, thereby removing some of the limiting factors of spatial analyses and giving researchers a better indication of the existence and extend of spatial relationships. Using a Bayesian-estimation framework, the model shows promising results in the simulation study. The model is applied on intercropping data consisting of Belgian endive and beetroot, illustrating the usage of the proposed methodology. An R package containing the proposed methodology can be found on // CRAN.R-project.org/package=SAGM.
Learning algorithms that divide the data into batches are prevalent in many machine-learning applications, typically offering useful trade-offs between computational efficiency and performance. In this paper, we examine the benefits of batch-partitioning through the lens of a minimum-norm overparameterized linear regression model with isotropic Gaussian features. We suggest a natural small-batch version of the minimum-norm estimator, and derive an upper bound on its quadratic risk, showing it is inversely proportional to the noise level as well as to the overparameterization ratio, for the optimal choice of batch size. In contrast to minimum-norm, our estimator admits a stable risk behavior that is monotonically increasing in the overparameterization ratio, eliminating both the blowup at the interpolation point and the double-descent phenomenon. Interestingly, we observe that this implicit regularization offered by the batch partition is partially explained by feature overlap between the batches. Our bound is derived via a novel combination of techniques, in particular normal approximation in the Wasserstein metric of noisy projections over random subspaces.
Formal method-based analysis of the 5G Wireless Communication Protocol is crucial for identifying logical vulnerabilities and facilitating an all-encompassing security assessment, especially in the design phase. Natural Language Processing (NLP) assisted techniques and most of the tools are not widely adopted by the industry and research community. Traditional formal verification through a mathematics approach heavily relied on manual logical abstraction prone to being time-consuming, and error-prone. The reason that the NLP-assisted method did not apply in industrial research may be due to the ambiguity in the natural language of the protocol designs nature is controversial to the explicitness of formal verification. To address the challenge of adopting the formal methods in protocol designs, targeting (3GPP) protocols that are written in natural language, in this study, we propose a hybrid approach to streamline the analysis of protocols. We introduce a two-step pipeline that first uses NLP tools to construct data and then uses constructed data to extract identifiers and formal properties by using the NLP model. The identifiers and formal properties are further used for formal analysis. We implemented three models that take different dependencies between identifiers and formal properties as criteria. Our results of the optimal model reach valid accuracy of 39% for identifier extraction and 42% for formal properties predictions. Our work is proof of concept for an efficient procedure in performing formal analysis for largescale complicate specification and protocol analysis, especially for 5G and nextG communications.
We consider the problem of estimating the false-/ true-positive-rate (FPR/TPR) for a binary classification model when there are incorrect labels (label noise) in the validation set. Our motivating application is fraud prevention where accurate estimates of FPR are critical to preserving the experience for good customers, and where label noise is highly asymmetric. Existing methods seek to minimize the total error in the cleaning process - to avoid cleaning examples that are not noise, and to ensure cleaning of examples that are. This is an important measure of accuracy but insufficient to guarantee good estimates of the true FPR or TPR for a model, and we show that using the model to directly clean its own validation data leads to underestimates even if total error is low. This indicates a need for researchers to pursue methods that not only reduce total error but also seek to de-correlate cleaning error with model scores.
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is $\leq k$ for some constant $k$. We also show how our results translate to fractional vertex covers.
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems is assumed. Derivations relevant to successful implementation are covered. Some theory is covered, but the focus here is on implementation and results. Examples are given that illustrate the utility of the method. Numerical results are provided to help researchers implement and verify their own results.
Matching has been widely used to mimic a randomized experiment with observational data. Ideally, treated subjects are exactly matched with controls for the covariates, and randomization-based estimation can then be conducted as in a randomized experiment (assuming no unobserved covariates). However, when there exists continuous covariates or many covariates, matching typically should be inexact. Previous studies have routinely ignored inexact matching in the downstream randomization-based estimation as long as some covariate balance criteria are satisfied, which can cause severe estimation bias. Built on the covariate-adaptive randomization inference framework, in this research note, we propose two new classes of bias-corrected randomization-based estimators to reduce estimation bias due to inexact matching: the bias-corrected maximum $p$-value estimator for the constant treatment effect and the bias-corrected difference-in-means estimator for the average treatment effect. Our simulation results show that the proposed bias-corrected estimators can effectively reduce estimation bias due to inexact matching.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191