Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a pre-trained deep neural network's last layer to adapt it to a novel task when performing transfer learning. We address this gap for finite-rank kernel ridge regression (KRR) by deriving sharp non-asymptotic upper and lower bounds for the KRR test error of any finite-rank KRR. Our bounds are tighter than previously derived bounds on finite-rank KRR, and unlike comparable results, they also remain valid for any regularization parameters.
相關內容
This paper studies convergence rates for some value function approximations that arise in a collection of reproducing kernel Hilbert spaces (RKHS) $H(\Omega)$. By casting an optimal control problem in a specific class of native spaces, strong rates of convergence are derived for the operator equation that enables offline approximations that appear in policy iteration. Explicit upper bounds on error in value function and controller approximations are derived in terms of power function $\mathcal{P}_{H,N}$ for the space of finite dimensional approximants $H_N$ in the native space $H(\Omega)$. These bounds are geometric in nature and refine some well-known, now classical results concerning convergence of approximations of value functions.
This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate training data, cost-accuracy trade-offs, and nontrivial hyperparameter tuning. The unpredictability of the accuracy of neural operators impacts their applications in downstream problems of inference, optimization, and control. A framework based on the linear variational problem that gives the correction to the prediction furnished by neural operators is considered based on earlier work in JCP 486 (2023) 112104. The operator, called Residual-based Error Corrector Operator or simply Corrector Operator, associated with the corrector problem is analyzed further. Numerical results involving a nonlinear reaction-diffusion model in two dimensions with PCANet-type neural operators show almost two orders of increase in the accuracy of approximations when neural operators are corrected using the correction scheme. Further, topology optimization involving a nonlinear reaction-diffusion model is considered to highlight the limitations of neural operators and the efficacy of the correction scheme. Optimizers with neural operator surrogates are seen to make significant errors (as high as 80 percent). However, the errors are much lower (below 7 percent) when neural operators are corrected.
The transformer neural network architecture uses a form of attention in which the dot product of query and key is divided by the square root of the key dimension before applying softmax. This scaling of the dot product is designed to avoid the absolute value of the dot products becoming so large that applying softmax leads to vanishing gradients. In this paper, we propose some alternative scalings, including dividing the dot product instead by the sum of the key lengths before applying softmax. We use simulated keys and queries to show that in many situations this appears to be more effective at avoiding regions where applying softmax leads to vanishing gradients.
In low-bitrate speech coding, end-to-end speech coding networks aim to learn compact yet expressive features and a powerful decoder in a single network. A challenging problem as such results in unwelcome complexity increase and inferior speech quality. In this paper, we propose to separate the representation learning and information reconstruction tasks. We leverage an end-to-end codec for learning low-dimensional discrete tokens and employ a latent diffusion model to de-quantize coded features into a high-dimensional continuous space, relieving the decoder's burden of de-quantizing and upsampling. To mitigate the issue of over-smooth generation, we introduce midway-infilling with less noise reduction and stronger conditioning. In ablation studies, we investigate the hyperparameters for midway-infilling and latent diffusion space with different dimensions. Subjective listening tests show that our model outperforms the state-of-the-art at two low bitrates, 1.5 and 3 kbps. Codes and samples of this work are available on our webpage.
Exploring the application of powerful large language models (LLMs) on the fundamental named entity recognition (NER) task has drawn much attention recently. This work aims to investigate the possibilities of pushing the boundary of zero-shot NER with LLM via a training-free self-improving strategy. We propose a self-improving framework, which utilize an unlabeled corpus to stimulate the self-learning ability of LLMs on NER. First, we use LLM to make predictions on the unlabeled corpus and obtain the self-annotated data. Second, we explore various strategies to select reliable samples from the self-annotated dataset as demonstrations, considering the similarity, diversity and reliability of demonstrations. Finally, we conduct inference for the test query via in-context learning with the selected self-annotated demonstrations. Through comprehensive experimental analysis, our study yielded the following findings: (1) The self-improving framework further pushes the boundary of zero-shot NER with LLMs, and achieves an obvious performance improvement; (2) Iterative self-improving or naively increasing the size of unlabeled corpus does not guarantee improvements; (3) There might still be space for improvement via more advanced strategy for reliable entity selection.
Finite element models of electrical machines allow insights in electrothermal stresses which endanger the insulation system of the machine. This paper presents a thermal finite element model of a 3.7 kW squirrel-cage induction machine. The model resolves the conductors and the surrounding insulation materials in the stator slots. A set of transient thermal scenarios is defined and measured in the machine laboratory. These data are used to assess the finite element model.
Language models (LMs) have gained great achievement in various NLP tasks for both fine-tuning and in-context learning (ICL) methods. Despite its outstanding performance, evidence shows that spurious correlations caused by imbalanced label distributions in training data (or exemplars in ICL) lead to robustness issues. However, previous studies mostly focus on word- and phrase-level features and fail to tackle it from the concept level, partly due to the lack of concept labels and subtle and diverse expressions of concepts in text. In this paper, we first use the LLM to label the concept for each text and then measure the concept bias of models for fine-tuning or ICL on the test data. Second, we propose a data rebalancing method to mitigate the spurious correlations by adding the LLM-generated counterfactual data to make a balanced label distribution for each concept. We verify the effectiveness of our mitigation method and show its superiority over the token removal method. Overall, our results show that there exist label distribution biases in concepts across multiple text classification datasets, and LMs will utilize these shortcuts to make predictions in both fine-tuning and ICL methods.
The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.
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